Alpharabian comma: Difference between revisions
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Revision as of 09:38, 17 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 interval 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.