User:BudjarnLambeth/Sandbox2: Difference between revisions
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What follows is a comparison of stretched-octave 31edo tunings. | What follows is a comparison of stretched-octave 31edo tunings. | ||
; | ; 31edo | ||
* Step size: 38.710{{c}}, octave size: 1200.0{{c}} | * Step size: 38.710{{c}}, octave size: 1200.0{{c}} | ||
Pure-octaves 31edo approximates all harmonics up to 16 within NNN{{c}}. | Pure-octaves 31edo approximates all harmonics up to 16 within NNN{{c}}. | ||
{{Harmonics in equal|31|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in | {{Harmonics in equal|31|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 31edo}} | ||
{{Harmonics in equal|31|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in | {{Harmonics in equal|31|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 31edo (continued)}} | ||
; [[WE|31et, 13-limit WE tuning]] | ; [[WE|31et, 13-limit WE tuning]] | ||
* Step size: 38.725{{c}}, octave size: | * Step size: 38.725{{c}}, octave size: 1200.5{{c}} | ||
Stretching the octave of 31edo by around | Stretching the octave of 31edo by around 0.5{{c}} results in slightly improved primes 3, 7 and 11, but slightly worse primes 2, 5 and 13. This approximates all harmonics up to 16 within 12.8{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this. | ||
{{Harmonics in cet|38.725|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 31et, 13-limit WE tuning}} | {{Harmonics in cet|38.725|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 31et, 13-limit WE tuning}} | ||
{{Harmonics in cet|38.725|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 31et, SUBGROUP WE tuning (continued)}} | {{Harmonics in cet|38.725|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 31et, SUBGROUP WE tuning (continued)}} | ||
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* Step size: 38.737{{c}}, octave size: NNN{{c}} | * Step size: 38.737{{c}}, octave size: NNN{{c}} | ||
Stretching the octave of 31edo 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 127zpi does this. | Stretching the octave of 31edo 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 127zpi does this. | ||
{{Harmonics in cet| | {{Harmonics in cet|38.737|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 127zpi}} | ||
{{Harmonics in cet| | {{Harmonics in cet|38.737|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 127zpi (continued)}} | ||
; [[WE|31et, 11-limit WE tuning]] | ; [[WE|31et, 11-limit WE tuning]] | ||