User:BudjarnLambeth/Sandbox2: Difference between revisions

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26edo
26edo
* 13lim WE (46.249) (octave identical to 11lim within 1/20th of a cent)
* 13lim WE (46.249)
* 93ed12
* 93ed12
* 100zpi (46.268)
* 100zpi (46.268)
Line 46: Line 46:


30edo
30edo
* 39.918zpi (39.918) (octave identical to 104ed11 within 0.1{{c}})
* 39.918zpi (39.918)
* 13lim WE (39.904)
* 13lim WE (39.904)
* 11lim WE (79.770)
* 11lim WE (79.770)
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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
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37edo
37edo
* 59edt
* 137ed13
* [[161zpi]] (32.408) (octave identical to 123ed10 within 0.1{{c}})
* 86ed5
* 86ed5
* 96ed6
* 104ed7
* 104ed7
* 123ed10
* 13lim WE (32.383)
* 128ed11
* 11lim WE (32.377)
* 133ed12
* 133ed12
* 137ed13
* 96ed6
* 11lim WE (32.377)
* 13lim WE (32.383)
* [[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
* 76edt
* 13lim WE (25.005)
* 124ed6
* 226zpi (25.006)
* 152ed9
* 159ed10
* 166ed11
* 166ed11
* 172ed12
* 172ed12
* 28edf
* 124ed6 (octave identical to 11lim WE within 0.1{{c}})
* 11lim WE (25.017)
* 76edt
* 13lim WE (25.005)
* 28edf (octave identical to 159ed10 within 0.1{{c}})
* 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


10edo
10edo
* 16edt
* 2.5.7.13 WE (120.358)
* 23ed5
* 26ed6
* 28ed7
* 28ed7
* 32ed8
* 33ed10
* 36ed12
* 37ed13
* 37ed13
* 6edf
* 26zpi (119.899)
* 2.3.7.13 WE (119.785)
* 2.3.7.13 WE (119.785)
* 2.5.7.13 WE (120.358)
* 13lim WE (119.776)
* 13lim WE (119.776)
* 26zpi (119.899)
* 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]].
{{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
* 27ed6
* 28ed6
* 28ed6
* 31ed7
* 35ed9
* 37ed10
* 38ed10
* 38ed12
* 39ed12
* 39ed12
* 41ed13
* 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.
{{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))
((13lim WE's octave is only 1/10th of a cent different from 24edo))
* 38edt
* 56ed5
* 56ed5
* 62ed6
* 67ed7
* 9ed7/6
* 80ed10
* 80ed10
* 83ed11
* 86ed12
* 89ed13
* 89ed13
* 14edf
* 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)
* 90zpi (49.988)
* 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.
{{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
* 8edt
* 13ed6
* 14ed7
* 14ed7
* 2.3.7 WE (239.426)
* 18ed12
* 18ed12
* 3edf
* 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
* 14ed5
* 17ed7
* 19ed9
* 19ed9
* 20ed10
* 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]].
{{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}}