User:BudjarnLambeth/Sandbox2: Difference between revisions

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= Title1 =

33edo ~~(reduce # of edonoi)~~

== Octave stretch or compression ==

What follows is a comparison of stretched- and compressed-octave 33edo tunings.

76ed5

; [[76ed5]]

92ed7 (137zpi's octave differs by only 0.3 ¢)

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

52ed13

_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.

114ed11

{{Harmonics in equal|76|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

138zpi (36.394c) (122ed13's octave differs by only 0.1 ¢)

{{Harmonics in equal|76|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

13-limit WE (36.357c)

93ed7 (optimised for dual-fifths)

; [[92ed7]] (137zpi's octave differs by only 0.3 ¢)

77ed5 (139zpi's octave differs by only 0.2 ¢)

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

123ed13 / 1ed47/46 (identical within <0.1 ¢)

_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.

115ed11

{{Harmonics in equal|92|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|92|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

; [[52ed13]]

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

{{Harmonics in equal|52|13|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|52|13|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

; [[114ed11]]

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

{{Harmonics in equal|114|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|114|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

; [[zpi|138zpi]] (36.394c) (122ed13's octave differs by only 0.1 ¢)

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

{{Harmonics in cet|36.394|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}

{{Harmonics in cet|36.394|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}

; [[WE|33et, 13-limit WE tuning]] (36.357c)

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

{{Harmonics in cet|36.357|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}

{{Harmonics in cet|36.357|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}

; 33edo

* Step size: 36.363{{c}}, octave size: NNN{{c}}

Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.

{{Harmonics in equal|33|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}

{{Harmonics in equal|33|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}

; [[93ed7]] (optimised for dual-fifths)

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

{{Harmonics in equal|93|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|93|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

; [[77ed5]] (139zpi's octave differs by only 0.2 ¢)

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

{{Harmonics in equal|77|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|77|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

; [[123ed13 / 1ed47/46]] (identical within <0.1 ¢)

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

{{Harmonics in equal|123|13|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|123|13|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

; [[115ed11]]

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

{{Harmonics in equal|115|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}

{{Harmonics in equal|115|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}

= Title2 =

@@ Line 4: / Line 4: @@
 = Title1 =
-edo (reduce # of edonoi)
+== Octave stretch or compression ==
+What follows is a comparison of stretched- and compressed-octave 33edo tunings.
-ed5
+; [[76ed5]]
-ed7 (137zpi's octave differs by only 0.3 ¢)
+* Step size: NNN{{c}}, octave size: NNN{{c}}
-ed13
+_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.
-ed11
+{{Harmonics in equal|76|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
-zpi (36.394c) (122ed13's octave differs by only 0.1 ¢)
+{{Harmonics in equal|76|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
--limit WE (36.357c)
-ed7 (optimised for dual-fifths)
+; [[92ed7]] (137zpi's octave differs by only 0.3 ¢)
-ed5 (139zpi's octave differs by only 0.2 ¢)
+* Step size: NNN{{c}}, octave size: NNN{{c}}
-ed13 / 1ed47/46 (identical within <0.1 ¢)
+_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.
-ed11
+{{Harmonics in equal|92|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|92|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+; [[52ed13]]
+* Step size: NNN{{c}}, octave size: NNN{{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.
+{{Harmonics in equal|52|13|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|52|13|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+; [[114ed11]]
+* Step size: NNN{{c}}, octave size: NNN{{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.
+{{Harmonics in equal|114|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|114|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+; [[zpi|138zpi]] (36.394c) (122ed13's octave differs by only 0.1 ¢)
+* Step size: NNN{{c}}, octave size: NNN{{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.
+{{Harmonics in cet|36.394|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ZPINAME}}
+{{Harmonics in cet|36.394|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ZPINAME (continued)}}
+; [[WE|33et, 13-limit WE tuning]] (36.357c)
+* Step size: NNN{{c}}, octave size: NNN{{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.
+{{Harmonics in cet|36.357|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning}}
+{{Harmonics in cet|36.357|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in ETNAME, SUBGROUP WE tuning (continued)}}
+; 33edo
+* Step size: 36.363{{c}}, octave size: NNN{{c}}
+Pure-octaves EDONAME approximates all harmonics up to 16 within NNN{{c}}.
+{{Harmonics in equal|33|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONAME}}
+{{Harmonics in equal|33|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONAME (continued)}}
+; [[93ed7]] (optimised for dual-fifths)
+* Step size: NNN{{c}}, octave size: NNN{{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.
+{{Harmonics in equal|93|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|93|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+; [[77ed5]] (139zpi's octave differs by only 0.2 ¢)
+* Step size: NNN{{c}}, octave size: NNN{{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.
+{{Harmonics in equal|77|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|77|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+; [[123ed13 / 1ed47/46]] (identical within <0.1 ¢)
+* Step size: NNN{{c}}, octave size: NNN{{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.
+{{Harmonics in equal|123|13|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|123|13|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
+; [[115ed11]]
+* Step size: NNN{{c}}, octave size: NNN{{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.
+{{Harmonics in equal|115|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in EDONOI}}
+{{Harmonics in equal|115|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in EDONOI (continued)}}
 = Title2 =