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
Color name sz3g3, Satrizo-agu comma
FJS name [math]\text{dd3}^{7,7,7}_{5}[/math]
Special properties reduced
Tenney height (log2 nd) 26.8387
Weil height (log2 max(n, d)) 26.8441
Wilson height (sopfr (nd)) 57
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.58255 bits
Comma size small
S-expression S282 × S29
open this interval in xen-calc

The hemimage, 10976/10935, is a small 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 out this comma alone in the 7-limit leads to the rank-3 hemimage temperament. See Hemimage family for the rank-3 family where it is tempered out. See Hemimage temperaments for a collection of rank-2 temperaments where it is tempered out.


This comma was first named as parahemfi by Gene Ward Smith in 2005 as a contraction of parakleismic and hemififths[1]. It is not clear how it later became hemimage, but the root of hemimage is obvious, being a contraction of hemififths and magic.