19edo: Difference between revisions
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| {{monzo| -30 19 }} | | {{monzo| -30 19 }} | ||
| {{mapping| 19 30 }} | | {{mapping| 19 30 }} | ||
| +2. | | +2.277 | ||
| 2. | | 2.277 | ||
| 3. | | 3.612 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| 81/80, 3125/3072 | | 81/80, 3125/3072 | ||
| {{mapping| 19 30 44 }} | | {{mapping| 19 30 44 }} | ||
| +2. | | +2.578 | ||
| 1. | | 1.911 | ||
| 3. | | 3.025 | ||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 49/48, 81/80, 126/125 | | 49/48, 81/80, 126/125 | ||
| {{mapping| 19 30 44 53 }} | | {{mapping| 19 30 44 53 }} | ||
| +3. | | +3.848 | ||
| 2. | | 2.755 | ||
| 4. | | 4.362 | ||
|- | |- | ||
| 2.3.5.7.13 | | 2.3.5.7.13 | ||
| 49/48, 65/64, 81/80, 91/90 | | 49/48, 65/64, 81/80, 91/90 | ||
| {{mapping| 19 30 44 53 70 }} | | {{mapping| 19 30 44 53 70 }} | ||
| +4. | | +4.135 | ||
| 2. | | 2.530 | ||
| | | 4.006 | ||
|- | |- | ||
| 2.3.5.7.13.23 | | 2.3.5.7.13.23 | ||
| 49/48, 65/64, 70/69, 81/80, 91/90 | | 49/48, 65/64, 70/69, 81/80, 91/90 | ||
| {{mapping| 19 30 44 53 70 86 }} | | {{mapping| 19 30 44 53 70 86 }} | ||
| +3. | | +3.319 | ||
| 2. | | 2.936 | ||
| 4. | | 4.649 | ||
|} | |} | ||
* 19et is lower in relative error than any previous equal temperaments in the 5-, 7-, 13-, 17-, and 19-limit—''both'' 19 and 19e val achieve this in the case of 13-limit, 19eg val in the 17-limit, and 19egh val in the 19-limit. The next equal temperaments doing better in those subgroups are [[34edo|34]], [[31edo|31]], [[27edo|27e]], [[22edo|22]], and [[26edo|26]], respectively. | * 19et is lower in relative error than any previous equal temperaments in the 5-, 7-, 13-, 17-, and 19-limit—''both'' 19 and 19e val achieve this in the case of 13-limit, 19eg val in the 17-limit, and 19egh val in the 19-limit. The next equal temperaments doing better in those subgroups are [[34edo|34]], [[31edo|31]], [[27edo|27e]], [[22edo|22]], and [[26edo|26]], respectively. | ||