1029/1024
Ratio | 1029/1024 |
Factorization | 2^{-10} × 3 × 7^{3} |
Monzo | [-10 1 0 3⟩ |
Size in cents | 8.4327203¢ |
Names | gamelisma, gamelan residue |
Color name | Lz^{3}2, latrizo 2nd, Latrizo comma |
FJS name | [math]\text{m2}^{7,7,7}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 20.007 |
Weil height (log_{2} max(n, d)) | 20.0141 |
Wilson height (sopfr (nd)) | 44 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.69206 bits |
Comma size | small |
S-expression | S7 / S8 |
open this interval in xen-calc |
1029/1024, the gamelisma, is a 7-limit (also 2.3.7 subgroup) small comma measuring about 8.4 cents. It is the amount by which a stack of three 8/7s falls short of 3/2. Tempering out this comma for the 2.3.7 subgroup leads to slendric temperament. In addition to the perfect fifth being split into three equal parts, the Pythagorean limma (256/243) is also split into three in the same way, one for 64/63~49/48 and two for 28/27. It therefore provides the little interval known as quark.
Temperaments
Tempering out this comma alone in the 7-limit leads to the rank-3 gamelismic temperament, or in the 2.3.7 subgroup, the rank-2 slendric temperament. Either case, it enables the slendric pentad. See Gamelismic family for the rank-3 family where it is tempered out. See Gamelismic clan for the rank-2 clan where it is tempered out.
Etymology
This comma was known as the gamelan residue no later than May 2001. It was allegedly named by Adriaan Fokker^{[1]}.