User:BudjarnLambeth/Sandbox2: Difference between revisions

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

; [[ed5|76ed5]]  

* Octave size: 1209.8{{c}}

Stretching the octave of 33edo by around 10{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 76ed5 does this.

{{Harmonics in equal|76|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 76ed5}}

{{Harmonics in equal|76|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 76ed5 (continued)}}

; [[ed7|92ed7]]

* Octave size: 1208.4{{c}}

Stretching the octave of 33edo by around 8.5{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 92ed7 does this. So does the tuning [[zpi|137zpi]] whose octave differs by only 0.3{{c}}.

{{Harmonics in equal|92|7|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 92ed7}}

{{Harmonics in equal|92|7|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 92ed7 (continued)}}

; [[equal tuning|114ed11]]  

* Octave size: 1201.7{{c}}

Stretching the octave of 33edo 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 114ed11 does this.

{{Harmonics in equal|114|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 114ed11}}

{{Harmonics in equal|114|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 114ed11 (continued)}}

; [[zpi|138zpi]]

* Step size: 36.394{{c}}, octave size: 1201.0{{c}}

Stretching the octave of 33edo 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 138zpi does this. So does the tuning [[equal tuning|122ed13]] whose octave differs by only 0.1{{c}}.

{{Harmonics in cet|36.394|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 138zpi}}

{{Harmonics in cet|36.394|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 138zpi (continued)}}

; 33edo

* Step size: 36.363{{c}}, octave size: 1200.0{{c}}  

Pure-octaves 33edo 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 33edo}}

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

; [[WE|33et, 13-limit WE tuning]]

* Step size: 36.357{{c}}, octave size: 1199.8{{c}}

Compressing the octave of 33edo by a fifth of 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 cet|36.357|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 33et, 13-limit WE tuning}}

{{Harmonics in cet|36.357|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 33et, 13-limit WE tuning (continued)}}

; [[ed5|77ed5]]

* Octave size: 1194.1{{c}}

Compressing the octave of 33edo 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 77ed5 does this. So does the tuning [[zpi|139zpi]] whose octave differs by only 0.2{{c}}.

{{Harmonics in equal|77|5|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 77ed5}}

{{Harmonics in equal|77|5|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 77ed5 (continued)}}

; [[equal tuning|115ed11]]  

* Octave size: 1191.2{{c}}

Compressing the octave of 33edo by around 9{{c}} results in improved primes NNN, but worse primes NNN. This approximates all harmonics up to 16 within NNN{{c}}. The tuning 115ed11 does this. So do the tunings [[equal tuning|123ed13]] and [[AS|1ed47/46]] whose octaves are within 0.3{{c}} of 115ed11.

{{Harmonics in equal|115|11|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 115ed11}}

{{Harmonics in equal|115|11|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 115ed11 (continued)}}