1029/1000

Interval information

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]\displaystyle{ \text{dd3}^{7,7,7}_{5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	19.9728
Weil norm (log2 max(n, d))	20.0141
Wilson norm (sopfr(nd))	45
Comma size	medium
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1029/1000, the keega, is a medium 7-limit comma measuring about 49.5 cents. It is the difference between a stack of three 10/7's and a perfect twelfth (3/1), or 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]\displaystyle{ \sqrt[3]{3} }[/math].

It factors into simpler commas as (49/48)⋅(126/125) and (81/80)⋅(686/675).

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.