Quarter-comma meantone each kind, a perfect fifth of meantone contains four diatonic and three chromatic semitones, and an octave seven diatonic and five chromatic semitones, it follows that: Thus, in Pythagorean tuning, where sequences of just fifths (frequency ratio 3:2) and octaves are used to produce the other intervals, a whole tone is and a major third is An interval of a seventeenth, consisting of sixteen diatonic and twelve chromatic semitones, such as the interval from D to F, can be equivalently obtained using either This large interval of a seventeenth contains staff positions. In Pythagorean tuning, the size of a seventeenth
Octave an octave apart is therefore 2:1. Further octaves of a note occur at formula_1 times the frequency of that note (where "n" is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. For example, 55 Hz and 440 Hz are one and two octaves away from 110 Hz because they are (or formula_2) and 4 (or formula_3) times the frequency, respectively. The number of octaves between two frequencies is given by the formula: The octave is defined by ANSI as the unit of frequency level when the base of the logarithm is two. After