45ed5/2
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Prime factorization
32 × 5
Step size
35.2514¢
Octave
34\45ed5/2 (1198.55¢)
Twelfth
54\45ed5/2 (1903.58¢) (→6\5ed5/2)
Consistency limit
6
Distinct consistency limit
6
 |
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45 equal divisions of 5/2 (abbreviated 45ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 45 equal parts of about 35.3 ¢ each. Each step represents a frequency ratio of (5/2)1/45, or the 45th root of 5/2.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 35.251 | |
| 2 | 70.503 | 24/23, 25/24, 26/25, 27/26 |
| 3 | 105.754 | 16/15, 17/16 |
| 4 | 141.006 | 13/12, 25/23 |
| 5 | 176.257 | 10/9, 21/19, 31/28 |
| 6 | 211.508 | 17/15, 26/23 |
| 7 | 246.76 | 15/13, 23/20 |
| 8 | 282.011 | 20/17, 27/23 |
| 9 | 317.263 | 6/5 |
| 10 | 352.514 | 11/9, 27/22 |
| 11 | 387.766 | 5/4 |
| 12 | 423.017 | 14/11, 23/18 |
| 13 | 458.268 | 13/10, 17/13, 30/23 |
| 14 | 493.52 | 4/3 |
| 15 | 528.771 | 19/14, 23/17 |
| 16 | 564.023 | 18/13, 25/18 |
| 17 | 599.274 | 17/12, 24/17, 31/22 |
| 18 | 634.525 | 13/9, 23/16 |
| 19 | 669.777 | 25/17, 28/19, 31/21 |
| 20 | 705.028 | 3/2 |
| 21 | 740.28 | 20/13, 23/15, 26/17 |
| 22 | 775.531 | 25/16 |
| 23 | 810.783 | 8/5 |
| 24 | 846.034 | 13/8, 31/19 |
| 25 | 881.285 | 5/3 |
| 26 | 916.537 | 17/10, 22/13 |
| 27 | 951.788 | 19/11, 26/15 |
| 28 | 987.04 | 23/13, 30/17 |
| 29 | 1022.291 | 9/5 |
| 30 | 1057.542 | 24/13 |
| 31 | 1092.794 | 15/8 |
| 32 | 1128.045 | 23/12, 25/13 |
| 33 | 1163.297 | |
| 34 | 1198.548 | 2/1 |
| 35 | 1233.8 | |
| 36 | 1269.051 | 25/12, 27/13 |
| 37 | 1304.302 | 17/8 |
| 38 | 1339.554 | 13/6 |
| 39 | 1374.805 | 31/14 |
| 40 | 1410.057 | 9/4 |
| 41 | 1445.308 | 23/10, 30/13 |
| 42 | 1480.559 | |
| 43 | 1515.811 | 12/5 |
| 44 | 1551.062 | 22/9, 27/11 |
| 45 | 1586.314 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.5 | +1.6 | -2.9 | -1.5 | +0.2 | +15.3 | -4.4 | +3.2 | -2.9 | +8.3 | -1.3 |
| Relative (%) | -4.1 | +4.6 | -8.2 | -4.1 | +0.5 | +43.4 | -12.4 | +9.2 | -8.2 | +23.7 | -3.6 | |
| Steps (reduced) |
34 (34) |
54 (9) |
68 (23) |
79 (34) |
88 (43) |
96 (6) |
102 (12) |
108 (18) |
113 (23) |
118 (28) |
122 (32) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.2 | +13.9 | +0.2 | -5.8 | -5.0 | +1.8 | +13.9 | -4.4 | +16.9 | +6.9 | +0.4 |
| Relative (%) | +3.3 | +39.3 | +0.5 | -16.5 | -14.2 | +5.1 | +39.6 | -12.4 | +48.0 | +19.6 | +1.3 | |
| Steps (reduced) |
126 (36) |
130 (40) |
133 (43) |
136 (1) |
139 (4) |
142 (7) |
145 (10) |
147 (12) |
150 (15) |
152 (17) |
154 (19) | |