4394/4375
Ratio | 4394/4375 |
Factorization | 2 × 5^{-4} × 7^{-1} × 13^{3} |
Monzo | [1 0 -4 -1 0 3⟩ |
Size in cents | 7.5022234¢ |
Name | hebrewsma |
Color name | 3o^{3}rg^{4}2, tritho-aruquadgu 2nd |
FJS name | [math]\text{ddd2}^{13,13,13}_{5,5,5,5,7}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 24.1964 |
Weil height (log_{2} max(n, d)) | 24.2026 |
Wilson height (sopfr (nd)) | 68 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.63323 bits |
Comma size | small |
S-expression | S26^{2} × S27 |
open this interval in xen-calc |
4394/4375, the hebrewsma, is a small 13-limit comma of about 7.5 cents. When octave-reduced, 4394/4375 represents the difference between a stack of three 13/10's against 35/32.
Temperaments
Tempering out this comma in the 13-limit results in the rank-5 hebrewsmic temperament. Tempering it out in the 2.5.7.13 subgroup results in the rank-3 hebrew temperament. In either case 14/13 is split in two parts, each corresponding to 26/25.
Tempering it out alongside with 3136/3125 sets the rectified hebrew temperament, which is a 2.5.7.13 subgroup extension of didacus. The presence of 4394/4375 being tempered out is the defining factor which specifies the temperament as rectified hebrew.
The comma is tempered out in the Optimal ET sequence: 19(e), 34d, 38df, 53, 58, 72, 77, 111, 130, 19e. In addition, it is tempered out by 353edo, where it is connected to a proposal to reform the Hebrew calendar, hence its name.