44ed6
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| ← 43ed6 | 44ed6 | 45ed6 → |
(semiconvergent)
(semiconvergent)
44 equal divisions of the 6th harmonic (abbreviated 44ed6) is a nonoctave tuning system that divides the interval of 6/1 into 44 equal parts of about 70.5 ¢ each. Each step represents a frequency ratio of 61/44, or the 44th root of 6.
Theory
44ed6 is closely related to 17edo and 27edt, and like them is an excellent no-5 13-limit tuning. It also has good matches for the 23rd and 25th harmonics. Like 27edt, its octaves are slightly flat, albeit less so. The octave of 44ed6 is 1198.48 cents: about a cent and a half flat. The 3rd harmonic is sharp by the same amount, while the 7th, 11th, and 13th harmonics are all sharp by 15.1, 8.1, and 0.9 cents, respectively.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.5 | +1.5 | -3.0 | +33.6 | +0.0 | +15.1 | -4.6 | +3.0 | +32.1 | +8.1 | -1.5 |
| Relative (%) | -2.2 | +2.2 | -4.3 | +47.7 | +0.0 | +21.5 | -6.5 | +4.3 | +45.6 | +11.5 | -2.2 | |
| Steps (reduced) |
17 (17) |
27 (27) |
34 (34) |
40 (40) |
44 (0) |
48 (4) |
51 (7) |
54 (10) |
57 (13) |
59 (15) |
61 (17) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.9 | +13.6 | +35.2 | -6.1 | +30.0 | +1.5 | -21.6 | +30.6 | +16.6 | +6.6 | +0.1 | -3.0 |
| Relative (%) | +1.3 | +19.3 | +49.9 | -8.6 | +42.5 | +2.2 | -30.6 | +43.4 | +23.6 | +9.4 | +0.2 | -4.3 | |
| Steps (reduced) |
63 (19) |
65 (21) |
67 (23) |
68 (24) |
70 (26) |
71 (27) |
72 (28) |
74 (30) |
75 (31) |
76 (32) |
77 (33) |
78 (34) | |
Subsets and supersets
Since 44 factors into primes as 22 × 11, 44ed6 has subset ed6's 2, 4, 11, and 22.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 70.5 | 23/22, 24/23, 27/26 |
| 2 | 141 | 13/12 |
| 3 | 211.5 | 17/15, 26/23 |
| 4 | 282 | 20/17, 27/23 |
| 5 | 352.5 | 11/9, 27/22 |
| 6 | 423 | 14/11, 23/18 |
| 7 | 493.5 | 4/3 |
| 8 | 564 | 18/13, 29/21 |
| 9 | 634.5 | 13/9, 23/16 |
| 10 | 705 | 3/2 |
| 11 | 775.5 | |
| 12 | 846 | 13/8, 31/19 |
| 13 | 916.5 | 17/10, 22/13 |
| 14 | 987 | 23/13, 30/17 |
| 15 | 1057.5 | 24/13 |
| 16 | 1128 | 23/12 |
| 17 | 1198.5 | 2/1 |
| 18 | 1269 | 27/13 |
| 19 | 1339.5 | 13/6 |
| 20 | 1410 | 9/4 |
| 21 | 1480.5 | |
| 22 | 1551 | 22/9, 27/11 |
| 23 | 1621.5 | 23/9, 28/11 |
| 24 | 1692 | 8/3 |
| 25 | 1762.5 | |
| 26 | 1833 | 23/8, 26/9 |
| 27 | 1903.5 | 3/1 |
| 28 | 1974 | |
| 29 | 2044.5 | 13/4 |
| 30 | 2115 | 17/5 |
| 31 | 2185.5 | |
| 32 | 2256 | |
| 33 | 2326.5 | 23/6 |
| 34 | 2397 | 4/1 |
| 35 | 2467.5 | |
| 36 | 2538 | 13/3 |
| 37 | 2608.5 | 9/2 |
| 38 | 2679 | |
| 39 | 2749.5 | |
| 40 | 2820 | |
| 41 | 2890.5 | |
| 42 | 2961 | |
| 43 | 3031.5 | 23/4 |
| 44 | 3102 | 6/1 |