User:BudjarnLambeth/Draft related tunings section: Difference between revisions
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; [[21edf]] | ; [[21edf]] | ||
* Step size: 33.426{{c}} | |||
* Octave size: 1203.3{{c}} | |||
{{Harmonics in equal|21|3|2|columns=12|collapsed=true}} | {{Harmonics in equal|21|3|2|columns=12|collapsed=true}} | ||
{{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}} | {{Harmonics in equal|21|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 21edf (continued)}} | ||
Stretching the octave of 36edo by | Stretching the octave of 36edo by a little over 3{{c}} results in improved primes 5, 11, and 13, but worse primes 2, 3, and 7. This approximates all primes up to 11 within ''12.0{{c}}''. The tuning 21edf does this. | ||
; [[57edt]] | |||
; [[57edt]] | |||
* Step size: 33.368{{c}} | |||
* Octave size: 1201.2{{c}} | |||
{{Harmonics in equal|57|3|1|columns=12|collapsed=true}} | {{Harmonics in equal|57|3|1|columns=12|collapsed=true}} | ||
{{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}} | {{Harmonics in equal|57|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 57edt (continued)}} | ||
If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all primes up to 11 within ''16.6{{c}}''. | If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1{{c}} optimises 36edo for that dual-5 usage, while also making slight improvements to primes 3, 7, 11, and 13. This approximates all primes up to 11 within ''16.6{{c}}''. Five almost-identical tunings do this: 57edt, [[101ed7]], [[zpi|155zpi]], and the [[TE]] and [[WE]] 2.3.7.13 subgroup WE tunings of 36edo. | ||
; Pure-octaves 36edo | ; Pure-octaves 36edo | ||
* Step size: 33.333{{c}} | |||
* Octave size: 1200.0{{c}} | |||
Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''. | Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''. | ||
Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within ''9.7{{c}}''. The 11- and 13-limit | ; [[TE|11-limit TE 36edo]] | ||
* Step size: 33.287{{c}} | |||
* Octave size: 1198.3{{c}} | |||
{{Harmonics in cet|33.287|columns=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo}} | |||
{{Harmonics in cet|33.287|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo (continued)}} | |||
Compressing the octave of 36edo by about 2{{c}} results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within ''9.7{{c}}''. The 11- and 13-limit TE tunings of 36edo both do this, as do their respective WE tunings. | |||
= Example (36edo without table) = | = Example (36edo without table) = | ||