Xenharmonic Wiki

User:BudjarnLambeth/Sandbox2: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,723 edits
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,723 edits
 
(88 intermediate revisions by the same user not shown)
Line 5: Line 5:
= Title1 =
= Title1 =
== Octave stretch or compression ==
== Octave stretch or compression ==
{{main|23edo and octave stretching}}
38edo's approximation of [[JI]] can be improved by slightly [[octave stretch|stretching the octave]].


23edo is not typically taken seriously as a tuning except by those interested in extreme [[xenharmony]]. Its fifths are significantly flat, and is neighbors [[22edo]] and [[24edo]] generally get more attention.
What follows is a comparison of stretched-octave 38edo tunings.


However, when using a slightly [[stretched tuning|stretched octave]] of around 1216 [[cents]], 23edo looks much better, and it approximates the [[perfect fifth]] (and various other [[interval]]s involving the 5th, 7th, 11th, and 13th [[harmonic]]s) to within 18 cents or so. If we can tolerate errors around this size in [[12edo]], we can probably tolerate them in stretched-23 as well.
; 38edo
* Step size: 31.579{{c}}, octave size: 1200.00{{c}}
Pure-octaves 38edo approximates all harmonics up to 16 within NNN{{c}}.
{{Harmonics in equal|38|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 38edo}}
{{Harmonics in equal|38|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 38edo (continued)}}


Stretched 23edo is one of the best tunings to use for exploring the [[antidiatonic]] scale since its fifth is more [[consonant]] and less "[[Wolf interval|wolfish]]" than fifths in other [[pelogic family]] temperaments.
; [[WE|38et, 13-limit WE tuning]]  
* Step size: 31.599{{c}}, octave size: 1200.77{{c}}
Stretching the octave of 38edo by around 1{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
{{Harmonics in cet|31.599|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning}}
{{Harmonics in cet|31.599|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning (continued)}}


What follows is a comparison of stretched- and compressed-octave 23edo tunings.
; [[ed5|88ed5]]
* Step size: 31.663{{c}}, octave size: 1203.18{{c}}
Stretching the octave of 38edo by around 3{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 88ed5 does this.
{{Harmonics in equal|88|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 88ed5}}
{{Harmonics in equal|88|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 88ed5 (continued)}}


; [[zpi|86zpi]]  
; [[zpi|166zpi]]  
* Step size: 51.653{{c}}, octave size: 1188.0{{c}}
* Step size: 31.671{{c}}, octave size: 1203.48{{c}}
Compressing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning ZPINAME does this.
Stretching the octave of 38edo by around 3.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 166zpi does this.
{{Harmonics in cet|51.653|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in cet|31.671|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 166zpi}}
{{Harmonics in cet|51.653|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
{{Harmonics in cet|31.671|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 166zpi (continued)}}


; [[60ed6]]  
; [[60edt]]  
* Step size: 51.700{{c}}, octave size: 1189.1{{c}}
* Step size: 31.699{{c}}, octave size: 1204.57{{c}}
Compressing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 60ed6 does this. So does the tuning [[equal tuning|105ed23]] whose octave is identical within 0.01{{c}}.
Stretching the octave of 38edo by around 4.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 60edt does this.
{{Harmonics in equal|60|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|60|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60edt}}
{{Harmonics in equal|60|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in equal|60|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60edt (continued)}}


; [[zpi|85zpi]]
= Title2 =
* Step size: 52.114{{c}}, octave size: 1198.6{{c}}
=== Lab ===
Compressing the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 85zpi does this. So does the tuning [[ed9|73ed9]] whose octave is identical within 0.02{{c}}.
{{Harmonics in cet|52.114|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in cet|52.114|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}


; 23edo
Place holder
* Step size: NNN{{c}}, octave size: 1200.0{{c}}
Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
{{Harmonics in equal|23|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
{{Harmonics in equal|23|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}


; [[WE|23et, 13-limit WE tuning]]
* Step size: 52.237{{c}}, octave size: 1201.5{{c}}
Stretching the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do this.
{{Harmonics in cet|52.237|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in cet|52.237|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}


; [[WE|23et, 2.3.5.13 WE tuning]]
<br><br><br><br><br>
* Step size: 52.447{{c}}, octave size: 1206.3{{c}}
Stretching the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do this. So does the tuning [[ed10|76ed10]] whose octave is identical within 0.01{{c}}.
{{Harmonics in cet|52.447|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in cet|52.447|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}


; [[59ed6]]
* Step size: 52.575{{c}}, octave size: 1209.2{{c}}
Stretching the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 59ed6 does this. So does the tuning [[53ed5]] whose octave is identical within 0.01{{c}}.
{{Harmonics in equal|59|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|59|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}


; [[zpi|84zpi]]
{{harmonics in cet | 300 | intervals=prime}}
* Step size: 52.615{{c}}, octave size: 1210.1{{c}}
Stretching the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning ZPINAME does this.
{{Harmonics in cet|52.615|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in cet|52.615|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}


; [[36edt]]
* Step size: 52.832{{c}}, octave size: 1215.1{{c}}
Stretching the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.
{{Harmonics in equal|36|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|36|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
; [[84ed13]]
* Step size: 52.863{{c}}, octave size: 1215.9{{c}}
Stretching the octave of EDONAME by around NNN{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning EDONOI does this.
{{Harmonics in equal|84|13|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|84|13|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
= Title2 =
=== Lab ===
{{harmonics in cet | 300 | intervals=prime}}
{{harmonics in equal | 140 | 12 | 1 | intervals=prime}}
{{harmonics in equal | 140 | 12 | 1 | intervals=prime}}
* 207zpi (26.762)
{{harmonics in cet | 26.762 | intervals=prime}}
* 7-limit WE (26.745c)
{{harmonics in cet | 26.745 | intervals=prime}}
* pure octave 45edo
{{harmonics in equal | 45 | 2 | 1 | intervals=integer | columns=12}}
* 13-limit WE (26.695c)
{{harmonics in cet | 26.695 | intervals=prime}}
* 208zpi (26.646)
{{harmonics in cet | 26.646 | intervals=prime}}
* 209zpi (26.550)
{{harmonics in cet | 26.550 | intervals=prime}}
* 126ed7 (improves 3.5.7.11.13)
{{harmonics in equal | 126 | 7 | 1 | intervals=prime}}
* 13ed11/9 (improves 3.5.7.11.13.17)
{{harmonics in equal | 13 | 11 | 9 | intervals=prime}}


=== Possible tunings to be used on each page ===
=== Possible tunings to be used on each page ===
Line 104: Line 58:


; High-priority
; High-priority
60edo (narrow down edonoi & ZPIs)
* 35edf
* 139ed5
* 301zpi (20.027c)
* 95edt
* 13-limit WE (20.013c) (155ed6 has octaves only 0.02{{c}} different)
* 215ed12
* PURE OCTAVES 60EDO PURE OCTAVES 60EDO
* 302zpi (19.962c)
* 208ed11 (ideal for catnip temperament)
* 303zpi (19.913c)
32edo
* 13-limit WE (37.481c)
* 11-limit WE (37.453c)
* 90ed7 (optimal for dual-5) (133zpi's octave only differs by 0.4{{c}})
* 51edt
* 134zpi (37.176c)
* 75ed5
33edo
* 76ed5
* 92ed7 (137zpi's octave differs by only 0.3{{c}})
* 52ed13
* 114ed11
* 138zpi (36.394c) (122ed13's octave differs by only 0.1{{c}})
* 13-limit WE (36.357c)
* 11-limit WE (36.349c)
* 93ed7 (optimised for dual-fifths)
* 77ed5 (139zpi's octave differs by only 0.2{{c}})
* 123ed13 / 1ed47/46 (identical within <0.1{{c}})
* 115ed11
39edo
* 171zpi (30.973c) (optimised for dual-fifths use)
* 13-limit WE (30.757c) (octave of 135ed11 differs by only 0.2{{c}})
* 101ed6 (octave of 172zpi differs by only 0.4{{c}})
* 2.3.5.11 WE (30.703c)
* 173zpi (30.672c) (octave of 62edt differs by only 0.2{{c}})
* 110ed7 (octave of 145ed13 differs by only 0.1{{c}})
* 91ed5
42edo
*Good <27% rel err
*Okay <40% rel err
{{harmonics in equal | 42 | 2 | 1 | intervals=integer | columns=12}}
* 42ed257/128 (good 2.3.5.7; bad 11.13)
* 11ed6/5 (good 2.3.5; okay 7.11.13)
* 189zpi (28.689c) (good 2.5.13; okay 3.11; bad 7)
* 190zpi (28.572c)
* 13-limit WE (28.534c)
* 34ed7/4 (good 2.5.7.13; okay 3.11)
* 7-limit WE (28.484c) (good 2.3.5.11.13; bad 7)
* 191zpi (28.444c)
* 1ed123/121 (good 2.3.5.11; okay 13; bad 7)
45edo
{{harmonics in equal | 45 | 2 | 1 | intervals=integer | columns=12}}
* 207zpi (26.762)
* 7-limit WE (26.745c)
* 13-limit WE (26.695c)
* 208zpi (26.646)
* 209zpi (26.550)
* 126ed7 (improves 3.5.7.11.13)
* 13ed11/9 (improves 3.5.7.11.13.17)
54edo (possibly narrow down edonoi)
{{harmonics in equal | 54 | 2 | 1 | intervals=integer | columns=12}}
* 126ed5
* 38ed5/3 (stretch, improves 3.5.7.11.13.17.19.23)
* 262zpi (22.313c)
* 263zpi (22.243c)
* 13-limit WE (22.198c)
* 2.3.7.11.13 WE (22.180c)
* 264zpi (22.175c)
* 40ed5/3 (compress, improves 3.5.11.13.17.19 (not 7))
* 152ed7
* 86edt
59edo (narrow down ZPIs)
* (Nothing special abt these choices)
{{harmonics in equal | 59 | 2 | 1 | intervals=integer | columns=12}}
* 93edt
* 203ed11
* 293zpi (20.454c)
* 294zpi (20.399c)
* 295zpi (20.342c)
* 13-limit WE (20.320c)
* 11-limit WE (20.310c)
* 7-limit WE (20.301c)
* 296zpi (20.282c)
* 297zpi (20.229c)
* 166ed7
64edo (narrow down ZPIs)
{{harmonics in equal | 64 | 2 | 1 | intervals=integer | columns=12}}
* 47ed5/3 (like 221ed11 but benefits & drawbacks both amplified)
* 221ed11
* 325zpi (18.868c)
* 326zpi (18.816c)
* 327zpi (18.767c)
* 11-limit WE (18.755c)
* 13-limit WE (18.752c)
* 328zpi (18.721c)
* 329zpi (18.672c)
* 330zpi (18.630c)
* 180ed7
* 149ed5
; Medium priority


118edo (choose ZPIS)
118edo (choose ZPIS)
Line 222: Line 65:
* 13-limit WE (10.171c)
* 13-limit WE (10.171c)
* Best nearby ZPI(s)
* Best nearby ZPI(s)
13edo
{{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}}
* 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)


103edo (narrow down edonoi, choose ZPIS)
103edo (narrow down edonoi, choose ZPIS)
Line 252: Line 87:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Low priority
13edo
{{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}}
* 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
104edo
Line 260: Line 101:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


125edo
; Medium-priority
 
25edo
{{harmonics in equal | 25 | 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 266: Line 110:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


145edo
26edo
{{harmonics in equal | 26 | 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 272: Line 117:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


152edo
29edo
* 241edt
{{harmonics in equal | 29 | 2 | 1 | intervals=integer | columns=12}}
* 13-limit WE (7.894c)
* Best nearby ZPI(s)
 
159edo
* 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 283: Line 124:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


166edo
30edo
{{harmonics in equal | 30 | 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 289: Line 131:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


182edo
35edo
{{harmonics in equal | 35 | 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 295: Line 138:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


198edo
36edo
{{harmonics in equal | 36 | 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 301: Line 145:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


212edo
37edo
{{harmonics in equal | 37 | 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 307: Line 152:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


243edo
15edo
{{harmonics in equal | 15 | 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 313: Line 159:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


247edo
9edo
{{harmonics in equal | 9 | 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 319: Line 166:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Optional
18edo
 
{{harmonics in equal | 18 | 2 | 1 | intervals=integer | columns=12}}
25edo
{{harmonics in equal | 25 | 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 328: Line 173:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


26edo
24edo
{{harmonics in equal | 26 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 24 | 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(


29edo
48edo
{{harmonics in equal | 29 | 2 | 1 | intervals=integer | columns=12}}
{{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)
Line 342: Line 187:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


30edo
5edo
{{harmonics in equal | 30 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 5 | 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 349: Line 194:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


34edo
6edo
{{harmonics in equal | 34 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 6 | 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)s)


35edo
10edo
{{harmonics in equal | 35 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 10 | 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 363: Line 208:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


36edo
11edo
{{harmonics in equal | 36 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 11 | 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 370: Line 215:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


37edo
34edo
{{harmonics in equal | 37 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 34 | 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 377: Line 222:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


5edo
; Low priority
{{harmonics in equal | 5 | 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)


6edo
125edo
{{harmonics in equal | 6 | 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 391: Line 230:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


9edo
145edo
{{harmonics in equal | 9 | 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 398: Line 236:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


10edo
152edo
{{harmonics in equal | 10 | 2 | 1 | intervals=integer | columns=12}}
* 241edt
* Nearby edt, ed6, ed12 and/or edf
* 13-limit WE (7.894c)
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)


11edo
159edo
{{harmonics in equal | 11 | 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 412: Line 247:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


15edo
166edo
{{harmonics in equal | 15 | 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 419: Line 253:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


18edo
182edo
{{harmonics in equal | 18 | 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 426: Line 259:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


48edo
198edo
{{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)
Line 433: Line 265:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


20edo
212edo
{{harmonics in equal | 20 | 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 440: Line 271:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


24edo
243edo
{{harmonics in equal | 24 | 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 447: Line 277:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


28edo
247edo
{{harmonics in equal | 28 | 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)
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox2"