27edo: Difference between revisions
→Octave stretch or compression: the 11-limit patent val makes no sense either. Lol. Replace with 2.3.5.7.13-subgroup tunings. Misc. clarifications |
→Octave stretch or compression: The previous edit left in the names of some of the things it replaced in some places |
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; [[WE|27et, 2.3.5.7.13-subgroup WE tuning]] | ; [[WE|27et, 2.3.5.7.13-subgroup WE tuning]] | ||
* Step size: 44.326{{c}}, octave size: 1196.796{{c}} | * Step size: 44.326{{c}}, octave size: 1196.796{{c}} | ||
Compressing the octave of 27edo by around 3.2{{c}} results in substantially improved primes 3, 5 and 7 at little cost. This approximates all harmonics up to 16 but 11 within 12.8{{c}}. Both 2.3.5.7.13-subgroup TE and WE tunings do this. | Compressing the octave of 27edo by around 3.2{{c}} results in substantially improved primes 3, 5 and 7 at little cost. This approximates all harmonics up to 16 but 11 within 12.8{{c}}. Both the 2.3.5.7.13-subgroup [[TE]] and WE tunings do this. | ||
{{Harmonics in cet|44.325787|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 27et, | {{Harmonics in cet|44.325787|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 27et, 2.3.5.7.13-subgroup WE tuning}} | ||
{{Harmonics in cet|44.325787|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 27et, | {{Harmonics in cet|44.325787|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 27et, 2.3.5.7.13-subgroup WE tuning (continued)}} | ||
; [[ZPI|106zpi]] / [[WE|27et, 7-limit WE tuning]] / [[70ed6]] | ; [[ZPI|106zpi]] / [[WE|27et, 7-limit WE tuning]] / [[70ed6]] | ||
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* Step size (7-limit WE): 44.306, octave size (7-limit WE): 1196.273{{c}} | * Step size (7-limit WE): 44.306, octave size (7-limit WE): 1196.273{{c}} | ||
* Step size (106zpi): 44.302{{c}}, octave size (106zpi): 1196.163{{c}} | * Step size (106zpi): 44.302{{c}}, octave size (106zpi): 1196.163{{c}} | ||
Compressing the octave of 27edo by around 3.5 to 3.8{{c}} results in even more improvement to primes 3, 5 and 7 than the 13 | Compressing the octave of 27edo by around 3.5 to 3.8{{c}} results in even more improvement to primes 3, 5 and 7 than the 2.3.5.7.13 tuning, but now at the cost of moderate damage to 2 and 13. This approximates all harmonics up to 16 within 15.4{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this. So do the tunings 106zpi and 70ed6. | ||
{{Harmonics in cet|44.302326|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 106zpi}} | {{Harmonics in cet|44.302326|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 106zpi}} | ||
{{Harmonics in cet|44.302326|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 106zpi (continued)}} | {{Harmonics in cet|44.302326|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 106zpi (continued)}} | ||