User:BudjarnLambeth/Sandbox2: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,520 edits
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,520 edits
 
(52 intermediate revisions by the same user not shown)
Line 3: Line 3:
[[User:BudjarnLambeth/Draft related tunings section]]
[[User:BudjarnLambeth/Draft related tunings section]]


= Title1 =
== Octave stretch and compression ==
== Octave stretch or compression ==
{{main|23edo and octave stretching}}


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.
; [[zpi|209zpi]]  
* Step size: 26.550{{c}}, octave size: 1194.8{{c}}
Compressing the octave of 45edo by around 5{{c}} results in improved primes 5 and 7, but worse primes 2, 3, 11 and 13. This approximates all harmonics up to 16 within 11.1{{c}}. The tuning 209zpi does this.
{{Harmonics in cet|26.550|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 209zpi}}
{{Harmonics in cet|26.550|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 209zpi (continued)}}


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.
; 45edo
* Step size: 26.667{{c}}, octave size: 1200.0{{c}}
Pure-octaves 45edo approximates all harmonics up to 16 within 13.0{{c}}.
{{Harmonics in equal|45|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 45edo}}
{{Harmonics in equal|45|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 45edo (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|45et, 13-limit WE tuning]]  
* Step size: 26.695{{c}}, octave size: 1201.3{{c}}
Stretching the octave of 45edo by around 1{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 13.2{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
{{Harmonics in cet|26.695|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 45et, 13-limit WE tuning}}
{{Harmonics in cet|26.695|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 45et, 13-limit WE tuning (continued)}}


What follows is a comparison of stretched- and compressed-octave 23edo tunings.
; [[161ed12]]
* Step size: Octave size: 1202.4{{c}}
Stretching the octave of 45edo by around 2.5{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 12.2{{c}}. The tuning 161ed12 does this.
{{Harmonics in equal|161|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 161ed12}}
{{Harmonics in equal|161|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 161ed12 (continued)}}


; [[zpi|86zpi]]  
; [[116ed6]]  
* Step size: 51.653{{c}}, octave size: 1188.0{{c}}
* Step size: Octave size: 1203.3{{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 45edo by around 3{{c}} results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 13.4{{c}}. The tuning 116ed6 does this. So does [[ed7|126ed7]] whose octave is identical within 0.1{{c}}.
{{Harmonics in cet|51.653|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in equal|116|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 116ed6}}
{{Harmonics in cet|51.653|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
{{Harmonics in equal|116|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 116ed6 (continued)}}


; [[60ed6]]  
; [[WE|45et, 7-limit WE tuning]]  
* Step size: 51.700{{c}}, octave size: 1189.1{{c}}
* Step size: 26.745{{c}}, octave size: 1203.5{{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 45edo by around 3.5{{c}} results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 12.6{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this.
{{Harmonics in equal|60|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in cet|26.745|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 45et, 7-limit WE tuning}}
{{Harmonics in equal|60|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in cet|26.745|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 45et, 7-limit WE tuning (continued)}}


; [[zpi|85zpi]]  
; [[zpi|207zpi]]  
* Step size: 52.114{{c}}, octave size: 1198.6{{c}}
* Step size: 26.762{{c}}, octave size: 1204.3{{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 85zpi does this. So does the tuning [[ed9|73ed9]] whose octave is identical within 0.02{{c}}.
Stretching the octave of 45edo by around 4{{c}} results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 12.9{{c}}. The tuning 207zpi does this.
{{Harmonics in cet|52.114|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in cet|26.762|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 207zpi}}
{{Harmonics in cet|52.114|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
{{Harmonics in cet|26.762|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 207zpi (continued)}}


; 23edo
; [[71edt]]  
* Step size: NNN{{c}}, octave size: 1200.0{{c}}
* Step size: 26.788{{c}}, octave size: 1205.5{{c}}
Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
Stretching the octave of 45edo by around 5.5{{c}} results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 11.9{{c}}. The tuning 71edt does this. So does the tuning [[equal tuning|155ed11]] whose octave is identical within 0.3{{c}}.
{{Harmonics in equal|23|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
{{Harmonics in equal|71|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 71edt}}
{{Harmonics in equal|23|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}
{{Harmonics in equal|71|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 71edt (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]]
* 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]]
* 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 =
= Title2 =
=== Lab ===
=== Lab ===


54edo (possibly narrow down edonoi)
Place holder
* 38ed5/3 (stretch, improves 3.5.7.11.13.17.19.23)
{{harmonics in equal | 38 | 5 | 3 | intervals=prime}}
* 262zpi (22.313c)
{{harmonics in cet | 22.313 | intervals=prime}}
* 263zpi (22.243c)
{{harmonics in cet | 22.243 | intervals=prime}}
* pure octave 54edo
{{harmonics in equal | 54 | 2 | 1 | intervals=integer | columns=12}}
* 13-limit WE (22.198c)
{{harmonics in cet | 22.198 | intervals=prime}}
* 2.3.7.11.13 WE (22.180c)
{{harmonics in cet | 22.180 | intervals=prime}}
* 264zpi (22.175c)
{{harmonics in cet | 22.175 | intervals=prime}}
* 152ed7
{{harmonics in equal | 152 | 7 | 1 | intervals=prime}}
* 86edt
{{harmonics in equal | 86 | 3 | 1 | intervals=prime}}
* 126ed5
{{harmonics in equal | 126 | 5 | 1 | intervals=prime}}
* 40ed5/3 (compress, improves 3.5.11.13.17.19 (not 7))
{{harmonics in equal | 40 | 5 | 3 | intervals=prime}}
 
<br><br>
 
59edo (narrow down ZPIs) (Nothing special abt these choices)
* 293zpi (20.454c)
{{harmonics in cet | 20.454 | intervals=prime}}
* 93edt
{{harmonics in equal | 93 | 3 | 1 | intervals=prime}}
* 203ed11
{{harmonics in equal | 203 | 11 | 1 | intervals=prime}}
* 294zpi (20.399c)
{{harmonics in cet | 20.399 | intervals=prime}}
* pure octaves 59edo
{{harmonics in equal | 59 | 2 | 1 | intervals=integer | columns=12}}
* 295zpi (20.342c)
{{harmonics in cet | 20.342 | intervals=prime}}
* 13-limit WE (20.320c)
{{harmonics in cet | 20.320 | intervals=prime}}
* 11-limit WE (20.310c)
{{harmonics in cet | 20.310 | intervals=prime}}
* 7-limit WE (20.301c)
{{harmonics in cet | 20.301 | intervals=prime}}
* 166ed7
{{harmonics in equal | 166 | 7 | 1 | intervals=prime}}
* 296zpi (20.282c)
{{harmonics in cet | 20.282 | intervals=prime}}
* 297zpi (20.229c)
{{harmonics in cet | 20.229 | intervals=prime}}
 
<br><br>
 
64edo (narrow down ZPIs)
* 325zpi (18.868c)
{{harmonics in cet | 18.868 | intervals=prime}}
* 326zpi (18.816c)
{{harmonics in cet | 18.816 | intervals=prime}}
{{harmonics in equal | 47 | 5 | 3 | intervals=prime}}
* 221ed11
{{harmonics in equal | 221 | 11 | 1 | intervals=prime}}
* 327zpi (18.767c)
{{harmonics in cet | 18.767 | intervals=prime}}
* 11-limit WE (18.755c)
{{harmonics in cet | 18.755 | intervals=prime}}
* 13-limit WE (18.752c)
{{harmonics in cet | 18.752 | intervals=prime}}
* pure octaves 64edo
{{harmonics in equal | 64 | 2 | 1 | intervals=integer | columns=12}}
* 328zpi (18.721c)
{{harmonics in cet | 18.721 | intervals=prime}}
* 180ed7
{{harmonics in equal | 180 | 7 | 1 | intervals=prime}}
* 149ed5
{{harmonics in equal | 149 | 5 | 1 | intervals=prime}}
* 329zpi (18.672c)
{{harmonics in cet | 18.672 | intervals=prime}}
* 330zpi (18.630c)
{{harmonics in cet | 18.630 | intervals=prime}}




Line 164: Line 63:


{{harmonics in cet | 300 | intervals=prime}}
{{harmonics in cet | 300 | intervals=prime}}
{{harmonics in equal | 140 | 12 | 1 | intervals=prime}}
{{harmonics in equal | 140 | 12 | 1 | intervals=prime}}


Line 173: Line 73:
; High-priority
; High-priority


60edo (narrow down edonoi & ZPIs)
54edo
* 35edf
* 139ed6 (octave is identical to 262zpi within 0.2{{c}})
* 139ed5
* 151ed7
* 301zpi (20.027c)
* 193ed12
* 95edt
* 263zpi (22.243c)
* 13-limit WE (20.013c) (155ed6 has octaves only 0.02{{c}} different)
* 13-limit WE (22.198c) (octave is identical to 187ed11 within 0.1{{c}})
* 215ed12
* 264zpi (22.175c) (octave is identical to 194ed12 within 0.01{{c}})
* 302zpi (19.962c)
* 152ed7
* 208ed11 (ideal for catnip temperament)
* 140ed6
* 303zpi (19.913c)
* 126ed5 (octave is identical to 86edt within 0.1{{c}})


32edo
64edo
* 13-limit WE (37.481c)
* 179ed7 (octave is identical to 326zpi within 0.3{{c}})
* 11-limit WE (37.453c)
* 165ed6
* 90ed7 (optimal for dual-5) (133zpi's octave only differs by 0.4{{c}})
* 229ed12 (octave is identical to 221ed11 within 0.1{{c}})
* 51edt
* 327zpi (18.767c)
* 134zpi (37.176c)
* 11-limit WE (18.755c)
* 75ed5
''pure octaves 64edo (octave is identical to 13-limit WE within 0.13{{c}}''
* 328zpi (18.721c)
* 180ed7
* 230ed12
* 149ed5


33edo
42edo (reduce # of edonoi)
* 76ed5
* 108ed6 (octave is identical to 97ed5 within 0.1{{c}})
* 92ed7 (137zpi's octave differs by only 0.3{{c}})
* 189zpi (28.689c)
* 52ed13
* 150ed12
* 114ed11
* 145ed11
* 138zpi (36.394c) (122ed13's octave differs by only 0.1{{c}})
''190zpi's octave is within 0.05{{c}} of pure-octaves 42edo''
* 13-limit WE (36.357c)
* 118ed7
* 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)
* 13-limit WE (28.534c)
* 34ed7/4 (good 2.5.7.13; okay 3.11)
* 151ed12 (octave is identical to 7-limit WE within 0.3{{c}})
* 7-limit WE (28.484c) (good 2.3.5.11.13; bad 7)
* 109ed6
* 191zpi (28.444c)
* 191zpi (28.444c)
* 1ed123/121 (good 2.3.5.11; okay 13; bad 7)
* 67edt
 
45edo
* 209zpi (26.550)
* 13-limit WE (26.695c)
* 161ed12
* 116ed6 (octave identical to 126ed7 within 0.1{{c}})
* 7-limit WE (26.745c)
* 207zpi (26.762)
* 71edt (octave identical to 155ed11 within 0.3{{c}})
 
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)
59edo (reduce # of edonoi or zpi)
* (Nothing special abt these choices)
* 152ed6
{{harmonics in equal | 59 | 2 | 1 | intervals=integer | columns=12}}
* 93edt
* 203ed11
* 293zpi (20.454c)
* 294zpi (20.399c)
* 294zpi (20.399c)
* 211ed12
* 295zpi (20.342c)
* 295zpi (20.342c)
''pure octaves 59edo octave is identical to 137ed5 within 0.05{{c}}''
* 13-limit WE (20.320c)
* 13-limit WE (20.320c)
* 11-limit WE (20.310c)
* 7-limit WE (20.301c)
* 7-limit WE (20.301c)
* 166ed7
* 212ed12
* 296zpi (20.282c)
* 296zpi (20.282c)
* 297zpi (20.229c)
* 153ed6
* 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
; Medium priority


118edo (choose ZPIS)
25edo
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}}
{{harmonics in equal | 25 | 2 | 1 | intervals=integer | columns=12}}
* 187edt
* 69edf
* 13-limit WE (10.171c)
* 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)
{{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}}
* 163edt
* 239ed5
* 266ed6
* 289ed7
* 356ed11
* 369ed12
* 381ed13
* 421ed17
* 466ed23
* 13-limit WE (11.658c)
* Best nearby ZPI(s)
 
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 318: Line 131:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Low priority
26edo
 
{{harmonics in equal | 26 | 2 | 1 | intervals=integer | columns=12}}
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 326: Line 138:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


125edo
29edo
{{harmonics in equal | 29 | 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 332: Line 145:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


145edo
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 338: Line 152:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


152edo
34edo
* 241edt
{{harmonics in equal | 34 | 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 349: Line 159:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


166edo
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 355: Line 166:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


182edo
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 361: Line 173:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


198edo
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 367: Line 180:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


212edo
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 373: Line 187:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


243edo
10edo
{{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 379: Line 194:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


247edo
11edo
{{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 385: Line 201:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


; Optional
15edo
 
{{harmonics in equal | 15 | 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 394: Line 208:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


26edo
18edo
{{harmonics in equal | 26 | 2 | 1 | intervals=integer | columns=12}}
{{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 401: Line 215:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


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 408: Line 222:
* 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 415: Line 229:
* 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)
Line 422: Line 236:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


35edo
20edo
{{harmonics in equal | 35 | 2 | 1 | intervals=integer | columns=12}}
{{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 429: Line 243:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


36edo
24edo
{{harmonics in equal | 36 | 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)
Line 436: Line 250:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


37edo
28edo
{{harmonics in equal | 37 | 2 | 1 | intervals=integer | columns=12}}
{{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)
Line 443: Line 257:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


5edo
; Low priority
{{harmonics in equal | 5 | 2 | 1 | intervals=integer | columns=12}}
 
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)
 
118edo (choose ZPIS)
{{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}}
* 187edt
* 69edf
* 13-limit WE (10.171c)
* Best nearby ZPI(s)
 
103edo (narrow down edonoi, choose ZPIS)
{{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}}
* 163edt
* 239ed5
* 266ed6
* 289ed7
* 356ed11
* 369ed12
* 381ed13
* 421ed17
* 466ed23
* 13-limit WE (11.658c)
* Best nearby ZPI(s)
 
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 450: Line 295:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


6edo
104edo
{{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 457: Line 301:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


9edo
125edo
{{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 464: Line 307:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


10edo
145edo
{{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 471: Line 313:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


11edo
152edo
{{harmonics in equal | 11 | 2 | 1 | intervals=integer | columns=12}}
* 241edt
* 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 478: Line 324:
* 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 485: Line 330:
* 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 492: Line 336:
* 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 499: Line 342:
* 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 506: Line 348:
* 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 513: Line 354:
* 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)

Latest revision as of 03:42, 30 August 2025

Quick link

User:BudjarnLambeth/Draft related tunings section

Octave stretch and compression

209zpi
  • Step size: 26.550 ¢, octave size: 1194.8 ¢

Compressing the octave of 45edo by around 5 ¢ results in improved primes 5 and 7, but worse primes 2, 3, 11 and 13. This approximates all harmonics up to 16 within 11.1 ¢. The tuning 209zpi does this.

Approximation of harmonics in 209zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -5.2 +9.6 -10.5 +1.4 +4.4 +3.0 +10.8 -7.3 -3.8 -9.5 -0.9
Relative (%) -19.8 +36.3 -39.5 +5.4 +16.6 +11.4 +40.7 -27.3 -14.4 -35.8 -3.2
Step 45 72 90 105 117 127 136 143 150 156 162
Approximation of harmonics in 209zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -6.7 -2.2 +11.1 +5.6 +6.8 -12.5 +0.1 -9.1 +12.7 +11.8 -12.1 -6.1
Relative (%) -25.2 -8.4 +41.7 +20.9 +25.6 -47.1 +0.3 -34.1 +47.7 +44.4 -45.5 -23.0
Step 167 172 177 181 185 188 192 195 199 202 204 207
45edo
  • Step size: 26.667 ¢, octave size: 1200.0 ¢

Pure-octaves 45edo approximates all harmonics up to 16 within 13.0 ¢.

Approximation of harmonics in 45edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 -8.6 +0.0 -13.0 -8.6 -8.8 +0.0 +9.4 -13.0 +8.7 -8.6
Relative (%) +0.0 -32.3 +0.0 -48.7 -32.3 -33.1 +0.0 +35.3 -48.7 +32.6 -32.3
Steps
(reduced) 		45
(0) 		71
(26) 		90
(0) 		104
(14) 		116
(26) 		126
(36) 		135
(0) 		143
(8) 		149
(14) 		156
(21) 		161
(26)
Approximation of harmonics in 45edo (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +12.8 -8.8 +5.1 +0.0 +1.7 +9.4 -4.2 -13.0 +9.2 +8.7 +11.7 -8.6
Relative (%) +48.0 -33.1 +19.0 +0.0 +6.4 +35.3 -15.7 -48.7 +34.6 +32.6 +44.0 -32.3
Steps
(reduced) 		167
(32) 		171
(36) 		176
(41) 		180
(0) 		184
(4) 		188
(8) 		191
(11) 		194
(14) 		198
(18) 		201
(21) 		204
(24) 		206
(26)
45et, 13-limit WE tuning
  • Step size: 26.695 ¢, octave size: 1201.3 ¢

Stretching the octave of 45edo by around 1 ¢ results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 13.2 ¢. Its 13-limit WE tuning and 13-limit TE tuning both do this.

Approximation of harmonics in 45et, 13-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.3 -6.6 +2.5 -10.0 -5.3 -5.3 +3.8 -13.2 -8.8 +13.1 -4.1
Relative (%) +4.8 -24.8 +9.6 -37.6 -20.0 -19.7 +14.3 -49.5 -32.8 +49.1 -15.2
Step 45 71 90 104 116 126 135 142 149 156 161
Approximation of harmonics in 45et, 13-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -9.2 -4.0 +10.1 +5.1 +6.9 -11.9 +1.2 -7.5 -11.9 -12.3 -9.2 -2.8
Relative (%) -34.3 -14.9 +37.7 +19.1 +25.9 -44.7 +4.6 -28.0 -44.4 -46.1 -34.4 -10.4
Step 166 171 176 180 184 187 191 194 197 200 203 206
161ed12
  • Step size: Octave size: 1202.4 ¢

Stretching the octave of 45edo by around 2.5 ¢ results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 12.2 ¢. The tuning 161ed12 does this.

Approximation of harmonics in 161ed12
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.4 -4.8 +4.8 -7.4 -2.4 -2.1 +7.2 -9.6 -5.0 -9.7 +0.0
Relative (%) +9.0 -18.0 +18.0 -27.7 -9.0 -7.8 +27.1 -36.1 -18.7 -36.2 +0.0
Steps
(reduced) 		45
(45) 		71
(71) 		90
(90) 		104
(104) 		116
(116) 		126
(126) 		135
(135) 		142
(142) 		149
(149) 		155
(155) 		161
(0)
Approximation of harmonics in 161ed12 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -5.0 +0.3 -12.2 +9.6 +11.6 -7.2 +6.0 -2.6 -6.9 -7.3 -4.1 +2.4
Relative (%) -18.6 +1.2 -45.8 +36.1 +43.3 -27.1 +22.6 -9.7 -25.8 -27.2 -15.2 +9.0
Steps
(reduced) 		166
(5) 		171
(10) 		175
(14) 		180
(19) 		184
(23) 		187
(26) 		191
(30) 		194
(33) 		197
(36) 		200
(39) 		203
(42) 		206
(45)
116ed6
  • Step size: Octave size: 1203.3 ¢

Stretching the octave of 45edo by around 3 ¢ results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 13.4 ¢. The tuning 116ed6 does this. So does 126ed7 whose octave is identical within 0.1 ¢.

Approximation of harmonics in 116ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.3 -3.3 +6.7 -5.3 +0.0 +0.5 +10.0 -6.7 -1.9 -6.5 +3.3
Relative (%) +12.5 -12.5 +25.0 -19.6 +0.0 +2.0 +37.5 -25.0 -7.1 -24.2 +12.5
Steps
(reduced) 		45
(45) 		71
(71) 		90
(90) 		104
(104) 		116
(0) 		126
(10) 		135
(19) 		142
(26) 		149
(33) 		155
(39) 		161
(45)
Approximation of harmonics in 116ed6 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -1.5 +3.9 -8.6 -13.4 -11.4 -3.3 +10.0 +1.4 -2.8 -3.1 +0.1 +6.7
Relative (%) -5.7 +14.5 -32.1 -50.0 -42.5 -12.5 +37.5 +5.4 -10.5 -11.7 +0.5 +25.0
Steps
(reduced) 		166
(50) 		171
(55) 		175
(59) 		179
(63) 		183
(67) 		187
(71) 		191
(75) 		194
(78) 		197
(81) 		200
(84) 		203
(87) 		206
(90)
45et, 7-limit WE tuning
  • Step size: 26.745 ¢, octave size: 1203.5 ¢

Stretching the octave of 45edo by around 3.5 ¢ results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 12.6 ¢. Its 7-limit WE tuning and 7-limit TE tuning both do this.

Approximation of harmonics in 45et, 7-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.5 -3.1 +7.1 -4.8 +0.5 +1.0 +10.6 -6.1 -1.3 -5.8 +4.0
Relative (%) +13.2 -11.4 +26.4 -18.1 +1.7 +3.9 +39.5 -22.9 -4.9 -21.8 +14.9
Step 45 71 90 104 116 126 135 142 149 155 161
Approximation of harmonics in 45et, 7-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -0.9 +4.6 -7.9 -12.6 -10.6 -2.6 +10.8 +2.2 -2.0 -2.3 +1.0 +7.5
Relative (%) -3.2 +17.1 -29.5 -47.3 -39.7 -9.7 +40.3 +8.3 -7.5 -8.7 +3.6 +28.1
Step 166 171 175 179 183 187 191 194 197 200 203 206
207zpi
  • Step size: 26.762 ¢, octave size: 1204.3 ¢

Stretching the octave of 45edo by around 4 ¢ results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 12.9 ¢. The tuning 207zpi does this.

Approximation of harmonics in 207zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.3 -1.9 +8.6 -3.1 +2.4 +3.2 +12.9 -3.7 +1.2 -3.2 +6.7
Relative (%) +16.0 -6.9 +32.1 -11.5 +9.1 +11.9 +48.1 -13.8 +4.6 -12.0 +25.1
Step 45 71 90 104 116 126 135 142 149 155 161
Approximation of harmonics in 207zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +2.0 +7.5 -4.9 -9.6 -7.5 +0.6 -12.7 +5.5 +1.3 +1.1 +4.4 +11.0
Relative (%) +7.3 +27.9 -18.4 -35.9 -28.1 +2.2 -47.6 +20.6 +5.0 +4.0 +16.5 +41.2
Step 166 171 175 179 183 187 190 194 197 200 203 206
71edt
  • Step size: 26.788 ¢, octave size: 1205.5 ¢

Stretching the octave of 45edo by around 5.5 ¢ results in improved primes 3, 5, 7, 11 and 13, but a worse prime 2. This approximates all harmonics up to 16 within 11.9 ¢. The tuning 71edt does this. So does the tuning 155ed11 whose octave is identical within 0.3 ¢.

Approximation of harmonics in 71edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +5.5 +0.0 +10.9 -0.4 +5.5 +6.5 -10.4 +0.0 +5.1 +0.8 +10.9
Relative (%) +20.4 +0.0 +40.8 -1.3 +20.4 +24.2 -38.8 +0.0 +19.1 +3.1 +40.8
Steps
(reduced) 		45
(45) 		71
(0) 		90
(19) 		104
(33) 		116
(45) 		126
(55) 		134
(63) 		142
(0) 		149
(7) 		155
(13) 		161
(19)
Approximation of harmonics in 71edt (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +6.3 +11.9 -0.4 -4.9 -2.7 +5.5 -7.8 +10.6 +6.5 +6.3 +9.7 -10.4
Relative (%) +23.5 +44.6 -1.3 -18.4 -10.2 +20.4 -29.0 +39.5 +24.2 +23.5 +36.2 -38.8
Steps
(reduced) 		166
(24) 		171
(29) 		175
(33) 		179
(37) 		183
(41) 		187
(45) 		190
(48) 		194
(52) 		197
(55) 		200
(58) 		203
(61) 		205
(63)

Title2

Lab

Place holder








Approximation of prime harmonics in 1ed300c
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0 -102 -86 -69 +49 +59 -105 +2 -28 -130 +55
Relative (%) +0.0 -34.0 -28.8 -22.9 +16.2 +19.8 -35.0 +0.8 -9.4 -43.2 +18.3
Step 4 6 9 11 14 15 16 17 18 19 20


Approximation of prime harmonics in 140ed12
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -1.6 +3.2 +10.0 +11.3 -3.0 +15.1 +11.6 +3.4 +10.6 +8.8 -14.5
Relative (%) -5.2 +10.4 +32.4 +36.7 -9.8 +49.0 +37.6 +11.0 +34.6 +28.6 -47.1
Steps
(reduced) 		39
(39) 		62
(62) 		91
(91) 		110
(110) 		135
(135) 		145
(5) 		160
(20) 		166
(26) 		177
(37) 		190
(50) 		193
(53)

Possible tunings to be used on each page

You can remove some of these or add more that aren't listed here; this section is pretty much just brainstorming.

(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

54edo

  • 139ed6 (octave is identical to 262zpi within 0.2 ¢)
  • 151ed7
  • 193ed12
  • 263zpi (22.243c)
  • 13-limit WE (22.198c) (octave is identical to 187ed11 within 0.1 ¢)
  • 264zpi (22.175c) (octave is identical to 194ed12 within 0.01 ¢)
  • 152ed7
  • 140ed6
  • 126ed5 (octave is identical to 86edt within 0.1 ¢)

64edo

  • 179ed7 (octave is identical to 326zpi within 0.3 ¢)
  • 165ed6
  • 229ed12 (octave is identical to 221ed11 within 0.1 ¢)
  • 327zpi (18.767c)
  • 11-limit WE (18.755c)

pure octaves 64edo (octave is identical to 13-limit WE within 0.13 ¢

  • 328zpi (18.721c)
  • 180ed7
  • 230ed12
  • 149ed5

42edo (reduce # of edonoi)

  • 108ed6 (octave is identical to 97ed5 within 0.1 ¢)
  • 189zpi (28.689c)
  • 150ed12
  • 145ed11

190zpi's octave is within 0.05 ¢ of pure-octaves 42edo

  • 118ed7
  • 13-limit WE (28.534c)
  • 151ed12 (octave is identical to 7-limit WE within 0.3 ¢)
  • 109ed6
  • 191zpi (28.444c)
  • 67edt

59edo (reduce # of edonoi or zpi)

  • 152ed6
  • 294zpi (20.399c)
  • 211ed12
  • 295zpi (20.342c)

pure octaves 59edo octave is identical to 137ed5 within 0.05 ¢

  • 13-limit WE (20.320c)
  • 7-limit WE (20.301c)
  • 166ed7
  • 212ed12
  • 296zpi (20.282c)
  • 153ed6
Medium priority

25edo

Approximation of harmonics in 25edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 -2.3 +18.0 -8.8 +0.0 -11.9 -2.3 -23.3 +18.0 +23.5
Relative (%) +0.0 +37.6 +0.0 -4.8 +37.6 -18.4 +0.0 -24.8 -4.8 -48.6 +37.6 +48.9
Steps
(reduced) 		25
(0) 		40
(15) 		50
(0) 		58
(8) 		65
(15) 		70
(20) 		75
(0) 		79
(4) 		83
(8) 		86
(11) 		90
(15) 		93
(18)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

26edo

Approximation of harmonics in 26edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -9.6 +0.0 -17.1 -9.6 +0.4 +0.0 -19.3 -17.1 +2.5 -9.6 -9.8
Relative (%) +0.0 -20.9 +0.0 -37.0 -20.9 +0.9 +0.0 -41.8 -37.0 +5.5 -20.9 -21.1
Steps
(reduced) 		26
(0) 		41
(15) 		52
(0) 		60
(8) 		67
(15) 		73
(21) 		78
(0) 		82
(4) 		86
(8) 		90
(12) 		93
(15) 		96
(18)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

29edo

Approximation of harmonics in 29edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +1.5 +0.0 -13.9 +1.5 -17.1 +0.0 +3.0 -13.9 -13.4 +1.5 -12.9
Relative (%) +0.0 +3.6 +0.0 -33.6 +3.6 -41.3 +0.0 +7.2 -33.6 -32.4 +3.6 -31.3
Steps
(reduced) 		29
(0) 		46
(17) 		58
(0) 		67
(9) 		75
(17) 		81
(23) 		87
(0) 		92
(5) 		96
(9) 		100
(13) 		104
(17) 		107
(20)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

30edo

Approximation of harmonics in 30edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 +13.7 +18.0 -8.8 +0.0 -3.9 +13.7 +8.7 +18.0 -0.5
Relative (%) +0.0 +45.1 +0.0 +34.2 +45.1 -22.1 +0.0 -9.8 +34.2 +21.7 +45.1 -1.3
Steps
(reduced) 		30
(0) 		48
(18) 		60
(0) 		70
(10) 		78
(18) 		84
(24) 		90
(0) 		95
(5) 		100
(10) 		104
(14) 		108
(18) 		111
(21)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

34edo

Approximation of harmonics in 34edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +3.9 +0.0 +1.9 +3.9 -15.9 +0.0 +7.9 +1.9 +13.4 +3.9 +6.5
Relative (%) +0.0 +11.1 +0.0 +5.4 +11.1 -45.0 +0.0 +22.3 +5.4 +37.9 +11.1 +18.5
Steps
(reduced) 		34
(0) 		54
(20) 		68
(0) 		79
(11) 		88
(20) 		95
(27) 		102
(0) 		108
(6) 		113
(11) 		118
(16) 		122
(20) 		126
(24)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

35edo

Approximation of harmonics in 35edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -16.2 +0.0 -9.2 -16.2 -8.8 +0.0 +1.8 -9.2 -2.7 -16.2 +16.6
Relative (%) +0.0 -47.4 +0.0 -26.7 -47.4 -25.7 +0.0 +5.3 -26.7 -8.0 -47.4 +48.5
Steps
(reduced) 		35
(0) 		55
(20) 		70
(0) 		81
(11) 		90
(20) 		98
(28) 		105
(0) 		111
(6) 		116
(11) 		121
(16) 		125
(20) 		130
(25)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

36edo

Approximation of harmonics in 36edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 -2.2 +0.0 -3.9 +13.7 +15.3 -2.0 -7.2
Relative (%) +0.0 -5.9 +0.0 +41.1 -5.9 -6.5 +0.0 -11.7 +41.1 +46.0 -5.9 -21.6
Steps
(reduced) 		36
(0) 		57
(21) 		72
(0) 		84
(12) 		93
(21) 		101
(29) 		108
(0) 		114
(6) 		120
(12) 		125
(17) 		129
(21) 		133
(25)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

37edo

Approximation of harmonics in 37edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +11.6 +0.0 +2.9 +11.6 +4.1 +0.0 -9.3 +2.9 +0.0 +11.6 +2.7
Relative (%) +0.0 +35.6 +0.0 +8.9 +35.6 +12.8 +0.0 -28.7 +8.9 +0.1 +35.6 +8.4
Steps
(reduced) 		37
(0) 		59
(22) 		74
(0) 		86
(12) 		96
(22) 		104
(30) 		111
(0) 		117
(6) 		123
(12) 		128
(17) 		133
(22) 		137
(26)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

9edo

Approximation of harmonics in 9edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -35.3 +0.0 +13.7 -35.3 -35.5 +0.0 +62.8 +13.7 -18.0 -35.3 -40.5
Relative (%) +0.0 -26.5 +0.0 +10.3 -26.5 -26.6 +0.0 +47.1 +10.3 -13.5 -26.5 -30.4
Steps
(reduced) 		9
(0) 		14
(5) 		18
(0) 		21
(3) 		23
(5) 		25
(7) 		27
(0) 		29
(2) 		30
(3) 		31
(4) 		32
(5) 		33
(6)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

10edo

Approximation of harmonics in 10edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 -26.3 +18.0 -8.8 +0.0 +36.1 -26.3 +48.7 +18.0 -0.5
Relative (%) +0.0 +15.0 +0.0 -21.9 +15.0 -7.4 +0.0 +30.1 -21.9 +40.6 +15.0 -0.4
Steps
(reduced) 		10
(0) 		16
(6) 		20
(0) 		23
(3) 		26
(6) 		28
(8) 		30
(0) 		32
(2) 		33
(3) 		35
(5) 		36
(6) 		37
(7)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

11edo

Approximation of harmonics in 11edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -47.4 +0.0 +50.0 -47.4 +13.0 +0.0 +14.3 +50.0 -5.9 -47.4 +32.2
Relative (%) +0.0 -43.5 +0.0 +45.9 -43.5 +11.9 +0.0 +13.1 +45.9 -5.4 -43.5 +29.5
Steps
(reduced) 		11
(0) 		17
(6) 		22
(0) 		26
(4) 		28
(6) 		31
(9) 		33
(0) 		35
(2) 		37
(4) 		38
(5) 		39
(6) 		41
(8)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

15edo

Approximation of harmonics in 15edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 +13.7 +18.0 -8.8 +0.0 +36.1 +13.7 +8.7 +18.0 +39.5
Relative (%) +0.0 +22.6 +0.0 +17.1 +22.6 -11.0 +0.0 +45.1 +17.1 +10.9 +22.6 +49.3
Steps
(reduced) 		15
(0) 		24
(9) 		30
(0) 		35
(5) 		39
(9) 		42
(12) 		45
(0) 		48
(3) 		50
(5) 		52
(7) 		54
(9) 		56
(11)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

18edo

Approximation of harmonics in 18edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +31.4 +0.0 +13.7 +31.4 +31.2 +0.0 -3.9 +13.7 -18.0 +31.4 +26.1
Relative (%) +0.0 +47.1 +0.0 +20.5 +47.1 +46.8 +0.0 -5.9 +20.5 -27.0 +47.1 +39.2
Steps
(reduced) 		18
(0) 		29
(11) 		36
(0) 		42
(6) 		47
(11) 		51
(15) 		54
(0) 		57
(3) 		60
(6) 		62
(8) 		65
(11) 		67
(13)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

48edo

Approximation of harmonics in 48edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -2.0 +0.0 -11.3 -2.0 +6.2 +0.0 -3.9 -11.3 -1.3 -2.0 +9.5
Relative (%) +0.0 -7.8 +0.0 -45.3 -7.8 +24.7 +0.0 -15.6 -45.3 -5.3 -7.8 +37.9
Steps
(reduced) 		48
(0) 		76
(28) 		96
(0) 		111
(15) 		124
(28) 		135
(39) 		144
(0) 		152
(8) 		159
(15) 		166
(22) 		172
(28) 		178
(34)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

5edo

Approximation of harmonics in 5edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0 +18 +0 +94 +18 -9 +0 +36 +94 -71 +18 +119
Relative (%) +0.0 +7.5 +0.0 +39.0 +7.5 -3.7 +0.0 +15.0 +39.0 -29.7 +7.5 +49.8
Steps
(reduced) 		5
(0) 		8
(3) 		10
(0) 		12
(2) 		13
(3) 		14
(4) 		15
(0) 		16
(1) 		17
(2) 		17
(2) 		18
(3) 		19
(4)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

6edo

Approximation of harmonics in 6edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +98.0 +0.0 +13.7 +98.0 +31.2 +0.0 -3.9 +13.7 +48.7 +98.0 -40.5
Relative (%) +0.0 +49.0 +0.0 +6.8 +49.0 +15.6 +0.0 -2.0 +6.8 +24.3 +49.0 -20.3
Steps
(reduced) 		6
(0) 		10
(4) 		12
(0) 		14
(2) 		16
(4) 		17
(5) 		18
(0) 		19
(1) 		20
(2) 		21
(3) 		22
(4) 		22
(4)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

20edo

Approximation of harmonics in 20edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +18.0 +0.0 -26.3 +18.0 -8.8 +0.0 -23.9 -26.3 -11.3 +18.0 -0.5
Relative (%) +0.0 +30.1 +0.0 -43.9 +30.1 -14.7 +0.0 -39.9 -43.9 -18.9 +30.1 -0.9
Steps
(reduced) 		20
(0) 		32
(12) 		40
(0) 		46
(6) 		52
(12) 		56
(16) 		60
(0) 		63
(3) 		66
(6) 		69
(9) 		72
(12) 		74
(14)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

24edo

Approximation of harmonics in 24edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -2.0 +0.0 +13.7 -2.0 -18.8 +0.0 -3.9 +13.7 -1.3 -2.0 +9.5
Relative (%) +0.0 -3.9 +0.0 +27.4 -3.9 -37.7 +0.0 -7.8 +27.4 -2.6 -3.9 +18.9
Steps
(reduced) 		24
(0) 		38
(14) 		48
(0) 		56
(8) 		62
(14) 		67
(19) 		72
(0) 		76
(4) 		80
(8) 		83
(11) 		86
(14) 		89
(17)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

28edo

Approximation of harmonics in 28edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 -16.2 +0.0 -0.6 -16.2 +16.9 +0.0 +10.4 -0.6 +5.8 -16.2 +16.6
Relative (%) +0.0 -37.9 +0.0 -1.4 -37.9 +39.4 +0.0 +24.2 -1.4 +13.6 -37.9 +38.8
Steps
(reduced) 		28
(0) 		44
(16) 		56
(0) 		65
(9) 		72
(16) 		79
(23) 		84
(0) 		89
(5) 		93
(9) 		97
(13) 		100
(16) 		104
(20)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)
Low priority

13edo

Approximation of harmonics in 13edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.0 +36.5 +0.0 -17.1 +36.5 -45.7 +0.0 -19.3 -17.1 +2.5 +36.5 -9.8
Relative (%) +0.0 +39.5 +0.0 -18.5 +39.5 -49.6 +0.0 -20.9 -18.5 +2.7 +39.5 -10.6
Steps
(reduced) 		13
(0) 		21
(8) 		26
(0) 		30
(4) 		34
(8) 		36
(10) 		39
(0) 		41
(2) 		43
(4) 		45
(6) 		47
(8) 		48
(9)
  • 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)

Approximation of harmonics in 118edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.00 -0.26 +0.00 +0.13 -0.26 -2.72 +0.00 -0.52 +0.13 -2.17 -0.26 +3.54
Relative (%) +0.0 -2.6 +0.0 +1.2 -2.6 -26.8 +0.0 -5.1 +1.2 -21.3 -2.6 +34.8
Steps
(reduced) 		118
(0) 		187
(69) 		236
(0) 		274
(38) 		305
(69) 		331
(95) 		354
(0) 		374
(20) 		392
(38) 		408
(54) 		423
(69) 		437
(83)
  • 187edt
  • 69edf
  • 13-limit WE (10.171c)
  • Best nearby ZPI(s)

103edo (narrow down edonoi, choose ZPIS)

Approximation of harmonics in 103edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.00 -2.93 +0.00 -1.85 -2.93 -1.84 +0.00 +5.80 -1.85 -3.75 -2.93 -1.69
Relative (%) +0.0 -25.1 +0.0 -15.9 -25.1 -15.8 +0.0 +49.8 -15.9 -32.1 -25.1 -14.5
Steps
(reduced) 		103
(0) 		163
(60) 		206
(0) 		239
(33) 		266
(60) 		289
(83) 		309
(0) 		327
(18) 		342
(33) 		356
(47) 		369
(60) 		381
(72)
  • 163edt
  • 239ed5
  • 266ed6
  • 289ed7
  • 356ed11
  • 369ed12
  • 381ed13
  • 421ed17
  • 466ed23
  • 13-limit WE (11.658c)
  • Best nearby ZPI(s)

111edo (choose ZPIS)

Approximation of harmonics in 111edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13
Error Absolute (¢) +0.00 +0.75 +0.00 +2.88 +0.75 +4.15 +0.00 +1.50 +2.88 +0.03 +0.75 +2.72
Relative (%) +0.0 +6.9 +0.0 +26.6 +6.9 +38.4 +0.0 +13.8 +26.6 +0.3 +6.9 +25.1
Steps
(reduced) 		111
(0) 		176
(65) 		222
(0) 		258
(36) 		287
(65) 		312
(90) 		333
(0) 		352
(19) 		369
(36) 		384
(51) 		398
(65) 		411
(78)
  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

104edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

125edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

145edo

  • Nearby edt, ed6, ed12 and/or edf
  • Nearby ed5, ed10, ed7 and/or ed11 (optional)
  • 1-2 WE tunings
  • Best nearby ZPI(s)

152edo

  • 241edt
  • 13-limit WE (7.894c)
  • Best nearby ZPI(s)

159edo

  • 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)
Retrieved from "https://en.xen.wiki/index.php?title=User:BudjarnLambeth/Sandbox2&oldid=208830"