User:BudjarnLambeth/Draft related tunings section: Difference between revisions
| Line 237: | Line 237: | ||
15edo | 15edo | ||
* 52ed11 | * 52ed11 | ||
* 11lim WE (79.770) | * 11lim WE (79.770) | ||
* 50ed10 | |||
* 47zpi (79.715) | * 47zpi (79.715) | ||
* 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]]. | ||
18edo | 18edo | ||
* 42ed5 | * 42ed5 | ||
* | * 13lim WE (66.291) | ||
* | * 61zpi (66.228) | ||
* 65ed12 | * 65ed12 | ||
* 7lim WE (66.148) | * 7lim WE (66.148) | ||
* | * 47ed6 | ||
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]]. | ||
25edo | 25edo | ||
* 95zpi (48.067) | |||
* 13lim WE (47.946) | |||
* 90ed12 | |||
* 65ed6 | * 65ed6 | ||
* 96zpi (47.642) | * 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]]. | ||
26edo | 26edo | ||
* | * 13lim WE (46.249) | ||
* 93ed12 | * 93ed12 | ||
* 100zpi (46.268) | * 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]]. | ||
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29edo | 29edo | ||
* 46edt | * 46edt | ||
* | * [[116zpi]] (41.465) | ||
* 13lim WE (41.484) | |||
* 107ed13 | |||
* 100ed11 | |||
* 96ed10 | * 96ed10 | ||
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]]. | ||
30edo | 30edo | ||
* | * 39.918zpi (39.918) | ||
* 13lim WE (39.904) | |||
* 11lim WE (79.770) | |||
* 100ed10 | * 100ed10 | ||
* 108ed12 | * 108ed12 | ||
* | * 78ed6 | ||
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]]. | ||
34edo | 34edo | ||
* | * 11lim WE (35.284) | ||
* 13lim WE (35.276) (octave identical to 113ed10 within 0.1{{c}}) | |||
* 79ed5 | * 79ed5 | ||
* 122ed12 | |||
* 88ed6 | * 88ed6 | ||
* | * 144zpi (35.248) | ||
* 126ed13 | * 126ed13 | ||
* | * 54edt | ||
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]]. | ||
35edo | 35edo | ||
* 11lim WE (35.284) | * 11lim WE (35.284) | ||
* 13lim WE (35.276) | * 13lim WE (35.276) | ||
* 121ed11 | |||
* [[149zpi]] (34.359) | * [[149zpi]] (34.359) | ||
* 116ed10 | |||
* 98ed7 | |||
* 81ed5 | |||
* 125ed12 | |||
* 90ed6 | |||
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]]. | ||
37edo | 37edo | ||
* | * 137ed13 | ||
* [[161zpi]] (32.408) (octave identical to 123ed10 within 0.1{{c}}) | |||
* 86ed5 | * 86ed5 | ||
* 104ed7 | * 104ed7 | ||
* | * 13lim WE (32.383) | ||
* | * 11lim WE (32.377) | ||
* 133ed12 | * 133ed12 | ||
* | * 96ed6 | ||
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]]. | ||
48edo | 48edo | ||
* | * 13lim WE (25.005) | ||
* | * 226zpi (25.006) | ||
* 166ed11 | * 166ed11 | ||
* 172ed12 | * 172ed12 | ||
* | * 124ed6 (octave identical to 11lim WE within 0.1{{c}}) | ||
* 76edt | |||
* | * 28edf (octave identical to 159ed10 within 0.1{{c}}) | ||
* | |||
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]]. | ||
| Line 352: | Line 332: | ||
10edo | 10edo | ||
* | * 2.5.7.13 WE (120.358) | ||
* 28ed7 | * 28ed7 | ||
* 37ed13 | * 37ed13 | ||
* | * 26zpi (119.899) | ||
* 2.3.7.13 WE (119.785) | * 2.3.7.13 WE (119.785) | ||
* 13lim WE (119.776) | * 13lim WE (119.776) | ||
* | * 36ed12 | ||
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]]. | ||
11edo | 11edo | ||
* 28ed6 | * 28ed6 | ||
* 39ed12 | * 39ed12 | ||
* 2.7.11.13 WE (108.821) | * 2.7.11.13 WE (108.821) | ||
* 30zpi (108.722) | * 30zpi (108.722) | ||
* 35ed9 | |||
* 31ed7 | |||
* 41ed13 | |||
* 37ed10 | |||
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. | ||
24edo | 24edo | ||
((13lim WE's octave is only 1/10th of a cent different from 24edo)) | ((13lim WE's octave is only 1/10th of a cent different from 24edo)) | ||
* 56ed5 | * 56ed5 | ||
* 80ed10 | * 80ed10 | ||
* 89ed13 | * 89ed13 | ||
* 2.3.5.11.13 WE (49.942) | * 2.3.5.11.13 WE (49.942) | ||
* 90zpi (49.988) | |||
* 11lim WE (50.017) | * 11lim WE (50.017) | ||
* | * 83ed11 | ||
* 86ed12 | |||
* 62ed6 | |||
* 38edt | |||
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. | ||
5edo | 5edo | ||
* 14ed7 | * 14ed7 | ||
* 2.3.7 WE (239.426) | |||
* 18ed12 | * 18ed12 | ||
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. | ||
6edo | 6edo | ||
* 19ed9 | * 19ed9 | ||
* 2.9.5 WE (199.736) | * 2.9.5 WE (199.736) | ||
* 2.9.5.7 WE (199.329) | * 2.9.5.7 WE (199.329) | ||
* 20ed10 | |||
* 14ed5 | |||
* 12zpi (198.843) | * 12zpi (198.843) | ||
If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[ | * 17ed7 | ||
If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. | |||
; Low-priority | ; Low-priority | ||