Revopentisma
Factorization | 2^{47} × 3^{4} × 7^{-19} |
Monzo | [47 4 0 -19⟩ |
Size in cents | 0.12778055¢ |
Name | revopentisma |
Color name | ssr^{19}-8, sasa-neru negative octave |
FJS name | [math]\text{6d}{-8}_{7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 106.68 |
Weil height (log_{2} max(n, d)) | 106.68 |
Wilson height (sopfr (nd)) | 239 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.39756 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
Revopentisma is a 7-limit (and also 2.3.7 subgroup) unnoticeable comma associated with very high accuracy temperaments.
Theory
Revopentisma is the comma shared by 31edo and 270edo in the 2.3.7 subgroup and is notable as supported by many mega-edos. The associated temperament is named revopent, and it's remarkable in its short generator chains for edos in the thousands, with 7/4 being just four generators down and 3/2 being just nineteen, with octave reduction. Tempering it out in the full 7-limit produces rank-3 revopentismic temperament, as well as the 2.3.7 rank-2 revopentic temperament. The rank-2 revopent temperament adds mapping for 5 where it is reached in 287 generators.
Etymology
Comma's name is derived from two edos in the temperament-merging, number 1848 being associated with a year with a large number of revolutions in Europe, and 3125 being equal to 5 to the power of 5, hence pent- meaning five.