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

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 == Octave stretch or compression ==
 What follows is a comparison of stretched- and compressed-octave 36edo tunings.
-Of the stretched-octave tunings listed, ''36ed513/256'', with a step size about 33.4 cents, performs best in this comparison, approximating all 11-limit primes with less than 36% relative error (< 12 cents error).
-Of the compressed-octave tunings listed, ''36ed511/256'', with a step size about 33.25 cents, performs best in this comparison, approximating all 11-limit primes with less than 36% relative error (< 12 cents error).
-The [[edonoi]] scales of [[57edt]] and [[101ed7]] are almost exactly the same as 36edo. They are 36edo with the octave stretched by less than 1{{c}}. Their main usage is to optimise 36edo for use as a [[dual-n|dual-5]] tuning, while also making slight improvements to 3/1 and 7/1 as well. So if one intends to use both 36edo's vals for 5/1 at once, 57edt or 101ed7 may be worth considering.
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+; 36ed513/256
+Stretching the octave of 36edo by about 3.5 cents results in much improved primes 5 and 11, but a much worse prime 7. This approximates all primes up to 11 within 12 cents.
+; 57edt or 2.3.7.13 WE 36edo
+If one intends to use both 36edo's vals for 5/1 at once, stretching the octave of 36edo by about 1 cent 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 17 cents.
+; Pure-octaves 36edo
+Pure-octaves 36edo approximates all primes up to 11 within 16 cents.
+; 11-limit WE 36edo
+Compressing the octave of 36edo by about 2 cents results in much improved primes 5 and 11, but much worse primes 7 and 13. This approximates all primes up to 11 within 10 cent.