User:BudjarnLambeth/Sandbox2: Difference between revisions

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


== Octave stretch or compression ==
== Lab ==
18edo's [[prime]]s 3, 5, 7 and 13 are all tuned sharp, so it can benefit from [[octave shrinking]].
=== Compressed 49edo ===
{{Harmonics in equal|49|2|1|intervals=integer|columns=12}}
{{Harmonics in cet|24.419|intervals=integer|columns=12}}
{{Harmonics in equal|176|12|1|intervals=integer|columns=12}}
{{Harmonics in equal|170|11|1|intervals=integer|columns=12}}
{{Harmonics in equal|163|10|1|intervals=integer|columns=12}}
{{Harmonics in equal|138|7|1|intervals=integer|columns=12}}
{{Harmonics in equal|127|6|1|intervals=integer|columns=12}}
{{Harmonics in equal|114|5|1|intervals=integer|columns=12}}
{{Harmonics in equal|78|3|1|intervals=integer|columns=12}}


; 18edo
=== Stretched 50edo ===
* Step size: 66.667{{c}}, octave size: 1200.0{{c}}
{{Harmonics in equal|50|2|1|intervals=integer|columns=12}}
Pure-octaves 18edo approximates all harmonics up to 15 within 31.4{{c}}.
{{Harmonics in cet|24.030|intervals=integer|columns=12}}
{{Harmonics in equal|18|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18edo}}
{{Harmonics in equal|185|13|1|intervals=integer|columns=12}}
{{Harmonics in equal|18|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18edo (continued)}}
{{Harmonics in equal|179|12|1|intervals=integer|columns=12}}
 
{{Harmonics in equal|166|10|1|intervals=integer|columns=12}}
; [[WE|18et, 13-limit WE tuning]]
{{Harmonics in equal|140|7|1|intervals=integer|columns=12}}
* Step size: 66.291{{c}}, octave size: 1193.2{{c}}
{{Harmonics in equal|129|6|1|intervals=integer|columns=12}}
Compressing the octave of 18edo by around 7{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 15 within 25.3{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
{{Harmonics in equal|116|5|1|intervals=integer|columns=12}}
{{Harmonics in cet|66.291|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning}}
{{Harmonics in equal|79|3|1|intervals=integer|columns=12}}
{{Harmonics in cet|66.291|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 18et, 13-limit WE tuning (continued)}}
 
; [[zpi|61zpi]]
* Step size: 66.228{{c}}, octave size: 1192.1{{c}}
Compressing the octave of 18edo by around 8{{c}} results in improved primes 3, 5, 7 and 13, but worse primes 2 and 11. This approximates all harmonics up to 15 within 28.9{{c}}. The tuning 61zpi does this.
{{Harmonics in cet| 66.228 |intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 61zpi}}
{{Harmonics in cet| 66.228 |intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 61zpi (continued)}}
 
; [[65ed12]]
* Octave size: 1191.3{{c}}
Compressing the octave of 18edo by around 9{{c}} results in improved primes 3, 5, 7 and 13, but a worse primes 2. This approximates all harmonics up to 15 within 31.4{{c}}. The tuning 65ed12 does this.
{{Harmonics in equal|65|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 65ed12}}
{{Harmonics in equal|65|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 65ed12 (continued)}}
 
; [[47ed6]]
* Step size: NNN{{c}}, octave size: 1188.0{{c}}
Compressing the octave of 18edo by around 12{{c}} results in improved primes 3, 7, 11 and 13, but worse primes 2 and 5. This approximates all harmonics up to 15 within 29.9{{c}}. The tuning 47ed6 does this.
{{Harmonics in equal|47|6|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 47ed6}}
{{Harmonics in equal|47|6|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 47ed6 (continued)}}