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User:BudjarnLambeth/Sandbox2: Difference between revisions

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BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,282 edits
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118edo (choose ZPIS)
118edo (choose ZPIS)
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}}
* 187edt
* 187edt
* 69edf
* 69edf
Line 67: Line 66:


103edo (narrow down edonoi, choose ZPIS)
103edo (narrow down edonoi, choose ZPIS)
{{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}}
* 163edt
* 163edt
* 239ed5
* 239ed5
Line 81: Line 79:


111edo (choose ZPIS)
111edo (choose ZPIS)
{{harmonics in equal | 111 | 2 | 1 | intervals=integer | columns=12}}
* 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 88: Line 85:


13edo
13edo
{{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}}
* Main: "13edo and optimal octave stretching"
* Main: "13edo and optimal octave stretching"
* 2.5.11.13 WE (92.483c)
* 2.5.11.13 WE (92.483c)
Line 101: Line 97:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Medium-priority
; Medium-high priority
 
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
25edo
{{harmonics in equal | 25 | 2 | 1 | intervals=integer | columns=12}}
* 65ed6
* Nearby edt, ed6, ed12 and/or edf
* 90ed12
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* Nearby edf (optional)
* 1-2 WE tunings
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* 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
26edo
{{harmonics in equal | 26 | 2 | 1 | intervals=integer | columns=12}}
* 41edt
* Nearby edt, ed6, ed12 and/or edf
* 67ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 86ed10
* 1-2 WE tunings
* 93ed12
* 96ed14
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* 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
29edo
{{harmonics in equal | 29 | 2 | 1 | intervals=integer | columns=12}}
* 46edt
* Nearby edt, ed6, ed12 and/or edf
* 105ed12
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 96ed10
* 1-2 WE tunings
* 100ed11
* 107ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* 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
30edo
{{harmonics in equal | 30 | 2 | 1 | intervals=integer | columns=12}}
* 78ed6
* Nearby edt, ed6, ed12 and/or edf
* 100ed10
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 104ed11
* 1-2 WE tunings
* 108ed12
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* 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]].


35edo
34edo
{{harmonics in equal | 35 | 2 | 1 | intervals=integer | columns=12}}
* 54edt
* Nearby edt, ed6, ed12 and/or edf
* 79ed5
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 88ed6
* 1-2 WE tunings
* 108ed9
* 113ed10
* 122ed12
* 126ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* 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]].


36edo
35edo
{{harmonics in equal | 36 | 2 | 1 | intervals=integer | columns=12}}
* 81ed5
* Nearby edt, ed6, ed12 and/or edf
* 90ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 98ed7
* 1-2 WE tunings
* 116ed10
* 121ed11
* 125ed12
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* 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
37edo
{{harmonics in equal | 37 | 2 | 1 | intervals=integer | columns=12}}
* 59edt
* Nearby edt, ed6, ed12 and/or edf
* 86ed5
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 96ed6
* 1-2 WE tunings
* 104ed7
* 123ed10
* 128ed11
* 133ed12
* 137ed13
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* 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]].


15edo
48edo
{{harmonics in equal | 15 | 2 | 1 | intervals=integer | columns=12}}
* 76edt
* Nearby edt, ed6, ed12 and/or edf
* 124ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 152ed9
* 1-2 WE tunings
* 159ed10
* 166ed11
* 172ed12
* Nearby edf (optional)
* 11lim WE
* 13lim WE
* Best nearby ZPI(s)
* 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]].


9edo
; Medium-low priority
{{harmonics in equal | 9 | 2 | 1 | intervals=integer | columns=12}}
 
* Nearby edt, ed6, ed12 and/or edf
10edo
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 16edt
* 1-2 WE tunings
* 23ed5
* 26ed6
* 28ed7
* 32ed8
* 33ed10
* 36ed12
* 37ed13
* Nearby edf (optional)
* 2.3.7.13 WE
* 2.5.7.13 WE
* 13lim WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
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]].


18edo
11edo
{{harmonics in equal | 18 | 2 | 1 | intervals=integer | columns=12}}
* 27ed6
* Nearby edt, ed6, ed12 and/or edf
* 28ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 31ed7
* 1-2 WE tunings
* 35ed9
* 37ed10
* 38ed10
* 38ed12
* 39ed12
* 41ed13
* 2.7.11 WE
* 2.7.11.13 WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
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
24edo
{{harmonics in equal | 24 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(
48edo
{{harmonics in equal | 48 | 2 | 1 | intervals=integer | columns=12}}
* 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)
* 1-2 WE tunings
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)
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
5edo
{{harmonics in equal | 5 | 2 | 1 | intervals=integer | columns=12}}
* 8edt
* Nearby edt, ed6, ed12 and/or edf
* 13ed6
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 14ed7
* 1-2 WE tunings
* 18ed12
* Nearby edf (optional)
* 2.3.7 WE
* Best nearby ZPI(s)
* Best nearby ZPI(s)
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
6edo
{{harmonics in equal | 6 | 2 | 1 | intervals=integer | columns=12}}
* 14ed5
* Nearby edt, ed6, ed12 and/or edf
* 17ed7
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 19ed9
* 1-2 WE tunings
* 20ed10
* Best nearby ZPI(s)s)
* 2.9.5 WE
 
* 2.9.5.7 WE
10edo
{{harmonics in equal | 10 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
11edo
{{harmonics in equal | 11 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
 
34edo
{{harmonics in equal | 34 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)
If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[sugroup]] tuning, then it benefits from [[octave shrinking]].


; Low priority
; Low-priority


125edo
125edo
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