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~~]].

It factors into simpler commas as the sum of the [[Alpharabian comma]] and the [[243/242|rastma]]. In the [[2.3.5.11 subgroup]], it also factors as the sum of the [[32805/32768|schisma]] and the [[121/120|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.

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 ==

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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]].
+It factors into simpler commas as the sum of the [[Alpharabian comma]] and the [[243/242|rastma]]. In the [[2.3.5.11 subgroup]], it also factors as the sum of the [[32805/32768|schisma]] and the [[121/120|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.
+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 ==