|
|
| (121 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| Quick link
| | == Approximations of odd harmonics == |
| | | {{harmonics in equal|1|intervals=odd|columns=7}} |
| [[User:BudjarnLambeth/Draft related tunings section]]
| | {{harmonics in equal|2|intervals=odd|columns=7}} |
| | | {{harmonics in equal|3|intervals=odd|columns=7}} |
| = Title1 = | | {{harmonics in equal|4|intervals=odd|columns=7}} |
| == Octave stretch or compression ==
| | {{harmonics in equal|5|intervals=odd|columns=7}} |
| {{main|23edo and octave stretching}} | | {{harmonics in equal|6|intervals=odd|columns=7}} |
| | | {{harmonics in equal|7|intervals=odd|columns=7}} |
| 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.
| | {{harmonics in equal|8|intervals=odd|columns=7}} |
| | | {{harmonics in equal|9|intervals=odd|columns=7}} |
| 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.
| | {{harmonics in equal|10|intervals=odd|columns=7}} |
| | | {{harmonics in equal|11|intervals=odd|columns=7}} |
| 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.
| | {{harmonics in equal|12|intervals=odd|columns=7}} |
| | | {{harmonics in equal|13|intervals=odd|columns=7}} |
| What follows is a comparison of stretched- and compressed-octave 23edo tunings.
| | {{harmonics in equal|14|intervals=odd|columns=7}} |
| | | {{harmonics in equal|15|intervals=odd|columns=7}} |
| ; [[zpi|86zpi]]
| | {{harmonics in equal|16|intervals=odd|columns=7}} |
| * Step size: 51.653{{c}}, octave size: 1188.0{{c}}
| | {{harmonics in equal|17|intervals=odd|columns=7}} |
| 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.
| | {{harmonics in equal|18|intervals=odd|columns=7}} |
| {{Harmonics in cet|51.653|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
| | {{harmonics in equal|19|intervals=odd|columns=7}} |
| {{Harmonics in cet|51.653|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}} | | {{harmonics in equal|20|intervals=odd|columns=7}} |
| | | {{harmonics in equal|21|intervals=odd|columns=7}} |
| ; [[60ed6]]
| | {{harmonics in equal|22|intervals=odd|columns=7}} |
| * Step size: 51.700{{c}}, octave size: 1189.1{{c}}
| | {{harmonics in equal|23|intervals=odd|columns=7}} |
| 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}}.
| | {{harmonics in equal|24|intervals=odd|columns=7}} |
| {{Harmonics in equal|60|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}} | | {{harmonics in equal|25|intervals=odd|columns=7}} |
| {{Harmonics in equal|60|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}} | | {{harmonics in equal|26|intervals=odd|columns=7}} |
| | | {{harmonics in equal|27|intervals=odd|columns=7}} |
| ; [[zpi|85zpi]]
| | {{harmonics in equal|28|intervals=odd|columns=7}} |
| * Step size: 52.114{{c}}, octave size: 1198.6{{c}}
| | {{harmonics in equal|29|intervals=odd|columns=7}} |
| 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 equal|30|intervals=odd|columns=7}} |
| {{Harmonics in cet|52.114|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
| | {{harmonics in equal|31|intervals=odd|columns=7}} |
| {{Harmonics in cet|52.114|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}} | | {{harmonics in equal|32|intervals=odd|columns=7}} |
| | | {{harmonics in equal|33|intervals=odd|columns=7}} |
| ; 23edo
| | {{harmonics in equal|34|intervals=odd|columns=7}} |
| * Step size: NNN{{c}}, octave size: 1200.0{{c}}
| | {{harmonics in equal|35|intervals=odd|columns=7}} |
| Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
| | {{harmonics in equal|36|intervals=odd|columns=7}} |
| {{Harmonics in equal|23|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
| | {{harmonics in equal|37|intervals=odd|columns=7}} |
| {{Harmonics in equal|23|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}} | | {{harmonics in equal|38|intervals=odd|columns=7}} |
| | | {{harmonics in equal|39|intervals=odd|columns=7}} |
| ; [[WE|23et, 13-limit WE tuning]]
| | {{harmonics in equal|40|intervals=odd|columns=7}} |
| * Step size: 52.237{{c}}, octave size: 1201.5{{c}}
| | {{harmonics in equal|41|intervals=odd|columns=7}} |
| 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 equal|42|intervals=odd|columns=7}} |
| {{Harmonics in cet|52.237|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
| | {{harmonics in equal|43|intervals=odd|columns=7}} |
| {{Harmonics in cet|52.237|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}} | | {{harmonics in equal|44|intervals=odd|columns=7}} |
| | | {{harmonics in equal|45|intervals=odd|columns=7}} |
| ; [[WE|23et, 2.3.5.13 WE tuning]]
| | {{harmonics in equal|46|intervals=odd|columns=7}} |
| * Step size: 52.447{{c}}, octave size: 1206.3{{c}}
| | {{harmonics in equal|47|intervals=odd|columns=7}} |
| 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 equal|48|intervals=odd|columns=7}} |
| {{Harmonics in cet|52.447|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
| | {{harmonics in equal|49|intervals=odd|columns=7}} |
| {{Harmonics in cet|52.447|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}} | | {{harmonics in equal|50|intervals=odd|columns=7}} |
| | | {{harmonics in equal|51|intervals=odd|columns=7}} |
| ; [[59ed6]]
| | {{harmonics in equal|52|intervals=odd|columns=7}} |
| * Step size: 52.575{{c}}, octave size: 1209.2{{c}}
| | {{harmonics in equal|53|intervals=odd|columns=7}} |
| 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 =
| |
| === Lab ===
| |
| {{harmonics in cet | 300 | intervals=prime}} | |
| {{harmonics in equal | 140 | 12 | 1 | intervals=prime}} | |
| | |
| | |
| * 207zpi (26.762)
| |
| * 7-limit WE (26.745c)
| |
| * pure octave 45edo
| |
| {{harmonics in equal | 39 | 2 | 1 | intervals=integer | columns=12}} | |
| * 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)
| |
| | |
| === 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
| |
| | |
| 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)
| |
| {{harmonics in equal | 118 | 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 ed5, ed10, ed7 and/or ed11 (optional)
| |
| * 1-2 WE tunings
| |
| * Best nearby ZPI(s)
| |
| | |
| ; Low priority
| |
| | |
| 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)
| |
| | |
| ; Optional
| |
| | |
| 25edo
| |
| {{harmonics in equal | 25 | 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)
| |
| | |
| 26edo
| |
| {{harmonics in equal | 26 | 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)
| |
| | |
| 29edo
| |
| {{harmonics in equal | 29 | 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)
| |
| | |
| 30edo
| |
| {{harmonics in equal | 30 | 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)
| |
| | |
| 35edo
| |
| {{harmonics in equal | 35 | 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)
| |
| | |
| 36edo
| |
| {{harmonics in equal | 36 | 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)
| |
| | |
| 37edo
| |
| {{harmonics in equal | 37 | 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)
| |
| | |
| 5edo
| |
| {{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
| |
| {{harmonics in equal | 6 | 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)
| |
| | |
| 9edo
| |
| {{harmonics in equal | 9 | 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)
| |
| | |
| 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)
| |
| | |
| 15edo
| |
| {{harmonics in equal | 15 | 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)
| |
| | |
| 18edo
| |
| {{harmonics in equal | 18 | 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)
| |
| | |
| 48edo
| |
| {{harmonics in equal | 48 | 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)
| |
| | |
| 20edo
| |
| {{harmonics in equal | 20 | 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)
| |
| | |
| 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(s)
| |
| | |
| 28edo
| |
| {{harmonics in equal | 28 | 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)
| |