44ed11/5
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Prime factorization
22 × 11
Step size
31.0228¢
Octave
39\44ed11/5 (1209.89¢)
Twelfth
61\44ed11/5 (1892.39¢)
Consistency limit
2
Distinct consistency limit
2
| ← 43ed11/5 | 44ed11/5 | 45ed11/5 → |
44 equal divisions of 11/5 (abbreviated 44ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 44 equal parts of about 31 ¢ each. Each step represents a frequency ratio of (11/5)1/44, or the 44th root of 11/5.
Theory
This tuning tempers out 33/32 in the 11-limit; 78/77 in the 13-limit; 69/68 in the 23-limit; 63/62 in the 31-limit; 75/74 in the 37-limit; 41/40 in the 41-limit; 61/60 in the 61-limit; 71/70 in the 71-limit; 73/72 in the 73-limit; and 81/79 in the 79-limit.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 31 | |
| 2 | 62 | 26/25, 30/29, 31/30 |
| 3 | 93.1 | 18/17, 19/18 |
| 4 | 124.1 | |
| 5 | 155.1 | 12/11, 23/21 |
| 6 | 186.1 | 19/17, 29/26 |
| 7 | 217.2 | 17/15, 25/22, 26/23 |
| 8 | 248.2 | 15/13 |
| 9 | 279.2 | |
| 10 | 310.2 | 6/5, 31/26 |
| 11 | 341.3 | |
| 12 | 372.3 | 21/17, 26/21, 31/25 |
| 13 | 403.3 | 19/15, 29/23 |
| 14 | 434.3 | |
| 15 | 465.3 | 17/13, 30/23 |
| 16 | 496.4 | |
| 17 | 527.4 | 23/17 |
| 18 | 558.4 | 18/13, 29/21 |
| 19 | 589.4 | 31/22 |
| 20 | 620.5 | 10/7 |
| 21 | 651.5 | 19/13 |
| 22 | 682.5 | |
| 23 | 713.5 | |
| 24 | 744.5 | 23/15 |
| 25 | 775.6 | |
| 26 | 806.6 | |
| 27 | 837.6 | |
| 28 | 868.6 | |
| 29 | 899.7 | |
| 30 | 930.7 | 12/7, 29/17 |
| 31 | 961.7 | |
| 32 | 992.7 | 23/13 |
| 33 | 1023.8 | |
| 34 | 1054.8 | 11/6 |
| 35 | 1085.8 | |
| 36 | 1116.8 | 21/11 |
| 37 | 1147.8 | |
| 38 | 1178.9 | |
| 39 | 1209.9 | |
| 40 | 1240.9 | |
| 41 | 1271.9 | 23/11, 25/12 |
| 42 | 1303 | |
| 43 | 1334 | 13/6 |
| 44 | 1365 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.9 | -9.6 | +5.7 | +12.7 | +5.7 | -4.3 | -3.3 | -9.8 | +0.7 | +2.7 | +11.3 |
| Relative (%) | +31.9 | -30.8 | +18.5 | +40.8 | +18.5 | -13.7 | -10.8 | -31.5 | +2.3 | +8.7 | +36.6 | |
| Steps (reduced) |
39 (39) |
61 (17) |
90 (2) |
109 (21) |
134 (2) |
143 (11) |
158 (26) |
164 (32) |
175 (43) |
188 (12) |
192 (16) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +15.3 | -7.3 | +3.3 | +4.4 | +13.6 | +14.0 | -12.7 | +11.1 | +3.7 | -13.3 | +5.0 |
| Relative (%) | +49.2 | -23.7 | +10.6 | +14.2 | +43.7 | +45.2 | -40.8 | +35.6 | +12.0 | -43.0 | +16.2 | |
| Steps (reduced) |
202 (26) |
207 (31) |
210 (34) |
215 (39) |
222 (2) |
228 (8) |
229 (9) |
235 (15) |
238 (18) |
239 (19) |
244 (24) | |