Hemimage comma

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Interval information
Ratio 10976/10935
Factorization 25 × 3-7 × 5-1 × 73
Monzo [5 -7 -1 3
Size in cents 6.4789995¢
Name hemimage
FJS name [math]\text{dd3}^{7,7,7}_{5}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 26.8387
Weil height (max(n, d)) 10976
Benedetti height (n⋅d) 120022560
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.57607 bits
Comma size small
S-expression S282 × S29
open this interval in xen-calc

The hemimage, 10976/10935, is a 7-limit comma measuring about 6.5 cents. It marks the difference between a classic diatonic semitone (16/15) and a stack of three septimal major thirds (9/7) octave reduced, or between a classic whole tone (10/9) and a stack of three septimal third tones (28/27), therefore interesting to those who work extensively with third tones. It is also the difference between 245/243 and 225/224, the two simplest commas to define the 7-limit magic temperament. Tempering it out leads to the hemimage family of temperaments.

See also