36edo: Difference between revisions
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Another 5-limit alternative val is {{val| 36 57 83 }} (36c-edo), which is similar to the patent val but has 5/4 mapped to the 367{{c}} submajor third rather than the major third. This mapping supports very sharp [[porcupine]] temperament using 5\36 as a generator. | Another 5-limit alternative val is {{val| 36 57 83 }} (36c-edo), which is similar to the patent val but has 5/4 mapped to the 367{{c}} submajor third rather than the major third. This mapping supports very sharp [[porcupine]] temperament using 5\36 as a generator. | ||
=== Octave stretch === | === Octave stretch === | ||
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| 33.37 || 4 || 0 || 50 || 5 || 40 || 36 || 57 || 83 || 101 || 124 | | 33.37 || 4 || 0 || 50 || 5 || 40 || 36 || 57 || 83 || 101 || 124 | ||
|- | |- | ||
! 155zpi | ! 155zpi & 101ed7 (basically identical) | ||
| 33.35 || 2 || 3 || 45 || 1 || 48 || 36 || 57 || 84 || 101 || 124 | | 33.35 || 2 || 3 || 45 || 1 || 48 || 36 || 57 || 84 || 101 || 124 | ||
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| 33.145 || 21 || 38 || 6 || 36 || 25 || 36 || 57 || 84 || 102 || 125 | | 33.145 || 21 || 38 || 6 || 36 || 25 || 36 || 57 || 84 || 102 || 125 | ||
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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]]. | |||
=== Subsets and supersets === | === Subsets and supersets === | ||