1029/1000
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Ratio
1029/1000
Factorization
2-3 × 3 × 5-3 × 73
Monzo
[-3 1 -3 3⟩
Size in cents
49.49158¢
Name
Keega
Color name
z3g33, trizogu 3rd
FJS name
[math]\text{dd3}^{7,7,7}_{5,5,5}[/math]
Special properties
reduced
Tenney height (log2 nd)
19.9728
Weil height (log2 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
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
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].