4394/4375

Interval information

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
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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.