User:BudjarnLambeth/Sandbox2: Difference between revisions
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[[User:BudjarnLambeth/Draft related tunings section]] | [[User:BudjarnLambeth/Draft related tunings section]] | ||
= Lab = | |||
15edo | 15edo | ||
* | * 52ed11 | ||
* 11lim WE (79.770) | |||
* 50ed10 | * 50ed10 | ||
* | * 47zpi (79.715) | ||
* 54ed12 | * 54ed12 | ||
15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | 15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | ||
| Line 114: | Line 18: | ||
* 60ed10 | * 60ed10 | ||
* 65ed12 | * 65ed12 | ||
* 7lim WE | * 7lim WE (66.148) | ||
* | * 13lim WE (66.291) | ||
* | * 60zpi (67.090) | ||
* | * 61zpi (66.228) | ||
18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | 18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | ||
{{harmonics in equal | 18 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 42 | 5 | 1 | intervals=prime}} | |||
{{harmonics in equal | 47 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 60 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 65 | 12 | 1 | intervals=prime} | |||
{{harmonics in cet | 66.148 | intervals=prime}} | |||
{{harmonics in cet | 66.291 | intervals=prime}} | |||
{{harmonics in cet | 67.090 | intervals=prime}} | |||
{{harmonics in cet | 66.228 | intervals=prime}} | |||
25edo | 25edo | ||
* 65ed6 | * 65ed6 | ||
* 90ed12 | * 90ed12 | ||
* | * 13lim WE (47.946) | ||
* | * 95zpi (48.067) | ||
* 96zpi (47.642) | |||
* | |||
25edo's [[prime]] 3 is very sharp, and its sharp and flat mapping of 11 and 13 are about equally bad, it can benefit from [[octave shrinking]]. | 25edo's [[prime]] 3 is very sharp, and its sharp and flat mapping of 11 and 13 are about equally bad, it can benefit from [[octave shrinking]]. | ||
{{harmonics in equal | 25 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 65 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 90 | 12 | 1 | intervals=prime} | |||
{{harmonics in cet | 47.946 | intervals=prime}} | |||
{{harmonics in cet | 48.067 | intervals=prime}} | |||
{{harmonics in cet | 47.642 | intervals=prime}} | |||
26edo | 26edo | ||
| Line 135: | Line 53: | ||
* 93ed12 | * 93ed12 | ||
* 96ed14 | * 96ed14 | ||
* | * 13lim WE (46.249) (octave identical to 11lim within 1/20th of a cent) | ||
* 100zpi (46.268) | |||
* | |||
26edo's simple [[prime]]s with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from [[octave stretching]]. | 26edo's simple [[prime]]s with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from [[octave stretching]]. | ||
{{harmonics in equal | 26 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 41 | 3 | 1 | intervals=prime}} | |||
{{harmonics in equal | 67 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 86 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 93 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 96 | 14 | 1 | intervals=prime}} | |||
{{harmonics in cet | 46.249 | intervals=prime}} | |||
{{harmonics in cet | 46.268 | intervals=prime}} | |||
29edo | 29edo | ||
| Line 147: | Line 71: | ||
* 100ed11 | * 100ed11 | ||
* 107ed13 | * 107ed13 | ||
* | * 16edf | ||
* 11lim WE | * 11lim WE (41.482) | ||
* 13lim WE | * 13lim WE (41.484) | ||
* | * [[116zpi]] (41.465) | ||
29edo's [[prime]]s 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from [[octave stretching]]. | 29edo's [[prime]]s 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from [[octave stretching]]. | ||
{{harmonics in equal | 29 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 46 | 3 | 1 | intervals=prime}} | |||
{{harmonics in equal | 96 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 100 | 11 | 1 | intervals=prime}} | |||
{{harmonics in equal | 105 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 107 | 13 | 1 | intervals=prime}} | |||
{{harmonics in equal | 16 | 3 | 2 | intervals=prime}} | |||
{{harmonics in cet | 41.482 | intervals=prime}} | |||
{{harmonics in cet | 41.484 | intervals=prime}} | |||
{{harmonics in cet | 41.465 | intervals=prime}} | |||
30edo | 30edo | ||
| Line 158: | Line 92: | ||
* 104ed11 | * 104ed11 | ||
* 108ed12 | * 108ed12 | ||
* 11lim WE | * 11lim WE (79.770) | ||
* 13lim WE | * 13lim WE (39.904) | ||
* | * 39.918zpi (39.918) | ||
30edo's simple [[prime]]s with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from [[octave shrinking]]. | 30edo's simple [[prime]]s with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from [[octave shrinking]]. | ||
{{harmonics in equal | 30 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 78 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 100 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 104 | 11 | 1 | intervals=prime}} | |||
{{harmonics in equal | 108 | 12 | 1 | intervals=prime}} | |||
{{harmonics in cet | 79.770 | intervals=prime}} | |||
{{harmonics in cet | 39.904 | intervals=prime}} | |||
{{harmonics in cet | 39.918 | intervals=prime}} | |||
34edo | 34edo | ||
| Line 171: | Line 113: | ||
* 122ed12 | * 122ed12 | ||
* 126ed13 | * 126ed13 | ||
* | * 11lim WE (35.284) | ||
* 13lim WE (35.276) | |||
* 13lim WE | * 144zpi (35.248) | ||
* | |||
34edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, and it has two about equally bad mappings of 7, so 34edo can benefit from [[octave shrinking]]. | 34edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, and it has two about equally bad mappings of 7, so 34edo can benefit from [[octave shrinking]]. | ||
{{harmonics in equal | 34 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 54 | 3 | 1 | intervals=prime}} | |||
{{harmonics in equal | 79 | 5 | 1 | intervals=prime}} | |||
{{harmonics in equal | 88 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 108 | 9 | 1 | intervals=prime} | |||
{{harmonics in equal | 113 | 10 | 1 | intervals=prime} | |||
{{harmonics in equal | 122 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 126 | 13 | 1 | intervals=prime}} | |||
{{harmonics in cet | 35.284 | intervals=prime}} | |||
{{harmonics in cet | 35.276 | intervals=prime}} | |||
{{harmonics in cet | 35.248 | intervals=prime}} | |||
35edo | 35edo | ||
| Line 184: | Line 136: | ||
* 121ed11 | * 121ed11 | ||
* 125ed12 | * 125ed12 | ||
* | * 11lim WE (35.284) | ||
* 13lim WE (35.276) | |||
* 13lim WE | * [[149zpi]] (34.359) | ||
* | |||
35edo's [[prime]]s 3, 5, 7 and 11 are all tuned flat, and it has two about equally bad mappings of 13, so 35edo can benefit from [[octave stretching]]. | 35edo's [[prime]]s 3, 5, 7 and 11 are all tuned flat, and it has two about equally bad mappings of 13, so 35edo can benefit from [[octave stretching]]. | ||
{{harmonics in equal | 35 | 2 | 1 | intervals=prime} | |||
{{harmonics in equal | 81 | 5 | 1 | intervals=prime}} | |||
{{harmonics in equal | 90 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 98 | 7 | 1 | intervals=prime} | |||
{{harmonics in equal | 116 | 10 | 1 | intervals=prime} | |||
{{harmonics in equal | 121 | 11 | 1 | intervals=prime}} | |||
{{harmonics in equal | 125 | 12 | 1 | intervals=prime}} | |||
{{harmonics in cet | 35.284 | intervals=prime}} | |||
{{harmonics in cet | 35.276 | intervals=prime}} | |||
{{harmonics in cet | 34.359 | intervals=prime}} | |||
37edo | 37edo | ||
| Line 199: | Line 160: | ||
* 133ed12 | * 133ed12 | ||
* 137ed13 | * 137ed13 | ||
* | * 11lim WE (32.377) | ||
* 13lim WE (32.383) | |||
* 13lim WE | * [[161zpi]] (32.408) | ||
* | |||
37edo's [[prime]]s 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | 37edo's [[prime]]s 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]]. | ||
{{harmonics in equal | 37 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 59 | 3 | 1 | intervals=prime}} | |||
{{harmonics in equal | 86 | 5 | 1 | intervals=prime}} | |||
{{harmonics in equal | 96 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 104 | 7 | 1 | intervals=prime} | |||
{{harmonics in equal | 123 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 128 | 11 | 1 | intervals=prime}} | |||
{{harmonics in equal | 133 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 137 | 13 | 1 | intervals=prime}} | |||
{{harmonics in cet | 32.377 | intervals=prime}} | |||
{{harmonics in cet | 32.383 | intervals=prime}} | |||
{{harmonics in cet | 32.408 | intervals=prime}} | |||
48edo | 48edo | ||
| Line 212: | Line 184: | ||
* 166ed11 | * 166ed11 | ||
* 172ed12 | * 172ed12 | ||
* | * 28edf | ||
* 11lim WE | * 11lim WE (25.017) | ||
* 13lim WE | * 13lim WE (25.005) | ||
* | * 226zpi (25.006) | ||
Most of 48edo's simple [[prime]]s have low error, but its 5 is substantially flat, so 48edo can benefit from slight [[octave stretching]]. | Most of 48edo's simple [[prime]]s have low error, but its 5 is substantially flat, so 48edo can benefit from slight [[octave stretching]]. | ||
{{harmonics in equal | 48 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 76 | 3 | 1 | intervals=prime}} | |||
{{harmonics in equal | 124 | 6 | 1 | intervals=prime} | |||
{{harmonics in equal | 152 | 9 | 1 | intervals=prime} | |||
{{harmonics in equal | 159 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 166 | 11 | 1 | intervals=prime}} | |||
{{harmonics in equal | 172 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 28 | 3 | 2 | intervals=prime}} | |||
{{harmonics in cet | 25.017 | intervals=prime}} | |||
{{harmonics in cet | 25.005 | intervals=prime}} | |||
{{harmonics in cet | 25.006 | intervals=prime}} | |||
; Medium-low priority | ; Medium-low priority | ||
| Line 229: | Line 212: | ||
* 36ed12 | * 36ed12 | ||
* 37ed13 | * 37ed13 | ||
* | * 6edf | ||
* 2.3.7.13 WE | * 2.3.7.13 WE (119.785) | ||
* 2.5.7.13 WE | * 2.5.7.13 WE (120.358) | ||
* 13lim WE | * 13lim WE (119.776) | ||
* | * 26zpi (119.899) | ||
If one wishes to use 10edo as a no-5s, 19-or-lower-limit tuning, then it benefits from [[octave shrinking]]. If one wishes to use 10edo as a no-3s, 13-or-lower-limit tuning, then it benefits from [[octave stretching]]. | If one wishes to use 10edo as a no-5s, 19-or-lower-limit tuning, then it benefits from [[octave shrinking]]. If one wishes to use 10edo as a no-3s, 13-or-lower-limit tuning, then it benefits from [[octave stretching]]. | ||
{{harmonics in equal | 10 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 23 | 5 | 1 | intervals=prime}} | |||
{{harmonics in equal | 26 | 6 | 1 | intervals=prime} | |||
{{harmonics in equal | 28 | 7 | 1 | intervals=prime} | |||
{{harmonics in equal | 32 | 8 | 1 | intervals=prime}} | |||
{{harmonics in equal | 33 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 36 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 37 | 13 | 1 | intervals=prime}} | |||
{{harmonics in equal | 6 | 3 | 2 | intervals=prime}} | |||
{{harmonics in cet | 119.785 | intervals=prime}} | |||
{{harmonics in cet | 120.358 | intervals=prime}} | |||
{{harmonics in cet | 119.776 | intervals=prime}} | |||
{{harmonics in cet | 119.899 | intervals=prime}} | |||
11edo | 11edo | ||
| Line 246: | Line 242: | ||
* 39ed12 | * 39ed12 | ||
* 41ed13 | * 41ed13 | ||
* 2.7.11.13 WE (108.821) | |||
* 2.7.11.13 WE | * 30zpi (108.722) | ||
* | |||
11edo has about equally bad sharp and flat mappings of [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. To use its primes 3 or 5, extreme octave shrinking or [[octave stretching]] can be used, at the cost of making the octaves sound significantly weaker. | 11edo has about equally bad sharp and flat mappings of [[prime]]s 3 and 5. The 7 and 13 are quite sharp, but the 11 is a little flat. To use it as a 2.7.11.13 tuning, slight [[octave shrinking]] is advisable. To use its primes 3 or 5, extreme octave shrinking or [[octave stretching]] can be used, at the cost of making the octaves sound significantly weaker. | ||
{{harmonics in equal | 11 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 27 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 28 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 31 | 7 | 1 | intervals=prime}} | |||
{{harmonics in equal | 35 | 9 | 1 | intervals=prime} | |||
{{harmonics in equal | 37 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 38 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 38 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 39 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 41 | 13 | 1 | intervals=prime}} | |||
{{harmonics in cet | 108.821 | intervals=prime}} | |||
{{harmonics in cet | 108.722 | intervals=prime}} | |||
24edo | 24edo | ||
((13lim WE's octave is only 1/10th of a cent different from 24edo)) | |||
* 38edt | * 38edt | ||
* 56ed5 | * 56ed5 | ||
* 62ed6 | * 62ed6 | ||
* 67ed7 | * 67ed7 | ||
* | * 9ed7/6 | ||
* 80ed10 | * 80ed10 | ||
* 83ed11 | * 83ed11 | ||
| Line 262: | Line 270: | ||
* 89ed13 | * 89ed13 | ||
* 14edf | * 14edf | ||
* 2.3.5.11.13 WE | * 2.3.5.11.13 WE (49.942) | ||
* 11lim WE | * 11lim WE (50.017) | ||
* | * 90zpi (49.988) | ||
If one wishes to use 24edo as a full 19-or-lower-limit tuning, then it benefits from slight [[octave stretching]], mostly to improve its [[prime]] 7. If one wishes to use 24edo as a no-7s 19-or-lower-limit tuning, then it benefits from slight [[octave shrinking]], mostly to improve its primes 5 and 13. | If one wishes to use 24edo as a full 19-or-lower-limit tuning, then it benefits from slight [[octave stretching]], mostly to improve its [[prime]] 7. If one wishes to use 24edo as a no-7s 19-or-lower-limit tuning, then it benefits from slight [[octave shrinking]], mostly to improve its primes 5 and 13. | ||
{{harmonics in equal | 24 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 38 | 3 | 1 | intervals=prime}} | |||
{{harmonics in equal | 56 | 5 | 1 | intervals=prime}} | |||
{{harmonics in equal | 62 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 67 | 7 | 1 | intervals=prime}} | |||
{{harmonics in equal | 9 | 7 | 6 | intervals=prime}} | |||
{{harmonics in equal | 80 | 10 | 1 | intervals=prime}} | |||
{{harmonics in equal | 83 | 11 | 1 | intervals=prime}} | |||
{{harmonics in equal | 86 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 89 | 13 | 1 | intervals=prime}} | |||
{{harmonics in equal | 14 | 3 | 2 | intervals=prime}} | |||
{{harmonics in cet | 49.942 | intervals=prime}} | |||
{{harmonics in cet | 50.017 | intervals=prime}} | |||
{{harmonics in cet | 49.988 | intervals=prime}} | |||
5edo | 5edo | ||
| Line 273: | Line 294: | ||
* 14ed7 | * 14ed7 | ||
* 18ed12 | * 18ed12 | ||
* | * 3edf | ||
* 2.3.7 WE | * 2.3.7 WE (239.426) | ||
* | * 9zpi (238.357) | ||
If one wishes to use 5edo as a 2.3.7 [[subgroup]] tuning, then it benefits from slight [[octave shrinking]] to improve its prime 3. | If one wishes to use 5edo as a 2.3.7 [[subgroup]] tuning, then it benefits from slight [[octave shrinking]] to improve its prime 3. | ||
{{harmonics in equal | 5 | 2 | 1 | intervals=prime}} | |||
{{harmonics in equal | 8 | 3 | 1 | intervals=prime}} | |||
{{harmonics in equal | 13 | 6 | 1 | intervals=prime}} | |||
{{harmonics in equal | 14 | 7 | 1 | intervals=prime}} | |||
{{harmonics in equal | 18 | 12 | 1 | intervals=prime}} | |||
{{harmonics in equal | 3 | 3 | 2 | intervals=prime}} | |||
{{harmonics in cet | 239.426 | intervals=prime}} | |||
{{harmonics in cet | 238.357 | intervals=prime}} | |||
6edo | 6edo | ||
| Line 283: | Line 312: | ||
* 19ed9 | * 19ed9 | ||
* 20ed10 | * 20ed10 | ||
* 2.9.5 WE | * 2.9.5 WE (199.736) | ||
* 2.9.5.7 WE | * 2.9.5.7 WE (199.329) | ||
* | * 12zpi (198.843) | ||
If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[sugroup]] tuning, then it benefits from [[octave shrinking]]. | If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[sugroup]] tuning, then it benefits from [[octave shrinking]]. | ||
{{harmonics in equal | 14 | 5 | 1 | intervals=prime}} | |||
{{harmonics in equal | 17 | 7 | 1 | intervals=prime}} | |||
{{harmonics in equal | 19 | 9 | 1 | intervals=prime}} | |||
{{harmonics in equal | 20 | 10 | 1 | intervals=prime} | |||
{{harmonics in cet | 199.736 | intervals=prime}} | |||
{{harmonics in cet | 199.329 | intervals=prime}} | |||
{{harmonics in cet | 198.843 | intervals=prime}} | |||
; Low-priority | ; Low-priority | ||