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| 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}} |
| 38edo's approximation of [[JI]] can be improved by slightly [[octave stretch|stretching the octave]].
| | {{harmonics in equal|6|intervals=odd|columns=7}} |
| | | {{harmonics in equal|7|intervals=odd|columns=7}} |
| What follows is a comparison of stretched-octave 38edo tunings.
| | {{harmonics in equal|8|intervals=odd|columns=7}} |
| | | {{harmonics in equal|9|intervals=odd|columns=7}} |
| ; 38edo
| | {{harmonics in equal|10|intervals=odd|columns=7}} |
| * Step size: 31.579{{c}}, octave size: 1200.00{{c}}
| | {{harmonics in equal|11|intervals=odd|columns=7}} |
| Pure-octaves 38edo approximates all harmonics up to 16 within NNN{{c}}.
| | {{harmonics in equal|12|intervals=odd|columns=7}} |
| {{Harmonics in equal|38|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 38edo}} | | {{harmonics in equal|13|intervals=odd|columns=7}} |
| {{Harmonics in equal|38|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 38edo (continued)}} | | {{harmonics in equal|14|intervals=odd|columns=7}} |
| | | {{harmonics in equal|15|intervals=odd|columns=7}} |
| ; [[WE|38et, 13-limit WE tuning]]
| | {{harmonics in equal|16|intervals=odd|columns=7}} |
| * Step size: 31.599{{c}}, octave size: 1200.77{{c}}
| | {{harmonics in equal|17|intervals=odd|columns=7}} |
| 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 equal|18|intervals=odd|columns=7}} |
| {{Harmonics in cet|31.599|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning}} | | {{harmonics in equal|19|intervals=odd|columns=7}} |
| {{Harmonics in cet|31.599|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 38et, 13-limit WE tuning (continued)}} | | {{harmonics in equal|20|intervals=odd|columns=7}} |
| | | {{harmonics in equal|21|intervals=odd|columns=7}} |
| ; [[ed5|88ed5]]
| | {{harmonics in equal|22|intervals=odd|columns=7}} |
| * Step size: 31.663{{c}}, octave size: 1203.18{{c}}
| | {{harmonics in equal|23|intervals=odd|columns=7}} |
| 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|24|intervals=odd|columns=7}} |
| {{Harmonics in equal|88|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 88ed5}} | | {{harmonics in equal|25|intervals=odd|columns=7}} |
| {{Harmonics in equal|88|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 88ed5 (continued)}} | | {{harmonics in equal|26|intervals=odd|columns=7}} |
| | | {{harmonics in equal|27|intervals=odd|columns=7}} |
| ; [[zpi|166zpi]]
| | {{harmonics in equal|28|intervals=odd|columns=7}} |
| * Step size: 31.671{{c}}, octave size: 1203.48{{c}}
| | {{harmonics in equal|29|intervals=odd|columns=7}} |
| 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 equal|30|intervals=odd|columns=7}} |
| {{Harmonics in cet|31.671|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 166zpi}} | | {{harmonics in equal|31|intervals=odd|columns=7}} |
| {{Harmonics in cet|31.671|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 166zpi (continued)}} | | {{harmonics in equal|32|intervals=odd|columns=7}} |
| | | {{harmonics in equal|33|intervals=odd|columns=7}} |
| ; [[60edt]]
| | {{harmonics in equal|34|intervals=odd|columns=7}} |
| * Step size: 31.699{{c}}, octave size: 1204.57{{c}}
| | {{harmonics in equal|35|intervals=odd|columns=7}} |
| 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|36|intervals=odd|columns=7}} |
| {{Harmonics in equal|60|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 60edt}} | | {{harmonics in equal|37|intervals=odd|columns=7}} |
| {{Harmonics in equal|60|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 60edt (continued)}} | | {{harmonics in equal|38|intervals=odd|columns=7}} |
| | | {{harmonics in equal|39|intervals=odd|columns=7}} |
| = Title2 =
| | {{harmonics in equal|40|intervals=odd|columns=7}} |
| === Lab ===
| | {{harmonics in equal|41|intervals=odd|columns=7}} |
| | | {{harmonics in equal|42|intervals=odd|columns=7}} |
| Place holder
| | {{harmonics in equal|43|intervals=odd|columns=7}} |
| | | {{harmonics in equal|44|intervals=odd|columns=7}} |
| | | {{harmonics in equal|45|intervals=odd|columns=7}} |
| <br><br><br><br><br>
| | {{harmonics in equal|46|intervals=odd|columns=7}} |
| | | {{harmonics in equal|47|intervals=odd|columns=7}} |
| | | {{harmonics in equal|48|intervals=odd|columns=7}} |
| {{harmonics in cet | 300 | intervals=prime}} | | {{harmonics in equal|49|intervals=odd|columns=7}} |
| | | {{harmonics in equal|50|intervals=odd|columns=7}} |
| {{harmonics in equal | 140 | 12 | 1 | intervals=prime}} | | {{harmonics in equal|51|intervals=odd|columns=7}} |
| | | {{harmonics in equal|52|intervals=odd|columns=7}} |
| === Possible tunings to be used on each page ===
| | {{harmonics in equal|53|intervals=odd|columns=7}} |
| You can remove some of these or add more that aren't listed here; this section is pretty much just brainstorming.
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| (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)
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| ; High-priority
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| 118edo (choose ZPIS)
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| {{harmonics in equal | 118 | 2 | 1 | intervals=integer | columns=12}} | |
| * 187edt
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| * 69edf
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| * 13-limit WE (10.171c)
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| * Best nearby ZPI(s)
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| 103edo (narrow down edonoi, choose ZPIS)
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| {{harmonics in equal | 103 | 2 | 1 | intervals=integer | columns=12}} | |
| * 163edt
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| * 239ed5
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| * 266ed6
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| * 289ed7
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| * 356ed11
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| * 369ed12
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| * 381ed13
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| * 421ed17
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| * 466ed23
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| * 13-limit WE (11.658c)
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| * Best nearby ZPI(s)
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| 111edo (choose ZPIS)
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| {{harmonics in equal | 111 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 13edo
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| {{harmonics in equal | 13 | 2 | 1 | intervals=integer | columns=12}} | |
| * Main: "13edo and optimal octave stretching"
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| * 2.5.11.13 WE (92.483c)
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| * 2.5.7.13 WE (92.804c)
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| * 2.3 WE (91.405c) (good for opposite 7 mapping)
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| * 38zpi (92.531c)
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| 104edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| ; Medium-priority
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| 25edo
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| {{harmonics in equal | 25 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 26edo
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| {{harmonics in equal | 26 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 29edo
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| {{harmonics in equal | 29 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 30edo
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| {{harmonics in equal | 30 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 35edo
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| {{harmonics in equal | 35 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 36edo
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| {{harmonics in equal | 36 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 37edo
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| {{harmonics in equal | 37 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 38edo
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| {{harmonics in equal | 38 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 15edo
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| {{harmonics in equal | 15 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 9edo
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| {{harmonics in equal | 9 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 18edo
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| {{harmonics in equal | 18 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 24edo
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| {{harmonics in equal | 24 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(
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| 48edo
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| {{harmonics in equal | 48 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 5edo
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| {{harmonics in equal | 5 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 6edo
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| {{harmonics in equal | 6 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)s)
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| 10edo
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| {{harmonics in equal | 10 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 11edo
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| {{harmonics in equal | 11 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 34edo
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| {{harmonics in equal | 34 | 2 | 1 | intervals=integer | columns=12}} | |
| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| ; Low priority
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| 125edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 145edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 152edo
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| * 241edt
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| * 13-limit WE (7.894c)
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| * Best nearby ZPI(s)
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| 159edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 166edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 182edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 198edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 212edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 243edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 247edo
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| * Nearby edt, ed6, ed12 and/or edf
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| * Nearby ed5, ed10, ed7 and/or ed11 (optional)
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| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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