Alchemisma

Interval information

Factorization	2-82 × 3-1 × 536
Monzo	[-82 -1 36⟩
Size in cents	5.338698 ¢
Name	alchemisma
Color name	quinla-quadtritriyo negative 10th, L5y36-10
FJS name	[math]\displaystyle{ \text{20d}{-10}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	167.174
Weil norm (log2 max(n, d))	167.179
Wilson norm (sopfr(nd))	347
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The alchemisma is a small 5-limit comma measuring about 5+1⁄3 cents. It is the amount by which a stack of 36 5/4s exceeds a single 3/2, octave-reduced. Tempering it out leads to the alchemy temperament (28 & 87), which has its ~3/2 at 36 generators of ~5/4 and is supported by 28edo, 87edo, 289edo, 665edo, and 954edo using their patent vals. This temperament extends naturally to the 2.3.5.11 subgroup by adding the pine comma, 4000/3993, with ~11/8 found at -11 generators. This extension is supported by the same edos mentioned earlier except for 954edo.