Alpharabian comma: Difference between revisions

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| Ratio = 131769/131072

| Name = Alpharabian comma

| Color name = L1o<sup>4</sup>-2, Laquadlo comma

| Comma = yes

}}

The '''Alpharabian comma''' ({{monzo|legend=1| -17 2 0 0 4 }}, [[ratio]]: 131769/131072) is a [[small comma|small]] [[11-limit]] (also 2.3.11 [[subgroup]]) [[comma]] measuring about 9.2{{cent}}. It is the amount by which a stack of four [[33/32]] quartertones exceeds a [[9/8]] whole tone, and the amount by which a stack of two [[128/121]] diatonic semitones falls short of a 9/8 whole tone.

The '''Alpharabian ~~comma''' is the [[11-limit]] interval ''~~'~~131769/131072~~''' measuring about 9.2[[¢]]. It is the amount by which a stack of two [[128/121]] diatonic semitones falls short of a [[9/8]] whole tone, and the amount by which a stack of four [[33/32]] quartertones exceeds a 9/8 whole tone. The term "Alpharabian" comes from Alpharabius – another name for Al-Farabi – and was chosen due to the fact that 33/32, also known as the the Al-Farabi ~~Quartertone~~, is the primary ~~parachorma~~ of the 11-limit, a fact which lends itself to the idea of just 2.3.11 tuning being called "Alpharabian tuning" in the same way that just 3-limit tuning is called "Pythagorean tuning". Of note is that the Alpharabian comma and the [[Pythagorean comma]] are similar in that both commas represent the difference between two of their respective p-limit's primary diatonic semitones and a 9/8 whole tone. Tempering out the Alpharabian comma results in ~~one of~~ the ~~various~~ '''[[~~Alpharabian~~ temperaments]]'''.

The term ''Alpharabian'' comes from Alpharabius – another name for Al-Farabi – and was chosen due to the fact that 33/32, also known as the the Al-Farabi quartertone, is the primary parachroma of the 11-limit, a fact which lends itself to the idea of just 2.3.11 tuning being called ''[[Alpharabian tuning]]'' in the same way that just 3-limit tuning is called ''[[Pythagorean tuning]]''. Of note is that the Alpharabian comma and the [[Pythagorean comma]] are similar in that both commas represent the difference between two of their respective ''p''-limit's primary diatonic semitones and a 9/8 whole tone.

== Temperaments ==

Tempering out the Alpharabian comma in the 11-limit results in the rank-4 '''alphaxenic''' temperament (→ [[Catalog of rank-4 temperaments #Alphaxenic (131769/131072)]]), or in the 2.3.11 subgroup, the rank-2 '''alphaxenean''' temperament (→ [[No-fives subgroup temperaments #Alphaxenean]]).

== See also ==

* [[~~Alpharabian temperaments]]~~

* [[Alphaxenic rank-3 clan]]

* [[Small comma]]

[[Category:Alpharabian]]

[[Category:Alphaxenic]]

[[Category:Commas named for their regular temperament properties]]

[[Category:Commas named after polymaths]]

@@ Line 2: / Line 2: @@
 | Ratio = 131769/131072
 | Name = Alpharabian comma
+| Color name = L1o<sup>4</sup>-2, Laquadlo comma
 | Comma = yes
 }}
+The '''Alpharabian comma''' ({{monzo|legend=1| -17 2 0 0 4 }}, [[ratio]]: 131769/131072) is a [[small comma|small]] [[11-limit]] (also 2.3.11 [[subgroup]]) [[comma]] measuring about 9.2{{cent}}. It is the amount by which a stack of four [[33/32]] quartertones exceeds a [[9/8]] whole tone, and the amount by which a stack of two [[128/121]] diatonic semitones falls short of a 9/8 whole tone.
-The '''Alpharabian comma''' is the [[11-limit]] interval '''131769/131072''' measuring about 9.2[[¢]]. It is the amount by which a stack of two [[128/121]] diatonic semitones falls short of a [[9/8]] whole tone, and the amount by which a stack of four [[33/32]] quartertones exceeds a 9/8 whole tone. The term "Alpharabian" comes from Alpharabius – another name for Al-Farabi – and was chosen due to the fact that 33/32, also known as the the Al-Farabi Quartertone, is the primary parachorma of the 11-limit, a fact which lends itself to the idea of just 2.3.11 tuning being called "Alpharabian tuning" in the same way that just 3-limit tuning is called "Pythagorean tuning".  Of note is that the Alpharabian comma and the [[Pythagorean comma]] are similar in that both commas represent the difference between two of their respective p-limit's primary diatonic semitones and a 9/8 whole tone.  Tempering out the Alpharabian comma results in one of the various '''[[Alpharabian temperaments]]'''.
+The term ''Alpharabian'' comes from Alpharabius – another name for Al-Farabi – and was chosen due to the fact that 33/32, also known as the the Al-Farabi quartertone, is the primary parachroma of the 11-limit, a fact which lends itself to the idea of just 2.3.11 tuning being called ''[[Alpharabian tuning]]'' in the same way that just 3-limit tuning is called ''[[Pythagorean tuning]]''. Of note is that the Alpharabian comma and the [[Pythagorean comma]] are similar in that both commas represent the difference between two of their respective ''p''-limit's primary diatonic semitones and a 9/8 whole tone.
+== Temperaments ==
+Tempering out the Alpharabian comma in the 11-limit results in the rank-4 '''alphaxenic''' temperament (→ [[Catalog of rank-4 temperaments #Alphaxenic (131769/131072)]]), or in the 2.3.11 subgroup, the rank-2 '''alphaxenean''' temperament (→ [[No-fives subgroup temperaments #Alphaxenean]]).
 == See also ==
-* [[Alpharabian temperaments]]
+* [[Alphaxenic rank-3 clan]]
-* [[Small comma]]
 [[Category:Alpharabian]]
+[[Category:Alphaxenic]]
+[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named after polymaths]]