Diatonic range
The diatonic range is a size range of fifth interval defined by the corner intervals 4\7 and 3\5.
Stacked (octave-reduced) fifths (R5) within this range build scales with distinguishable "diatonic whole tones" (2*R5 - P8), "diatonic semitones" (3*P8 - 5*R5), and "chromatic semitones" (M2 - m2) of a non-negative size. Some examples:
| 5th definition | Interval sizes (cents) | Comments | |||
|---|---|---|---|---|---|
| R5 | M2 | m2 | A1 | ||
| 4\7 | 686 | 171 | 171 | 0 | lower limit |
| 11\19 | 695 | 189 | 126 | 63 | 3:2 (L:s) |
| 7\12 | 700 | 200 | 100 | 100 | 2:1 (L:s) |
| 10\17 | 706 | 212 | 71 | 141 | 3:1 (L:s) |
| 3\5 | 720 | 240 | 0 | 240 | upper limit |