User:MisterShafXen/9ed88: Difference between revisions
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Prime factorization
32
Step size
861.258 ¢
Octave
1\9ed88 (861.258 ¢)
Twelfth
2\9ed88 (1722.52 ¢)
(semiconvergent)
Consistency limit
3
Distinct consistency limit
2
Created page with "{{Infobox ET}} {{ED intro}} == Intervals == {{Interval table|9ed88}} == Harmonics == {{Harmonics in equal|steps=9|num=88|intervals=prime}}" Tags: Visual edit Mobile edit Mobile web edit |
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Latest revision as of 14:43, 1 August 2025
| ← 8ed88 | 9ed88 | 10ed88 → |
(semiconvergent)
9 equal divisions of the 88th harmonic (abbreviated 9ed88) is a nonoctave tuning system that divides the interval of 88/1 into 9 equal parts of about 861 ¢ each. Each step represents a frequency ratio of 881/9, or the 9th root of 88.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 861.3 | 5/3, 21/13 |
| 2 | 1722.5 | 19/7 |
| 3 | 2583.8 | 9/2, 22/5 |
| 4 | 3445 | 22/3 |
| 5 | 4306.3 | |
| 6 | 5167.5 | |
| 7 | 6028.8 | |
| 8 | 6890.1 | |
| 9 | 7751.3 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -339 | -179 | -203 | +76 | +155 | -134 | +263 | +70 | -261 | +199 | +84 |
| Relative (%) | -39.3 | -20.8 | -23.5 | +8.8 | +18.0 | -15.6 | +30.5 | +8.1 | -30.3 | +23.1 | +9.7 | |
| Steps (reduced) |
1 (1) |
2 (2) |
3 (3) |
4 (4) |
5 (5) |
5 (5) |
6 (6) |
6 (6) |
6 (6) |
7 (7) |
7 (7) | |