User:BudjarnLambeth/Draft related tunings section: Difference between revisions

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BudjarnLambeth (talk | contribs)
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''Done''
''Done''
* Done (with table): {{EDOs| 36 }}.
* Done (with table): {{EDOs| 36 }}.
* Done (table not added yet): {{EDOs| 7, 8, 12, 14, 16, 17, 19, 22, 23, 27, 31, 32, 38, 41, 58, 60, 72, 99 }}.
* Done (table not added yet): {{EDOs| 7, 8, 9, 12, 14, 16, 17, 19, 22, 23, 27, 31, 32, 38, 41, 58, 60, 72, 99 }}.
* Done (table & some step sizes not added yet): {{EDOs| 33, 39, 42, 45, 54, 59, 64 }}.
* Done (table & some step sizes not added yet): {{EDOs| 33, 39, 42, 45, 54, 59, 64 }}.


''To-do''
''To-do''
* High priority: {{EDOs| 118, 103, 111, 13, 104 }}.
* High priority: {{EDOs| 118, 103, 111, 13, 104 }}.
* Medium-high priority: {{EDOs| 9, 15, 18, 25, 26, 29, 30, 34, 35, 37, 48 }}.
* Medium-high priority: {{EDOs| 15, 18, 25, 26, 29, 30, 34, 35, 37, 48 }}.
* Medium-low priority: {{EDOs| 10, 11, 24, 5, 6 }}.
* Medium-low priority: {{EDOs| 10, 11, 24, 5, 6 }}.
* Low priority: {{EDOs| 125, 145, 152, 159, 166, 182, 198, 212, 243, 247 }}.  
* Low priority: {{EDOs| 125, 145, 152, 159, 166, 182, 198, 212, 243, 247 }}.  
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; Medium-high priority
; Medium-high priority
9edo
* 23ed6
* 31ed11
* 32ed12
* 11lim WE
* 13lim WE
* 2.3.5.11 WE
* Best nearby ZPI(s)
9edo's [[prime]]s 3, 7, 11 and 13 are all tuned flat, so it can benefit from [[octave stretching]].


15edo
15edo
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* 54ed12
* 54ed12
* Nearby edf (optional)
* Nearby edf (optional)
* 11lim WE
* 11lim WE (79.770)
* Best nearby ZPI(s)
* 47zpi (79.715)
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]].


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* 60ed10
* 60ed10
* 65ed12
* 65ed12
* 7lim WE
* 7lim WE (66.148)
* 11lim WE
* 13lim WE (66.291)
* 13lim WE
* 60zpi (67.090)
* Best nearby ZPI(s)
* 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]].


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* 90ed12
* 90ed12
* Nearby edf (optional)
* Nearby edf (optional)
* 11lim WE
* 13lim WE (47.946)
* 13lim WE
* 95zpi (48.067)
* Best nearby ZPI(s)
* 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]].


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* 96ed14
* 96ed14
* Nearby edf (optional)
* Nearby edf (optional)
* 11lim WE
* 13lim WE (46.249) (octave identical to 11lim within 1/20th of a cent)
* 13lim WE
* 100zpi (46.268)
* Best nearby ZPI(s)
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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* 107ed13
* 107ed13
* Nearby edf (optional)
* Nearby edf (optional)
* 11lim WE
* 11lim WE (41.482)
* 13lim WE
* 13lim WE (41.484)
* Best nearby ZPI(s)
* [[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]].


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* 104ed11
* 104ed11
* 108ed12
* 108ed12
* 11lim WE
* 11lim WE (79.770)
* 13lim WE
* 13lim WE (39.904)
* Best nearby ZPI(s)
* 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]].


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* 126ed13
* 126ed13
* Nearby edf (optional)
* Nearby edf (optional)
* 11lim WE
* 11lim WE (35.284)
* 13lim WE
* 13lim WE (35.276)
* Best nearby ZPI(s)
* 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]].


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* 125ed12
* 125ed12
* Nearby edf (optional)
* Nearby edf (optional)
* 11lim WE
* 11lim WE (35.284)
* 13lim WE
* 13lim WE (35.276)
* Best nearby ZPI(s)
* [[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]].


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* 137ed13
* 137ed13
* Nearby edf (optional)
* Nearby edf (optional)
* 11lim WE
* 11lim WE (32.377)
* 13lim WE
* 13lim WE (32.383)
* Best nearby ZPI(s)
* [[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]].


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* 172ed12
* 172ed12
* Nearby edf (optional)
* Nearby edf (optional)
* 11lim WE
* 11lim WE (25.017)
* 13lim WE
* 13lim WE (25.005)
* Best nearby ZPI(s)
* 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]].


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* 37ed13
* 37ed13
* Nearby edf (optional)
* Nearby edf (optional)
* 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)
* Best nearby ZPI(s)
* 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]].


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* 39ed12
* 39ed12
* 41ed13
* 41ed13
* 2.7.11 WE
* 2.7.11.13 WE (108.821)
* 2.7.11.13 WE
* 30zpi (108.722)
* Best nearby ZPI(s)
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))
* 38edt
* 38edt
* 56ed5
* 56ed5
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* 89ed13
* 89ed13
* 14edf
* 14edf
* 2.3.5.11.13 WE
* 2.3.5.11.13 WE (49.942)
* 11lim WE
* 11lim WE (50.017)
* 13lim WE
* 90zpi (49.988)
* Best nearby ZPI(s)
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.


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* 18ed12
* 18ed12
* Nearby edf (optional)
* Nearby edf (optional)
* 2.3.7 WE
* 2.3.7 WE (239.426)
* Best nearby ZPI(s)
* 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.


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* 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)
* Best nearby ZPI(s)
* 12zpi (198.843)
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 [[sugroup]] tuning, then it benefits from [[octave shrinking]].


; Low-priority
; Low-priority