Wadisma

Todo: research , add etymology

Interval information

Factorization	2-26 × 3-1 × 5 × 79
Monzo	[-26 -1 1 9⟩
Size in cents	3.791871¢
Name	Wadisma
FJS name	[math]\displaystyle{ \text{dd4}^{5,7,7,7,7,7,7,7,7,7} }[/math]
Special properties	reduced
Tenney height (log2 nd)	55.1731
Weil height (log2 max(n, d))	55.1762
Wilson height (sopfr(nd))	123
Comma size	small
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The wadisma is a 7-limit comma of about 3.792 cents, the amount by which 10/3 exceeds a stack of nine 8/7s. It has the monzo [-26 -1 1 9⟩ and the ratio 201768035/201326592.

This comma is closely related to mothra temperament, as three 8/7s in mothra reach a meantone fifth, three of which are identified with 10/3. Therefore, the wadisma is tempered out in EDOs supporting mothra, such as 5, 26, 31, and 36. However, there are other more accurate 7-limit tuning systems tempering it out that do not make the equivalence of (8/7)³ to 3/2, and therefore do not temper out 81/80 nor 1029/1024, notable examples of which include 140edo, 171edo, and their sum, 311edo.

Etymology

This comma was described and named some time prior to June 2011. It is unclear by whom.