Alpharabian comma: Difference between revisions
Reclassified 33/32 as a "limma" in this system, as when you take 11/8 into account, you realize that 33/32 is actually a derivative of 11/8 by means of subtracting 4/3 |
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The '''Alpharabian comma''' (about 9.18177[[Cent|¢]]), is the interval '''131769/131072''' or {{Monzo| -17 2 0 0 4 }} in [[monzo]] notation. 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''' (about 9.18177[[Cent|¢]]), is the interval '''131769/131072''' or {{Monzo| -17 2 0 0 4}} in [[monzo]] notation. 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'''. | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category:Small comma]] | [[Category:Small comma]] | ||
[[Category:Alpharabian]] | [[Category:Alpharabian]] | ||
Revision as of 04:16, 18 October 2020
The Alpharabian comma (about 9.18177¢), is the interval 131769/131072 or [-17 2 0 0 4⟩ in monzo notation. 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.