User:BudjarnLambeth/Draft related tunings section: Difference between revisions

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{{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}}''. Four almost identical tunings do this: 57edt, [[101ed7]], [[zpi|155zpi]], and the [[WE|2.3.7.13 subgroup WE tuning of 36edo]].
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.




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; [[WE|11-limit WE 36edo]]
; [[TE|11-limit TE 36edo]]
* Step size: 33.286{{c}}
* Step size: 33.287{{c}}
* Octave size: 1198.3{{c}}
* Octave size: 1198.3{{c}}
{{Harmonics in cet|33.286|columns=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo}}
{{Harmonics in cet|33.287|columns=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo}}
{{Harmonics in cet|33.286|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11lim WE-tuned 36edo (continued)}}
{{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 WE tunings of 36edo both do this, as do their respective [[TE]] tunings.
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.