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'''ABANDONED.'''
'''These guidelines have been retracted due to them being largely not liked by most commenters on the XA Discord.'''
{{Editable user page}}
{{Editable user page}}


<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.'''
Line 169: Line 174:
''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, 28, 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| 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, 49, 50, 62, 65, 66 }}.''


''To-do''
''To-do (optional)''
* High priority: {{EDOs| 118, 103, 111, 13, 104 }}.
* Highest priority: {{EDOs| 13, 118, 159, 270, 103, 104, 107, 111, 117, 125 }}.
* Medium-high priority: {{EDOs| 9, 15, 18, 25, 26, 29, 30, 34, 35, 37, 48 }}.
* High priority: {{EDOs| 140, 145, 152, 166, 171, 182, 183, 198, 212, 224, 243, 247, 342 }}.
* Medium-low priority: {{EDOs| 10, 11, 24, 5, 6 }}.
* Medium-high priority: {{EDOs| 5, 6, 10, 11, 24, 25, 26, 29, 30, 34, 35, 37, 47, 48, 49, 50, 62, 65, 66}}.
* Low priority: {{EDOs| 125, 145, 152, 159, 166, 182, 198, 212, 243, 247 }}.  
* Medium-low priority: {{EDOs| 73, 76, 80, 81, 83, 84, 88, 89, 91, 95, 96, 101, 106, 110, 112, 113, 121, 122, 123, 124 }}.
* 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 }}.
* Lowest priority: All other EDOs above 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).''


; Things to note:
; Things to note:
Line 194: Line 203:
(Used https://x31eq.com/temper-pyscript/net.html, used WE instead of TE cause it kept defaulting to WE and I kept not remembering to switch it)
(Used https://x31eq.com/temper-pyscript/net.html, used WE instead of TE cause it kept defaulting to WE and I kept not remembering to switch it)


; High-priority
13edo
* Main: "13edo and optimal octave stretching"
* 2.5.11.13 WE (92.483c)
* 2.5.7.13 WE (92.804c)
* 2.3 WE (91.405c) (good for opposite 7 mapping)
* 38zpi (92.531c)


118edo (choose ZPIS)
118edo (choose ZPIS)
Line 215: Line 229:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


111edo (choose ZPIS)
Default
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
13edo
* Main: "13edo and optimal octave stretching"
* 2.5.11.13 WE (92.483c)
* 2.5.7.13 WE (92.804c)
* 2.3 WE (91.405c) (good for opposite 7 mapping)
* 38zpi (92.531c)
 
104edo
* 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)
Line 234: Line 235:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Medium-high priority
=== Reasoning for priority levels ===
 
^^currently has a zeta peak section with only the graph/table and little/no description, or another existing non-standard similar tunings section
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
* 39ed6
* 50ed10
* 52ed11
* 54ed12
* Nearby edf (optional)
* 11lim WE
* Best nearby ZPI(s)
15edo's [[prime]]s 3, 5, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
 
18edo
* 42ed5
* 47ed6
* 60ed10
* 65ed12
* 7lim WE
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
 
25edo
* 65ed6
* 90ed12
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
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]].
 
26edo
* 41edt
* 67ed6
* 86ed10
* 93ed12
* 96ed14
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* 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]].
 
29edo
* 46edt
* 105ed12
* 96ed10
* 100ed11
* 107ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
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]].
 
30edo
* 78ed6
* 100ed10
* 104ed11
* 108ed12
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
30edo's simple [[prime]]s with the most error - 3, 5 and 11 - are all tuned sharp, so it can benefit from [[octave shrinking]].
 
34edo
* 54edt
* 79ed5
* 88ed6
* 108ed9
* 113ed10
* 122ed12
* 126ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
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
* 81ed5
* 90ed6
* 98ed7
* 116ed10
* 121ed11
* 125ed12
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
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
* 59edt
* 86ed5
* 96ed6
* 104ed7
* 123ed10
* 128ed11
* 133ed12
* 137ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
37edo's [[prime]]s 3, 5, 7, 11 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
 
48edo
* 76edt
* 124ed6
* 152ed9
* 159ed10
* 166ed11
* 172ed12
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
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
* 49edo mostly sharp
* 16edt
* 50edo mostly flat
* 23ed5
* 51edo stretch/compression unhelpful
* 26ed6
* 52edo stretch/compression unhelpful
* 28ed7
* 53edo stretch/compression unhelpful
* 32ed8
* 54edo stretch/compression unhelpful
* 33ed10
* 55edo stretch/compression unhelpful
* 36ed12
* 56edo stretch/compression unhelpful
* 37ed13
* 57edo mostly flat (on closer inspection octave stretch doesn't help all that much)
* Nearby edf (optional)
* 58edo mostly sharp
* 2.3.7.13 WE
* 59edo mostly sharp
* 2.5.7.13 WE
* ''60edo already done''
* 13lim WE
* 61edo stretch/compression unhelpful
* Best nearby ZPI(s)
* 62edo mostly flat
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]].
* 63edo stretch/compression unhelpful
 
* 64edo stretch/compression unhelpful
11edo
* 65edo mostly sharp
* 27ed6
* 66edo mostly flat
* 28ed6
* 67edo stretch/compression unhelpful
* 31ed7
* 68edo stretch/compression unhelpful
* 35ed9
* 69edo stretch/compression unhelpful
* 37ed10
* 70edo complicated
* 38ed10
* 71edo stretch/compression unhelpful
* 38ed12
* ''72edo already done''
* 39ed12
* 73edo mostly sharp
* 41ed13
* 74edo stretch/compression unhelpful
* 2.7.11 WE
* 75edo complicated
* 2.7.11.13 WE
* 76edo mostly flat
* Best nearby ZPI(s)
* 77edo stretch/compression unhelpful
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.
* 78edo stretch/compression unhelpful
 
* 79edo stretch/compression unhelpful
24edo
* 80edo mostly sharp
* Nearby edt, ed6, ed12 and/or edf
* 81edo mostly flat
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 82edo stretch/compression unhelpful
* 1-2 WE tunings
* 83edo mostly sharp
* Best nearby ZPI(s)
* 84edo mostly sharp
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.
* 85edo stretch/compression unhelpful
 
* 86edo stretch/compression unhelpful
5edo
* 87edo stretch/compression unhelpful
* 8edt
* 88edo mostly flat
* 13ed6
* ^^89edo mostly sharp
* 14ed7
* 90edo stretch/compression unhelpful
* 18ed12
* 91edo mostly flat
* Nearby edf (optional)
* 92edo stretch/compression unhelpful
* 2.3.7 WE
* 93edo stretch/compression unhelpful
* Best nearby ZPI(s)
* 94edo stretch/compression unhelpful
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.
* 95edo mostly sharp
 
* 96edo mostly flat
6edo
* 97edo stretch/compression unhelpful
* 14ed5
* 98edo stretch/compression unhelpful
* 17ed7
* 99edo mostly sharp
* 19ed9
* 100edo complicated
* 20ed10
* 101edo mostly sharp
* 2.9.5 WE
* 102edo stretch/compression unhelpful
* 2.9.5.7 WE
* ^^103edo mostly flat
* Best nearby ZPI(s)
* ^^104edo mostly sharp
If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]].
* 105edo stretch/compression unhelpful
 
* 106edo mostly sharp
; Low-priority
* ^^107edo mostly flat
 
* 108edo stretch/compression unhelpful
125edo
* 109edo stretch/compression unhelpful
* Nearby edt, ed6, ed12 and/or edf
* 110edo mostly flat
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* ^^111edo mostly sharp
* 1-2 WE tunings
* 112edo mostly flat
* Best nearby ZPI(s)
* 113edo mostly flat
 
* 114edo stretch/compression unhelpful
145edo
* 115edo stretch/compression unhelpful
* Nearby edt, ed6, ed12 and/or edf
* 116edo stretch/compression unhelpful
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* ^^117edo slightly sharp
* 1-2 WE tunings
* ^^118edo stretch/compression unhelpful
* Best nearby ZPI(s)
* 119edo stretch/compression unhelpful
 
* 120edo stretch/compression unhelpful
152edo
* 121edo mostly sharp
* 241edt
* 122edo mostly flat
* 13-limit WE (7.894c)
* 123edo mostly flat
* Best nearby ZPI(s)
* 124edo mostly sharp
 
* ^^125edo mostly flat
159edo
</pre>
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
166edo
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
182edo
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
198edo
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
212edo
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
243edo
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
247edo
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
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