1029/1000: Difference between revisions

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'''1029/1000''', the '''keega''', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 49.5 [[cent]]s. 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>.
'''1029/1000''', the '''keega''', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 49.5 [[cent]]s. 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>.



Revision as of 11:33, 21 January 2026

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
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]\displaystyle{ \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].

Notes