User:BudjarnLambeth/Draft related tunings section: Difference between revisions
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* It is okay to add only the descriptive text and collapsed harmonic tables to an edo page initially, and to add the full comparison table at a later date; this should make life easier for editors on mobile devices who might want to help but find tables difficult to edit. | * It is okay to add only the descriptive text and collapsed harmonic tables to an edo page initially, and to add the full comparison table at a later date; this should make life easier for editors on mobile devices who might want to help but find tables difficult to edit. | ||
= Example (36edo) = | = Example (36edo with table) = | ||
== Octave stretch or compression == | == Octave stretch or compression == | ||
What follows is a comparison of stretched- and compressed-octave 36edo tunings. | What follows is a comparison of stretched- and compressed-octave 36edo tunings. | ||
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; [[21edf]] | |||
{{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)}} | |||
Stretching the octave of 36edo by about 3.5{{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]] / [[ed7|101ed7]] / [[zpi|155zpi]] / [[WE|2.3.7.13 WE-tuned 36edo]] | |||
{{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)}} | |||
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, 155zpi, and the 2.3.7.13 subgroup WE tuning of 36edo. | |||
; Pure-octaves 36edo | |||
Pure-octaves 36edo approximates all primes up to 11 within ''15.3{{c}}''. | |||
; [[WE|11-limit WE 36edo / 13-limit WE 36edo]] | |||
{{Harmonics in cet|33.286|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)}} | |||
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. | |||
= Example (36edo without table) = | |||
== Octave stretch or compression == | |||
What follows is a comparison of stretched- and compressed-octave 36edo tunings. | |||
; [[21edf]] | ; [[21edf]] | ||