39ed15/8: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''Division of the [[15/8|just major seventh]] into 39 equal parts''' (39ED15/8) is almost identical to [[43edo|43 EDO]], but with the [[15/8]] rather than the 2/1 being just. The octave is about 0.11 [[cent]]s [[stretched and compressed tuning|compressed]] and the step size is about 44.35 cents. | '''Division of the [[15/8|just major seventh]] into 39 equal parts''' (39ED15/8) is almost identical to [[43edo|43 EDO]], but with the [[15/8]] rather than the 2/1 being just. The octave is about 0.11 [[cent]]s [[stretched and compressed tuning|compressed]] and the step size is about 44.35 cents. | ||
==Intervals== | |||
{{Interval table}} | |||
==Harmonics== | ==Harmonics== | ||
{{Harmonics in equal|39|15|8|prec=2|columns=15}} | {{Harmonics in equal|39|15|8|prec=2|columns=15}} | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 09:03, 1 October 2024
| ← 38ed15/8 | 39ed15/8 | 40ed15/8 → |
(convergent)
(semiconvergent)
Division of the just major seventh into 39 equal parts (39ED15/8) is almost identical to 43 EDO, but with the 15/8 rather than the 2/1 being just. The octave is about 0.11 cents compressed and the step size is about 44.35 cents.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 27.9 | |
| 2 | 55.8 | 29/28 |
| 3 | 83.7 | 20/19, 21/20, 22/21, 23/22 |
| 4 | 111.6 | 16/15, 17/16 |
| 5 | 139.5 | 13/12, 25/23 |
| 6 | 167.4 | 11/10, 21/19 |
| 7 | 195.3 | 19/17, 28/25, 29/26 |
| 8 | 223.2 | 17/15, 25/22 |
| 9 | 251.1 | 15/13, 22/19, 29/25 |
| 10 | 279 | 20/17 |
| 11 | 306.9 | 25/21 |
| 12 | 334.9 | 17/14, 23/19, 28/23, 29/24 |
| 13 | 362.8 | 16/13, 21/17, 26/21 |
| 14 | 390.7 | 5/4 |
| 15 | 418.6 | 14/11 |
| 16 | 446.5 | 22/17 |
| 17 | 474.4 | 21/16, 25/19, 29/22 |
| 18 | 502.3 | 4/3 |
| 19 | 530.2 | 15/11, 19/14, 23/17 |
| 20 | 558.1 | 11/8, 18/13, 29/21 |
| 21 | 586 | 7/5 |
| 22 | 613.9 | 10/7 |
| 23 | 641.8 | 13/9, 16/11, 29/20 |
| 24 | 669.7 | 22/15, 25/17, 28/19 |
| 25 | 697.6 | 3/2 |
| 26 | 725.5 | 29/19 |
| 27 | 753.4 | 17/11 |
| 28 | 781.3 | 11/7 |
| 29 | 809.2 | 8/5 |
| 30 | 837.1 | 13/8, 21/13 |
| 31 | 865 | 23/14, 28/17 |
| 32 | 892.9 | |
| 33 | 920.8 | 17/10, 29/17 |
| 34 | 948.7 | 19/11, 26/15 |
| 35 | 976.7 | |
| 36 | 1004.6 | 25/14 |
| 37 | 1032.5 | 20/11, 29/16 |
| 38 | 1060.4 | 24/13 |
| 39 | 1088.3 | 15/8 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.11 | -4.46 | -0.23 | +4.12 | -4.57 | +7.60 | -0.34 | -8.92 | +4.00 | +6.43 | -4.69 | -3.74 | +7.48 | -0.34 | -0.46 |
| Relative (%) | -0.4 | -16.0 | -0.8 | +14.8 | -16.4 | +27.2 | -1.2 | -32.0 | +14.4 | +23.0 | -16.8 | -13.4 | +26.8 | -1.2 | -1.6 | |
| Steps (reduced) |
43 (4) |
68 (29) |
86 (8) |
100 (22) |
111 (33) |
121 (4) |
129 (12) |
136 (19) |
143 (26) |
149 (32) |
154 (37) |
159 (3) |
164 (8) |
168 (12) |
172 (16) | |