Alpharabian comma
| 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 one of the various Alpharabian temperaments.