User:BudjarnLambeth/Sandbox2: Difference between revisions

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[[User:BudjarnLambeth/Draft related tunings section]]

= Title1 =

== Octave stretch or compression ==

What follows is a comparison of stretched- and compressed-octave ~~EDONAME~~ tunings.

What follows is a comparison of stretched- and compressed-octave 42edo tunings.

; [[~~zpi~~|~~ZPINAME~~]]

; [[ed6|108ed6]]

* Step size: NNN{{c}}, octave size: ~~NNN~~{{c}}

* Step size: NNN{{c}}, octave size: 1206.3{{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.

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 ~~cet~~|~~100~~|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~ZPINAME~~}}

{{Harmonics in equal|108|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 108ed6}}

{{Harmonics in ~~cet~~|~~100~~|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~ZPINAME~~ (continued)}}

{{Harmonics in equal|108|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 108ed6 (continued)}}

; [[~~EDONOI~~]]

; [[zpi|189zpi]]

* Step size: ~~NNN~~{{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}}. The tuning ~~EDONOI~~ does 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 ~~equal~~|~~12|2|1~~|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~}}

{{Harmonics in cet|28.689|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 189zpi}}

{{Harmonics in ~~equal~~|~~12|2|1~~|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~ (continued)}}

{{Harmonics in cet|28.689|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 189zpi (continued)}}

; [[WE|~~ETNAME, SUBGROUP WE tuning~~]]

; [[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}}. ~~Its SUBGROUP WE~~ tuning ~~and SUBGROUP [[TE]] tuning both do~~ 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 ~~cet~~|~~100~~|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~ETNAME, SUBGROUP WE tuning~~}}

{{Harmonics in equal|150|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 150ed12}}

{{Harmonics in ~~cet~~|~~100~~|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~ETNAME, SUBGROUP WE tuning~~ (continued)}}

{{Harmonics in equal|150|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 150ed12 (continued)}}

; ~~EDONAME~~

; [[equal tuning|145ed11]]

* Step size: NNN{{c}}, octave size: ~~NNN~~{{c}}

* Step size: NNN{{c}}, octave size: 1202.5{{c}}

~~Pure-octaves EDONAME~~ approximates all harmonics up to 16 within NNN{{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|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~EDONAME~~}}

{{Harmonics in equal|145|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 145ed11}}

{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~EDONAME~~ (continued)}}

{{Harmonics in equal|145|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 145ed11 (continued)}}

; ~~[[WE|ETNAME, SUBGROUP WE tuning]]~~

; 42edo

* Step size: NNN{{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~~|~~100~~|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~~|~~100~~|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)}}

; [[~~EDONOI~~]]

; [[ed7|118ed7]]

* Step size: NNN{{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 ~~EDONOI~~ 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 equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~}}

{{Harmonics in equal|118|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 118ed7}}

{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~EDONOI~~ (continued)}}

{{Harmonics in equal|118|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 118ed7 (continued)}}

; [[~~zpi~~|~~ZPINAME~~]]

; [[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 ~~ZPINAME~~ does this.

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 cet|~~100~~|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ~~ZPINAME~~}}

{{Harmonics in cet|28.534|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 42et, 13-limit WE tuning}}

{{Harmonics in cet|~~100~~|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ~~ZPINAME~~ (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 =

Line 67:

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; High-priority

~~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

54edo

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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)

38edo

{{harmonics in equal | 38 | 2 | 1 | intervals=integer | columns=12}}

* Nearby edt, ed6, ed12 and/or edf

* Nearby ed5, ed10, ed7 and/or ed11 (optional)

Line 217:

Line 236:

* 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 ed5, ed10, ed7 and/or ed11 (optional)

Line 224:

Line 243:

* 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 ed5, ed10, ed7 and/or ed11 (optional)

Line 231:

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* 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 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)

@@ Line 3: / Line 3: @@
 [[User:BudjarnLambeth/Draft related tunings section]]
+= Title1 =
 == Octave stretch or compression ==
-What follows is a comparison of stretched- and compressed-octave EDONAME tunings.
+What follows is a comparison of stretched- and compressed-octave 42edo tunings.
-; [[zpi|ZPINAME]]
+; [[ed6|108ed6]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1206.3{{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.
+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 cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
+{{Harmonics in equal|108|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 108ed6}}
-{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
+{{Harmonics in equal|108|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 108ed6 (continued)}}
-; [[EDONOI]]
+; [[zpi|189zpi]]
-* Step size: NNN{{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}}. The tuning EDONOI does 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 equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in cet|28.689|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 189zpi}}
-{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+{{Harmonics in cet|28.689|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 189zpi (continued)}}
-; [[WE|ETNAME, SUBGROUP WE tuning]]
+; [[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}}. Its SUBGROUP WE tuning and SUBGROUP [[TE]] tuning both do 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 cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
+{{Harmonics in equal|150|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 150ed12}}
-{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
+{{Harmonics in equal|150|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 150ed12 (continued)}}
-; EDONAME
+; [[equal tuning|145ed11]]
-* Step size: NNN{{c}}, octave size: NNN{{c}}
+* Step size: NNN{{c}}, octave size: 1202.5{{c}}
-Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{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|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
+{{Harmonics in equal|145|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 145ed11}}
-{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}
+{{Harmonics in equal|145|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 145ed11 (continued)}}
-; [[WE|ETNAME, SUBGROUP WE tuning]]
+; 42edo
-* Step size: NNN{{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|100|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|100|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)}}
-; [[EDONOI]]
+; [[ed7|118ed7]]
-* Step size: NNN{{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 EDONOI 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 equal|12|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|118|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 118ed7}}
-{{Harmonics in equal|12|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+{{Harmonics in equal|118|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 118ed7 (continued)}}
-; [[zpi|ZPINAME]]
+; [[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 ZPINAME does this.
+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 cet|100|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
+{{Harmonics in cet|28.534|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 42et, 13-limit WE tuning}}
-{{Harmonics in cet|100|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (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 =
@@ Line 67: / Line 92: @@
 ; High-priority
-edo (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
 edo
@@ Line 170: / Line 182: @@
 edo
 {{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)
+edo
+{{harmonics in equal | 38 | 2 | 1 | intervals=integer | columns=12}}
 * Nearby edt, ed6, ed12 and/or edf
 * Nearby ed5, ed10, ed7 and/or ed11 (optional)
@@ Line 217: / Line 236: @@
 * Best nearby ZPI(s)
 edo
-{{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 ed5, ed10, ed7 and/or ed11 (optional)
@@ Line 224: / Line 243: @@
 * Best nearby ZPI(s)
 edo
-{{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 ed5, ed10, ed7 and/or ed11 (optional)
@@ Line 231: / Line 250: @@
 * Best nearby ZPI(s)
 edo
-{{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)
-edo
-{{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)
-edo
-{{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)