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Betarabian comma: Difference between revisions

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Created page with "The '''Betarabian comma''' (about 16.32089¢), is the interval '''264627/262144''' or {{Monzo| -18 7 0 0 2}} in monzo notation. It is the sum of the 32805/3276..."
 
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The '''Betarabian comma''' (about 16.32089[[Cent|¢]]), is the interval '''264627/262144''' or {{Monzo| -18 7 0 0 2}} in [[monzo]] notation.  It is the sum of the [[32805/32768|schisma]] and the [[121/120|biyatisma]], as well as the sum of the [[Alpharabian comma]] and the [[243/242|rastma]]. Furthermore, it forms the difference between various pairs of enharmonic quartertone-based intervals in no-fives no-sevens just 11-limit tuning. The term "Betarabian" is a derivative of "Alpharabian", and was coined on account of both the rastma being the comma which separates primary and secondary 11-limit intervals and the term "Alpharabian" itself containing the word "Alpha" within it.  As the Betarabian comma is the sum of the Alpharabian comma and the rastma, it is automatically tempered out whenever the rastma is added to the list of commas tempered out by members of the Alpharabian family.
{{Infobox Interval
| Ratio = 264627/262144
| Name = Betarabian comma
| Color name = L1oo-2, Lalolo comma
| 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]].  


[[Category:11-limit]]
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]].
[[Category:Small comma]]
 
== 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:Betaxenic]]
[[Category:Commas named after polymaths]]
[[Category:Commas named for their regular temperament properties]]
Retrieved from "https://en.xen.wiki/w/Betarabian_comma"