Betarabian comma

Interval information

Ratio	264627/262144
Factorization	2-18 × 37 × 112
Monzo	[-18 7 0 0 2⟩
Size in cents	16.32089 ¢
Name	Betarabian comma
Color name	L1oo-2, Lalolo comma
FJS name	[math]\displaystyle{ \text{m}{-2}^{11,11} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	36.0136
Weil norm (log2 max(n, d))	36.0272
Wilson norm (sopfr(nd))	79
Comma size	small
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The Betarabian comma (monzo: [-18 7 0 0 2⟩, ratio: 264627/262144) is a small 11-limit comma measuring about 16.3 ¢. It forms the difference between various pairs of enharmonic quartertone-based intervals in the 2.3.11 subgroup. Specifically, it is the amount by which a stack of two 33/32's exceeds the Pythagorean limma, or the amount by which a stack of two 11/8's exceeds the Pythagorean diminished octave.

It factors into simpler commas as the sum of the Alpharabian comma and the rastma. In the 2.3.5.11 subgroup, it also factors as the sum of the schisma and the biyatisma.

Temperaments

As the Betarabian comma is the sum of the Alpharabian comma and the rastma, it is automatically tempered out whenever the rastma and the Alpharabian comma are tempered out; however, there are other temperaments that temper out just the Betarabian comma itself. When tempered out in the 11-limit, it is the betaxenic temperament, or in the 2.3.11 subgroup, the betaxenean temperament.

Etymology

The term Betarabian is a derivative of Alpharabian, and was coined on account of both the rastma being a comma which separates primary and secondary 11-limit intervals and the term Alpharabian itself containing the word alpha within it.