Alpharabian comma

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Interval information
Ratio 131769/131072
Factorization 2-17 × 32 × 114
Monzo [-17 2 0 0 4
Size in cents 9.1817712¢
Name Alpharabian comma
Color name L1o4-2, Laquadlo comma
FJS name [math]\text{M}{-2}^{11,11,11,11}[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 n⋅d) 34.0077
Weil height (max(n, d)) 131769
Benedetti height (n⋅d) 17271226368
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.74395 bits
Comma size small
open this interval in xen-calc

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 parachorma 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. Tempering out the Alpharabian comma results in one of the various Alpharabian temperaments.

See also