9-odd-limit: Difference between revisions
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The '''9-[[odd-limit]]''' consists of all intervals where the largest allowable odd factor in the numerator and denominator is 9. Reduced to an octave, these are: | The '''9-[[odd-limit]]''' consists of all intervals where the largest allowable odd factor in the numerator and denominator is 9. Reduced to an octave, these are: | ||
==Table of 9-odd-limit intervals== | |||
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| Octave | | Octave | ||
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==Approximation by edos== | |||
The first edo to be consistent to the 9-odd-limit is [[5edo]], giving a rough outline for harmony with its relatively accurate 3/2 and 7/4 of 720 and 960 cents respectively, while very sharply mapping 5/4 to 480 cents. The first edo to be distinctly consistent in this limit is [[41edo]]. | |||
Latest revision as of 21:20, 1 June 2026
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The 9-odd-limit consists of all intervals where the largest allowable odd factor in the numerator and denominator is 9. Reduced to an octave, these are:
Table of 9-odd-limit intervals
| Interval | Cents | Name |
|---|---|---|
| 1/1 | 0.0 | Unison |
| 10/9 | 182.4 | Minor whole tone, Ptolemaic major 2nd |
| 9/8 | 203.9 | Major whole tone, Pythagorean major 2nd |
| 8/7 | 231.2 | Septimal major 2nd |
| 7/6 | 266.9 | Septimal minor 3rd |
| 6/5 | 315.6 | Classical minor 3rd |
| 5/4 | 386.4 | Classical major 3rd |
| 9/7 | 435.1 | Septimal major 3rd |
| 4/3 | 498.0 | Perfect 4th |
| 7/5 | 582.5 | Lesser septimal tritone |
| 10/7 | 617.5 | Greater septimal tritone |
| 3/2 | 702.0 | Perfect 5th |
| 14/9 | 764.9 | Septimal minor 6th |
| 8/5 | 813.6 | Classical minor 6th |
| 5/3 | 884.4 | Classical major 6th |
| 12/7 | 933.1 | Septimal major 6th |
| 7/4 | 968.8 | Septimal minor 7th |
| 16/9 | 996.1 | Pythagoran minor 7th |
| 9/5 | 1017.6 | Classical minor 7th |
| 2/1 | 1200.0 | Octave |
Approximation by edos
The first edo to be consistent to the 9-odd-limit is 5edo, giving a rough outline for harmony with its relatively accurate 3/2 and 7/4 of 720 and 960 cents respectively, while very sharply mapping 5/4 to 480 cents. The first edo to be distinctly consistent in this limit is 41edo.
