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| | '''ABANDONED.''' |
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| | '''These guidelines have been retracted due to them being largely not liked by most commenters on the XA Discord.''' |
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| {{Editable user page}} | | {{Editable user page}} |
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| | <pre> |
| == The guidelines == | | == The guidelines == |
| '''These are draft guidelines for what a standard "related tunings"-type section should look like on edo pages, using [[36edo]] as an example.''' | | '''These are draft guidelines for what a standard "related tunings"-type section should look like on edo pages, using [[36edo]] as an example.''' |
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| ''Done'' | | ''Done'' |
| * Done (with table): {{EDOs| 36 }}. | | * Done (with table): {{EDOs| 36 }}. |
| * 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 not added yet): {{EDOs| 7, 8, 9, 12, 14, 16, 17, 19, 22, 23, 27, 28, 31, 32, 38, 41, 58, 60, 72, 99 }}. |
| * Done (table & some step sizes not added yet): {{EDOs| 15, 18, 33, 39, 42, 45, 54, 59, 64 }}. | | * Done (table & some step sizes not added yet): {{EDOs| 15, 18, 33, 39, 42, 45, 54, 59, 64 }}. |
| * ''Started (brief summary only): {{EDOs| 5, 6, 10, 11, 24, 25, 26, 29, 30, 34, 35, 37, 47, 48 }}.'' | | * ''Started (brief summary only): {{EDOs| 5, 6, 10, 11, 24, 25, 26, 29, 30, 34, 35, 37, 47, 48, 49, 50, 62, 65, 66 }}.'' |
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| ''To-do (optional)'' | | ''To-do (optional)'' |
| * Highest priority: {{EDOs| 72, 13, 62, 65, 89, 103, 104, 111, 118, 159, 270 }}. | | * Highest priority: {{EDOs| 13, 118, 159, 270, 103, 104, 107, 111, 117, 125 }}. |
| * High priority: {{EDOs| 63, 68, 82, 10, 11, 24, 25, 26, 29, 30, 34, 35, 37, 47, 48, 5, 6 }}. | | * High priority: {{EDOs| 140, 145, 152, 166, 171, 182, 183, 198, 212, 224, 243, 247, 342 }}. |
| * Medium-high priority: {{EDOs| 107, 117, 125, 140, 145, 152, 166, 171, 182, 183, 198, 212, 224, 243, 247, 342 }}. (''Most of these are here because they have or had a "zeta peak" section on their page that needs to be replaced.'') | | * Medium-high priority: {{EDOs| 5, 6, 10, 11, 24, 25, 26, 29, 30, 34, 35, 37, 47, 48, 49, 50, 62, 65, 66}}. |
| * Medium priority: {{EDOs| 49, 50, 57, 58, 59, 66, 73, 76, 80, 81, 83, 84, 88, }}. | | * Medium-low priority: {{EDOs| 73, 76, 80, 81, 83, 84, 88, 89, 91, 95, 96, 101, 106, 110, 112, 113, 121, 122, 123, 124 }}. |
| * Medium-low priority: {{EDOs| (others from 91-246 which are well suited to octave stretch/compression) }}.
| | * Low priority: {{EDOs| 20, 21, 40, 43, 44, 46, 51, 52, 53, 55, 56, 57, 63, 67, 68, 69, 70, 71, 74, 75, 77, 78, 79, 82, 85, 86, 87, 90, 92, 93, 94, 97, 98, 102, 105, 108, 109, 114, 115, 116, 119, 120 }}. |
| * Low priority: {{EDOs| 20, 21, 28, 40, 43, 44, 46, 51, 52, 53, 54, 55, 56, 64, 67, 69, 70, 71, 74, 75, 77, 78, 79, 85, 86, 87, 90, (others from 91-124 which are not well suited) }}. | | * Lowest priority: All other EDOs above 125. |
| * Lowest priority: {{EDOs| (others bigger than 125) }}. | | ''Priority is higher if: there is already a section for stretch, compression, nearby tunings or zeta on the page / the edo lends itself to stretch or compression (e.g. of the primes with 20-40% relative error, most tend in the same direction) / the edo gets a lot of attention (it's small, or especially good by some prominent metric, or the page is especially long, or it gets used a lot by composers).'' |
| ''Priority is higher if: there is or was already discussion about stretch, compression, nearby tunings or zeta on the page / the edo lends itself to stretch or compression (e.g. of the primes with 20-40% relative error, most tend in the same direction) / the edo gets a lot of attention (it's small, or especially good, or the page is especially long, or it gets used a lot by composers).'' | |
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| ; Things to note: | | ; Things to note: |
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| * 2.3 WE (91.405c) (good for opposite 7 mapping) | | * 2.3 WE (91.405c) (good for opposite 7 mapping) |
| * 38zpi (92.531c) | | * 38zpi (92.531c) |
| | |
| | 118edo (choose ZPIS) |
| | * 187edt |
| | * 69edf |
| | * 13-limit WE (10.171c) |
| | * Best nearby ZPI(s) |
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| 103edo (narrow down edonoi, choose ZPIS) | | 103edo (narrow down edonoi, choose ZPIS) |
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| * Best nearby ZPI(s) | | * Best nearby ZPI(s) |
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| 104edo
| | Default |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 111edo (choose ZPIS)
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 118edo (choose ZPIS)
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| * 187edt
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| * 69edf
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| * 13-limit WE (10.171c)
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| * Best nearby ZPI(s)
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| 159edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 10edo
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| * 2.5.7.13 WE (120.358)
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| * 28ed7
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| * 37ed13
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| * 26zpi (119.899)
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| * 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
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| * 28ed6
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| * 39ed12
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| * 2.7.11.13 WE (108.821)
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| * 30zpi (108.722)
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| * 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
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| ((13lim WE's octave is only 1/10th of a cent different from 24edo))
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| * 56ed5
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| * 80ed10
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| * 89ed13
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| * 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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| 25edo
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| * 95zpi (48.067)
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| * 13lim WE (47.946)
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| * 90ed12
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| * 65ed6
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| * 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
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| 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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| 47edo
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| * 220zpi
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| * 174ed13
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| * 13lim WE (with 2nd best fifth)
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| * 25.5cET
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| * 8ed9/8
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| * 169ed12
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| 47edo's [[prime]] 11 is very sharp, and its sharp and flat mapping of 3 are about equally bad, it can benefit from slight [[octave shrinking]]. [[APS|25.5cET]] or [[ed9/8|8ed9/8]] make good compressed-octave versions of 47edo.
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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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| 5edo
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| * 14ed7
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| * 2.3.7 WE (239.426)
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| * 18ed12
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| 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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| 6edo
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| * 19ed9
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| * 2.9.5 WE (199.736)
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| * 2.9.5.7 WE (199.329)
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| * 20ed10
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| * 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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| 125edo
| |
| * Nearby edt, ed6, ed12 and/or edf
| |
| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 145edo
| |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 152edo
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| * 241edt
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| * 13-limit WE (7.894c)
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| * Best nearby ZPI(s)
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| 166edo
| |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 182edo
| |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 198edo
| |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 212edo
| |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 243edo
| |
| * Nearby edt, ed6, ed12 and/or edf | | * Nearby edt, ed6, ed12 and/or edf |
| * Nearby ed5, ed10, ed7 and/or ed11 (optional) | | * Nearby ed5, ed10, ed7 and/or ed11 (optional) |
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| * Best nearby ZPI(s) | | * Best nearby ZPI(s) |
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| 247edo
| | === Reasoning for priority levels === |
| * Nearby edt, ed6, ed12 and/or edf
| | ^^currently has a zeta peak section with only the graph/table and little/no description, or another existing non-standard similar tunings section |
| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
| |
| * 1-2 WE tunings
| |
| * Best nearby ZPI(s)
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|
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|
| Others
| |
| * 49edo mostly sharp | | * 49edo mostly sharp |
| * 50edo mostly flat | | * 50edo mostly flat |
| Line 441: |
Line 246: |
| * 55edo stretch/compression unhelpful | | * 55edo stretch/compression unhelpful |
| * 56edo stretch/compression unhelpful | | * 56edo stretch/compression unhelpful |
| * 57edo mostly flat | | * 57edo mostly flat (on closer inspection octave stretch doesn't help all that much) |
| * 58edo mostly sharp | | * 58edo mostly sharp |
| * 59edo mostly sharp | | * 59edo mostly sharp |
| * 60edo already done | | * ''60edo already done'' |
| * 61edo stretch/compression unhelpful | | * 61edo stretch/compression unhelpful |
| * ^^62edo mostly flat | | * 62edo mostly flat |
| * ^^63edo stretch/compression unhelpful | | * 63edo stretch/compression unhelpful |
| * 64edo stretch/compression unhelpful | | * 64edo stretch/compression unhelpful |
| * ^^65edo mostly sharp | | * 65edo mostly sharp |
| * 66edo mostly flat | | * 66edo mostly flat |
| * 67edo stretch/compression unhelpful | | * 67edo stretch/compression unhelpful |
| * ^^68edo stretch/compression unhelpful | | * 68edo stretch/compression unhelpful |
| * 69edo stretch/compression unhelpful | | * 69edo stretch/compression unhelpful |
| * 70edo complicated | | * 70edo complicated |
| * 71edo stretch/compression unhelpful | | * 71edo stretch/compression unhelpful |
| * ^^72edo mostly flat | | * ''72edo already done'' |
| * 73edo mostly sharp | | * 73edo mostly sharp |
| * 74edo stretch/compression unhelpful | | * 74edo stretch/compression unhelpful |
| Line 466: |
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| * 80edo mostly sharp | | * 80edo mostly sharp |
| * 81edo mostly flat | | * 81edo mostly flat |
| * ^^82edo stretch/compression unhelpful | | * 82edo stretch/compression unhelpful |
| * 83edo mostly sharp | | * 83edo mostly sharp |
| * 84edo mostly sharp | | * 84edo mostly sharp |
| Line 475: |
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| * ^^89edo mostly sharp | | * ^^89edo mostly sharp |
| * 90edo stretch/compression unhelpful | | * 90edo stretch/compression unhelpful |
| | | * 91edo mostly flat |
| ^^currently has a zeta peak section with only the graph and little/no description | | * 92edo stretch/compression unhelpful |
| | * 93edo stretch/compression unhelpful |
| | * 94edo stretch/compression unhelpful |
| | * 95edo mostly sharp |
| | * 96edo mostly flat |
| | * 97edo stretch/compression unhelpful |
| | * 98edo stretch/compression unhelpful |
| | * 99edo mostly sharp |
| | * 100edo complicated |
| | * 101edo mostly sharp |
| | * 102edo stretch/compression unhelpful |
| | * ^^103edo mostly flat |
| | * ^^104edo mostly sharp |
| | * 105edo stretch/compression unhelpful |
| | * 106edo mostly sharp |
| | * ^^107edo mostly flat |
| | * 108edo stretch/compression unhelpful |
| | * 109edo stretch/compression unhelpful |
| | * 110edo mostly flat |
| | * ^^111edo mostly sharp |
| | * 112edo mostly flat |
| | * 113edo mostly flat |
| | * 114edo stretch/compression unhelpful |
| | * 115edo stretch/compression unhelpful |
| | * 116edo stretch/compression unhelpful |
| | * ^^117edo slightly sharp |
| | * ^^118edo stretch/compression unhelpful |
| | * 119edo stretch/compression unhelpful |
| | * 120edo stretch/compression unhelpful |
| | * 121edo mostly sharp |
| | * 122edo mostly flat |
| | * 123edo mostly flat |
| | * 124edo mostly sharp |
| | * ^^125edo mostly flat |
| | </pre> |