9ed4/3
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Prime factorization
32
Step size
55.3383¢
Octave
22\9ed4/3 (1217.44¢)
Twelfth
34\9ed4/3 (1881.5¢)
Consistency limit
2
Distinct consistency limit
2
 |
Todo: add source, research, cleanup |
| ← 8ed4/3 | 9ed4/3 | 10ed4/3 → |
9ed4/3, also known as Noleta, is a tuning system based on the division of the perfect fourth (4/3) into 9 equal parts, each 55.3383 cents in size. The name ‘Noleta’ seems to be coined by Ron Sword: Nonoctave.com: Messages: 9197
Regular temperaments that divide 4/3 into 9 equal parts include:
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 55.338 | 21/20 |
| 2 | 110.677 | 13/12, 19/18, 20/19, 22/21 |
| 3 | 166.015 | 11/10, 12/11, 14/13, 19/17, 21/19 |
| 4 | 221.353 | 10/9, 15/13 |
| 5 | 276.692 | 7/6, 13/11, 20/17, 22/19 |
| 6 | 332.03 | 6/5, 17/14, 21/17 |
| 7 | 387.368 | |
| 8 | 442.707 | 13/10, 14/11, 19/15, 22/17 |
| 9 | 498.045 | 15/11, 17/13, 19/14 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +17.4 | -20.5 | -20.5 | -19.4 | -3.0 | +6.8 | -3.0 | +14.4 | -2.0 | -0.9 | +14.4 |
| Relative (%) | +31.5 | -37.0 | -37.0 | -35.1 | -5.4 | +12.3 | -5.4 | +26.1 | -3.5 | -1.7 | +26.1 | |
| Steps (reduced) |
22 (4) |
34 (7) |
43 (7) |
50 (5) |
56 (2) |
61 (7) |
65 (2) |
69 (6) |
72 (0) |
75 (3) |
78 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -13.5 | +24.3 | +15.5 | +14.4 | +20.2 | -23.5 | -6.4 | +15.5 | -13.6 | +16.5 | -5.1 |
| Relative (%) | -24.3 | +43.8 | +28.0 | +26.1 | +36.4 | -42.4 | -11.5 | +28.0 | -24.6 | +29.8 | -9.2 | |
| Steps (reduced) |
80 (8) |
83 (2) |
85 (4) |
87 (6) |
89 (8) |
90 (0) |
92 (2) |
94 (4) |
95 (5) |
97 (7) |
98 (8) | |