36edo: Difference between revisions

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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, 101ed7 may be worth considering.

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=== Additional properties ===

36edo also offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament.

The [[edonoi]] scales of [[57edt]] and [[101ed7]] are almost exactly the same as 36edo. It is 36edo with the [[stretched octave|octave stretched]] by less than 1{{c}}. Its 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, 101ed7 may be worth considering.

Thanks to its sevenths, 36edo is an ideal tuning for its size for [[metallic harmony]].

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 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, 101ed7 may be worth considering.
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 === Additional properties ===
 edo also offers a good approximation to the [[acoustic phi|acoustic golden ratio]], as 25\36. [[Heinz Bohlen]] proposed 36edo as a suitable temperament for approximating his 833-cents scale. The 13th harmonic (octave reduced) is so closely mapped on [[acoustic phi]] that 36edo could be treated as a 2.3.7.ϕ.17 temperament.
-The [[edonoi]] scales of [[57edt]] and [[101ed7]] are almost exactly the same as 36edo. It is 36edo with the [[stretched octave|octave stretched]] by less than 1{{c}}. Its 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, 101ed7 may be worth considering.
 Thanks to its sevenths, 36edo is an ideal tuning for its size for [[metallic harmony]].