24ed7: Difference between revisions
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'''[[Ed7|Division of the 7th harmonic]] into 24 equal parts''' (24ed7) is related to the [[Hemifamity temperaments|quanic temperament]], which tempers out 352/351, 540/539, 729/728, and 1331/1323 in the 13-limit; 352/351, 442/441, 540/539, 561/560, and 715/714 in the 17-limit | '''[[Ed7|Division of the 7th harmonic]] into 24 equal parts''' (24ed7) is related to the [[Hemifamity temperaments|quanic temperament]], which tempers out 352/351, 540/539, 729/728, and 1331/1323 in the 13-limit; 352/351, 442/441, 540/539, 561/560, and 715/714 in the 17-limit. The step size is about 140.3677 cents, corresponding to 8.5490 [[edo]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 25: | Line 25: | ||
| | 3 | | | 3 | ||
| | 421.1032 | | | 421.1032 | ||
| | [[14/11]], 23/18, [[32/25]] | | | [[14/11]], 65/51, 51/40, 23/18, [[32/25]] | ||
| | | | | | ||
|- | |- | ||
| Line 70: | Line 70: | ||
| | 12 | | | 12 | ||
| | 1684.4130 | | | 1684.4130 | ||
| | | | | 119/45, 45/17 | ||
| | | | | | ||
|- | |- | ||
| Line 85: | Line 85: | ||
| | 15 | | | 15 | ||
| | 2105.5162 | | | 2105.5162 | ||
| | [[27/16|27/8]] | | | 91/27, [[27/16|27/8]] | ||
| | | | | | ||
|- | |- | ||
| Line 95: | Line 95: | ||
| | 17 | | | 17 | ||
| | 2386.2517 | | | 2386.2517 | ||
| | 119/30, | | | 119/30, 143/36 | ||
| | | | | | ||
|- | |- | ||
| | 18 | | | 18 | ||
| | 2526.6194 | | | 2526.6194 | ||
| | 56/13 | | | [[14/13|56/13]] | ||
| | | | | | ||
|- | |- | ||
Revision as of 02:02, 6 January 2019
Division of the 7th harmonic into 24 equal parts (24ed7) is related to the quanic temperament, which tempers out 352/351, 540/539, 729/728, and 1331/1323 in the 13-limit; 352/351, 442/441, 540/539, 561/560, and 715/714 in the 17-limit. The step size is about 140.3677 cents, corresponding to 8.5490 edo.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 140.3677 | 13/12, 25/23 | |
| 2 | 280.7355 | 20/17 | |
| 3 | 421.1032 | 14/11, 65/51, 51/40, 23/18, 32/25 | |
| 4 | 561.4710 | 18/13 | |
| 5 | 701.8387 | 3/2 | |
| 6 | 842.2065 | 13/8, 80/49 | |
| 7 | 982.5742 | 30/17 | |
| 8 | 1122.9420 | 21/11 | |
| 9 | 1263.3097 | 56/27, 27/13 | |
| 10 | 1403.6775 | 9/4 | |
| 11 | 1544.0452 | 56/23, 39/16, 22/9, 120/49 | |
| 12 | 1684.4130 | 119/45, 45/17 | |
| 13 | 1824.7807 | 63/22, 112/39, 23/8 | |
| 14 | 1965.1484 | 28/9 | |
| 15 | 2105.5162 | 91/27, 27/8 | |
| 16 | 2245.8839 | 11/3 | |
| 17 | 2386.2517 | 119/30, 143/36 | |
| 18 | 2526.6194 | 56/13 | |
| 19 | 2666.9872 | 14/3 | |
| 20 | 2807.3549 | 91/18 | |
| 21 | 2947.7227 | 11/2 | |
| 22 | 3088.0904 | 119/20 | |
| 23 | 3228.4582 | 84/13 | |
| 24 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |