Betarabian comma: Difference between revisions
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The '''Betarabian comma''' ({{monzo|legend=1| -18 7 0 0 2 }}, [[ratio]]: 264627/262144) is a [[small comma|small]] [[11-limit]] [[comma]] measuring about 16.3{{cent}}. 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 [[4096/2187|Pythagorean diminished octave]]. | |||
It is the sum of the [[Alpharabian comma]] and the [[243/242|rastma]], as well as the sum of the [[32805/32768|schisma]] and the [[121/120|biyatisma]] in the [[2.3.5.11 subgroup]]. | |||
== Temperaments == | == 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. | 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. | |||
[[Category:Alpharabian]] | [[Category:Alpharabian]] | ||
Revision as of 04:13, 17 August 2026
| Interval information |
reduced harmonic
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 is the sum of the Alpharabian comma and the rastma, as well as the sum of the schisma and the biyatisma in the 2.3.5.11 subgroup.
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.