Diatonic scale are major scales (those with a major third/triad: Ionian, Lydian, and Mixolydian), three are minor (those with a minor third/triad: Dorian, Phrygian, and Aeolian). To these may be added the seventh diatonic scale, with a diminished fifth above the reference note, the Locrian scale. These could be transposed not only to include one flat in the signature (as described by Glarean), but to all twelve notes of the chromatic scale, resulting in a total of eighty-four diatonic scales. The modern musical keyboard originated as a diatonic keyboard with only white keys. The black keys were progressively added for several purposes:
Bohlen–Pierce scale Bohlen–Pierce scale The Bohlen–Pierce scale (BP scale) is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal tempered diatonic scale. The interval 3:1 (often called by a new name, tritave) serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the octave). For any pitch that is part of the BP scale, all pitches one or more tritaves higher or lower are part of the system as well, and are considered equivalent. The BP scale divides the tritave into 13 steps,