4394/4375
| Ratio | 4394/4375 |
| Factorization | 2 × 5-4 × 7-1 × 133 |
| Monzo | [1 0 -4 -1 0 3⟩ |
| Size in cents | 7.5022234¢ |
| Name | hebrewsma |
| Color name | 3o3rg42, tritho-aruquadgu 2nd |
| FJS name | [math]\text{ddd2}^{13,13,13}_{5,5,5,5,7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 24.1964 |
| Weil height (log2 max(n, d)) | 24.2026 |
| Wilson height (sopfr (nd)) | 68 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.70921 bits |
| Comma size | small |
| S-expression | S262 × 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.