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| [[User:BudjarnLambeth/Draft related tunings section]] | | [[User:BudjarnLambeth/Draft related tunings section]] |
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| = Lab = | | == Octave stretch or compression == |
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| 15edo
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| * 52ed11
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| * 11lim WE (79.770)
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| * 50ed10
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| * 47zpi (79.715)
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| * 54ed12
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| 15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
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| 18edo
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| * 42ed5
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| * 13lim WE (66.291)
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| * 61zpi (66.228)
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| * 65ed12
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| * 7lim WE (66.148)
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| * 47ed6
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| 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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| 25edo
| | ; 18edo |
| * 95zpi (48.067)
| | * Step size: NNN{{c}}, octave size: NNN{{c}} |
| * 13lim WE (47.946)
| | Pure-octaves 18edo approximates all harmonics up to 16 within NNN{{c}}. |
| * 90ed12
| | {{Harmonics in equal|18|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18edo}} |
| * 65ed6
| | {{Harmonics in equal|18|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18edo (continued)}} |
| * 96zpi (47.642)
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| 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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| 26edo
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| * 13lim WE (46.249)
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| * 93ed12
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| * 100zpi (46.268)
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| 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
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| * 46edt
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| * [[116zpi]] (41.465)
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| * 13lim WE (41.484)
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| * 107ed13
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| * 100ed11
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| * 96ed10
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| 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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| 30edo
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| * 39.918zpi (39.918)
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| * 13lim WE (39.904)
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| * 11lim WE (79.770)
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| * 100ed10
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| * 108ed12
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| * 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]].
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| 34edo
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| * 11lim WE (35.284)
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| * 13lim WE (35.276) (octave identical to 113ed10 within 0.1{{c}})
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| * 79ed5
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| * 122ed12
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| * 88ed6
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| * 144zpi (35.248)
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| * 126ed13
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| * 54edt
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| 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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| 35edo
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| * 11lim WE (35.284)
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| * 13lim WE (35.276)
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| * 121ed11
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| * [[149zpi]] (34.359)
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| * 116ed10
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| * 98ed7
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| * 81ed5
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| * 125ed12
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| * 90ed6
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| 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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| 37edo
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| * 137ed13
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| * [[161zpi]] (32.408) (octave identical to 123ed10 within 0.1{{c}})
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| * 86ed5
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| * 104ed7
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| * 13lim WE (32.383)
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| * 11lim WE (32.377)
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| * 133ed12
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| * 96ed6
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| 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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| 48edo
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| * 13lim WE (25.005)
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| * 226zpi (25.006)
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| * 166ed11
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| * 172ed12
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| * 124ed6 (octave identical to 11lim WE within 0.1{{c}})
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| * 76edt
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| * 28edf (octave identical to 159ed10 within 0.1{{c}})
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| 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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| ; Medium-low priority
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| 10edo
| | ; [[WE|18et, 13-limit WE tuning]] |
| * 2.5.7.13 WE (120.358)
| | * Step size: 66.291{{c}}, octave size: 1193.2{{c}} |
| * 28ed7 | | Compressing the octave of 18edo by around 7{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this. |
| * 37ed13
| | {{Harmonics in cet|66.291|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning}} |
| * 26zpi (119.899)
| | {{Harmonics in cet|66.291|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning (continued)}} |
| * 2.3.7.13 WE (119.785)
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| * 13lim WE (119.776)
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| * 36ed12
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| 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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| 11edo
| | ; [[zpi|61zpi]] |
| * 28ed6
| | * Step size: 66.228{{c}}, octave size: 1192.1{{c}} |
| * 39ed12
| | Compressing the octave of 18edo by around 8{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 61zpi does this. |
| * 2.7.11.13 WE (108.821) | | {{Harmonics in cet| 66.228 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 61zpi}} |
| * 30zpi (108.722)
| | {{Harmonics in cet| 66.228 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 61zpi (continued)}} |
| * 35ed9
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| * 31ed7
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| * 41ed13
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| * 37ed10
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| 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 can be used, at the cost of making the octaves sound significantly weaker.
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| 24edo
| | ; [[65ed12]] |
| ((13lim WE's octave is only 1/10th of a cent different from 24edo))
| | * Step size: NNN{{c}}, octave size: 1191.3{{c}} |
| * 56ed5
| | Compressing the octave of 18edo by around 9{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 65ed12 does this. |
| * 80ed10
| | {{Harmonics in equal|65|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 65ed12}} |
| * 89ed13
| | {{Harmonics in equal|65|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 65ed12 (continued)}} |
| * 2.3.5.11.13 WE (49.942)
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| * 90zpi (49.988)
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| * 11lim WE (50.017)
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| * 83ed11
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| * 86ed12
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| * 62ed6
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| * 38edt
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| 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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| 5edo
| | ; [[WE|18et, 7-limit WE tuning]] |
| * 14ed7
| | * Step size: 66.148{{c}}, octave size: 1190.7{{c}} |
| * 2.3.7 WE (239.426) | | Compressing the octave of 18edo by around 9.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this. |
| * 18ed12
| | {{Harmonics in cet| 66.148 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 7-limit WE tuning}} |
| 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 cet| 66.148 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 7-limit WE tuning (continued)}} |
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| 6edo
| | ; [[47ed6]] |
| * 19ed9 | | * Step size: NNN{{c}}, octave size: 1188.0{{c}} |
| * 2.9.5 WE (199.736)
| | Compressing the octave of 18edo by around 12{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 47ed6 does this. |
| * 2.9.5.7 WE (199.329)
| | {{Harmonics in equal|47|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 47ed6}} |
| * 20ed10
| | {{Harmonics in equal|47|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 47ed6 (continued)}} |
| * 14ed5
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| * 12zpi (198.843)
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| * 17ed7
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| If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]].
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