82edo: Difference between revisions
+subsets and supersets |
Note the alt val. Rework on the interval table |
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== Theory == | == Theory == | ||
82edo's [[patent val]] is [[contorted]] in the [[11-limit]], from 82 = 2 × 41. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. | 82edo's [[patent val]] is [[contorted]] in the [[11-limit]], from 82 = 2 × 41. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The alternative 82e val tempers out [[121/120]] instead. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 18: | Line 18: | ||
! # | ! # | ||
! Cents | ! Cents | ||
! | ! Approximate Ratios* | ||
! Additional Ratios<br>with 11's (82e Val) | ! Additional Ratios<br>with 11's (82e Val) | ||
! Additional Ratios<br>with 11's (Patent Val) | ! Additional Ratios<br>with 11's (Patent Val) | ||
| Line 30: | Line 30: | ||
| 1 | | 1 | ||
| 14.634 | | 14.634 | ||
| | | ''65/64'', 91/90 | ||
| | | ''55/54'' | ||
| | | | ||
|- | |- | ||
| 2 | | 2 | ||
| 29.268 | | 29.268 | ||
| 49/48, 50/49, ''81/80'', ''126/125'' | |||
| | | | ||
| | | 45/44, 55/54 | ||
|- | |- | ||
| 3 | | 3 | ||
| 43.902 | | 43.902 | ||
| | | 40/39 | ||
| | | ''33/32'', ''45/44'' | ||
| | | | ||
|- | |- | ||
| 4 | | 4 | ||
| 58.537 | | 58.537 | ||
| ''25/24'', 28/27, ''36/35'' | |||
| | | | ||
| | | 33/32 | ||
|- | |- | ||
| 5 | | 5 | ||
| 73.171 | | 73.171 | ||
| | | 26/25, ''27/26'' | ||
| 22/21 | | 22/21 | ||
| | | | ||
| Line 60: | Line 60: | ||
| 6 | | 6 | ||
| 87.805 | | 87.805 | ||
| | | 19/18, 20/19, 21/20 | ||
| | | | ||
| 22/21 | | ''22/21'' | ||
|- | |- | ||
| 7 | | 7 | ||
| 102.439 | | 102.439 | ||
| 18/17 | | 17/16, 18/17 | ||
| | | | ||
| | | | ||
| Line 72: | Line 72: | ||
| 8 | | 8 | ||
| 117.073 | | 117.073 | ||
| 16/15 | | 15/14, 16/15 | ||
| | | | ||
| | | | ||
| Line 91: | Line 91: | ||
| 160.976 | | 160.976 | ||
| | | | ||
| 12/11 | | 11/10, ''12/11'' | ||
| | | | ||
|- | |- | ||
| Line 98: | Line 98: | ||
| 10/9, 21/19 | | 10/9, 21/19 | ||
| | | | ||
| 11/10 | | ''11/10'' | ||
|- | |- | ||
| 13 | | 13 | ||
| Line 134: | Line 134: | ||
| 7/6 | | 7/6 | ||
| | | | ||
| 22/19 | | ''22/19'' | ||
|- | |- | ||
| 19 | | 19 | ||
| Line 140: | Line 140: | ||
| 20/17 | | 20/17 | ||
| | | | ||
| 13/11 | | ''13/11'' | ||
|- | |- | ||
| 20 | | 20 | ||
| Line 163: | Line 163: | ||
| 336.585 | | 336.585 | ||
| 17/14 | | 17/14 | ||
| 11/9 | | ''11/9'' | ||
| | | | ||
|- | |- | ||
| Line 192: | Line 192: | ||
| 28 | | 28 | ||
| 409.756 | | 409.756 | ||
| 24/19 | | 19/15, 24/19 | ||
| | | | ||
| 14/11 | | ''14/11'' | ||
|- | |- | ||
| 29 | | 29 | ||
| Line 205: | Line 205: | ||
| 439.024 | | 439.024 | ||
| 9/7 | | 9/7 | ||
| 22/17 | | ''22/17'' | ||
| | | | ||
|- | |- | ||
| Line 242: | Line 242: | ||
| 19/14 | | 19/14 | ||
| | | | ||
| 15/11 | | ''15/11'' | ||
|- | |- | ||
| 37 | | 37 | ||
| 541.463 | | 541.463 | ||
| 26/19 | | 26/19 | ||
| 15/11 | | ''11/8'', 15/11 | ||
| | | | ||
|- | |- | ||
| Line 258: | Line 258: | ||
| 39 | | 39 | ||
| 570.732 | | 570.732 | ||
| 18/13 | | ''18/13'' | ||
| | | | ||
| | | | ||
| Line 270: | Line 270: | ||
| 41 | | 41 | ||
| 600.000 | | 600.000 | ||
| 24/17 | | 17/12, 24/17 | ||
| | | | ||
| | | | ||
| Line 280: | Line 280: | ||
| | | | ||
|} | |} | ||
<nowiki>*</nowiki> as a no-11 19-limit temperament | |||