<gh_stars>1-10
# -----------------------------------------------------------------------------
# Name:        MidiFile.py
# Purpose:     MIDI file manipulation utilities
#
# Author:      <NAME> <emergentmusics) at (gmail . com>
#
# Created:     2008/04/17
# Copyright:   (c) 2009-2016 <NAME>
# License:     Please see License.txt for the terms under which this
#              software is distributed.
# -----------------------------------------------------------------------------

from __future__ import division, print_function
import math
import struct
import warnings

__version__ = 'HEAD'

# TICKSPERQUARTERNOTE is the number of "ticks" (time measurement in the MIDI file) that
# corresponds to one quarter note. This number is somewhat arbitrary, but should
# be chosen to provide adequate temporal resolution.
TICKSPERQUARTERNOTE = 960

controllerEventTypes = {'pan': 0x0a}

# Define some constants

MAJOR = 0
MINOR = 1
SHARPS = 1
FLATS = -1

__all__ = ['MIDIFile', 'MAJOR', 'MINOR', 'SHARPS', 'FLATS']


class GenericEvent(object):
    '''
    The event class from which specific events are derived
    '''
    evtname = None
    sec_sort_order = 0

    def __init__(self, tick, insertion_order):
        self.tick = tick
        self.insertion_order = insertion_order

    def __eq__(self, other):
        '''
        Equality operator.

        In the processing of the event list, we have need to remove duplicates.
        To do this we rely on the fact that the classes are hashable, and must
        therefore have an equality operator (__hash__() and __eq__() must both
        be defined).

        Some derived classes will need to override and consider their specific
        attributes in the comparison.
        '''
        return (self.evtname == other.evtname and self.tick == other.tick)

    def __hash__(self):
        '''
        Return a hash code for the object.

        This is needed in order to allow GenericObject classes to be used
        as the key in a dict or set. duplicate objects are removed from
        the event list by storing all the objects in a set, and then
        reconstructing the list from the set.  The only real requirement
        for the algorithm is that the hash of equal objects must be equal.
        There is probably great opportunity for improvements in the hashing
        function.
        '''
        # <NAME>'s 32 bit hash.
        a = int(self.tick)
        a = (a + 0x7ed55d16) + (a << 12)
        a = (a ^ 0xc761c23c) ^ (a >> 19)
        a = (a + 0x165667b1) + (a << 5)
        a = (a + 0xd3a2646c) ^ (a << 9)
        a = (a + 0xfd7046c5) + (a << 3)
        a = (a ^ 0xb55a4f09) ^ (a >> 16)
        return a


class NoteOn(GenericEvent):
    '''
    A class that encapsulates a note
    '''
    evtname = 'NoteOn'
    midi_status = 0x90    # 0x9x is Note On
    sec_sort_order = 3

    def __init__(self, channel, pitch, tick, duration, volume,
                 annotation=None, insertion_order=0):
        self.pitch = pitch
        self.duration = duration
        self.volume = volume
        self.channel = channel
        self.annotation = annotation
        super(NoteOn, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and self.tick == other.tick and
                self.pitch == other.pitch and self.channel == other.channel)

    # In Python 3, a class which overrides __eq__ also needs to provide __hash__,
    # because in Python 3 parent __hash__ is not inherited.
    __hash__ = GenericEvent.__hash__

    def __str__(self):
        return 'NoteOn %d at tick %d duration %d ch %d vel %d' % (
            self.pitch, self.tick, self.duration, self.channel, self.volume)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.pitch)
        midibytes += struct.pack('>B', self.volume)
        return midibytes


class NoteOff (GenericEvent):
    '''
    A class that encapsulates a Note Off event
    '''
    evtname = 'NoteOff'
    midi_status = 0x80  # 0x8x is Note Off
    sec_sort_order = 2  # must be less than that of NoteOn
    # If two events happen at the same time, the secondary sort key is
    # ``sec_sort_order``. Thus a class of events can be processed earlier than
    # another. One place this is used in the code is to make sure that note
    # off events are processed before note on events.

    def __init__(self, channel, pitch, tick, volume,
                 annotation=None, insertion_order=0):
        self.pitch = pitch
        self.volume = volume
        self.channel = channel
        self.annotation = annotation
        super(NoteOff, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and self.tick == other.tick and
                self.pitch == other.pitch and self.channel == other.channel)

    __hash__ = GenericEvent.__hash__

    def __str__(self):
        return 'NoteOff %d at tick %d ch %d vel %d' % (
            self.pitch, self.tick, self.channel, self.volume)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.pitch)
        midibytes += struct.pack('>B', self.volume)
        return midibytes


class Tempo(GenericEvent):
    '''
    A class that encapsulates a tempo meta-event
    '''
    evtname = 'Tempo'
    sec_sort_order = 3

    def __init__(self, tick, tempo, insertion_order=0):
        self.tempo = int(60000000 / tempo)
        super(Tempo, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and
                self.tick == other.tick and
                self.tempo == other.tempo)

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        # Standard MIDI File Format says:
        #
        # FF 51 03 tttttt Set Tempo (in microseconds per MIDI quarter-note)
        # This event indicates a tempo change. Another way of putting
        # "microseconds per quarter-note" is "24ths of a microsecond per MIDI
        # clock". Representing tempos as time per beat instead of beat per time
        # allows absolutely exact long-term synchronisation with a time-based
        # sync protocol such as SMPTE time code or MIDI time code. The amount
        # of accuracy provided by this tempo resolution allows a four-minute
        # piece at 120 beats per minute to be accurate within 500 usec at the
        # end of the piece. Ideally, these events should only occur where MIDI
        # clocks would be located -- this convention is intended to guarantee,
        # or at least increase the likelihood, of compatibility with other
        # synchronisation devices so that a time signature/tempo map stored in
        # this format may easily be transferred to another device.
        #
        # Six identical lower-case letters such as tttttt refer to a 24-bit value, stored
        # most-significant-byte first. The notation len refers to the

        midibytes = b""
        code = 0xFF
        subcode = 0x51
        fourbite = struct.pack('>L', self.tempo)  # big-endian uint32
        threebite = fourbite[1:4]  # Just discard the MSB
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        midibytes += struct.pack('>B', 0x03)  # length in bytes of 24-bit tempo
        midibytes += threebite
        return midibytes


class Copyright(GenericEvent):
    '''
    A class that encapsulates a copyright event
    '''
    evtname = 'Copyright'
    sec_sort_order = 1

    def __init__(self, tick, notice, insertion_order=0):
        self.notice = notice.encode("ISO-8859-1")
        super(Copyright, self).__init__(tick, insertion_order)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        # Standard MIDI File Format says:
        #
        # FF 02 len text Copyright Notice
        # Contains a copyright notice as printable ASCII text. The notice should
        # contain the characters (C), the year of the copyright, and the owner
        # of the copyright. If several pieces of music are in the same MIDI
        # File, all of the copyright notices should be placed together in this
        # event so that it will be at the beginning of the file. This event
        # should be the first event in the track chunk, at tick 0.
        midibytes = b""
        code = 0xFF
        subcode = 0x02
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        payloadLength = len(self.notice)
        payloadLengthVar = writeVarLength(payloadLength)
        for i in payloadLengthVar:
            midibytes += struct.pack("b", i)
        midibytes += self.notice
        return midibytes


class Text(GenericEvent):
    '''
    A class that encapsulates a text event
    '''
    evtname = 'Text'
    sec_sort_order = 1

    def __init__(self, tick, text, insertion_order=0):
        self.text = text.encode("ISO-8859-1")
        super(Text, self).__init__(tick, insertion_order)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xFF
        subcode = 0x01
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        payloadLength = len(self.text)
        payloadLengthVar = writeVarLength(payloadLength)
        for i in payloadLengthVar:
            midibytes += struct.pack("B", i)
        midibytes += self.text
        return midibytes


class KeySignature(GenericEvent):
    '''
    A class that encapsulates a text event
    '''
    evtname = 'KeySignature'
    sec_sort_order = 1

    def __init__(self, tick, accidentals, accidental_type, mode,
                 insertion_order=0):
        self.accidentals = accidentals
        self.accidental_type = accidental_type
        self.mode = mode
        super(KeySignature, self).__init__(tick, insertion_order)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xFF
        subcode = 0x59
        event_subtype = 0x02
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        midibytes += struct.pack('>B', event_subtype)
        midibytes += struct.pack('>b', self.accidentals * self.accidental_type)
        midibytes += struct.pack('>B', self.mode)
        return midibytes


class ProgramChange(GenericEvent):
    '''
    A class that encapsulates a program change event.
    '''
    evtname = 'ProgramChange'
    midi_status = 0xc0   # 0xcx is Program Change
    sec_sort_order = 1

    def __init__(self, channel, tick, programNumber,
                 insertion_order=0):
        self.programNumber = programNumber
        self.channel = channel
        super(ProgramChange, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and
                self.tick == other.tick and
                self.programNumber == other.programNumber and
                self.channel == other.channel)

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.programNumber)
        return midibytes


class SysExEvent(GenericEvent):
    '''
    A class that encapsulates a System Exclusive  event.
    '''
    evtname = 'SysEx'  # doesn't match class name like most others
    sec_sort_order = 1

    def __init__(self, tick, manID, payload, insertion_order=0):
        self.manID = manID
        self.payload = payload
        super(SysExEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return False

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xF0
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)

        payloadLength = writeVarLength(len(self.payload) + 2)
        for lenByte in payloadLength:
            midibytes += struct.pack('>B', lenByte)

        midibytes += struct.pack('>B', self.manID)
        midibytes += self.payload
        midibytes += struct.pack('>B', 0xF7)
        return midibytes


class UniversalSysExEvent(GenericEvent):
    '''
    A class that encapsulates a Universal System Exclusive  event.
    '''
    evtname = 'UniversalSysEx'  # doesn't match class name like most others
    sec_sort_order = 1

    def __init__(self, tick, realTime, sysExChannel, code, subcode,
                 payload, insertion_order=0):
        self.realTime = realTime
        self.sysExChannel = sysExChannel
        self.code = code
        self.subcode = subcode
        self.payload = payload
        super(UniversalSysExEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return False

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xF0
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)

        # Do we need to add a length?
        payloadLength = writeVarLength(len(self.payload) + 5)
        for lenByte in payloadLength:
            midibytes += struct.pack('>B', lenByte)

        if self.realTime:
            midibytes += struct.pack('>B', 0x7F)
        else:
            midibytes += struct.pack('>B', 0x7E)

        midibytes += struct.pack('>B', self.sysExChannel)
        midibytes += struct.pack('>B', self.code)
        midibytes += struct.pack('>B', self.subcode)
        midibytes += self.payload
        midibytes += struct.pack('>B', 0xF7)
        return midibytes


class ControllerEvent(GenericEvent):
    '''
    A class that encapsulates a program change event.
    '''
    evtname = 'ControllerEvent'
    midi_status = 0xB0  # 0xBx is Control Change
    sec_sort_order = 1

    def __init__(self, channel, tick, controller_number, parameter,
                 insertion_order=0):
        self.parameter = parameter
        self.channel = channel
        self.controller_number = controller_number
        super(ControllerEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return False

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.controller_number)
        midibytes += struct.pack('>B', self.parameter)
        return midibytes


class ChannelPressureEvent(GenericEvent):
    '''
    A class that encapsulates a Channel Pressure (Aftertouch) event.
    '''
    evtname = 'ChannelPressure'
    midi_status = 0xD0  # 0xDx is Channel Pressure (Aftertouch)
    sec_sort_order = 1

    def __init__(self, channel, tick, pressure_value, insertion_order=0):
        self.channel = channel
        self.pressure_value = pressure_value
        super(ChannelPressureEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.__class__.__name__ == other.__class__.__name__ and
                self.tick == other.tick and
                self.pressure_value == other.pressure_value and
                self.channel == other.channel)

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        vartick = writeVarLength(self.tick - previous_event_tick)
        for x in vartick:
            midibytes += struct.pack('>B', x)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.pressure_value)
        return midibytes


class PitchWheelEvent(GenericEvent):
    '''
    A class that encapsulates a pitch wheel change event.
    '''
    evtname = 'PitchWheelEvent'
    midi_status = 0xE0  # 0xEx is Pitch Wheel Change
    sec_sort_order = 1

    def __init__(self, channel, tick, pitch_wheel_value, insertion_order=0):
        self.channel = channel
        self.pitch_wheel_value = pitch_wheel_value
        super(PitchWheelEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return False

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes = midibytes + struct.pack('>B', timeByte)
        MSB = (self.pitch_wheel_value + 8192) >> 7
        LSB = (self.pitch_wheel_value + 8192) & 0x7F
        midibytes = midibytes + struct.pack('>B', code)
        midibytes = midibytes + struct.pack('>B', LSB)
        midibytes = midibytes + struct.pack('>B', MSB)
        return midibytes


class TrackName(GenericEvent):
    '''
    A class that encapsulates a program change event.
    '''
    evtname = 'TrackName'
    sec_sort_order = 0

    def __init__(self, tick, trackName, insertion_order=0):
        # GenericEvent.__init__(self, tick)
        self.trackName = trackName.encode("ISO-8859-1")
        super(TrackName, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and
                self.tick == other.tick and
                self.trackName == other.trackName)

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('B', 0xFF)
        midibytes += struct.pack('B', 0X03)
        dataLength = len(self.trackName)
        dataLengthVar = writeVarLength(dataLength)
        for i in dataLengthVar:
            midibytes += struct.pack("B", i)
        midibytes += self.trackName
        return midibytes


class TimeSignature(GenericEvent):
    '''
    A class that encapsulates a time signature.
    '''
    evtname = 'TimeSignature'
    sec_sort_order = 0

    def __init__(self, tick, numerator, denominator, clocks_per_tick,
                 notes_per_quarter, insertion_order=0):
        self.numerator = numerator
        self.denominator = denominator
        self.clocks_per_tick = clocks_per_tick
        self.notes_per_quarter = notes_per_quarter
        super(TimeSignature, self).__init__(tick, insertion_order)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xFF
        subcode = 0x58
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        midibytes += struct.pack('>B', 0x04)
        midibytes += struct.pack('>B', self.numerator)
        midibytes += struct.pack('>B', self.denominator)
        midibytes += struct.pack('>B', self.clocks_per_tick)
        # 32nd notes per quarter note
        midibytes += struct.pack('>B', self.notes_per_quarter)
        return midibytes


class MIDITrack(object):
    '''
    A class that encapsulates a MIDI track
    '''

    def __init__(self, removeDuplicates, deinterleave):
        '''Initialize the MIDITrack object.
        '''
        self.headerString = struct.pack('cccc', b'M', b'T', b'r', b'k')
        self.dataLength = 0  # Is calculated after the data is in place
        self.MIDIdata = b""
        self.closed = False
        self.eventList = []
        self.MIDIEventList = []
        self.remdep = removeDuplicates
        self.deinterleave = deinterleave

    def addNoteByNumber(self, channel, pitch, tick, duration, volume,
                        annotation=None, insertion_order=0):
        '''
        Add a note by chromatic MIDI number
        '''
        self.eventList.append(NoteOn(channel, pitch, tick, duration, volume,
                                     annotation=annotation,
                                     insertion_order=insertion_order))

        # This event is not in chronological order. But before writing all the
        # events to the file, I sort self.eventlist on (tick, sec_sort_order, insertion_order)
        # which puts the events in chronological order.
        self.eventList.append(NoteOff(channel, pitch, tick + duration, volume,
                                      annotation=annotation,
                                      insertion_order=insertion_order))

    def addControllerEvent(self, channel, tick, controller_number, parameter,
                           insertion_order=0):
        '''
        Add a controller event.
        '''

        self.eventList.append(ControllerEvent(channel, tick, controller_number,
                                              parameter,
                                              insertion_order=insertion_order))

    def addPitchWheelEvent(self, channel, tick, pitch_wheel_value, insertion_order=0):
        '''
        Add a pitch wheel event.
        '''
        self.eventList.append(PitchWheelEvent(channel, tick, pitch_wheel_value, insertion_order=insertion_order))

    def addTempo(self, tick, tempo, insertion_order=0):
        '''
        Add a tempo change (or set) event.
        '''
        self.eventList.append(Tempo(tick, tempo,
                                    insertion_order=insertion_order))

    def addSysEx(self, tick, manID, payload, insertion_order=0):
        '''
        Add a SysEx event.
        '''
        self.eventList.append(SysExEvent(tick, manID, payload,
                                         insertion_order=insertion_order))

    def addUniversalSysEx(self, tick, code, subcode, payload,
                          sysExChannel=0x7F, realTime=False,
                          insertion_order=0):
        '''
        Add a Universal SysEx event.
        '''
        self.eventList.append(UniversalSysExEvent(tick, realTime, sysExChannel,
                              code, subcode, payload,
                              insertion_order=insertion_order))

    def addProgramChange(self, channel, tick, program, insertion_order=0):
        '''
        Add a program change event.
        '''
        self.eventList.append(ProgramChange(channel, tick, program,
                                            insertion_order=insertion_order))

    def addChannelPressure(self, channel, tick, pressure_value, insertion_order=0):
        '''
        Add a channel pressure event.
        '''
        self.eventList.append(ChannelPressureEvent(channel, tick, pressure_value,
                                                   insertion_order=insertion_order))

    def addTrackName(self, tick, trackName, insertion_order=0):
        '''
        Add a track name event.
        '''
        self.eventList.append(TrackName(tick, trackName,
                                        insertion_order=insertion_order))

    def addTimeSignature(self, tick, numerator, denominator, clocks_per_tick,
                         notes_per_quarter, insertion_order=0):
        '''
        Add a time signature.
        '''
        self.eventList.append(TimeSignature(tick, numerator, denominator,
                                            clocks_per_tick, notes_per_quarter,
                                            insertion_order=insertion_order))

    def addCopyright(self, tick, notice, insertion_order=0):
        '''
        Add a copyright notice
        '''
        self.eventList.append(Copyright(tick, notice,
                                        insertion_order=insertion_order))

    def addKeySignature(self, tick, accidentals, accidental_type, mode,
                        insertion_order=0):
        '''
        Add a copyright notice
        '''
        self.eventList.append(KeySignature(tick, accidentals, accidental_type,
                                           mode,
                                           insertion_order=insertion_order))

    def addText(self, tick, text, insertion_order=0):
        '''
        Add a text event
        '''
        self.eventList.append(Text(tick, text,
                              insertion_order=insertion_order))

    def changeNoteTuning(self, tunings, sysExChannel=0x7F, realTime=True,
                         tuningProgam=0, insertion_order=0):
        '''
        Change the tuning of MIDI notes
        '''
        payload = struct.pack('>B', tuningProgam)
        payload = payload + struct.pack('>B', len(tunings))
        for (noteNumber, frequency) in tunings:
            payload = payload + struct.pack('>B', noteNumber)
            MIDIFreqency = frequencyTransform(frequency)
            for byte in MIDIFreqency:
                payload = payload + struct.pack('>B', byte)

        self.eventList.append(UniversalSysExEvent(0, realTime, sysExChannel,
                              8, 2, payload, insertion_order=insertion_order))

    def processEventList(self):
        '''
        Process the event list, creating a MIDIEventList,
        which is then sorted to be in chronological order by start tick.
        '''

        self.MIDIEventList = [evt for evt in self.eventList]
        # Assumptions in the code expect the list to be time-sorted.
        self.MIDIEventList.sort(key=sort_events)

        if self.deinterleave:
            self.deInterleaveNotes()

    def removeDuplicates(self):
        '''
        Remove duplicates from the eventList.

        This function will remove duplicates from the eventList. This is
        necessary because we the MIDI event stream can become confused
        otherwise.
        '''

        # For this algorithm to work, the events in the eventList must be
        # hashable (that is, they must have a __hash__() and __eq__() function
        # defined).

        s = set(self.eventList)
        self.eventList = list(s)
        self.eventList.sort(key=sort_events)

    def closeTrack(self):
        '''
        Called to close a track before writing

        This function should be called to "close a track," that is to
        prepare the actual data stream for writing. Duplicate events are
        removed from the eventList, and the MIDIEventList is created.

        Called by the parent MIDIFile object.
        '''

        if self.closed:
            return
        self.closed = True

        if self.remdep:
            self.removeDuplicates()

        self.processEventList()

    def writeMIDIStream(self):
        '''
        Write the meta data and note data to the packed MIDI stream.
        '''

        # Process the events in the eventList

        self.writeEventsToStream()

        # Write MIDI close event.

        self.MIDIdata += struct.pack('BBBB', 0x00, 0xFF, 0x2F, 0x00)

        # Calculate the entire length of the data and write to the header

        self.dataLength = struct.pack('>L', len(self.MIDIdata))

    def writeEventsToStream(self):
        '''
        Write the events in MIDIEvents to the MIDI stream.
        MIDIEventList is presumed to be already sorted in chronological order.
        '''
        previous_event_tick = 0
        for event in self.MIDIEventList:
            self.MIDIdata += event.serialize(previous_event_tick)
            # previous_event_tick = event.tick
            # I do not like that adjustTimeAndOrigin() changes GenericEvent.tick
            # from absolute to relative. I intend to change that, and just
            # calculate the relative tick here, without changing GenericEvent.tick

    def deInterleaveNotes(self):
        '''
        Correct Interleaved notes.

        Because we are writing multiple notes in no particular order, we
        can have notes which are interleaved with respect to their start
        and stop times. This method will correct that. It expects that the
        MIDIEventList has been time-ordered.
        '''

        tempEventList = []
        stack = {}

        for event in self.MIDIEventList:
            if event.evtname in ['NoteOn', 'NoteOff']:
                # !!! Pitch 101 channel 5 produces the same key as pitch 10 channel 15.
                # !!! This is not the only pair of pitch,channel tuples which
                # !!! collide to the same key, just one example.  Should fix by
                # !!! putting a separator char between pitch and channel.
                noteeventkey = str(event.pitch) + str(event.channel)
                if event.evtname == 'NoteOn':
                    if noteeventkey in stack:
                        stack[noteeventkey].append(event.tick)
                    else:
                        stack[noteeventkey] = [event.tick]
                    tempEventList.append(event)
                elif event.evtname == 'NoteOff':
                    if len(stack[noteeventkey]) > 1:
                        event.tick = stack[noteeventkey].pop()
                        tempEventList.append(event)
                    else:
                        stack[noteeventkey].pop()
                        tempEventList.append(event)
            else:
                tempEventList.append(event)

        self.MIDIEventList = tempEventList

        # Note NoteOff events have a lower secondary sort key than NoteOn
        # events, so this sort will make concomitant NoteOff events
        # processed first.

        self.MIDIEventList.sort(key=sort_events)

    def adjustTimeAndOrigin(self, origin, adjust):
        '''
        Adjust Times to be relative, and zero-origined.

        If adjust is True, the track will be shifted. Regardelss times
        are converted to relative values here.
        '''

        if len(self.MIDIEventList) == 0:
            return
        tempEventList = []
        internal_origin = origin if adjust else 0
        runningTick = 0

        for event in self.MIDIEventList:
            adjustedTick = event.tick - internal_origin
            event.tick = adjustedTick - runningTick
            runningTick = adjustedTick
            tempEventList.append(event)

        self.MIDIEventList = tempEventList

    def writeTrack(self, fileHandle):
        '''
        Write track to disk.
        '''

        fileHandle.write(self.headerString)
        fileHandle.write(self.dataLength)
        fileHandle.write(self.MIDIdata)


class MIDIHeader(object):
    '''
    Class to encapsulate the MIDI header structure.

    This class encapsulates a MIDI header structure. It isn't used for much,
    but it will create the appropriately packed identifier string that all
    MIDI files should contain. It is used by the MIDIFile class to create a
    complete and well formed MIDI pattern.

    '''
    def __init__(self, numTracks, file_format, ticks_per_quarternote):
        ''' Initialize the data structures

        :param numTracks: The number of tracks the file contains. Integer,
            one or greater
        :param file_format: The format of the multi-track file. This should
            either be ``1`` (the default, and the most widely supported
            format) or ``2``.
        :param ticks_per_quarternote: The number of ticks per quarter
            note is what the Standard MIDI File Format Specification calls
            "division".  Ticks are the integer unit of time in the SMF, and in
            every MIDI sequencer I am aware of.  Common values are 120, 240,
            384, 480, 960. Note that all these numbers are evenly divisible by
            2,3,4,6,8,12,16, and 24, except 120 does not have 16 as a divisor.
        '''
        self.headerString = struct.pack('cccc', b'M', b'T', b'h', b'd')
        self.headerSize = struct.pack('>L', 6)
        # Format 1 = multi-track file
        self.formatnum = struct.pack('>H', file_format)
        self.numeric_format = file_format
        self.numTracks = struct.pack('>H', numTracks)
        self.ticks_per_quarternote = struct.pack('>H', ticks_per_quarternote)

    def writeFile(self, fileHandle):
        fileHandle.write(self.headerString)
        fileHandle.write(self.headerSize)
        fileHandle.write(self.formatnum)
        fileHandle.write(self.numTracks)
        fileHandle.write(self.ticks_per_quarternote)


class MIDIFile(object):
    '''
    A class that encapsulates a full, well-formed MIDI file object.

    This is a container object that contains a header (:class:`MIDIHeader`),
    one or more tracks (class:`MIDITrack`), and the data associated with a
    proper and well-formed MIDI file.
    '''

    def __init__(self, numTracks=1, removeDuplicates=True, deinterleave=True,
                 adjust_origin=False, file_format=1,
                 ticks_per_quarternote=TICKSPERQUARTERNOTE, eventtime_is_ticks=False):
        '''Initialize the MIDIFile class

        :param numTracks: The number of tracks the file contains. Integer,
            one or greater
        :param removeDuplicates: If set to ``True`` remove duplicate events
            before writing to disk
        :param deinterleave: If set to ``True`` deinterleave the notes in
            the stream
        :param adjust_origin: If set to ``True`` shift all the events in the tracks 
            so that the first event takes place at time t=0. Default is ``False``
        :param file_format: The format of the multi-track file. This should
            either be ``1`` (the default, and the most widely supported
            format) or ``2``.
        :param ticks_per_quarternote: The number of ticks per quarter note is
            what the Standard MIDI File Format Specification calls "division".
            Ticks are the integer unit of time in the SMF, and in most if
            not all MIDI sequencers.  Common values are 120, 240, 384,
            480, 960. Note that all these numbers are evenly divisible by
            2,3,4,6,8,12,16, and 24, except 120 does not have 16 as a divisor.

        :param eventtime_is_ticks: If set True means event time and duration
            argument values are integer ticks instead of fractional quarter
            notes.

        Note that the default for ``adjust_origin`` will change in a future
        release, so one should probably explicitly set it.

        In a format 1 file, it would be a rare cirumstance where adjusting the
        origin of each track to the track's first note makes any sense.

        Example:

        .. code::

            # Create a two-track MIDIFile

            from midiutil.MidiFile import MIDIFile
            midi_file = MIDIFile(1, adjust_origin=False)

        A Note on File Formats
        ----------------------

        In previous versions of this code the file written was format 2
        (which can be thought of as a collection of independent tracks) but
        was identified as format 1. In this version one can specify either
        format 1 or 2.

        In format 1 files there is a separate tempo track which contains
        tempo and time signature data, but contains no note data. If one
        creates a single track format 1 file the actual file has two tracks
        -- one for tempo data and one for note data. In the track indexing
        the tempo track can be ignored. In other words track 0 is the note
        track (the second track in the file). However, tempo and time
        signature data will be written to the first, tempo track. This is
        done to try and preserve as much interoperability with previous
        versions as possible.

        In a format 2 file all tracks are indexed and the track parameter
        is interpreted literally.
        '''

        self.tracks = list()
        if file_format == 1:
            self.numTracks = numTracks + 1  # self.tracks[0] is the baked-in tempo track
        else:
            self.numTracks = numTracks
        self.header = MIDIHeader(self.numTracks, file_format, ticks_per_quarternote)

        self.adjust_origin = adjust_origin
        self.closed = False

        self.ticks_per_quarternote = ticks_per_quarternote
        self.eventtime_is_ticks = eventtime_is_ticks
        if self.eventtime_is_ticks:
            self.time_to_ticks = lambda x: x
        else:
            self.time_to_ticks = self.quarter_to_tick

        for i in range(0, self.numTracks):
            self.tracks.append(MIDITrack(removeDuplicates, deinterleave))
        # to keep track of the order of insertion for new sorting
        self.event_counter = 0

    # Public Functions. These (for the most part) wrap the MIDITrack functions,
    # where most Processing takes place.

    def quarter_to_tick(self, quarternote_time):
        return int(quarternote_time * self.ticks_per_quarternote)

    def tick_to_quarter(self, ticknum):
        return float(ticknum) / self.ticks_per_quarternote

    def addNote(self, track, channel, pitch, time, duration, volume,
                annotation=None):
        """

        Add notes to the MIDIFile object

        :param track: The track to which the note is added.
        :param channel: the MIDI channel to assign to the note. [Integer, 0-15]
        :param pitch: the MIDI pitch number [Integer, 0-127].
        :param time: the time at which the note sounds. The value can be either
            quarter notes [Float], or ticks [Integer]. Ticks may be specified by
            passing eventtime_is_ticks=True to the MIDIFile constructor.
            The default is quarter notes.
        :param duration: the duration of the note. Like the time argument, the
            value can be either quarter notes [Float], or ticks [Integer].
        :param volume: the volume (velocity) of the note. [Integer, 0-127].
        :param annotation: Arbitrary data to attach to the note.

        The ``annotation`` parameter attaches arbitrary data to the note. This
        is not used in the code, but can be useful anyway. As an example,
        I have created a project that uses MIDIFile to write
        `csound <http://csound.github.io/>`_ orchestra files directly from the
        class ``EventList``.
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addNoteByNumber(channel, pitch,
                                           self.time_to_ticks(time), self.time_to_ticks(duration),
                                           volume, annotation=annotation,
                                           insertion_order=self.event_counter)
        self.event_counter += 1

    def addTrackName(self, track, time, trackName):
        """
        Name a track.

        :param track: The track to which the name is assigned.
        :param time: The time (in beats) at which the track name event is
            placed.  In general this should probably be time 0 (the beginning
            of the track).
        :param trackName: The name to assign to the track [String]
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addTrackName(self.time_to_ticks(time), trackName,
                                        insertion_order=self.event_counter)
        self.event_counter += 1

    def addTimeSignature(self, track, time, numerator, denominator,
                         clocks_per_tick, notes_per_quarter=8):
        '''
        Add a time signature event.

        :param track: The track to which the signature is assigned. Note that
            in a format 1 file this parameter is ignored and the event is
            written to the tempo track
        :param time: The time (in beats) at which the event is placed.
            In general this should probably be time 0 (the beginning of the
            track).
        :param numerator: The numerator of the time signature. [Int]
        :param denominator: The denominator of the time signature, expressed as
            a power of two (see below). [Int]
        :param clocks_per_tick: The number of MIDI clock ticks per metronome
            click (see below).
        :param notes_per_quarter: The number of annotated 32nd notes in a MIDI
            quarter note. This is almost always 8 (the default), but some
            sequencers allow this value to be changed. Unless you know that
            your sequencing software supports it, this should be left at its
            default value.

        The data format for this event is a little obscure.

        The ``denominator`` should be specified as a power of 2, with
        a half note being one, a quarter note being two, and eight note
        being three, etc. Thus, for example, a 4/4 time signature would
        have a ``numerator`` of 4 and a ``denominator`` of 2. A 7/8 time
        signature would be a ``numerator`` of 7 and a ``denominator``
        of 3.

        The ``clocks_per_tick`` argument specifies the number of clock
        ticks per metronome click. By definition there are 24 ticks in
        a quarter note, so a metronome click per quarter note would be
        24. A click every third eighth note would be 3 * 12 = 36.

        The ``notes_per_quarter`` value is also a little confusing. It
        specifies the number of 32nd notes in a MIDI quarter note. Usually
        there are 8 32nd notes in a quarter note (8/32 = 1/4), so
        the default value is 8. However, one can change this value if
        needed. Setting it to 16, for example, would cause the music to
        play at double speed, as there would be 16/32 (or what could be
        considered *two* quarter notes for every one MIDI quarter note.

        Note that both the ``clocks_per_tick`` and the
        ``notes_per_quarter`` are specified in terms of quarter notes,
        even is the score is not a quarter-note based score (i.e.,
        even if the denominator is not ``4``). So if you're working with a
        time signature of, say, 6/8, one still needs to specify the clocks
        per quarter note.
        '''
        if self.header.numeric_format == 1:
            track = 0

        self.tracks[track].addTimeSignature(self.time_to_ticks(time), numerator, denominator,
                                            clocks_per_tick, notes_per_quarter,
                                            insertion_order=self.event_counter)
        self.event_counter += 1

    def addTempo(self, track, time, tempo):
        """

        Add notes to the MIDIFile object

        :param track: The track to which the tempo event  is added. Note that
            in a format 1 file this parameter is ignored and the tempo is
            written to the tempo track
        :param time: The time (in beats) at which tempo event is placed
        :param tempo: The tempo, in Beats per Minute. [Integer]
        """
        if self.header.numeric_format == 1:
            track = 0
        self.tracks[track].addTempo(self.time_to_ticks(time), tempo,
                                    insertion_order=self.event_counter)
        self.event_counter += 1

    def addCopyright(self, track, time, notice):
        """

        Add a copyright notice to the MIDIFile object

        :param track: The track to which the notice is added.
        :param time: The time (in beats) at which notice event is placed. In
            general this sould be time t=0
        :param notice: The copyright notice [String]
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addCopyright(self.time_to_ticks(time), notice,
                                        insertion_order=self.event_counter)
        self.event_counter += 1

    def addKeySignature(self, track, time, accidentals, accidental_type, mode,
                        insertion_order=0):
        '''
        Add a Key Signature to a track

        :param track: The track to which this should be added
        :param time: The time at which the signature should be placed
        :param accidentals: The number of accidentals in the key signature
        :param accidental_type: The type of accidental
        :param mode: The mode of the scale

        The easiest way to use this function is to make sure that the symbolic
        constants for accidental_type and mode are imported. By doing this:

        .. code::

            from midiutil.MidiFile import *

        one gets the following constants defined:

        * ``SHARPS``
        * ``FLATS``
        * ``MAJOR``
        * ``MINOR``

        So, for example, if one wanted to create a key signature for a minor
        scale with three sharps:

        .. code::

            MyMIDI.addKeySignature(0, 0, 3, SHARPS, MINOR)
        '''
        if self.header.numeric_format == 1:
            track = 0  # User reported that this is needed.
        self.tracks[track].addKeySignature(self.time_to_ticks(time), accidentals, accidental_type,
                                           mode, insertion_order=self.event_counter)
        self.event_counter += 1

    def addText(self, track, time, text):
        """

        Add a text event

        :param track: The track to which the notice is added.
        :param time: The time (in beats) at which text event is placed.
        :param text: The text to adde [ASCII String]
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addText(self.time_to_ticks(time), text,
                                   insertion_order=self.event_counter)
        self.event_counter += 1

    def addProgramChange(self, tracknum, channel, time, program):
        """

        Add a MIDI program change event.

        :param tracknum: The zero-based track number to which program change event is added.
        :param channel: the MIDI channel to assign to the event.
            [Integer, 0-15]
        :param time: The time (in beats) at which the program change event is
            placed [Float].
        :param program: the program number. [Integer, 0-127].
        """
        if self.header.numeric_format == 1:
            tracknum += 1
        self.tracks[tracknum].addProgramChange(channel, self.time_to_ticks(time), program,
                                               insertion_order=self.event_counter)
        self.event_counter += 1

    def addChannelPressure(self, tracknum, channel, time, pressure_value):
        """
        Add a Channel Pressure event.

        :param tracknum: The zero-based track number to which channel pressure event is added.
        :param channel: the MIDI channel to assign to the event.
            [Integer, 0-15]
        :param time: The time (in beats) at which the channel pressure event is
            placed [Float].
        :param pressure_value: the pressure value. [Integer, 0-127].
        """
        if self.header.numeric_format == 1:
            tracknum += 1
        track = self.tracks[tracknum]
        track.addChannelPressure(channel, self.time_to_ticks(time), pressure_value,
                                 insertion_order=self.event_counter)
        self.event_counter += 1

    def addControllerEvent(self, track, channel, time, controller_number,
                           parameter):
        """

        Add a channel control event

        :param track: The track to which the event is added.
        :param channel: the MIDI channel to assign to the event.
            [Integer, 0-15]
        :param time: The time (in beats) at which the event is placed [Float].
        :param controller_number: The controller ID of the event.
        :param parameter: The event's parameter, the meaning of which varies by
            event type.
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addControllerEvent(channel, self.time_to_ticks(time), controller_number,
                                              parameter, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1

    def addPitchWheelEvent(self, track, channel, time, pitchWheelValue):
        """

        Add a channel pitch wheel event

        :param track: The track to which the event is added.
        :param channel: the MIDI channel to assign to the event. [Integer, 0-15]
        :param time: The time (in beats) at which the event is placed [Float].
        :param pitchWheelValue: 0 for no pitch change. [Integer, -8192-8192]
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addPitchWheelEvent(channel, self.time_to_ticks(time), pitchWheelValue,
                                              insertion_order=self.event_counter)
        self.event_counter += 1

    def makeRPNCall(self, track, channel, time, controller_msb, controller_lsb,
                    data_msb, data_lsb, time_order=False):
        '''

        Perform a Registered Parameter Number Call

        :param track: The track to which this applies
        :param channel: The channel to which this applies
        :param time: The time of the event
        :param controller_msb: The Most significant byte of the controller. In
            common usage this will usually be 0
        :param controller_lsb: The Least significant Byte for the controller
            message. For example, for a fine-tuning change this would be 01.
        :param data_msb: The Most Significant Byte of the controller's
            parameter.
        :param data_lsb: The Least Significant Byte of the controller's
            parameter. If not needed this should be set to ``None``
        :param time_order: Order the control events in time (see below)

        As an example, if one were to change a channel's tuning program::

            makeRPNCall(track, channel, time, 0, 3, 0, program)

        (Note, however, that there is a convenience function,
        ``changeTuningProgram``, that does this for you.)

        Registered/Non-Registered Parameter Number (RPN / NRPN)
        -------------------------------------------------------
        Controller number 6 (Data Entry), in conjunction with Controller numbers 96
        (Data Increment), 97 (Data Decrement), 98 (Registered Parameter Number LSB),
        99 (Registered Parameter Number MSB), 100 (Non-Registered Parameter Number
        LSB), and 101 (Non-Registered Parameter Number MSB), extend the number of
        controllers available via MIDI. Parameter data is transferred by first
        selecting the parameter number to be edited using controllers 98 and 99 or
        100 and 101, and then adjusting the data value for that parameter using
        controller number 6, 96, or 97.

        RPN and NRPN are typically used to send parameter data to a synthesizer in
        order to edit sound patches or other data. Registered parameters are those
        which have been assigned some particular function by the MIDI Manufacturers
        Association (MMA) and the Japan MIDI Standards Committee (JMSC). For
        example, there are Registered Parameter numbers assigned to control pitch
        bend sensitivity and master tuning for a synthesizer. Non-Registered
        parameters have not been assigned specific functions, and may be used for
        different functions by different manufacturers.

        The ``time_order`` parameter is something of a work-around for
        sequencers that do not preserve the order of events from the MIDI files
        they import. Within this code care is taken to preserve the order of
        events as specified, but some sequencers seem to transmit events
        occurring at the same time in an arbitrary order.  By setting this
        parameter to ``True`` something of a work-around is performed: each
        successive event (of which there are three or four for this event type)
        is placed in the time stream a small delta from the preceding one.
        Thus, for example, the controllers are set before the data bytes in
        this call.
        '''
        tick = self.time_to_ticks(time)

        if self.header.numeric_format == 1:
            track += 1
        track = self.tracks[track]

        tick_incr = 1 if time_order else 0
        track.addControllerEvent(channel, tick, 101,  # parameter number MSB
                                 controller_msb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        track.addControllerEvent(channel, tick, 100,
                                 controller_lsb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        track.addControllerEvent(channel, tick, 6,
                                 data_msb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        if data_lsb is not None:
            track.addControllerEvent(channel, tick, 38,
                                     data_lsb, insertion_order=self.event_counter)  # noqa: E128
            self.event_counter += 1

    def makeNRPNCall(self, track, channel, time, controller_msb,
                     controller_lsb, data_msb, data_lsb, time_order=False):
        '''

        Perform a Non-Registered Parameter Number Call

        :param track: The track to which this applies
        :param channel: The channel to which this applies
        :param time: The time of the event
        :param controller_msb: The Most significant byte of thecontroller. In
            common usage this will usually be 0
        :param controller_lsb: The least significant byte for the controller
            message. For example, for a fine-tunning change this would be 01.
        :param data_msb: The most significant byte of the controller's
            parameter.
        :param data_lsb: The least significant byte of the controller's
            parameter. If none is needed this should be set to ``None``
        :param time_order: Order the control events in time (see below)

        The ``time_order`` parameter is something of a work-around for
        sequencers that do not preserve the order of events from the MIDI files
        they import. Within this code care is taken to preserve the order of
        events as specified, but some sequencers seem to transmit events
        occurring at the same time in an arbitrary order.  By setting this
        parameter to ``True`` something of a work-around is performed: each
        successive event (of which there are three or four for this event type)
        is placed in the time stream a small delta from the preceding one.
        Thus, for example, the controllers are set before the data bytes in
        this call.

        '''
        tick = self.time_to_ticks(time)

        if self.header.numeric_format == 1:
            track += 1
        track = self.tracks[track]

        tick_incr = 1 if time_order else 0
        track.addControllerEvent(channel, tick, 99,
                                 controller_msb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        track.addControllerEvent(channel, tick, 98,
                                 controller_lsb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        track.addControllerEvent(channel, tick, 6,
                                 data_msb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        if data_lsb is not None:
            track.addControllerEvent(channel, tick, 38,
                                     data_lsb, insertion_order=self.event_counter)  # noqa: E128
            self.event_counter += 1

    def changeTuningBank(self, track, channel, time, bank, time_order=False):
        '''

        Change the tuning bank for a selected track

        :param track: The track to which the data should be written
        :param channel: The channel for the event
        :param time: The time of the event
        :param bank: The tuning bank (0-127)
        :param time_order: Preserve the ordering of the component events by
            ordering in time. See ``makeRPNCall()`` for a discussion of when
            this may be necessary

        Note that this is a convenience function, as the same
        functionality is available from directly sequencing controller
        events.

        The specified tuning should already have been written to the
        stream with ``changeNoteTuning``.  '''
        self.makeRPNCall(track, channel, time, 0, 4, 0, bank,
                         time_order=time_order)

    def changeTuningProgram(self, track, channel, time, program,
                            time_order=False):
        '''

        Change the tuning program for a selected track

        :param track: The track to which the data should be written
        :param channel: The channel for the event
        :param time: The time of the event
        :param program: The tuning program number (0-127)
        :param time_order: Preserve the ordering of the component events by
            ordering in time. See ``makeRPNCall()`` for a discussion of when
            this may be necessary

        Note that this is a convenience function, as the same
        functionality is available from directly sequencing controller
        events.

        The specified tuning should already have been written to the
        stream with ``changeNoteTuning``.
        '''
        self.makeRPNCall(track, channel, time, 0, 3, 0, program,
                         time_order=time_order)

    def changeNoteTuning(self, track, tunings, sysExChannel=0x7F,
                         realTime=True, tuningProgam=0):
        """
        Add a real-time MIDI tuning standard update to a track.

        :param track: The track to which the tuning is applied.
        :param tunings: A list to tuples representing the tuning. See below for
            an explanation.
        :param sysExChannel: The SysEx channel of the event. This is mapped to
            "manufacturer ID" in the event which is written. Unless there is a
            specific reason for changing it, it should be left at its default
            value.
        :param realTime: Speicifes if the Universal SysEx event should be
            flagged as real-time or non-real-time. As with the ``sysExChannel``
            argument, this should in general be left at it's default value.
        :param tuningProgram: The tuning program number.

        This function specifically implements the "real time single note tuning
        change" (although the name is misleading, as multiple notes can be
        included in each event). It should be noted that not all hardware or
        software implements the MIDI tuning standard, and that which does often
        does not implement it in its entirety.

        The ``tunings`` argument is a list of tuples, in (*note number*,
        *frequency*) format.  As an example, if one wanted to change the
        frequency on MIDI note 69 to 500 (it is normally 440 Hz), one could do
        it thus:

        .. code:: python

            from midiutil.MidiFile import MIDIFile
            MyMIDI = MIDIFile(1)
            tuning = [(69, 500)]
            MyMIDI.changeNoteTuning(0, tuning, tuningProgam=0)
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].changeNoteTuning(tunings, sysExChannel, realTime,
                                            tuningProgam,
                                            insertion_order=self.event_counter)
        self.event_counter += 1

    def addSysEx(self, track, time, manID, payload):
        '''

        Add a System Exclusive event.

        :param track: The track to which the event should be written
        :param time: The time of the event.
        :param manID: The manufacturer ID for the event
        :param payload: The payload for the event. This should be a
            binary-packed value, and will vary for each type and function.

        **Note**: This is a low-level MIDI function, so care must be used in
        constructing the payload. It is recommended that higher-level helper
        functions be written to wrap this function and construct the payload if
        a developer finds him or herself using the function heavily.

        '''
        tick = self.time_to_ticks(time)
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addSysEx(tick, manID, payload,
                                    insertion_order=self.event_counter)
        self.event_counter += 1

    def addUniversalSysEx(self, track, time, code, subcode, payload,
                          sysExChannel=0x7F, realTime=False):
        '''

        Add a Univeral System Exclusive event.

        :param track: The track to which the event should be written
        :param time: The time of the event, in beats.
        :param code: The event code. [Integer]
        :param subcode: The event sub-code [Integer]
        :param payload: The payload for the event. This should be a
            binary-packed value, and will vary for each type and function.
        :param sysExChannel: The SysEx channel.
        :param realTime: Sets the real-time flag. Defaults to non-real-time.
        :param manID: The manufacturer ID for the event


        **Note**: This is a low-level MIDI function, so care must be used in
        constructing the payload. It is recommended that higher-level helper
        functions be written to wrap this function and construct the payload if
        a developer finds him or herself using the function heavily. As an
        example of such a helper function, see the ``changeNoteTuning()``
        function, which uses the event to create a real-time note tuning
        update.

        '''
        tick = self.time_to_ticks(time)
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addUniversalSysEx(tick, code, subcode, payload,
                                             sysExChannel, realTime,
                                             insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1

    def writeFile(self, fileHandle):
        '''
        Write the MIDI File.

        :param fileHandle: A file handle that has been opened for binary
            writing.
        '''

        self.header.writeFile(fileHandle)

        # Close the tracks and have them create the MIDI event data structures.
        self.close()

        # Write the MIDI Events to file.
        for i in range(0, self.numTracks):
            self.tracks[i].writeTrack(fileHandle)

    def shiftTracks(self, offset=0):
        """Shift tracks to be zero-origined, or origined at offset.

        Note that the shifting of the time in the tracks uses the MIDIEventList
        -- in other words it is assumed to be called in the stage where the
        MIDIEventList has been created. This function, however, it meant to
        operate on the eventList itself.
        """
        origin = 100000000  # A little silly, but we'll assume big enough
        tick_offset = self.time_to_ticks(offset)

        for track in self.tracks:
            if len(track.eventList) > 0:
                for event in track.eventList:
                    if event.tick < origin:
                        origin = event.tick

        for track in self.tracks:
            tempEventList = []
            # runningTick = 0

            for event in track.eventList:
                adjustedTick = event.tick - origin
                # event.time = adjustedTime - runningTick + tick_offset
                event.tick = adjustedTick + tick_offset
                # runningTick = adjustedTick
                tempEventList.append(event)

            track.eventList = tempEventList

    # End Public Functions ########################

    def close(self):
        '''
        Close the MIDIFile for further writing.

        To close the File for events, we must close the tracks, adjust the time
        to be zero-origined, and have the tracks write to their MIDI Stream
        data structure.
        '''

        if self.closed:
            return

        for i in range(0, self.numTracks):
            self.tracks[i].closeTrack()
            # We want things like program changes to come before notes when
            # they are at the same time, so we sort the MIDI events by both
            # their start time and a secondary ordinality defined for each kind
            # of event.
            self.tracks[i].MIDIEventList.sort(key=sort_events)

        origin = self.findOrigin()

        for i in range(0, self.numTracks):
            self.tracks[i].adjustTimeAndOrigin(origin, self.adjust_origin)
            self.tracks[i].writeMIDIStream()

        self.closed = True

    def findOrigin(self):
        '''
        Find the earliest time in the file's tracks.append.
        '''
        origin = 100000000  # A little silly, but we'll assume big enough

    # Note: This code assumes that the MIDIEventList has been sorted, so this
    # should be insured before it is called. It is probably a poor design to do
    # this.
    # TODO: -- Consider making this less efficient but more robust by not
    #          assuming the list to be sorted.

        for track in self.tracks:
            if len(track.MIDIEventList) > 0:
                if track.MIDIEventList[0].tick < origin:
                    origin = track.MIDIEventList[0].tick

        return origin


def writeVarLength(i):
    '''
    Accept an integer, and serialize it as a MIDI file variable length quantity

    Some numbers in MTrk chunks are represented in a form called a variable-
    length quantity.  These numbers are represented in a sequence of bytes,
    each byte holding seven bits of the number, and ordered most significant
    bits first. All bytes in the sequence except the last have bit 7 set,
    and the last byte has bit 7 clear.  This form allows smaller numbers to
    be stored in fewer bytes.  For example, if the number is between 0 and
    127, it is thus represented exactly as one byte.  A number between 128
    and 16383 uses two bytes, and so on.

    Examples:
    Number  VLQ
    128     81 00
    8192    C0 00
    16383   FF 7F
    16384   81 80 00
    '''
    if i == 0:
        return [0]

    vlbytes = []
    hibit = 0x00  # low-order byte has high bit cleared.
    while i > 0:
        vlbytes.append(((i & 0x7f) | hibit) & 0xff)
        i >>= 7
        hibit = 0x80
    vlbytes.reverse()  # put most-significant byte first, least significant last
    return vlbytes


# readVarLength is taken from the MidiFile class.

def readVarLength(offset, buffer):
    '''
    A function to read a MIDI variable length variable.

    It returns a tuple of the value read and the number of bytes processed. The
    input is an offset into the buffer, and the buffer itself.
    '''
    toffset = offset
    output = 0
    bytesRead = 0
    while True:
        output = output << 7
        byte = struct.unpack_from('>B', buffer, toffset)[0]
        toffset = toffset + 1
        bytesRead = bytesRead + 1
        output = output + (byte & 127)
        if (byte & 128) == 0:
            break
    return (output, bytesRead)


def frequencyTransform(freq):
    '''
    Returns a three-byte transform of a frequency.
    '''
    resolution = 16384
    freq = float(freq)
    dollars = 69 + 12 * math.log(freq / (float(440)), 2)
    firstByte = int(dollars)
    lowerFreq = 440 * pow(2.0, ((float(firstByte) - 69.0) / 12.0))
    centDif = 1200 * math.log((freq / lowerFreq), 2) if freq != lowerFreq else 0
    cents = round(centDif / 100 * resolution)  # round?
    secondByte = min([int(cents) >> 7, 0x7F])
    thirdByte = cents - (secondByte << 7)
    thirdByte = min([thirdByte, 0x7f])
    if thirdByte == 0x7f and secondByte == 0x7F and firstByte == 0x7F:
        thirdByte = 0x7e
    thirdByte = int(thirdByte)
    return [firstByte, secondByte, thirdByte]


def returnFrequency(freqBytes):
    '''
    The reverse of frequencyTransform. Given a byte stream, return a frequency.
    '''
    resolution = 16384.0
    baseFrequency = 440 * pow(2.0, (float(freqBytes[0] - 69.0) / 12.0))
    frac = (float((int(freqBytes[1]) << 7) + int(freqBytes[2])) * 100.0) / resolution
    frequency = baseFrequency * pow(2.0, frac / 1200.0)
    return frequency


def sort_events(event):
    '''
    .. py:function:: sort_events(event)

        The key function used to sort events (both MIDI and Generic)

        :param event: An object of type :class:`MIDIEvent` or (a derrivative)
            :class:`GenericEvent`

        This function should be provided as the ``key`` for both
        ``list.sort()`` and ``sorted()``. By using it sorting will be as
        follows:

        * Events are ordered in time. An event that takes place earlier will
          appear earlier
        * If two events happen at the same time, the secondary sort key is
          ``sec_sort_order``. Thus a class of events can be processed earlier
          than another. One place this is used in the code is to make sure that
          note off events are processed before note on events.
        * If event time and event ordinality are the same, they are sorted in
          the order in which they were originally added to the list. Thus, for
          example, if one is making an RPN call one can specify the controller
          change events in the proper order and be sure that they will end up in
          the file that way.
    '''

    return (event.tick, event.sec_sort_order, event.insertion_order)
# -----------------------------------------------------------------------------
# Name:        MidiFile.py
# Purpose:     MIDI file manipulation utilities
#
# Author:      <NAME> <emergentmusics) at (gmail . com>
#
# Created:     2008/04/17
# Copyright:   (c) 2009-2016 <NAME>
# License:     Please see License.txt for the terms under which this
#              software is distributed.
# -----------------------------------------------------------------------------

from __future__ import division, print_function
import math
import struct
import warnings

__version__ = 'HEAD'

# TICKSPERQUARTERNOTE is the number of "ticks" (time measurement in the MIDI file) that
# corresponds to one quarter note. This number is somewhat arbitrary, but should
# be chosen to provide adequate temporal resolution.
TICKSPERQUARTERNOTE = 960

controllerEventTypes = {'pan': 0x0a}

# Define some constants

MAJOR = 0
MINOR = 1
SHARPS = 1
FLATS = -1

__all__ = ['MIDIFile', 'MAJOR', 'MINOR', 'SHARPS', 'FLATS']


class GenericEvent(object):
    '''
    The event class from which specific events are derived
    '''
    evtname = None
    sec_sort_order = 0

    def __init__(self, tick, insertion_order):
        self.tick = tick
        self.insertion_order = insertion_order

    def __eq__(self, other):
        '''
        Equality operator.

        In the processing of the event list, we have need to remove duplicates.
        To do this we rely on the fact that the classes are hashable, and must
        therefore have an equality operator (__hash__() and __eq__() must both
        be defined).

        Some derived classes will need to override and consider their specific
        attributes in the comparison.
        '''
        return (self.evtname == other.evtname and self.tick == other.tick)

    def __hash__(self):
        '''
        Return a hash code for the object.

        This is needed in order to allow GenericObject classes to be used
        as the key in a dict or set. duplicate objects are removed from
        the event list by storing all the objects in a set, and then
        reconstructing the list from the set.  The only real requirement
        for the algorithm is that the hash of equal objects must be equal.
        There is probably great opportunity for improvements in the hashing
        function.
        '''
        # <NAME>'s 32 bit hash.
        a = int(self.tick)
        a = (a + 0x7ed55d16) + (a << 12)
        a = (a ^ 0xc761c23c) ^ (a >> 19)
        a = (a + 0x165667b1) + (a << 5)
        a = (a + 0xd3a2646c) ^ (a << 9)
        a = (a + 0xfd7046c5) + (a << 3)
        a = (a ^ 0xb55a4f09) ^ (a >> 16)
        return a


class NoteOn(GenericEvent):
    '''
    A class that encapsulates a note
    '''
    evtname = 'NoteOn'
    midi_status = 0x90    # 0x9x is Note On
    sec_sort_order = 3

    def __init__(self, channel, pitch, tick, duration, volume,
                 annotation=None, insertion_order=0):
        self.pitch = pitch
        self.duration = duration
        self.volume = volume
        self.channel = channel
        self.annotation = annotation
        super(NoteOn, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and self.tick == other.tick and
                self.pitch == other.pitch and self.channel == other.channel)

    # In Python 3, a class which overrides __eq__ also needs to provide __hash__,
    # because in Python 3 parent __hash__ is not inherited.
    __hash__ = GenericEvent.__hash__

    def __str__(self):
        return 'NoteOn %d at tick %d duration %d ch %d vel %d' % (
            self.pitch, self.tick, self.duration, self.channel, self.volume)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.pitch)
        midibytes += struct.pack('>B', self.volume)
        return midibytes


class NoteOff (GenericEvent):
    '''
    A class that encapsulates a Note Off event
    '''
    evtname = 'NoteOff'
    midi_status = 0x80  # 0x8x is Note Off
    sec_sort_order = 2  # must be less than that of NoteOn
    # If two events happen at the same time, the secondary sort key is
    # ``sec_sort_order``. Thus a class of events can be processed earlier than
    # another. One place this is used in the code is to make sure that note
    # off events are processed before note on events.

    def __init__(self, channel, pitch, tick, volume,
                 annotation=None, insertion_order=0):
        self.pitch = pitch
        self.volume = volume
        self.channel = channel
        self.annotation = annotation
        super(NoteOff, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and self.tick == other.tick and
                self.pitch == other.pitch and self.channel == other.channel)

    __hash__ = GenericEvent.__hash__

    def __str__(self):
        return 'NoteOff %d at tick %d ch %d vel %d' % (
            self.pitch, self.tick, self.channel, self.volume)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.pitch)
        midibytes += struct.pack('>B', self.volume)
        return midibytes


class Tempo(GenericEvent):
    '''
    A class that encapsulates a tempo meta-event
    '''
    evtname = 'Tempo'
    sec_sort_order = 3

    def __init__(self, tick, tempo, insertion_order=0):
        self.tempo = int(60000000 / tempo)
        super(Tempo, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and
                self.tick == other.tick and
                self.tempo == other.tempo)

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        # Standard MIDI File Format says:
        #
        # FF 51 03 tttttt Set Tempo (in microseconds per MIDI quarter-note)
        # This event indicates a tempo change. Another way of putting
        # "microseconds per quarter-note" is "24ths of a microsecond per MIDI
        # clock". Representing tempos as time per beat instead of beat per time
        # allows absolutely exact long-term synchronisation with a time-based
        # sync protocol such as SMPTE time code or MIDI time code. The amount
        # of accuracy provided by this tempo resolution allows a four-minute
        # piece at 120 beats per minute to be accurate within 500 usec at the
        # end of the piece. Ideally, these events should only occur where MIDI
        # clocks would be located -- this convention is intended to guarantee,
        # or at least increase the likelihood, of compatibility with other
        # synchronisation devices so that a time signature/tempo map stored in
        # this format may easily be transferred to another device.
        #
        # Six identical lower-case letters such as tttttt refer to a 24-bit value, stored
        # most-significant-byte first. The notation len refers to the

        midibytes = b""
        code = 0xFF
        subcode = 0x51
        fourbite = struct.pack('>L', self.tempo)  # big-endian uint32
        threebite = fourbite[1:4]  # Just discard the MSB
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        midibytes += struct.pack('>B', 0x03)  # length in bytes of 24-bit tempo
        midibytes += threebite
        return midibytes


class Copyright(GenericEvent):
    '''
    A class that encapsulates a copyright event
    '''
    evtname = 'Copyright'
    sec_sort_order = 1

    def __init__(self, tick, notice, insertion_order=0):
        self.notice = notice.encode("ISO-8859-1")
        super(Copyright, self).__init__(tick, insertion_order)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        # Standard MIDI File Format says:
        #
        # FF 02 len text Copyright Notice
        # Contains a copyright notice as printable ASCII text. The notice should
        # contain the characters (C), the year of the copyright, and the owner
        # of the copyright. If several pieces of music are in the same MIDI
        # File, all of the copyright notices should be placed together in this
        # event so that it will be at the beginning of the file. This event
        # should be the first event in the track chunk, at tick 0.
        midibytes = b""
        code = 0xFF
        subcode = 0x02
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        payloadLength = len(self.notice)
        payloadLengthVar = writeVarLength(payloadLength)
        for i in payloadLengthVar:
            midibytes += struct.pack("b", i)
        midibytes += self.notice
        return midibytes


class Text(GenericEvent):
    '''
    A class that encapsulates a text event
    '''
    evtname = 'Text'
    sec_sort_order = 1

    def __init__(self, tick, text, insertion_order=0):
        self.text = text.encode("ISO-8859-1")
        super(Text, self).__init__(tick, insertion_order)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xFF
        subcode = 0x01
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        payloadLength = len(self.text)
        payloadLengthVar = writeVarLength(payloadLength)
        for i in payloadLengthVar:
            midibytes += struct.pack("B", i)
        midibytes += self.text
        return midibytes


class KeySignature(GenericEvent):
    '''
    A class that encapsulates a text event
    '''
    evtname = 'KeySignature'
    sec_sort_order = 1

    def __init__(self, tick, accidentals, accidental_type, mode,
                 insertion_order=0):
        self.accidentals = accidentals
        self.accidental_type = accidental_type
        self.mode = mode
        super(KeySignature, self).__init__(tick, insertion_order)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xFF
        subcode = 0x59
        event_subtype = 0x02
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        midibytes += struct.pack('>B', event_subtype)
        midibytes += struct.pack('>b', self.accidentals * self.accidental_type)
        midibytes += struct.pack('>B', self.mode)
        return midibytes


class ProgramChange(GenericEvent):
    '''
    A class that encapsulates a program change event.
    '''
    evtname = 'ProgramChange'
    midi_status = 0xc0   # 0xcx is Program Change
    sec_sort_order = 1

    def __init__(self, channel, tick, programNumber,
                 insertion_order=0):
        self.programNumber = programNumber
        self.channel = channel
        super(ProgramChange, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and
                self.tick == other.tick and
                self.programNumber == other.programNumber and
                self.channel == other.channel)

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.programNumber)
        return midibytes


class SysExEvent(GenericEvent):
    '''
    A class that encapsulates a System Exclusive  event.
    '''
    evtname = 'SysEx'  # doesn't match class name like most others
    sec_sort_order = 1

    def __init__(self, tick, manID, payload, insertion_order=0):
        self.manID = manID
        self.payload = payload
        super(SysExEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return False

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xF0
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)

        payloadLength = writeVarLength(len(self.payload) + 2)
        for lenByte in payloadLength:
            midibytes += struct.pack('>B', lenByte)

        midibytes += struct.pack('>B', self.manID)
        midibytes += self.payload
        midibytes += struct.pack('>B', 0xF7)
        return midibytes


class UniversalSysExEvent(GenericEvent):
    '''
    A class that encapsulates a Universal System Exclusive  event.
    '''
    evtname = 'UniversalSysEx'  # doesn't match class name like most others
    sec_sort_order = 1

    def __init__(self, tick, realTime, sysExChannel, code, subcode,
                 payload, insertion_order=0):
        self.realTime = realTime
        self.sysExChannel = sysExChannel
        self.code = code
        self.subcode = subcode
        self.payload = payload
        super(UniversalSysExEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return False

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xF0
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)

        # Do we need to add a length?
        payloadLength = writeVarLength(len(self.payload) + 5)
        for lenByte in payloadLength:
            midibytes += struct.pack('>B', lenByte)

        if self.realTime:
            midibytes += struct.pack('>B', 0x7F)
        else:
            midibytes += struct.pack('>B', 0x7E)

        midibytes += struct.pack('>B', self.sysExChannel)
        midibytes += struct.pack('>B', self.code)
        midibytes += struct.pack('>B', self.subcode)
        midibytes += self.payload
        midibytes += struct.pack('>B', 0xF7)
        return midibytes


class ControllerEvent(GenericEvent):
    '''
    A class that encapsulates a program change event.
    '''
    evtname = 'ControllerEvent'
    midi_status = 0xB0  # 0xBx is Control Change
    sec_sort_order = 1

    def __init__(self, channel, tick, controller_number, parameter,
                 insertion_order=0):
        self.parameter = parameter
        self.channel = channel
        self.controller_number = controller_number
        super(ControllerEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return False

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.controller_number)
        midibytes += struct.pack('>B', self.parameter)
        return midibytes


class ChannelPressureEvent(GenericEvent):
    '''
    A class that encapsulates a Channel Pressure (Aftertouch) event.
    '''
    evtname = 'ChannelPressure'
    midi_status = 0xD0  # 0xDx is Channel Pressure (Aftertouch)
    sec_sort_order = 1

    def __init__(self, channel, tick, pressure_value, insertion_order=0):
        self.channel = channel
        self.pressure_value = pressure_value
        super(ChannelPressureEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.__class__.__name__ == other.__class__.__name__ and
                self.tick == other.tick and
                self.pressure_value == other.pressure_value and
                self.channel == other.channel)

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        vartick = writeVarLength(self.tick - previous_event_tick)
        for x in vartick:
            midibytes += struct.pack('>B', x)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', self.pressure_value)
        return midibytes


class PitchWheelEvent(GenericEvent):
    '''
    A class that encapsulates a pitch wheel change event.
    '''
    evtname = 'PitchWheelEvent'
    midi_status = 0xE0  # 0xEx is Pitch Wheel Change
    sec_sort_order = 1

    def __init__(self, channel, tick, pitch_wheel_value, insertion_order=0):
        self.channel = channel
        self.pitch_wheel_value = pitch_wheel_value
        super(PitchWheelEvent, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return False

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = self.midi_status | self.channel
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes = midibytes + struct.pack('>B', timeByte)
        MSB = (self.pitch_wheel_value + 8192) >> 7
        LSB = (self.pitch_wheel_value + 8192) & 0x7F
        midibytes = midibytes + struct.pack('>B', code)
        midibytes = midibytes + struct.pack('>B', LSB)
        midibytes = midibytes + struct.pack('>B', MSB)
        return midibytes


class TrackName(GenericEvent):
    '''
    A class that encapsulates a program change event.
    '''
    evtname = 'TrackName'
    sec_sort_order = 0

    def __init__(self, tick, trackName, insertion_order=0):
        # GenericEvent.__init__(self, tick)
        self.trackName = trackName.encode("ISO-8859-1")
        super(TrackName, self).__init__(tick, insertion_order)

    def __eq__(self, other):
        return (self.evtname == other.evtname and
                self.tick == other.tick and
                self.trackName == other.trackName)

    __hash__ = GenericEvent.__hash__

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('B', 0xFF)
        midibytes += struct.pack('B', 0X03)
        dataLength = len(self.trackName)
        dataLengthVar = writeVarLength(dataLength)
        for i in dataLengthVar:
            midibytes += struct.pack("B", i)
        midibytes += self.trackName
        return midibytes


class TimeSignature(GenericEvent):
    '''
    A class that encapsulates a time signature.
    '''
    evtname = 'TimeSignature'
    sec_sort_order = 0

    def __init__(self, tick, numerator, denominator, clocks_per_tick,
                 notes_per_quarter, insertion_order=0):
        self.numerator = numerator
        self.denominator = denominator
        self.clocks_per_tick = clocks_per_tick
        self.notes_per_quarter = notes_per_quarter
        super(TimeSignature, self).__init__(tick, insertion_order)

    def serialize(self, previous_event_tick):
        """Return a bytestring representation of the event, in the format required for
        writing into a standard midi file.
        """
        midibytes = b""
        code = 0xFF
        subcode = 0x58
        varTime = writeVarLength(self.tick - previous_event_tick)
        for timeByte in varTime:
            midibytes += struct.pack('>B', timeByte)
        midibytes += struct.pack('>B', code)
        midibytes += struct.pack('>B', subcode)
        midibytes += struct.pack('>B', 0x04)
        midibytes += struct.pack('>B', self.numerator)
        midibytes += struct.pack('>B', self.denominator)
        midibytes += struct.pack('>B', self.clocks_per_tick)
        # 32nd notes per quarter note
        midibytes += struct.pack('>B', self.notes_per_quarter)
        return midibytes


class MIDITrack(object):
    '''
    A class that encapsulates a MIDI track
    '''

    def __init__(self, removeDuplicates, deinterleave):
        '''Initialize the MIDITrack object.
        '''
        self.headerString = struct.pack('cccc', b'M', b'T', b'r', b'k')
        self.dataLength = 0  # Is calculated after the data is in place
        self.MIDIdata = b""
        self.closed = False
        self.eventList = []
        self.MIDIEventList = []
        self.remdep = removeDuplicates
        self.deinterleave = deinterleave

    def addNoteByNumber(self, channel, pitch, tick, duration, volume,
                        annotation=None, insertion_order=0):
        '''
        Add a note by chromatic MIDI number
        '''
        self.eventList.append(NoteOn(channel, pitch, tick, duration, volume,
                                     annotation=annotation,
                                     insertion_order=insertion_order))

        # This event is not in chronological order. But before writing all the
        # events to the file, I sort self.eventlist on (tick, sec_sort_order, insertion_order)
        # which puts the events in chronological order.
        self.eventList.append(NoteOff(channel, pitch, tick + duration, volume,
                                      annotation=annotation,
                                      insertion_order=insertion_order))

    def addControllerEvent(self, channel, tick, controller_number, parameter,
                           insertion_order=0):
        '''
        Add a controller event.
        '''

        self.eventList.append(ControllerEvent(channel, tick, controller_number,
                                              parameter,
                                              insertion_order=insertion_order))

    def addPitchWheelEvent(self, channel, tick, pitch_wheel_value, insertion_order=0):
        '''
        Add a pitch wheel event.
        '''
        self.eventList.append(PitchWheelEvent(channel, tick, pitch_wheel_value, insertion_order=insertion_order))

    def addTempo(self, tick, tempo, insertion_order=0):
        '''
        Add a tempo change (or set) event.
        '''
        self.eventList.append(Tempo(tick, tempo,
                                    insertion_order=insertion_order))

    def addSysEx(self, tick, manID, payload, insertion_order=0):
        '''
        Add a SysEx event.
        '''
        self.eventList.append(SysExEvent(tick, manID, payload,
                                         insertion_order=insertion_order))

    def addUniversalSysEx(self, tick, code, subcode, payload,
                          sysExChannel=0x7F, realTime=False,
                          insertion_order=0):
        '''
        Add a Universal SysEx event.
        '''
        self.eventList.append(UniversalSysExEvent(tick, realTime, sysExChannel,
                              code, subcode, payload,
                              insertion_order=insertion_order))

    def addProgramChange(self, channel, tick, program, insertion_order=0):
        '''
        Add a program change event.
        '''
        self.eventList.append(ProgramChange(channel, tick, program,
                                            insertion_order=insertion_order))

    def addChannelPressure(self, channel, tick, pressure_value, insertion_order=0):
        '''
        Add a channel pressure event.
        '''
        self.eventList.append(ChannelPressureEvent(channel, tick, pressure_value,
                                                   insertion_order=insertion_order))

    def addTrackName(self, tick, trackName, insertion_order=0):
        '''
        Add a track name event.
        '''
        self.eventList.append(TrackName(tick, trackName,
                                        insertion_order=insertion_order))

    def addTimeSignature(self, tick, numerator, denominator, clocks_per_tick,
                         notes_per_quarter, insertion_order=0):
        '''
        Add a time signature.
        '''
        self.eventList.append(TimeSignature(tick, numerator, denominator,
                                            clocks_per_tick, notes_per_quarter,
                                            insertion_order=insertion_order))

    def addCopyright(self, tick, notice, insertion_order=0):
        '''
        Add a copyright notice
        '''
        self.eventList.append(Copyright(tick, notice,
                                        insertion_order=insertion_order))

    def addKeySignature(self, tick, accidentals, accidental_type, mode,
                        insertion_order=0):
        '''
        Add a copyright notice
        '''
        self.eventList.append(KeySignature(tick, accidentals, accidental_type,
                                           mode,
                                           insertion_order=insertion_order))

    def addText(self, tick, text, insertion_order=0):
        '''
        Add a text event
        '''
        self.eventList.append(Text(tick, text,
                              insertion_order=insertion_order))

    def changeNoteTuning(self, tunings, sysExChannel=0x7F, realTime=True,
                         tuningProgam=0, insertion_order=0):
        '''
        Change the tuning of MIDI notes
        '''
        payload = struct.pack('>B', tuningProgam)
        payload = payload + struct.pack('>B', len(tunings))
        for (noteNumber, frequency) in tunings:
            payload = payload + struct.pack('>B', noteNumber)
            MIDIFreqency = frequencyTransform(frequency)
            for byte in MIDIFreqency:
                payload = payload + struct.pack('>B', byte)

        self.eventList.append(UniversalSysExEvent(0, realTime, sysExChannel,
                              8, 2, payload, insertion_order=insertion_order))

    def processEventList(self):
        '''
        Process the event list, creating a MIDIEventList,
        which is then sorted to be in chronological order by start tick.
        '''

        self.MIDIEventList = [evt for evt in self.eventList]
        # Assumptions in the code expect the list to be time-sorted.
        self.MIDIEventList.sort(key=sort_events)

        if self.deinterleave:
            self.deInterleaveNotes()

    def removeDuplicates(self):
        '''
        Remove duplicates from the eventList.

        This function will remove duplicates from the eventList. This is
        necessary because we the MIDI event stream can become confused
        otherwise.
        '''

        # For this algorithm to work, the events in the eventList must be
        # hashable (that is, they must have a __hash__() and __eq__() function
        # defined).

        s = set(self.eventList)
        self.eventList = list(s)
        self.eventList.sort(key=sort_events)

    def closeTrack(self):
        '''
        Called to close a track before writing

        This function should be called to "close a track," that is to
        prepare the actual data stream for writing. Duplicate events are
        removed from the eventList, and the MIDIEventList is created.

        Called by the parent MIDIFile object.
        '''

        if self.closed:
            return
        self.closed = True

        if self.remdep:
            self.removeDuplicates()

        self.processEventList()

    def writeMIDIStream(self):
        '''
        Write the meta data and note data to the packed MIDI stream.
        '''

        # Process the events in the eventList

        self.writeEventsToStream()

        # Write MIDI close event.

        self.MIDIdata += struct.pack('BBBB', 0x00, 0xFF, 0x2F, 0x00)

        # Calculate the entire length of the data and write to the header

        self.dataLength = struct.pack('>L', len(self.MIDIdata))

    def writeEventsToStream(self):
        '''
        Write the events in MIDIEvents to the MIDI stream.
        MIDIEventList is presumed to be already sorted in chronological order.
        '''
        previous_event_tick = 0
        for event in self.MIDIEventList:
            self.MIDIdata += event.serialize(previous_event_tick)
            # previous_event_tick = event.tick
            # I do not like that adjustTimeAndOrigin() changes GenericEvent.tick
            # from absolute to relative. I intend to change that, and just
            # calculate the relative tick here, without changing GenericEvent.tick

    def deInterleaveNotes(self):
        '''
        Correct Interleaved notes.

        Because we are writing multiple notes in no particular order, we
        can have notes which are interleaved with respect to their start
        and stop times. This method will correct that. It expects that the
        MIDIEventList has been time-ordered.
        '''

        tempEventList = []
        stack = {}

        for event in self.MIDIEventList:
            if event.evtname in ['NoteOn', 'NoteOff']:
                # !!! Pitch 101 channel 5 produces the same key as pitch 10 channel 15.
                # !!! This is not the only pair of pitch,channel tuples which
                # !!! collide to the same key, just one example.  Should fix by
                # !!! putting a separator char between pitch and channel.
                noteeventkey = str(event.pitch) + str(event.channel)
                if event.evtname == 'NoteOn':
                    if noteeventkey in stack:
                        stack[noteeventkey].append(event.tick)
                    else:
                        stack[noteeventkey] = [event.tick]
                    tempEventList.append(event)
                elif event.evtname == 'NoteOff':
                    if len(stack[noteeventkey]) > 1:
                        event.tick = stack[noteeventkey].pop()
                        tempEventList.append(event)
                    else:
                        stack[noteeventkey].pop()
                        tempEventList.append(event)
            else:
                tempEventList.append(event)

        self.MIDIEventList = tempEventList

        # Note NoteOff events have a lower secondary sort key than NoteOn
        # events, so this sort will make concomitant NoteOff events
        # processed first.

        self.MIDIEventList.sort(key=sort_events)

    def adjustTimeAndOrigin(self, origin, adjust):
        '''
        Adjust Times to be relative, and zero-origined.

        If adjust is True, the track will be shifted. Regardelss times
        are converted to relative values here.
        '''

        if len(self.MIDIEventList) == 0:
            return
        tempEventList = []
        internal_origin = origin if adjust else 0
        runningTick = 0

        for event in self.MIDIEventList:
            adjustedTick = event.tick - internal_origin
            event.tick = adjustedTick - runningTick
            runningTick = adjustedTick
            tempEventList.append(event)

        self.MIDIEventList = tempEventList

    def writeTrack(self, fileHandle):
        '''
        Write track to disk.
        '''

        fileHandle.write(self.headerString)
        fileHandle.write(self.dataLength)
        fileHandle.write(self.MIDIdata)


class MIDIHeader(object):
    '''
    Class to encapsulate the MIDI header structure.

    This class encapsulates a MIDI header structure. It isn't used for much,
    but it will create the appropriately packed identifier string that all
    MIDI files should contain. It is used by the MIDIFile class to create a
    complete and well formed MIDI pattern.

    '''
    def __init__(self, numTracks, file_format, ticks_per_quarternote):
        ''' Initialize the data structures

        :param numTracks: The number of tracks the file contains. Integer,
            one or greater
        :param file_format: The format of the multi-track file. This should
            either be ``1`` (the default, and the most widely supported
            format) or ``2``.
        :param ticks_per_quarternote: The number of ticks per quarter
            note is what the Standard MIDI File Format Specification calls
            "division".  Ticks are the integer unit of time in the SMF, and in
            every MIDI sequencer I am aware of.  Common values are 120, 240,
            384, 480, 960. Note that all these numbers are evenly divisible by
            2,3,4,6,8,12,16, and 24, except 120 does not have 16 as a divisor.
        '''
        self.headerString = struct.pack('cccc', b'M', b'T', b'h', b'd')
        self.headerSize = struct.pack('>L', 6)
        # Format 1 = multi-track file
        self.formatnum = struct.pack('>H', file_format)
        self.numeric_format = file_format
        self.numTracks = struct.pack('>H', numTracks)
        self.ticks_per_quarternote = struct.pack('>H', ticks_per_quarternote)

    def writeFile(self, fileHandle):
        fileHandle.write(self.headerString)
        fileHandle.write(self.headerSize)
        fileHandle.write(self.formatnum)
        fileHandle.write(self.numTracks)
        fileHandle.write(self.ticks_per_quarternote)


class MIDIFile(object):
    '''
    A class that encapsulates a full, well-formed MIDI file object.

    This is a container object that contains a header (:class:`MIDIHeader`),
    one or more tracks (class:`MIDITrack`), and the data associated with a
    proper and well-formed MIDI file.
    '''

    def __init__(self, numTracks=1, removeDuplicates=True, deinterleave=True,
                 adjust_origin=False, file_format=1,
                 ticks_per_quarternote=TICKSPERQUARTERNOTE, eventtime_is_ticks=False):
        '''Initialize the MIDIFile class

        :param numTracks: The number of tracks the file contains. Integer,
            one or greater
        :param removeDuplicates: If set to ``True`` remove duplicate events
            before writing to disk
        :param deinterleave: If set to ``True`` deinterleave the notes in
            the stream
        :param adjust_origin: If set to ``True`` shift all the events in the tracks 
            so that the first event takes place at time t=0. Default is ``False``
        :param file_format: The format of the multi-track file. This should
            either be ``1`` (the default, and the most widely supported
            format) or ``2``.
        :param ticks_per_quarternote: The number of ticks per quarter note is
            what the Standard MIDI File Format Specification calls "division".
            Ticks are the integer unit of time in the SMF, and in most if
            not all MIDI sequencers.  Common values are 120, 240, 384,
            480, 960. Note that all these numbers are evenly divisible by
            2,3,4,6,8,12,16, and 24, except 120 does not have 16 as a divisor.

        :param eventtime_is_ticks: If set True means event time and duration
            argument values are integer ticks instead of fractional quarter
            notes.

        Note that the default for ``adjust_origin`` will change in a future
        release, so one should probably explicitly set it.

        In a format 1 file, it would be a rare cirumstance where adjusting the
        origin of each track to the track's first note makes any sense.

        Example:

        .. code::

            # Create a two-track MIDIFile

            from midiutil.MidiFile import MIDIFile
            midi_file = MIDIFile(1, adjust_origin=False)

        A Note on File Formats
        ----------------------

        In previous versions of this code the file written was format 2
        (which can be thought of as a collection of independent tracks) but
        was identified as format 1. In this version one can specify either
        format 1 or 2.

        In format 1 files there is a separate tempo track which contains
        tempo and time signature data, but contains no note data. If one
        creates a single track format 1 file the actual file has two tracks
        -- one for tempo data and one for note data. In the track indexing
        the tempo track can be ignored. In other words track 0 is the note
        track (the second track in the file). However, tempo and time
        signature data will be written to the first, tempo track. This is
        done to try and preserve as much interoperability with previous
        versions as possible.

        In a format 2 file all tracks are indexed and the track parameter
        is interpreted literally.
        '''

        self.tracks = list()
        if file_format == 1:
            self.numTracks = numTracks + 1  # self.tracks[0] is the baked-in tempo track
        else:
            self.numTracks = numTracks
        self.header = MIDIHeader(self.numTracks, file_format, ticks_per_quarternote)

        self.adjust_origin = adjust_origin
        self.closed = False

        self.ticks_per_quarternote = ticks_per_quarternote
        self.eventtime_is_ticks = eventtime_is_ticks
        if self.eventtime_is_ticks:
            self.time_to_ticks = lambda x: x
        else:
            self.time_to_ticks = self.quarter_to_tick

        for i in range(0, self.numTracks):
            self.tracks.append(MIDITrack(removeDuplicates, deinterleave))
        # to keep track of the order of insertion for new sorting
        self.event_counter = 0

    # Public Functions. These (for the most part) wrap the MIDITrack functions,
    # where most Processing takes place.

    def quarter_to_tick(self, quarternote_time):
        return int(quarternote_time * self.ticks_per_quarternote)

    def tick_to_quarter(self, ticknum):
        return float(ticknum) / self.ticks_per_quarternote

    def addNote(self, track, channel, pitch, time, duration, volume,
                annotation=None):
        """

        Add notes to the MIDIFile object

        :param track: The track to which the note is added.
        :param channel: the MIDI channel to assign to the note. [Integer, 0-15]
        :param pitch: the MIDI pitch number [Integer, 0-127].
        :param time: the time at which the note sounds. The value can be either
            quarter notes [Float], or ticks [Integer]. Ticks may be specified by
            passing eventtime_is_ticks=True to the MIDIFile constructor.
            The default is quarter notes.
        :param duration: the duration of the note. Like the time argument, the
            value can be either quarter notes [Float], or ticks [Integer].
        :param volume: the volume (velocity) of the note. [Integer, 0-127].
        :param annotation: Arbitrary data to attach to the note.

        The ``annotation`` parameter attaches arbitrary data to the note. This
        is not used in the code, but can be useful anyway. As an example,
        I have created a project that uses MIDIFile to write
        `csound <http://csound.github.io/>`_ orchestra files directly from the
        class ``EventList``.
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addNoteByNumber(channel, pitch,
                                           self.time_to_ticks(time), self.time_to_ticks(duration),
                                           volume, annotation=annotation,
                                           insertion_order=self.event_counter)
        self.event_counter += 1

    def addTrackName(self, track, time, trackName):
        """
        Name a track.

        :param track: The track to which the name is assigned.
        :param time: The time (in beats) at which the track name event is
            placed.  In general this should probably be time 0 (the beginning
            of the track).
        :param trackName: The name to assign to the track [String]
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addTrackName(self.time_to_ticks(time), trackName,
                                        insertion_order=self.event_counter)
        self.event_counter += 1

    def addTimeSignature(self, track, time, numerator, denominator,
                         clocks_per_tick, notes_per_quarter=8):
        '''
        Add a time signature event.

        :param track: The track to which the signature is assigned. Note that
            in a format 1 file this parameter is ignored and the event is
            written to the tempo track
        :param time: The time (in beats) at which the event is placed.
            In general this should probably be time 0 (the beginning of the
            track).
        :param numerator: The numerator of the time signature. [Int]
        :param denominator: The denominator of the time signature, expressed as
            a power of two (see below). [Int]
        :param clocks_per_tick: The number of MIDI clock ticks per metronome
            click (see below).
        :param notes_per_quarter: The number of annotated 32nd notes in a MIDI
            quarter note. This is almost always 8 (the default), but some
            sequencers allow this value to be changed. Unless you know that
            your sequencing software supports it, this should be left at its
            default value.

        The data format for this event is a little obscure.

        The ``denominator`` should be specified as a power of 2, with
        a half note being one, a quarter note being two, and eight note
        being three, etc. Thus, for example, a 4/4 time signature would
        have a ``numerator`` of 4 and a ``denominator`` of 2. A 7/8 time
        signature would be a ``numerator`` of 7 and a ``denominator``
        of 3.

        The ``clocks_per_tick`` argument specifies the number of clock
        ticks per metronome click. By definition there are 24 ticks in
        a quarter note, so a metronome click per quarter note would be
        24. A click every third eighth note would be 3 * 12 = 36.

        The ``notes_per_quarter`` value is also a little confusing. It
        specifies the number of 32nd notes in a MIDI quarter note. Usually
        there are 8 32nd notes in a quarter note (8/32 = 1/4), so
        the default value is 8. However, one can change this value if
        needed. Setting it to 16, for example, would cause the music to
        play at double speed, as there would be 16/32 (or what could be
        considered *two* quarter notes for every one MIDI quarter note.

        Note that both the ``clocks_per_tick`` and the
        ``notes_per_quarter`` are specified in terms of quarter notes,
        even is the score is not a quarter-note based score (i.e.,
        even if the denominator is not ``4``). So if you're working with a
        time signature of, say, 6/8, one still needs to specify the clocks
        per quarter note.
        '''
        if self.header.numeric_format == 1:
            track = 0

        self.tracks[track].addTimeSignature(self.time_to_ticks(time), numerator, denominator,
                                            clocks_per_tick, notes_per_quarter,
                                            insertion_order=self.event_counter)
        self.event_counter += 1

    def addTempo(self, track, time, tempo):
        """

        Add notes to the MIDIFile object

        :param track: The track to which the tempo event  is added. Note that
            in a format 1 file this parameter is ignored and the tempo is
            written to the tempo track
        :param time: The time (in beats) at which tempo event is placed
        :param tempo: The tempo, in Beats per Minute. [Integer]
        """
        if self.header.numeric_format == 1:
            track = 0
        self.tracks[track].addTempo(self.time_to_ticks(time), tempo,
                                    insertion_order=self.event_counter)
        self.event_counter += 1

    def addCopyright(self, track, time, notice):
        """

        Add a copyright notice to the MIDIFile object

        :param track: The track to which the notice is added.
        :param time: The time (in beats) at which notice event is placed. In
            general this sould be time t=0
        :param notice: The copyright notice [String]
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addCopyright(self.time_to_ticks(time), notice,
                                        insertion_order=self.event_counter)
        self.event_counter += 1

    def addKeySignature(self, track, time, accidentals, accidental_type, mode,
                        insertion_order=0):
        '''
        Add a Key Signature to a track

        :param track: The track to which this should be added
        :param time: The time at which the signature should be placed
        :param accidentals: The number of accidentals in the key signature
        :param accidental_type: The type of accidental
        :param mode: The mode of the scale

        The easiest way to use this function is to make sure that the symbolic
        constants for accidental_type and mode are imported. By doing this:

        .. code::

            from midiutil.MidiFile import *

        one gets the following constants defined:

        * ``SHARPS``
        * ``FLATS``
        * ``MAJOR``
        * ``MINOR``

        So, for example, if one wanted to create a key signature for a minor
        scale with three sharps:

        .. code::

            MyMIDI.addKeySignature(0, 0, 3, SHARPS, MINOR)
        '''
        if self.header.numeric_format == 1:
            track = 0  # User reported that this is needed.
        self.tracks[track].addKeySignature(self.time_to_ticks(time), accidentals, accidental_type,
                                           mode, insertion_order=self.event_counter)
        self.event_counter += 1

    def addText(self, track, time, text):
        """

        Add a text event

        :param track: The track to which the notice is added.
        :param time: The time (in beats) at which text event is placed.
        :param text: The text to adde [ASCII String]
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addText(self.time_to_ticks(time), text,
                                   insertion_order=self.event_counter)
        self.event_counter += 1

    def addProgramChange(self, tracknum, channel, time, program):
        """

        Add a MIDI program change event.

        :param tracknum: The zero-based track number to which program change event is added.
        :param channel: the MIDI channel to assign to the event.
            [Integer, 0-15]
        :param time: The time (in beats) at which the program change event is
            placed [Float].
        :param program: the program number. [Integer, 0-127].
        """
        if self.header.numeric_format == 1:
            tracknum += 1
        self.tracks[tracknum].addProgramChange(channel, self.time_to_ticks(time), program,
                                               insertion_order=self.event_counter)
        self.event_counter += 1

    def addChannelPressure(self, tracknum, channel, time, pressure_value):
        """
        Add a Channel Pressure event.

        :param tracknum: The zero-based track number to which channel pressure event is added.
        :param channel: the MIDI channel to assign to the event.
            [Integer, 0-15]
        :param time: The time (in beats) at which the channel pressure event is
            placed [Float].
        :param pressure_value: the pressure value. [Integer, 0-127].
        """
        if self.header.numeric_format == 1:
            tracknum += 1
        track = self.tracks[tracknum]
        track.addChannelPressure(channel, self.time_to_ticks(time), pressure_value,
                                 insertion_order=self.event_counter)
        self.event_counter += 1

    def addControllerEvent(self, track, channel, time, controller_number,
                           parameter):
        """

        Add a channel control event

        :param track: The track to which the event is added.
        :param channel: the MIDI channel to assign to the event.
            [Integer, 0-15]
        :param time: The time (in beats) at which the event is placed [Float].
        :param controller_number: The controller ID of the event.
        :param parameter: The event's parameter, the meaning of which varies by
            event type.
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addControllerEvent(channel, self.time_to_ticks(time), controller_number,
                                              parameter, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1

    def addPitchWheelEvent(self, track, channel, time, pitchWheelValue):
        """

        Add a channel pitch wheel event

        :param track: The track to which the event is added.
        :param channel: the MIDI channel to assign to the event. [Integer, 0-15]
        :param time: The time (in beats) at which the event is placed [Float].
        :param pitchWheelValue: 0 for no pitch change. [Integer, -8192-8192]
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addPitchWheelEvent(channel, self.time_to_ticks(time), pitchWheelValue,
                                              insertion_order=self.event_counter)
        self.event_counter += 1

    def makeRPNCall(self, track, channel, time, controller_msb, controller_lsb,
                    data_msb, data_lsb, time_order=False):
        '''

        Perform a Registered Parameter Number Call

        :param track: The track to which this applies
        :param channel: The channel to which this applies
        :param time: The time of the event
        :param controller_msb: The Most significant byte of the controller. In
            common usage this will usually be 0
        :param controller_lsb: The Least significant Byte for the controller
            message. For example, for a fine-tuning change this would be 01.
        :param data_msb: The Most Significant Byte of the controller's
            parameter.
        :param data_lsb: The Least Significant Byte of the controller's
            parameter. If not needed this should be set to ``None``
        :param time_order: Order the control events in time (see below)

        As an example, if one were to change a channel's tuning program::

            makeRPNCall(track, channel, time, 0, 3, 0, program)

        (Note, however, that there is a convenience function,
        ``changeTuningProgram``, that does this for you.)

        Registered/Non-Registered Parameter Number (RPN / NRPN)
        -------------------------------------------------------
        Controller number 6 (Data Entry), in conjunction with Controller numbers 96
        (Data Increment), 97 (Data Decrement), 98 (Registered Parameter Number LSB),
        99 (Registered Parameter Number MSB), 100 (Non-Registered Parameter Number
        LSB), and 101 (Non-Registered Parameter Number MSB), extend the number of
        controllers available via MIDI. Parameter data is transferred by first
        selecting the parameter number to be edited using controllers 98 and 99 or
        100 and 101, and then adjusting the data value for that parameter using
        controller number 6, 96, or 97.

        RPN and NRPN are typically used to send parameter data to a synthesizer in
        order to edit sound patches or other data. Registered parameters are those
        which have been assigned some particular function by the MIDI Manufacturers
        Association (MMA) and the Japan MIDI Standards Committee (JMSC). For
        example, there are Registered Parameter numbers assigned to control pitch
        bend sensitivity and master tuning for a synthesizer. Non-Registered
        parameters have not been assigned specific functions, and may be used for
        different functions by different manufacturers.

        The ``time_order`` parameter is something of a work-around for
        sequencers that do not preserve the order of events from the MIDI files
        they import. Within this code care is taken to preserve the order of
        events as specified, but some sequencers seem to transmit events
        occurring at the same time in an arbitrary order.  By setting this
        parameter to ``True`` something of a work-around is performed: each
        successive event (of which there are three or four for this event type)
        is placed in the time stream a small delta from the preceding one.
        Thus, for example, the controllers are set before the data bytes in
        this call.
        '''
        tick = self.time_to_ticks(time)

        if self.header.numeric_format == 1:
            track += 1
        track = self.tracks[track]

        tick_incr = 1 if time_order else 0
        track.addControllerEvent(channel, tick, 101,  # parameter number MSB
                                 controller_msb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        track.addControllerEvent(channel, tick, 100,
                                 controller_lsb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        track.addControllerEvent(channel, tick, 6,
                                 data_msb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        if data_lsb is not None:
            track.addControllerEvent(channel, tick, 38,
                                     data_lsb, insertion_order=self.event_counter)  # noqa: E128
            self.event_counter += 1

    def makeNRPNCall(self, track, channel, time, controller_msb,
                     controller_lsb, data_msb, data_lsb, time_order=False):
        '''

        Perform a Non-Registered Parameter Number Call

        :param track: The track to which this applies
        :param channel: The channel to which this applies
        :param time: The time of the event
        :param controller_msb: The Most significant byte of thecontroller. In
            common usage this will usually be 0
        :param controller_lsb: The least significant byte for the controller
            message. For example, for a fine-tunning change this would be 01.
        :param data_msb: The most significant byte of the controller's
            parameter.
        :param data_lsb: The least significant byte of the controller's
            parameter. If none is needed this should be set to ``None``
        :param time_order: Order the control events in time (see below)

        The ``time_order`` parameter is something of a work-around for
        sequencers that do not preserve the order of events from the MIDI files
        they import. Within this code care is taken to preserve the order of
        events as specified, but some sequencers seem to transmit events
        occurring at the same time in an arbitrary order.  By setting this
        parameter to ``True`` something of a work-around is performed: each
        successive event (of which there are three or four for this event type)
        is placed in the time stream a small delta from the preceding one.
        Thus, for example, the controllers are set before the data bytes in
        this call.

        '''
        tick = self.time_to_ticks(time)

        if self.header.numeric_format == 1:
            track += 1
        track = self.tracks[track]

        tick_incr = 1 if time_order else 0
        track.addControllerEvent(channel, tick, 99,
                                 controller_msb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        track.addControllerEvent(channel, tick, 98,
                                 controller_lsb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        track.addControllerEvent(channel, tick, 6,
                                 data_msb, insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1
        tick += tick_incr
        if data_lsb is not None:
            track.addControllerEvent(channel, tick, 38,
                                     data_lsb, insertion_order=self.event_counter)  # noqa: E128
            self.event_counter += 1

    def changeTuningBank(self, track, channel, time, bank, time_order=False):
        '''

        Change the tuning bank for a selected track

        :param track: The track to which the data should be written
        :param channel: The channel for the event
        :param time: The time of the event
        :param bank: The tuning bank (0-127)
        :param time_order: Preserve the ordering of the component events by
            ordering in time. See ``makeRPNCall()`` for a discussion of when
            this may be necessary

        Note that this is a convenience function, as the same
        functionality is available from directly sequencing controller
        events.

        The specified tuning should already have been written to the
        stream with ``changeNoteTuning``.  '''
        self.makeRPNCall(track, channel, time, 0, 4, 0, bank,
                         time_order=time_order)

    def changeTuningProgram(self, track, channel, time, program,
                            time_order=False):
        '''

        Change the tuning program for a selected track

        :param track: The track to which the data should be written
        :param channel: The channel for the event
        :param time: The time of the event
        :param program: The tuning program number (0-127)
        :param time_order: Preserve the ordering of the component events by
            ordering in time. See ``makeRPNCall()`` for a discussion of when
            this may be necessary

        Note that this is a convenience function, as the same
        functionality is available from directly sequencing controller
        events.

        The specified tuning should already have been written to the
        stream with ``changeNoteTuning``.
        '''
        self.makeRPNCall(track, channel, time, 0, 3, 0, program,
                         time_order=time_order)

    def changeNoteTuning(self, track, tunings, sysExChannel=0x7F,
                         realTime=True, tuningProgam=0):
        """
        Add a real-time MIDI tuning standard update to a track.

        :param track: The track to which the tuning is applied.
        :param tunings: A list to tuples representing the tuning. See below for
            an explanation.
        :param sysExChannel: The SysEx channel of the event. This is mapped to
            "manufacturer ID" in the event which is written. Unless there is a
            specific reason for changing it, it should be left at its default
            value.
        :param realTime: Speicifes if the Universal SysEx event should be
            flagged as real-time or non-real-time. As with the ``sysExChannel``
            argument, this should in general be left at it's default value.
        :param tuningProgram: The tuning program number.

        This function specifically implements the "real time single note tuning
        change" (although the name is misleading, as multiple notes can be
        included in each event). It should be noted that not all hardware or
        software implements the MIDI tuning standard, and that which does often
        does not implement it in its entirety.

        The ``tunings`` argument is a list of tuples, in (*note number*,
        *frequency*) format.  As an example, if one wanted to change the
        frequency on MIDI note 69 to 500 (it is normally 440 Hz), one could do
        it thus:

        .. code:: python

            from midiutil.MidiFile import MIDIFile
            MyMIDI = MIDIFile(1)
            tuning = [(69, 500)]
            MyMIDI.changeNoteTuning(0, tuning, tuningProgam=0)
        """
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].changeNoteTuning(tunings, sysExChannel, realTime,
                                            tuningProgam,
                                            insertion_order=self.event_counter)
        self.event_counter += 1

    def addSysEx(self, track, time, manID, payload):
        '''

        Add a System Exclusive event.

        :param track: The track to which the event should be written
        :param time: The time of the event.
        :param manID: The manufacturer ID for the event
        :param payload: The payload for the event. This should be a
            binary-packed value, and will vary for each type and function.

        **Note**: This is a low-level MIDI function, so care must be used in
        constructing the payload. It is recommended that higher-level helper
        functions be written to wrap this function and construct the payload if
        a developer finds him or herself using the function heavily.

        '''
        tick = self.time_to_ticks(time)
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addSysEx(tick, manID, payload,
                                    insertion_order=self.event_counter)
        self.event_counter += 1

    def addUniversalSysEx(self, track, time, code, subcode, payload,
                          sysExChannel=0x7F, realTime=False):
        '''

        Add a Univeral System Exclusive event.

        :param track: The track to which the event should be written
        :param time: The time of the event, in beats.
        :param code: The event code. [Integer]
        :param subcode: The event sub-code [Integer]
        :param payload: The payload for the event. This should be a
            binary-packed value, and will vary for each type and function.
        :param sysExChannel: The SysEx channel.
        :param realTime: Sets the real-time flag. Defaults to non-real-time.
        :param manID: The manufacturer ID for the event


        **Note**: This is a low-level MIDI function, so care must be used in
        constructing the payload. It is recommended that higher-level helper
        functions be written to wrap this function and construct the payload if
        a developer finds him or herself using the function heavily. As an
        example of such a helper function, see the ``changeNoteTuning()``
        function, which uses the event to create a real-time note tuning
        update.

        '''
        tick = self.time_to_ticks(time)
        if self.header.numeric_format == 1:
            track += 1
        self.tracks[track].addUniversalSysEx(tick, code, subcode, payload,
                                             sysExChannel, realTime,
                                             insertion_order=self.event_counter)  # noqa: E128
        self.event_counter += 1

    def writeFile(self, fileHandle):
        '''
        Write the MIDI File.

        :param fileHandle: A file handle that has been opened for binary
            writing.
        '''

        self.header.writeFile(fileHandle)

        # Close the tracks and have them create the MIDI event data structures.
        self.close()

        # Write the MIDI Events to file.
        for i in range(0, self.numTracks):
            self.tracks[i].writeTrack(fileHandle)

    def shiftTracks(self, offset=0):
        """Shift tracks to be zero-origined, or origined at offset.

        Note that the shifting of the time in the tracks uses the MIDIEventList
        -- in other words it is assumed to be called in the stage where the
        MIDIEventList has been created. This function, however, it meant to
        operate on the eventList itself.
        """
        origin = 100000000  # A little silly, but we'll assume big enough
        tick_offset = self.time_to_ticks(offset)

        for track in self.tracks:
            if len(track.eventList) > 0:
                for event in track.eventList:
                    if event.tick < origin:
                        origin = event.tick

        for track in self.tracks:
            tempEventList = []
            # runningTick = 0

            for event in track.eventList:
                adjustedTick = event.tick - origin
                # event.time = adjustedTime - runningTick + tick_offset
                event.tick = adjustedTick + tick_offset
                # runningTick = adjustedTick
                tempEventList.append(event)

            track.eventList = tempEventList

    # End Public Functions ########################

    def close(self):
        '''
        Close the MIDIFile for further writing.

        To close the File for events, we must close the tracks, adjust the time
        to be zero-origined, and have the tracks write to their MIDI Stream
        data structure.
        '''

        if self.closed:
            return

        for i in range(0, self.numTracks):
            self.tracks[i].closeTrack()
            # We want things like program changes to come before notes when
            # they are at the same time, so we sort the MIDI events by both
            # their start time and a secondary ordinality defined for each kind
            # of event.
            self.tracks[i].MIDIEventList.sort(key=sort_events)

        origin = self.findOrigin()

        for i in range(0, self.numTracks):
            self.tracks[i].adjustTimeAndOrigin(origin, self.adjust_origin)
            self.tracks[i].writeMIDIStream()

        self.closed = True

    def findOrigin(self):
        '''
        Find the earliest time in the file's tracks.append.
        '''
        origin = 100000000  # A little silly, but we'll assume big enough

    # Note: This code assumes that the MIDIEventList has been sorted, so this
    # should be insured before it is called. It is probably a poor design to do
    # this.
    # TODO: -- Consider making this less efficient but more robust by not
    #          assuming the list to be sorted.

        for track in self.tracks:
            if len(track.MIDIEventList) > 0:
                if track.MIDIEventList[0].tick < origin:
                    origin = track.MIDIEventList[0].tick

        return origin


def writeVarLength(i):
    '''
    Accept an integer, and serialize it as a MIDI file variable length quantity

    Some numbers in MTrk chunks are represented in a form called a variable-
    length quantity.  These numbers are represented in a sequence of bytes,
    each byte holding seven bits of the number, and ordered most significant
    bits first. All bytes in the sequence except the last have bit 7 set,
    and the last byte has bit 7 clear.  This form allows smaller numbers to
    be stored in fewer bytes.  For example, if the number is between 0 and
    127, it is thus represented exactly as one byte.  A number between 128
    and 16383 uses two bytes, and so on.

    Examples:
    Number  VLQ
    128     81 00
    8192    C0 00
    16383   FF 7F
    16384   81 80 00
    '''
    if i == 0:
        return [0]

    vlbytes = []
    hibit = 0x00  # low-order byte has high bit cleared.
    while i > 0:
        vlbytes.append(((i & 0x7f) | hibit) & 0xff)
        i >>= 7
        hibit = 0x80
    vlbytes.reverse()  # put most-significant byte first, least significant last
    return vlbytes


# readVarLength is taken from the MidiFile class.

def readVarLength(offset, buffer):
    '''
    A function to read a MIDI variable length variable.

    It returns a tuple of the value read and the number of bytes processed. The
    input is an offset into the buffer, and the buffer itself.
    '''
    toffset = offset
    output = 0
    bytesRead = 0
    while True:
        output = output << 7
        byte = struct.unpack_from('>B', buffer, toffset)[0]
        toffset = toffset + 1
        bytesRead = bytesRead + 1
        output = output + (byte & 127)
        if (byte & 128) == 0:
            break
    return (output, bytesRead)


def frequencyTransform(freq):
    '''
    Returns a three-byte transform of a frequency.
    '''
    resolution = 16384
    freq = float(freq)
    dollars = 69 + 12 * math.log(freq / (float(440)), 2)
    firstByte = int(dollars)
    lowerFreq = 440 * pow(2.0, ((float(firstByte) - 69.0) / 12.0))
    centDif = 1200 * math.log((freq / lowerFreq), 2) if freq != lowerFreq else 0
    cents = round(centDif / 100 * resolution)  # round?
    secondByte = min([int(cents) >> 7, 0x7F])
    thirdByte = cents - (secondByte << 7)
    thirdByte = min([thirdByte, 0x7f])
    if thirdByte == 0x7f and secondByte == 0x7F and firstByte == 0x7F:
        thirdByte = 0x7e
    thirdByte = int(thirdByte)
    return [firstByte, secondByte, thirdByte]


def returnFrequency(freqBytes):
    '''
    The reverse of frequencyTransform. Given a byte stream, return a frequency.
    '''
    resolution = 16384.0
    baseFrequency = 440 * pow(2.0, (float(freqBytes[0] - 69.0) / 12.0))
    frac = (float((int(freqBytes[1]) << 7) + int(freqBytes[2])) * 100.0) / resolution
    frequency = baseFrequency * pow(2.0, frac / 1200.0)
    return frequency


def sort_events(event):
    '''
    .. py:function:: sort_events(event)

        The key function used to sort events (both MIDI and Generic)

        :param event: An object of type :class:`MIDIEvent` or (a derrivative)
            :class:`GenericEvent`

        This function should be provided as the ``key`` for both
        ``list.sort()`` and ``sorted()``. By using it sorting will be as
        follows:

        * Events are ordered in time. An event that takes place earlier will
          appear earlier
        * If two events happen at the same time, the secondary sort key is
          ``sec_sort_order``. Thus a class of events can be processed earlier
          than another. One place this is used in the code is to make sure that
          note off events are processed before note on events.
        * If event time and event ordinality are the same, they are sorted in
          the order in which they were originally added to the list. Thus, for
          example, if one is making an RPN call one can specify the controller
          change events in the proper order and be sure that they will end up in
          the file that way.
    '''

    return (event.tick, event.sec_sort_order, event.insertion_order)
# ----------------------------------------------------------------------------- # Name:        MidiFile.py # Purpose:     MIDI file manipulation utilities # # Author:      <NAME> <emergentmusics) at (gmail . com> # # Created:     2008/04/17 # Copyright:   (c) 2009-2016 <NAME> # License:     Please see License.txt for the terms under which this #              software is distributed. # ----------------------------------------------------------------------------- # TICKSPERQUARTERNOTE is the number of "ticks" (time measurement in the MIDI file) that # corresponds to one quarter note. This number is somewhat arbitrary, but should # be chosen to provide adequate temporal resolution. # Define some constants The event class from which specific events are derived Equality operator.          In the processing of the event list, we have need to remove duplicates.         To do this we rely on the fact that the classes are hashable, and must         therefore have an equality operator (__hash__() and __eq__() must both         be defined).          Some derived classes will need to override and consider their specific         attributes in the comparison. Return a hash code for the object.          This is needed in order to allow GenericObject classes to be used         as the key in a dict or set. duplicate objects are removed from         the event list by storing all the objects in a set, and then         reconstructing the list from the set.  The only real requirement         for the algorithm is that the hash of equal objects must be equal.         There is probably great opportunity for improvements in the hashing         function. # <NAME>'s 32 bit hash. A class that encapsulates a note # 0x9x is Note On # In Python 3, a class which overrides __eq__ also needs to provide __hash__, # because in Python 3 parent __hash__ is not inherited. Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a Note Off event # 0x8x is Note Off # must be less than that of NoteOn # If two events happen at the same time, the secondary sort key is # ``sec_sort_order``. Thus a class of events can be processed earlier than # another. One place this is used in the code is to make sure that note # off events are processed before note on events. Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a tempo meta-event Return a bytestring representation of the event, in the format required for         writing into a standard midi file. # Standard MIDI File Format says: # # FF 51 03 tttttt Set Tempo (in microseconds per MIDI quarter-note) # This event indicates a tempo change. Another way of putting # "microseconds per quarter-note" is "24ths of a microsecond per MIDI # clock". Representing tempos as time per beat instead of beat per time # allows absolutely exact long-term synchronisation with a time-based # sync protocol such as SMPTE time code or MIDI time code. The amount # of accuracy provided by this tempo resolution allows a four-minute # piece at 120 beats per minute to be accurate within 500 usec at the # end of the piece. Ideally, these events should only occur where MIDI # clocks would be located -- this convention is intended to guarantee, # or at least increase the likelihood, of compatibility with other # synchronisation devices so that a time signature/tempo map stored in # this format may easily be transferred to another device. # # Six identical lower-case letters such as tttttt refer to a 24-bit value, stored # most-significant-byte first. The notation len refers to the # big-endian uint32 # Just discard the MSB # length in bytes of 24-bit tempo A class that encapsulates a copyright event Return a bytestring representation of the event, in the format required for         writing into a standard midi file. # Standard MIDI File Format says: # # FF 02 len text Copyright Notice # Contains a copyright notice as printable ASCII text. The notice should # contain the characters (C), the year of the copyright, and the owner # of the copyright. If several pieces of music are in the same MIDI # File, all of the copyright notices should be placed together in this # event so that it will be at the beginning of the file. This event # should be the first event in the track chunk, at tick 0. A class that encapsulates a text event Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a text event Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a program change event. # 0xcx is Program Change Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a System Exclusive  event. # doesn't match class name like most others Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a Universal System Exclusive  event. # doesn't match class name like most others Return a bytestring representation of the event, in the format required for         writing into a standard midi file. # Do we need to add a length? A class that encapsulates a program change event. # 0xBx is Control Change Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a Channel Pressure (Aftertouch) event. # 0xDx is Channel Pressure (Aftertouch) Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a pitch wheel change event. # 0xEx is Pitch Wheel Change Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a program change event. # GenericEvent.__init__(self, tick) Return a bytestring representation of the event, in the format required for         writing into a standard midi file. A class that encapsulates a time signature. Return a bytestring representation of the event, in the format required for         writing into a standard midi file. # 32nd notes per quarter note A class that encapsulates a MIDI track Initialize the MIDITrack object. # Is calculated after the data is in place Add a note by chromatic MIDI number # This event is not in chronological order. But before writing all the # events to the file, I sort self.eventlist on (tick, sec_sort_order, insertion_order) # which puts the events in chronological order. Add a controller event. Add a pitch wheel event. Add a tempo change (or set) event. Add a SysEx event. Add a Universal SysEx event. Add a program change event. Add a channel pressure event. Add a track name event. Add a time signature. Add a copyright notice Add a copyright notice Add a text event Change the tuning of MIDI notes Process the event list, creating a MIDIEventList,         which is then sorted to be in chronological order by start tick. # Assumptions in the code expect the list to be time-sorted. Remove duplicates from the eventList.          This function will remove duplicates from the eventList. This is         necessary because we the MIDI event stream can become confused         otherwise. # For this algorithm to work, the events in the eventList must be # hashable (that is, they must have a __hash__() and __eq__() function # defined). Called to close a track before writing          This function should be called to "close a track," that is to         prepare the actual data stream for writing. Duplicate events are         removed from the eventList, and the MIDIEventList is created.          Called by the parent MIDIFile object. Write the meta data and note data to the packed MIDI stream. # Process the events in the eventList # Write MIDI close event. # Calculate the entire length of the data and write to the header Write the events in MIDIEvents to the MIDI stream.         MIDIEventList is presumed to be already sorted in chronological order. # previous_event_tick = event.tick # I do not like that adjustTimeAndOrigin() changes GenericEvent.tick # from absolute to relative. I intend to change that, and just # calculate the relative tick here, without changing GenericEvent.tick Correct Interleaved notes.          Because we are writing multiple notes in no particular order, we         can have notes which are interleaved with respect to their start         and stop times. This method will correct that. It expects that the         MIDIEventList has been time-ordered. # !!! Pitch 101 channel 5 produces the same key as pitch 10 channel 15. # !!! This is not the only pair of pitch,channel tuples which # !!! collide to the same key, just one example.  Should fix by # !!! putting a separator char between pitch and channel. # Note NoteOff events have a lower secondary sort key than NoteOn # events, so this sort will make concomitant NoteOff events # processed first. Adjust Times to be relative, and zero-origined.          If adjust is True, the track will be shifted. Regardelss times         are converted to relative values here. Write track to disk. Class to encapsulate the MIDI header structure.      This class encapsulates a MIDI header structure. It isn't used for much,     but it will create the appropriately packed identifier string that all     MIDI files should contain. It is used by the MIDIFile class to create a     complete and well formed MIDI pattern. Initialize the data structures          :param numTracks: The number of tracks the file contains. Integer,             one or greater         :param file_format: The format of the multi-track file. This should             either be ``1`` (the default, and the most widely supported             format) or ``2``.         :param ticks_per_quarternote: The number of ticks per quarter             note is what the Standard MIDI File Format Specification calls             "division".  Ticks are the integer unit of time in the SMF, and in             every MIDI sequencer I am aware of.  Common values are 120, 240,             384, 480, 960. Note that all these numbers are evenly divisible by             2,3,4,6,8,12,16, and 24, except 120 does not have 16 as a divisor. # Format 1 = multi-track file A class that encapsulates a full, well-formed MIDI file object.      This is a container object that contains a header (:class:`MIDIHeader`),     one or more tracks (class:`MIDITrack`), and the data associated with a     proper and well-formed MIDI file. Initialize the MIDIFile class          :param numTracks: The number of tracks the file contains. Integer,             one or greater         :param removeDuplicates: If set to ``True`` remove duplicate events             before writing to disk         :param deinterleave: If set to ``True`` deinterleave the notes in             the stream         :param adjust_origin: If set to ``True`` shift all the events in the tracks              so that the first event takes place at time t=0. Default is ``False``         :param file_format: The format of the multi-track file. This should             either be ``1`` (the default, and the most widely supported             format) or ``2``.         :param ticks_per_quarternote: The number of ticks per quarter note is             what the Standard MIDI File Format Specification calls "division".             Ticks are the integer unit of time in the SMF, and in most if             not all MIDI sequencers.  Common values are 120, 240, 384,             480, 960. Note that all these numbers are evenly divisible by             2,3,4,6,8,12,16, and 24, except 120 does not have 16 as a divisor.          :param eventtime_is_ticks: If set True means event time and duration             argument values are integer ticks instead of fractional quarter             notes.          Note that the default for ``adjust_origin`` will change in a future         release, so one should probably explicitly set it.          In a format 1 file, it would be a rare cirumstance where adjusting the         origin of each track to the track's first note makes any sense.          Example:          .. code::              # Create a two-track MIDIFile              from midiutil.MidiFile import MIDIFile             midi_file = MIDIFile(1, adjust_origin=False)          A Note on File Formats         ----------------------          In previous versions of this code the file written was format 2         (which can be thought of as a collection of independent tracks) but         was identified as format 1. In this version one can specify either         format 1 or 2.          In format 1 files there is a separate tempo track which contains         tempo and time signature data, but contains no note data. If one         creates a single track format 1 file the actual file has two tracks         -- one for tempo data and one for note data. In the track indexing         the tempo track can be ignored. In other words track 0 is the note         track (the second track in the file). However, tempo and time         signature data will be written to the first, tempo track. This is         done to try and preserve as much interoperability with previous         versions as possible.          In a format 2 file all tracks are indexed and the track parameter         is interpreted literally. # self.tracks[0] is the baked-in tempo track # to keep track of the order of insertion for new sorting # Public Functions. These (for the most part) wrap the MIDITrack functions, # where most Processing takes place. Add notes to the MIDIFile object          :param track: The track to which the note is added.         :param channel: the MIDI channel to assign to the note. [Integer, 0-15]         :param pitch: the MIDI pitch number [Integer, 0-127].         :param time: the time at which the note sounds. The value can be either             quarter notes [Float], or ticks [Integer]. Ticks may be specified by             passing eventtime_is_ticks=True to the MIDIFile constructor.             The default is quarter notes.         :param duration: the duration of the note. Like the time argument, the             value can be either quarter notes [Float], or ticks [Integer].         :param volume: the volume (velocity) of the note. [Integer, 0-127].         :param annotation: Arbitrary data to attach to the note.          The ``annotation`` parameter attaches arbitrary data to the note. This         is not used in the code, but can be useful anyway. As an example,         I have created a project that uses MIDIFile to write         `csound <http://csound.github.io/>`_ orchestra files directly from the         class ``EventList``. Name a track.          :param track: The track to which the name is assigned.         :param time: The time (in beats) at which the track name event is             placed.  In general this should probably be time 0 (the beginning             of the track).         :param trackName: The name to assign to the track [String] Add a time signature event.          :param track: The track to which the signature is assigned. Note that             in a format 1 file this parameter is ignored and the event is             written to the tempo track         :param time: The time (in beats) at which the event is placed.             In general this should probably be time 0 (the beginning of the             track).         :param numerator: The numerator of the time signature. [Int]         :param denominator: The denominator of the time signature, expressed as             a power of two (see below). [Int]         :param clocks_per_tick: The number of MIDI clock ticks per metronome             click (see below).         :param notes_per_quarter: The number of annotated 32nd notes in a MIDI             quarter note. This is almost always 8 (the default), but some             sequencers allow this value to be changed. Unless you know that             your sequencing software supports it, this should be left at its             default value.          The data format for this event is a little obscure.          The ``denominator`` should be specified as a power of 2, with         a half note being one, a quarter note being two, and eight note         being three, etc. Thus, for example, a 4/4 time signature would         have a ``numerator`` of 4 and a ``denominator`` of 2. A 7/8 time         signature would be a ``numerator`` of 7 and a ``denominator``         of 3.          The ``clocks_per_tick`` argument specifies the number of clock         ticks per metronome click. By definition there are 24 ticks in         a quarter note, so a metronome click per quarter note would be         24. A click every third eighth note would be 3 * 12 = 36.          The ``notes_per_quarter`` value is also a little confusing. It         specifies the number of 32nd notes in a MIDI quarter note. Usually         there are 8 32nd notes in a quarter note (8/32 = 1/4), so         the default value is 8. However, one can change this value if         needed. Setting it to 16, for example, would cause the music to         play at double speed, as there would be 16/32 (or what could be         considered *two* quarter notes for every one MIDI quarter note.          Note that both the ``clocks_per_tick`` and the         ``notes_per_quarter`` are specified in terms of quarter notes,         even is the score is not a quarter-note based score (i.e.,         even if the denominator is not ``4``). So if you're working with a         time signature of, say, 6/8, one still needs to specify the clocks         per quarter note. Add notes to the MIDIFile object          :param track: The track to which the tempo event  is added. Note that             in a format 1 file this parameter is ignored and the tempo is             written to the tempo track         :param time: The time (in beats) at which tempo event is placed         :param tempo: The tempo, in Beats per Minute. [Integer] Add a copyright notice to the MIDIFile object          :param track: The track to which the notice is added.         :param time: The time (in beats) at which notice event is placed. In             general this sould be time t=0         :param notice: The copyright notice [String] Add a Key Signature to a track          :param track: The track to which this should be added         :param time: The time at which the signature should be placed         :param accidentals: The number of accidentals in the key signature         :param accidental_type: The type of accidental         :param mode: The mode of the scale          The easiest way to use this function is to make sure that the symbolic         constants for accidental_type and mode are imported. By doing this:          .. code::              from midiutil.MidiFile import *          one gets the following constants defined:          * ``SHARPS``         * ``FLATS``         * ``MAJOR``         * ``MINOR``          So, for example, if one wanted to create a key signature for a minor         scale with three sharps:          .. code::              MyMIDI.addKeySignature(0, 0, 3, SHARPS, MINOR) # User reported that this is needed. Add a text event          :param track: The track to which the notice is added.         :param time: The time (in beats) at which text event is placed.         :param text: The text to adde [ASCII String] Add a MIDI program change event.          :param tracknum: The zero-based track number to which program change event is added.         :param channel: the MIDI channel to assign to the event.             [Integer, 0-15]         :param time: The time (in beats) at which the program change event is             placed [Float].         :param program: the program number. [Integer, 0-127]. Add a Channel Pressure event.          :param tracknum: The zero-based track number to which channel pressure event is added.         :param channel: the MIDI channel to assign to the event.             [Integer, 0-15]         :param time: The time (in beats) at which the channel pressure event is             placed [Float].         :param pressure_value: the pressure value. [Integer, 0-127]. Add a channel control event          :param track: The track to which the event is added.         :param channel: the MIDI channel to assign to the event.             [Integer, 0-15]         :param time: The time (in beats) at which the event is placed [Float].         :param controller_number: The controller ID of the event.         :param parameter: The event's parameter, the meaning of which varies by             event type. # noqa: E128 Add a channel pitch wheel event          :param track: The track to which the event is added.         :param channel: the MIDI channel to assign to the event. [Integer, 0-15]         :param time: The time (in beats) at which the event is placed [Float].         :param pitchWheelValue: 0 for no pitch change. [Integer, -8192-8192] Perform a Registered Parameter Number Call          :param track: The track to which this applies         :param channel: The channel to which this applies         :param time: The time of the event         :param controller_msb: The Most significant byte of the controller. In             common usage this will usually be 0         :param controller_lsb: The Least significant Byte for the controller             message. For example, for a fine-tuning change this would be 01.         :param data_msb: The Most Significant Byte of the controller's             parameter.         :param data_lsb: The Least Significant Byte of the controller's             parameter. If not needed this should be set to ``None``         :param time_order: Order the control events in time (see below)          As an example, if one were to change a channel's tuning program::              makeRPNCall(track, channel, time, 0, 3, 0, program)          (Note, however, that there is a convenience function,         ``changeTuningProgram``, that does this for you.)          Registered/Non-Registered Parameter Number (RPN / NRPN)         -------------------------------------------------------         Controller number 6 (Data Entry), in conjunction with Controller numbers 96         (Data Increment), 97 (Data Decrement), 98 (Registered Parameter Number LSB),         99 (Registered Parameter Number MSB), 100 (Non-Registered Parameter Number         LSB), and 101 (Non-Registered Parameter Number MSB), extend the number of         controllers available via MIDI. Parameter data is transferred by first         selecting the parameter number to be edited using controllers 98 and 99 or         100 and 101, and then adjusting the data value for that parameter using         controller number 6, 96, or 97.          RPN and NRPN are typically used to send parameter data to a synthesizer in         order to edit sound patches or other data. Registered parameters are those         which have been assigned some particular function by the MIDI Manufacturers         Association (MMA) and the Japan MIDI Standards Committee (JMSC). For         example, there are Registered Parameter numbers assigned to control pitch         bend sensitivity and master tuning for a synthesizer. Non-Registered         parameters have not been assigned specific functions, and may be used for         different functions by different manufacturers.          The ``time_order`` parameter is something of a work-around for         sequencers that do not preserve the order of events from the MIDI files         they import. Within this code care is taken to preserve the order of         events as specified, but some sequencers seem to transmit events         occurring at the same time in an arbitrary order.  By setting this         parameter to ``True`` something of a work-around is performed: each         successive event (of which there are three or four for this event type)         is placed in the time stream a small delta from the preceding one.         Thus, for example, the controllers are set before the data bytes in         this call. # parameter number MSB # noqa: E128 # noqa: E128 # noqa: E128 # noqa: E128 Perform a Non-Registered Parameter Number Call          :param track: The track to which this applies         :param channel: The channel to which this applies         :param time: The time of the event         :param controller_msb: The Most significant byte of thecontroller. In             common usage this will usually be 0         :param controller_lsb: The least significant byte for the controller             message. For example, for a fine-tunning change this would be 01.         :param data_msb: The most significant byte of the controller's             parameter.         :param data_lsb: The least significant byte of the controller's             parameter. If none is needed this should be set to ``None``         :param time_order: Order the control events in time (see below)          The ``time_order`` parameter is something of a work-around for         sequencers that do not preserve the order of events from the MIDI files         they import. Within this code care is taken to preserve the order of         events as specified, but some sequencers seem to transmit events         occurring at the same time in an arbitrary order.  By setting this         parameter to ``True`` something of a work-around is performed: each         successive event (of which there are three or four for this event type)         is placed in the time stream a small delta from the preceding one.         Thus, for example, the controllers are set before the data bytes in         this call. # noqa: E128 # noqa: E128 # noqa: E128 # noqa: E128 Change the tuning bank for a selected track          :param track: The track to which the data should be written         :param channel: The channel for the event         :param time: The time of the event         :param bank: The tuning bank (0-127)         :param time_order: Preserve the ordering of the component events by             ordering in time. See ``makeRPNCall()`` for a discussion of when             this may be necessary          Note that this is a convenience function, as the same         functionality is available from directly sequencing controller         events.          The specified tuning should already have been written to the         stream with ``changeNoteTuning``. Change the tuning program for a selected track          :param track: The track to which the data should be written         :param channel: The channel for the event         :param time: The time of the event         :param program: The tuning program number (0-127)         :param time_order: Preserve the ordering of the component events by             ordering in time. See ``makeRPNCall()`` for a discussion of when             this may be necessary          Note that this is a convenience function, as the same         functionality is available from directly sequencing controller         events.          The specified tuning should already have been written to the         stream with ``changeNoteTuning``. Add a real-time MIDI tuning standard update to a track.          :param track: The track to which the tuning is applied.         :param tunings: A list to tuples representing the tuning. See below for             an explanation.         :param sysExChannel: The SysEx channel of the event. This is mapped to             "manufacturer ID" in the event which is written. Unless there is a             specific reason for changing it, it should be left at its default             value.         :param realTime: Speicifes if the Universal SysEx event should be             flagged as real-time or non-real-time. As with the ``sysExChannel``             argument, this should in general be left at it's default value.         :param tuningProgram: The tuning program number.          This function specifically implements the "real time single note tuning         change" (although the name is misleading, as multiple notes can be         included in each event). It should be noted that not all hardware or         software implements the MIDI tuning standard, and that which does often         does not implement it in its entirety.          The ``tunings`` argument is a list of tuples, in (*note number*,         *frequency*) format.  As an example, if one wanted to change the         frequency on MIDI note 69 to 500 (it is normally 440 Hz), one could do         it thus:          .. code:: python              from midiutil.MidiFile import MIDIFile             MyMIDI = MIDIFile(1)             tuning = [(69, 500)]             MyMIDI.changeNoteTuning(0, tuning, tuningProgam=0) Add a System Exclusive event.          :param track: The track to which the event should be written         :param time: The time of the event.         :param manID: The manufacturer ID for the event         :param payload: The payload for the event. This should be a             binary-packed value, and will vary for each type and function.          **Note**: This is a low-level MIDI function, so care must be used in         constructing the payload. It is recommended that higher-level helper         functions be written to wrap this function and construct the payload if         a developer finds him or herself using the function heavily. Add a Univeral System Exclusive event.          :param track: The track to which the event should be written         :param time: The time of the event, in beats.         :param code: The event code. [Integer]         :param subcode: The event sub-code [Integer]         :param payload: The payload for the event. This should be a             binary-packed value, and will vary for each type and function.         :param sysExChannel: The SysEx channel.         :param realTime: Sets the real-time flag. Defaults to non-real-time.         :param manID: The manufacturer ID for the event           **Note**: This is a low-level MIDI function, so care must be used in         constructing the payload. It is recommended that higher-level helper         functions be written to wrap this function and construct the payload if         a developer finds him or herself using the function heavily. As an         example of such a helper function, see the ``changeNoteTuning()``         function, which uses the event to create a real-time note tuning         update. # noqa: E128 Write the MIDI File.          :param fileHandle: A file handle that has been opened for binary             writing. # Close the tracks and have them create the MIDI event data structures. # Write the MIDI Events to file. Shift tracks to be zero-origined, or origined at offset.          Note that the shifting of the time in the tracks uses the MIDIEventList         -- in other words it is assumed to be called in the stage where the         MIDIEventList has been created. This function, however, it meant to         operate on the eventList itself. # A little silly, but we'll assume big enough # runningTick = 0 # event.time = adjustedTime - runningTick + tick_offset # runningTick = adjustedTick # End Public Functions ######################## Close the MIDIFile for further writing.          To close the File for events, we must close the tracks, adjust the time         to be zero-origined, and have the tracks write to their MIDI Stream         data structure. # We want things like program changes to come before notes when # they are at the same time, so we sort the MIDI events by both # their start time and a secondary ordinality defined for each kind # of event. Find the earliest time in the file's tracks.append. # A little silly, but we'll assume big enough # Note: This code assumes that the MIDIEventList has been sorted, so this # should be insured before it is called. It is probably a poor design to do # this. # TODO: -- Consider making this less efficient but more robust by not #          assuming the list to be sorted. Accept an integer, and serialize it as a MIDI file variable length quantity      Some numbers in MTrk chunks are represented in a form called a variable-     length quantity.  These numbers are represented in a sequence of bytes,     each byte holding seven bits of the number, and ordered most significant     bits first. All bytes in the sequence except the last have bit 7 set,     and the last byte has bit 7 clear.  This form allows smaller numbers to     be stored in fewer bytes.  For example, if the number is between 0 and     127, it is thus represented exactly as one byte.  A number between 128     and 16383 uses two bytes, and so on.      Examples:     Number  VLQ     128     81 00     8192    C0 00     16383   FF 7F     16384   81 80 00 # low-order byte has high bit cleared. # put most-significant byte first, least significant last # readVarLength is taken from the MidiFile class. A function to read a MIDI variable length variable.      It returns a tuple of the value read and the number of bytes processed. The     input is an offset into the buffer, and the buffer itself. Returns a three-byte transform of a frequency. # round? The reverse of frequencyTransform. Given a byte stream, return a frequency. .. py:function:: sort_events(event)          The key function used to sort events (both MIDI and Generic)          :param event: An object of type :class:`MIDIEvent` or (a derrivative)             :class:`GenericEvent`          This function should be provided as the ``key`` for both         ``list.sort()`` and ``sorted()``. By using it sorting will be as         follows:          * Events are ordered in time. An event that takes place earlier will           appear earlier         * If two events happen at the same time, the secondary sort key is           ``sec_sort_order``. Thus a class of events can be processed earlier           than another. One place this is used in the code is to make sure that           note off events are processed before note on events.         * If event time and event ordinality are the same, they are sorted in           the order in which they were originally added to the list. Thus, for           example, if one is making an RPN call one can specify the controller           change events in the proper order and be sure that they will end up in           the file that way.