1029/1024
| Ratio | 1029/1024 |
| Factorization | 2-10 × 3 × 73 |
| Monzo | [-10 1 0 3⟩ |
| Size in cents | 8.4327203¢ |
| Names | slendric comma, gamelisma, gamelan residue |
| Color name | Lz32, latrizo 2nd, Latrizo comma |
| FJS name | [math]\text{m2}^{7,7,7}[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 20.007 |
| Weil height (log2 max(n, d)) | 20.0141 |
| Wilson height (sopfr(nd)) | 44 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.83722 bits |
| Comma size | small |
| S-expression | S7 / S8 |
| open this interval in xen-calc | |
1029/1024, the slendric comma or 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 a 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. In 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].