Alpharabian comma: Difference between revisions
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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 | 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 limma 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". 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 temperaments]]. | ||
== See also == | == See also == | ||
Revision as of 08:36, 2 December 2020
| Interval information |
reduced harmonic
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 limma 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". 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 temperaments.