Xenharmonic Wiki

User:BudjarnLambeth/Sandbox2: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,543 edits
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,543 edits
 
(11 intermediate revisions by the same user not shown)
Line 4: Line 4:


= Title1 =
= Title1 =
; [[zpi|209zpi]]
== Octave stretch or compression ==
* Step size: 26.550{{c}}, octave size: NNN{{c}}
What follows is a comparison of stretched- and compressed-octave 42edo tunings.
_ing 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|26.550|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in cet|26.550|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}


; 45edo
; [[ed6|108ed6]]
* Step size: 26.667{{c}}, octave size: NNN{{c}}  
* Step size: NNN{{c}}, octave size: 1206.3{{c}}
Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
Stretching the octave of 42edo 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 108ed6 does this. So does the tuning [[97ed5]] whose octave differs by only 0.1{{c}}.
{{Harmonics in equal|45|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
{{Harmonics in equal|108|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 108ed6}}
{{Harmonics in equal|45|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}
{{Harmonics in equal|108|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 108ed6 (continued)}}


; [[WE|ETNAME, SUBGROUP WE tuning]]  
; [[zpi|189zpi]]  
* Step size: 26.695{{c}}, octave size: NNN{{c}}
* Step size: 28.689{{c}}, octave size: 1204.9{{c}}
_ing 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.
Stretching the octave of 42edo by around 5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 189zpi does this.
{{Harmonics in cet|26.695|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in cet|28.689|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 189zpi}}
{{Harmonics in cet|26.695|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
{{Harmonics in cet|28.689|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 189zpi (continued)}}


; [[161ed12]]  
; [[ed12|150ed12]]  
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: NNN{{c}}, octave size: 1204.5{{c}}
_ing 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.
Stretcing the octave of 42edo 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 150ed12 does this.
{{Harmonics in equal|161|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|150|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 150ed12}}
{{Harmonics in equal|161|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in equal|150|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 150ed12 (continued)}}


; [[116ed6]]  
; [[equal tuning|145ed11]]  
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: NNN{{c}}, octave size: 1202.5{{c}}
_ing 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. So does [[ed7|126ed7]] whose octave is identical within 0.1{{c}}.
Stretching the octave of 42edo by around 2.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 145ed11 does this.
{{Harmonics in equal|116|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in equal|145|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 145ed11}}
{{Harmonics in equal|116|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in equal|145|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 145ed11 (continued)}}


; [[WE|45et, 7-limit WE tuning]]
; 42edo
* Step size: 26.745{{c}}, octave size: NNN{{c}}
* Step size: NNN{{c}}, octave size: 1200.0{{c}}  
_ing 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.
Pure-octaves 42edo approximates all harmonics up to 16 within NNN{{c}}. The tuning [[zpi|190zpi]] is almost exactly the same as pure-octaves 42edo, its octave differing by less than 0.05{{c}}.
{{Harmonics in cet|26.745|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
{{Harmonics in equal|42|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 42edo}}
{{Harmonics in cet|26.745|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
{{Harmonics in equal|42|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 42edo (continued)}}


; [[zpi|207zpi]]  
; [[ed7|118ed7]]  
* Step size: 26.762{{c}}, octave size: NNN{{c}}
* Step size: NNN{{c}}, octave size: 1199.1{{c}}
_ing 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.
Compressing the octave of 42edo by around 1{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 118ed7 does this.
{{Harmonics in cet|26.762|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
{{Harmonics in equal|118|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 118ed7}}
{{Harmonics in cet|26.762|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
{{Harmonics in equal|118|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 118ed7 (continued)}}


; [[71edt]]  
; [[WE|42et, 13-limit WE tuning]]
* Step size: NNN{{c}}, octave size: NNN{{c}}
* Step size: 28.534{{c}}, octave size: 1198.4{{c}}
_ing 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. So does the tuning [[equal tuning|155ed11]] whose octave is identical within 0.3{{c}}.
Compressing the octave of 42edo by around 1.5{{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|71|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
{{Harmonics in cet|28.534|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 42et, 13-limit WE tuning}}
{{Harmonics in equal|71|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
{{Harmonics in cet|28.534|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 42et, 13-limit WE tuning (continued)}}
 
; [[ed12|151ed12]]  
* Step size: NNN{{c}}, octave size: 1196.6{{c}}
Compressing the octave of 42edo 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 151ed12 does this. So do the 7-limit [[WE]] and [[TE]] tunings of 42et, whose octaves are within 0.3{{c}} of 151ed12.
{{Harmonics in equal|151|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 151ed12}}
{{Harmonics in equal|151|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 151ed12 (continued)}}
 
; [[ed6|109ed6]]
* Step size: NNN{{c}}, octave size: 1195.2{{c}}
Compressing the octave of 42edo by around 5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 109ed6 does this.
{{Harmonics in equal|109|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 109ed6}}
{{Harmonics in equal|109|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 109ed6 (continued)}}
 
; [[zpi|191zpi]]  
* Step size: 28.444{{c}}, octave size: 1194.6{{c}}
Compressing the octave of 42edo 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 191zpi does this.
{{Harmonics in cet|28.444|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 191zpi}}
{{Harmonics in cet|28.444|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 191zpi (continued)}}
 
; [[67edt]]
* Step size: NNN{{c}}, octave size: 1192.3{{c}}
Compressing the octave of 42edo by around 7.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 67edt does this.
{{Harmonics in equal|67|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 67edt}}
{{Harmonics in equal|67|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 67edt (continued)}}


= Title2 =
= Title2 =
Line 71: Line 92:


; High-priority
; High-priority
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
54edo
Line 103: Line 115:
* 230ed12
* 230ed12
* 149ed5
* 149ed5
42edo (reduce # of edonoi)
* 108ed6 (octave is identical to 97ed5 within 0.1{{c}})
* 189zpi (28.689c)
* 150ed12
* 145ed11
''190zpi's octave is within 0.05{{c}} of pure-octaves 42edo''
* 118ed7
* 13-limit WE (28.534c)
* 151ed12 (octave is identical to 7-limit WE within 0.3{{c}})
* 109ed6
* 191zpi (28.444c)
* 67edt


59edo (reduce # of edonoi or zpi)
59edo (reduce # of edonoi or zpi)
Line 183: Line 182:
37edo
37edo
{{harmonics in equal | 37 | 2 | 1 | intervals=integer | columns=12}}
{{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)
38edo
{{harmonics in equal | 38 | 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 230: Line 236:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


5edo
24edo
{{harmonics in equal | 5 | 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 237: Line 243:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


6edo
5edo
{{harmonics in equal | 6 | 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 244: Line 250:
* Best nearby ZPI(s)
* Best nearby ZPI(s)


20edo
6edo
{{harmonics in equal | 20 | 2 | 1 | intervals=integer | columns=12}}
{{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)
 
24edo
{{harmonics in equal | 24 | 2 | 1 | intervals=integer | columns=12}}
* Nearby edt, ed6, ed12 and/or edf
* Nearby edt, ed6, ed12 and/or edf
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* Nearby ed5, ed10, ed7 and/or ed11 (optional)
* 1-2 WE tunings
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(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)
; Low priority


13edo
13edo
Line 302: Line 292:
* 1-2 WE tunings
* 1-2 WE tunings
* Best nearby ZPI(s)
* Best nearby ZPI(s)
; Low priority


104edo
104edo
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Sandbox2"