Alpharabian comma: Difference between revisions

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 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'''.