Alpharabian comma

Revision as of 20:41, 17 October 2020 by Aura (talk | contribs) (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)

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.