Alpharabian comma
Ratio | 131769/131072 |
Factorization | 2^{-17} × 3^{2} × 11^{4} |
Monzo | [-17 2 0 0 4⟩ |
Size in cents | 9.1817712¢ |
Name | Alpharabian comma |
Color name | L1o^{4}-2, Laquadlo comma |
FJS name | [math]\text{M}{-2}^{11,11,11,11}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 34.0077 |
Weil height (log_{2} max(n, d)) | 34.0153 |
Wilson height (sopfr (nd)) | 84 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.94991 bits |
Comma size | small |
open this interval in xen-calc |
The Alpharabian comma (monzo: [-17 2 0 0 4⟩, ratio: 131769/131072) is an 11-limit (also 2.3.11 subgroup) comma 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 parachroma 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". Of note is 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.
Temperaments
Tempering out the Alpharabian comma in the 11-limit results in the alphaxenic temperament, or in the 2.3.11 subgroup the alphaxenean temperament.