Alpharabian comma: Difference between revisions

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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'~~'' ({{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 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.

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 ==

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+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''' ({{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 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.
+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 ==