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| | == Approximations of odd harmonics == |
| | | {{harmonics in equal|1|intervals=odd|columns=7}} |
| [[User:BudjarnLambeth/Draft related tunings section]]
| | {{harmonics in equal|2|intervals=odd|columns=7}} |
| | | {{harmonics in equal|3|intervals=odd|columns=7}} |
| = Lab = | | {{harmonics in equal|4|intervals=odd|columns=7}} |
| | | {{harmonics in equal|5|intervals=odd|columns=7}} |
| 15edo
| | {{harmonics in equal|6|intervals=odd|columns=7}} |
| * 52ed11
| | {{harmonics in equal|7|intervals=odd|columns=7}} |
| * 11lim WE (79.770)
| | {{harmonics in equal|8|intervals=odd|columns=7}} |
| * 50ed10
| | {{harmonics in equal|9|intervals=odd|columns=7}} |
| * 47zpi (79.715)
| | {{harmonics in equal|10|intervals=odd|columns=7}} |
| * 54ed12
| | {{harmonics in equal|11|intervals=odd|columns=7}} |
| 15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
| | {{harmonics in equal|12|intervals=odd|columns=7}} |
| | | {{harmonics in equal|13|intervals=odd|columns=7}} |
| 18edo
| | {{harmonics in equal|14|intervals=odd|columns=7}} |
| * 42ed5
| | {{harmonics in equal|15|intervals=odd|columns=7}} |
| * 13lim WE (66.291)
| | {{harmonics in equal|16|intervals=odd|columns=7}} |
| * 61zpi (66.228)
| | {{harmonics in equal|17|intervals=odd|columns=7}} |
| * 65ed12
| | {{harmonics in equal|18|intervals=odd|columns=7}} |
| * 7lim WE (66.148)
| | {{harmonics in equal|19|intervals=odd|columns=7}} |
| * 47ed6
| | {{harmonics in equal|20|intervals=odd|columns=7}} |
| 18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
| | {{harmonics in equal|21|intervals=odd|columns=7}} |
| | | {{harmonics in equal|22|intervals=odd|columns=7}} |
| 25edo
| | {{harmonics in equal|23|intervals=odd|columns=7}} |
| * 95zpi (48.067)
| | {{harmonics in equal|24|intervals=odd|columns=7}} |
| * 13lim WE (47.946)
| | {{harmonics in equal|25|intervals=odd|columns=7}} |
| * 90ed12
| | {{harmonics in equal|26|intervals=odd|columns=7}} |
| * 65ed6
| | {{harmonics in equal|27|intervals=odd|columns=7}} |
| * 96zpi (47.642)
| | {{harmonics in equal|28|intervals=odd|columns=7}} |
| 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]].
| | {{harmonics in equal|29|intervals=odd|columns=7}} |
| | | {{harmonics in equal|30|intervals=odd|columns=7}} |
| 26edo
| | {{harmonics in equal|31|intervals=odd|columns=7}} |
| * 13lim WE (46.249)
| | {{harmonics in equal|32|intervals=odd|columns=7}} |
| * 93ed12
| | {{harmonics in equal|33|intervals=odd|columns=7}} |
| * 100zpi (46.268)
| | {{harmonics in equal|34|intervals=odd|columns=7}} |
| 26edo's simple [[prime]]s with the most error - 3, 5 and 13 - are all tuned flat, so it can benefit from [[octave stretching]].
| | {{harmonics in equal|35|intervals=odd|columns=7}} |
| | | {{harmonics in equal|36|intervals=odd|columns=7}} |
| 29edo
| | {{harmonics in equal|37|intervals=odd|columns=7}} |
| * 46edt
| | {{harmonics in equal|38|intervals=odd|columns=7}} |
| * [[116zpi]] (41.465)
| | {{harmonics in equal|39|intervals=odd|columns=7}} |
| * 13lim WE (41.484)
| | {{harmonics in equal|40|intervals=odd|columns=7}} |
| * 107ed13
| | {{harmonics in equal|41|intervals=odd|columns=7}} |
| * 100ed11
| | {{harmonics in equal|42|intervals=odd|columns=7}} |
| * 96ed10
| | {{harmonics in equal|43|intervals=odd|columns=7}} |
| 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]].
| | {{harmonics in equal|44|intervals=odd|columns=7}} |
| | | {{harmonics in equal|45|intervals=odd|columns=7}} |
| 30edo
| | {{harmonics in equal|46|intervals=odd|columns=7}} |
| * 39.918zpi (39.918)
| | {{harmonics in equal|47|intervals=odd|columns=7}} |
| * 13lim WE (39.904)
| | {{harmonics in equal|48|intervals=odd|columns=7}} |
| * 11lim WE (79.770)
| | {{harmonics in equal|49|intervals=odd|columns=7}} |
| * 100ed10
| | {{harmonics in equal|50|intervals=odd|columns=7}} |
| * 108ed12
| | {{harmonics in equal|51|intervals=odd|columns=7}} |
| * 78ed6
| | {{harmonics in equal|52|intervals=odd|columns=7}} |
| 30edo's simple [[prime]]s with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from [[octave shrinking]].
| | {{harmonics in equal|53|intervals=odd|columns=7}} |
| | |
| 34edo
| |
| * 11lim WE (35.284)
| |
| * 13lim WE (35.276) (octave identical to 113ed10 within 0.1{{c}})
| |
| * 79ed5
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| * 122ed12
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| * 88ed6
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| * 144zpi (35.248)
| |
| * 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]].
| |
| | |
| 35edo
| |
| * 11lim WE (35.284)
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| * 13lim WE (35.276)
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| * 121ed11
| |
| * [[149zpi]] (34.359)
| |
| * 116ed10
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| * 98ed7
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| * 81ed5
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| * 125ed12
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| * 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]].
| |
| | |
| 37edo
| |
| * 137ed13
| |
| * [[161zpi]] (32.408) (octave identical to 123ed10 within 0.1{{c}})
| |
| * 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
| |
| 37edo's [[prime]]s 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
| |
| | |
| 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}})
| |
| * 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]].
| |
| | |
| ; Medium-low priority
| |
| | |
| 10edo
| |
| * 2.5.7.13 WE (120.358)
| |
| * 28ed7
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| * 37ed13
| |
| * 26zpi (119.899)
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| * 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)
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| * 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.
| |
| | |
| 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)
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| * 2.9.5.7 WE (199.329)
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| * 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]].
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