Alpharabian comma: Difference between revisions

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{{Infobox Interval

~~| JI glyph =~~

| Ratio = 131769/131072

~~| Monzo = -17 2 0 0 4~~

~~| Cents = 9.18177~~

| Name = Alpharabian comma

| Color name =

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

| ~~FJS name =~~

| Comma = yes

~~| Sound~~ =

}}

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. 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 ~~limma~~ of the 11-limit, a fact which lends itself to the idea of just 11~~-limit~~ tuning being called "Alpharabian tuning" in the same way that just 3-limit tuning is called "Pythagorean tuning". ~~Given~~ 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~~, it follows that tempering~~ out the Alpharabian comma results in ~~a member of~~ the '''~~Alpharabian family~~'''.

The '''Alpharabian comma''' ({{monzo|legend=1| -17 2 0 0 4 }}, [[ratio]]: 131769/131072) is an [[11-limit]] (also 2.3.11 [[subgroup]]) [[comma]] measuring about 9.2{{cent}}. 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 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 '''alphaxenic temperament''', or in the 2.3.11 subgroup the '''alphaxenean temperament'''.

== See also ==

* [[Alphaxenic rank three clan]]

* [[Small comma]]

~~[[Category:11-limit]]~~

~~[[Category:Small comma]]~~

[[Category:Alpharabian]]

[[Category:Alphaxenic]]

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

[[Category:Commas named after polymaths]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
 | Ratio = 131769/131072
-| Monzo = -17 2 0 0 4
-| Cents = 9.18177
 | Name = Alpharabian comma
-| Color name =
+| Color name = L1o<sup>4</sup>-2, Laquadlo comma
-| FJS name =
+| Comma = yes
-| Sound =
 }}
-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. 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 limma of the 11-limit, a fact which lends itself to the idea of just 11-limit tuning being called "Alpharabian tuning" in the same way that just 3-limit tuning is called "Pythagorean tuning". Given 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, it follows that tempering out the Alpharabian comma results in a member of the '''Alpharabian family'''.
+The '''Alpharabian comma''' ({{monzo|legend=1| -17 2 0 0 4 }}, [[ratio]]: 131769/131072) is an [[11-limit]] (also 2.3.11 [[subgroup]]) [[comma]] measuring about 9.2{{cent}}. 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 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 '''alphaxenic temperament''', or in the 2.3.11 subgroup the '''alphaxenean temperament'''.
 == See also ==
+* [[Alphaxenic rank three clan]]
 * [[Small comma]]
-[[Category:11-limit]]
-[[Category:Small comma]]
 [[Category:Alpharabian]]
+[[Category:Alphaxenic]]
+[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named after polymaths]]