1029/1000
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Ratio | 1029/1000 |
Factorization | 2^{-3} × 3 × 5^{-3} × 7^{3} |
Monzo | [-3 1 -3 3⟩ |
Size in cents | 49.491579¢ |
Name | Keega |
Color name | z^{3}g^{3}3, trizogu 3rd |
FJS name | [math]\text{dd3}^{7,7,7}_{5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 19.9728 |
Weil height (log_{2} max(n, d)) | 20.0141 |
Wilson height (sopfr (nd)) | 45 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.47404 bits |
Comma size | medium |
open this interval in xen-calc |
1029/1000, the keega, is a medium 7-limit comma measuring about 49.5 cents. It is the difference between a stack of three 7/5's and a perfect eleventh (8/3), and arises from 10/7 being a convergent in the continued fraction of [math]\sqrt[3]{3}[/math].
Temperaments
Tempering out this comma in the 7-limit leads to the rank-3 keegic temperament. See keegic temperaments for a collection of rank-2 temperaments where it is tempered out.
Etymology
The name keega was given by Gene Ward Smith in 2005. It is a contraction of keemun and gawel, although gawel was later renamed to liese^{[1]}.