Diatonic range: Difference between revisions
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complete definition of intervals M2, m2, and A1 in pseudo code |
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The '''diatonic range''' is a size range of the [[fifth]] interval defined by the bounds 4\7 and 3\5. | The '''diatonic range''' is a size range of the [[fifth]] interval defined by the bounds 4\7 and 3\5. | ||
Stacked ([[octave-reduced]]) fifths (<code>R5</code>) within this range build scales with distinguishable "diatonic whole tones" (<code>2*R5 - P8</code>), "diatonic semitones" (<code>3*P8 - 5*R5</code>), and "chromatic semitones" (<code>M2 - m2</code>) of a non-negative size. Some examples: | Stacked ([[octave-reduced]]) fifths (<code>R5</code>) within this range build scales with distinguishable | ||
* "diatonic whole tones" (<code>M2 := 2*R5 - P8</code>), | |||
* "diatonic semitones" (<code>m2 := 3*P8 - 5*R5</code>), and | |||
* "chromatic semitones" (<code>A1 := M2 - m2</code>) | |||
of a non-negative size. Some examples: | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
Revision as of 17:31, 10 June 2021
The diatonic range is a size range of the fifth interval defined by the bounds 4\7 and 3\5.
Stacked (octave-reduced) fifths (R5) within this range build scales with distinguishable
- "diatonic whole tones" (
M2 := 2*R5 - P8), - "diatonic semitones" (
m2 := 3*P8 - 5*R5), and - "chromatic semitones" (
A1 := 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 |