Betarabian comma: Difference between revisions
Rework |
m Linking |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 5: | Line 5: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
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 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. | |||
== | == 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]] | ||