User:BudjarnLambeth/Sandbox2: Difference between revisions
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| Line 31: | Line 31: | ||
26edo | 26edo | ||
* 13lim WE (46.249 | * 13lim WE (46.249) | ||
* 93ed12 | * 93ed12 | ||
* 100zpi (46.268) | * 100zpi (46.268) | ||
| Line 46: | Line 46: | ||
30edo | 30edo | ||
* 39.918zpi (39.918 | * 39.918zpi (39.918) | ||
* 13lim WE (39.904) | * 13lim WE (39.904) | ||
* 11lim WE (79.770) | * 11lim WE (79.770) | ||
| Line 56: | Line 56: | ||
34edo | 34edo | ||
* 11lim WE (35.284) | * 11lim WE (35.284) | ||
* 13lim WE (35.276) (identical to 113ed10) | * 13lim WE (35.276) (octave identical to 113ed10 within 0.1{{c}}) | ||
* 79ed5 | * 79ed5 | ||
* 122ed12 | * 122ed12 | ||
| Line 78: | Line 78: | ||
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]]. | ||
; Medium-low priority | ; Medium-low priority | ||
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) | ||
* 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]]. | If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. | ||
Revision as of 09:35, 14 September 2025
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User:BudjarnLambeth/Draft related tunings section
Lab
15edo
- 52ed11
- 11lim WE (79.770)
- 50ed10
- 47zpi (79.715)
- 54ed12
15edo's primes 3, 5, 11 and 13 are all tuned sharp, so it can benefit from octave shrinking.
18edo
- 42ed5
- 13lim WE (66.291)
- 61zpi (66.228)
- 65ed12
- 7lim WE (66.148)
- 47ed6
18edo's primes 3, 5, 7 and 13 are all tuned sharp, so it can benefit from octave shrinking.
25edo
- 95zpi (48.067)
- 13lim WE (47.946)
- 90ed12
- 65ed6
- 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.
26edo
- 13lim WE (46.249)
- 93ed12
- 100zpi (46.268)
26edo's simple primes with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from octave stretching.
29edo
- 46edt
- 116zpi (41.465)
- 13lim WE (41.484)
- 107ed13
- 100ed11
- 96ed10
29edo's primes 5, 7, 11 and 13 are all tuned flat and the 3 has relatively little error, so 29edo can benefit from octave stretching.
30edo
- 39.918zpi (39.918)
- 13lim WE (39.904)
- 11lim WE (79.770)
- 100ed10
- 108ed12
- 78ed6
30edo's simple primes with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from octave shrinking.
34edo
- 11lim WE (35.284)
- 13lim WE (35.276) (octave identical to 113ed10 within 0.1 ¢)
- 79ed5
- 122ed12
- 88ed6
- 144zpi (35.248)
- 126ed13
- 54edt
34edo's primes 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
- 11lim WE (35.284)
- 13lim WE (35.276)
- 121ed11
- 149zpi (34.359)
- 116ed10
- 98ed7
- 81ed5
- 125ed12
- 90ed6
35edo's primes 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
- 137ed13
- 161zpi (32.408) (octave identical to 123ed10 within 0.1 ¢)
- 86ed5
- 104ed7
- 13lim WE (32.383)
- 11lim WE (32.377)
- 133ed12
- 96ed6
37edo's primes 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from octave shrinking.
48edo
- 13lim WE (25.005)
- 226zpi (25.006)
- 166ed11
- 172ed12
- 124ed6 (octave identical to 11lim WE within 0.1 ¢)
- 76edt
- 28edf (octave identical to 159ed10 within 0.1 ¢)
Most of 48edo's simple primes have low error, but its 5 is substantially flat, so 48edo can benefit from slight octave stretching.
- Medium-low priority
10edo
- 2.5.7.13 WE (120.358)
- 28ed7
- 37ed13
- 26zpi (119.899)
- 2.3.7.13 WE (119.785)
- 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.
11edo
- 28ed6
- 39ed12
- 2.7.11.13 WE (108.821)
- 30zpi (108.722)
- 35ed9
- 31ed7
- 41ed13
- 37ed10
11edo has about equally bad sharp and flat mappings of primes 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 ((13lim WE's octave is only 1/10th of a cent different from 24edo))
- 56ed5
- 80ed10
- 89ed13
- 2.3.5.11.13 WE (49.942)
- 90zpi (49.988)
- 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.
5edo
- 14ed7
- 2.3.7 WE (239.426)
- 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.
6edo
- 19ed9
- 2.9.5 WE (199.736)
- 2.9.5.7 WE (199.329)
- 20ed10
- 14ed5
- 12zpi (198.843)
- 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.