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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}} |
| What follows is a comparison of stretched- and compressed-octave 39edo tunings.
| | {{harmonics in equal|6|intervals=odd|columns=7}} |
| | | {{harmonics in equal|7|intervals=odd|columns=7}} |
| ; [[zpi|171zpi]]
| | {{harmonics in equal|8|intervals=odd|columns=7}} |
| * Step size: 30.973{{c}}, octave size: 107.9{{c}}
| | {{harmonics in equal|9|intervals=odd|columns=7}} |
| Stretching the octave of 39edo by around 8{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 171zpi does this. Because it shares error evenly between 39edo's fifths, it is suited for use as a [[dual-fifths tuning]] of 39edo.
| | {{harmonics in equal|10|intervals=odd|columns=7}} |
| {{Harmonics in cet|30.973|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 171zpi}} | | {{harmonics in equal|11|intervals=odd|columns=7}} |
| {{Harmonics in cet|30.973|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 171zpi (continued)}} | | {{harmonics in equal|12|intervals=odd|columns=7}} |
| | | {{harmonics in equal|13|intervals=odd|columns=7}} |
| ; 39edo
| | {{harmonics in equal|14|intervals=odd|columns=7}} |
| * Step size: 30.769{{c}}, octave size: 1200.00{{c}}
| | {{harmonics in equal|15|intervals=odd|columns=7}} |
| Pure-octaves 39edo approximates all harmonics up to 16 within NNN{{c}}.
| | {{harmonics in equal|16|intervals=odd|columns=7}} |
| {{Harmonics in equal|39|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 39edo}}
| | {{harmonics in equal|17|intervals=odd|columns=7}} |
| {{Harmonics in equal|39|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 39edo (continued)}} | | {{harmonics in equal|18|intervals=odd|columns=7}} |
| | | {{harmonics in equal|19|intervals=odd|columns=7}} |
| ; [[WE|39et, 13-limit WE tuning]]
| | {{harmonics in equal|20|intervals=odd|columns=7}} |
| * Step size: 30.757{{c}}, octave size: 1199.5{{c}}
| | {{harmonics in equal|21|intervals=odd|columns=7}} |
| Compressing the octave of 39edo by about half a cent 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|22|intervals=odd|columns=7}} |
| {{Harmonics in cet|30.757|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 39et, 13-limit WE tuning}}
| | {{harmonics in equal|23|intervals=odd|columns=7}} |
| {{Harmonics in cet|30.757|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 39et, 13-limit WE tuning (continued)}} | | {{harmonics in equal|24|intervals=odd|columns=7}} |
| | | {{harmonics in equal|25|intervals=odd|columns=7}} |
| ; [[ed6|101ed6]]
| | {{harmonics in equal|26|intervals=odd|columns=7}} |
| * Octave size: 1197.8{{c}}
| | {{harmonics in equal|27|intervals=odd|columns=7}} |
| Compressing the octave of 101ed6 by around 2{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 101ed6 does this. So does [[zpi|172zpi]] whose octave differs by only 0.4{{c}}.
| | {{harmonics in equal|28|intervals=odd|columns=7}} |
| {{Harmonics in equal|101|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 101ed6}} | | {{harmonics in equal|29|intervals=odd|columns=7}} |
| {{Harmonics in equal|101|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 101ed6 (continued)}} | | {{harmonics in equal|30|intervals=odd|columns=7}} |
| | | {{harmonics in equal|31|intervals=odd|columns=7}} |
| ; [[WE|39et, 2.3.5.11 WE tuning]]
| | {{harmonics in equal|32|intervals=odd|columns=7}} |
| * Step size: 30.703{{c}}, octave size: 1197.4{{c}}
| | {{harmonics in equal|33|intervals=odd|columns=7}} |
| Compressing the octave of 39edo by around 2.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. Its 2.3.5.11 WE tuning and 2.3.5.11 [[TE]] tuning both do this.
| | {{harmonics in equal|34|intervals=odd|columns=7}} |
| {{Harmonics in cet|30.703|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 39et, 2.3.5.11 WE tuning}}
| | {{harmonics in equal|35|intervals=odd|columns=7}} |
| {{Harmonics in cet|30.703|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 39et, 2.3.5.11 WE tuning (continued)}} | | {{harmonics in equal|36|intervals=odd|columns=7}} |
| | | {{harmonics in equal|37|intervals=odd|columns=7}} |
| ; [[zpi|173zpi]]
| | {{harmonics in equal|38|intervals=odd|columns=7}} |
| * Step size: 30.672{{c}}, octave size: 1196.2{{c}}
| | {{harmonics in equal|39|intervals=odd|columns=7}} |
| Compressing the octave of 39edo by around 4{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 173zpi does this. So does [[62edt]] whose octave differs by only 0.2{{c}}.
| | {{harmonics in equal|40|intervals=odd|columns=7}} |
| {{Harmonics in cet|30.672|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 173zpi}} | | {{harmonics in equal|41|intervals=odd|columns=7}} |
| {{Harmonics in cet|30.672|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 173zpi (continued)}} | | {{harmonics in equal|42|intervals=odd|columns=7}} |
| | | {{harmonics in equal|43|intervals=odd|columns=7}} |
| ; [[ed7|110ed7]]
| | {{harmonics in equal|44|intervals=odd|columns=7}} |
| * Octave size: 1194.4{{c}}
| | {{harmonics in equal|45|intervals=odd|columns=7}} |
| Compressing the octave of 39edo by around 5.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 110ed7 does this. So does [[equal tuning|145ed13]] whose octave differs by only 0.1{{c}}.
| | {{harmonics in equal|46|intervals=odd|columns=7}} |
| {{Harmonics in equal|110|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 110ed7}} | | {{harmonics in equal|47|intervals=odd|columns=7}} |
| {{Harmonics in equal|110|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 110ed7 (continued)}} | | {{harmonics in equal|48|intervals=odd|columns=7}} |
| | | {{harmonics in equal|49|intervals=odd|columns=7}} |
| ; [[ed5|91ed5]]
| | {{harmonics in equal|50|intervals=odd|columns=7}} |
| * Octave size: 1194.1{{c}}
| | {{harmonics in equal|51|intervals=odd|columns=7}} |
| Compressing the octave of 39edo by around 6{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 91ed5 does this.
| | {{harmonics in equal|52|intervals=odd|columns=7}} |
| {{Harmonics in equal|91|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 91ed5}}
| | {{harmonics in equal|53|intervals=odd|columns=7}} |
| {{Harmonics in equal|91|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 91ed5 (continued)}} | |
| | |
| = Title2 =
| |
| === Lab ===
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| Place holder
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| <br><br><br><br><br>
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| {{harmonics in cet | 300 | intervals=prime}} | |
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| {{harmonics in equal | 140 | 12 | 1 | intervals=prime}} | |
| | |
| === 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.
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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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| 39edo
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| * 171zpi (30.973c) (optimised for dual-fifths use)
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| * 13-limit WE (30.757c) (octave of 135ed11 differs by only 0.2{{c}})
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| * 101ed6 (octave of 172zpi differs by only 0.4{{c}})
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| * 173zpi (30.672c) (octave of 62edt differs by only 0.2{{c}})
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| * 110ed7 (octave of 145ed13 differs by only 0.1{{c}})
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| * 91ed5
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| 45edo
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| * 209zpi (26.550)
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| * 13-limit WE (26.695c)
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| * 161ed12
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| * 116ed6 (octave identical to 126ed7 within 0.1{{c}})
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| * 7-limit WE (26.745c)
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| * 207zpi (26.762)
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| * 71edt (octave identical to 155ed11 within 0.3{{c}})
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| 54edo
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| * 139ed6 (octave is identical to 262zpi within 0.2{{c}})
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| * 151ed7
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| * 193ed12
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| * 263zpi (22.243c)
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| * 13-limit WE (22.198c) (octave is identical to 187ed11 within 0.1{{c}})
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| * 264zpi (22.175c) (octave is identical to 194ed12 within 0.01{{c}})
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| * 152ed7
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| * 140ed6
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| * 126ed5 (octave is identical to 86edt within 0.1{{c}})
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| 64edo
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| * 179ed7 (octave is identical to 326zpi within 0.3{{c}})
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| * 165ed6
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| * 229ed12 (octave is identical to 221ed11 within 0.1{{c}})
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| * 327zpi (18.767c)
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| * 11-limit WE (18.755c)
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| ''pure octaves 64edo (octave is identical to 13-limit WE within 0.13{{c}}''
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| * 328zpi (18.721c)
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| * 180ed7
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| * 230ed12
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| * 149ed5
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| 42edo (reduce # of edonoi)
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| * 108ed6 (octave is identical to 97ed5 within 0.1{{c}})
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| * 189zpi (28.689c)
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| * 150ed12
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| * 145ed11
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| ''190zpi's octave is within 0.05{{c}} of pure-octaves 42edo''
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| * 118ed7
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| * 13-limit WE (28.534c)
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| * 151ed12 (octave is identical to 7-limit WE within 0.3{{c}})
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| * 109ed6
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| * 191zpi (28.444c)
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| * 67edt
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| 59edo (reduce # of edonoi or zpi)
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| * 152ed6
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| * 294zpi (20.399c)
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| * 211ed12
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| * 295zpi (20.342c)
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| ''pure octaves 59edo octave is identical to 137ed5 within 0.05{{c}}''
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| * 13-limit WE (20.320c)
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| * 7-limit WE (20.301c)
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| * 166ed7
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| * 212ed12
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| * 296zpi (20.282c)
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| * 153ed6
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| ; Medium 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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| 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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| 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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| ; Low priority
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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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| 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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| ; Optional
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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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| 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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| 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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| 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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| 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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| 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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| 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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| 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)
| |
| * 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)
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| 20edo
| |
| {{harmonics in equal | 20 | 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
| |
| {{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)
| |
| * 1-2 WE tunings
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| * Best nearby ZPI(s)
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| 28edo
| |
| {{harmonics in equal | 28 | 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)
| |
| * 1-2 WE tunings
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| * Best nearby ZPI(s)
| |