Hemimage comma
Ratio | 10976/10935 |
Factorization | 2^{5} × 3^{-7} × 5^{-1} × 7^{3} |
Monzo | [5 -7 -1 3⟩ |
Size in cents | 6.4789995¢ |
Name | hemimage |
Color name | sz^{3}g3, Satrizo-agu comma |
FJS name | [math]\text{dd3}^{7,7,7}_{5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 26.8387 |
Weil height (log_{2} max(n, d)) | 26.8441 |
Wilson height (sopfr (nd)) | 57 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.57607 bits |
Comma size | small |
S-expression | S28^{2} × 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.
Temperaments
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.
Etymology
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.