1029/1000
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| Ratio | 1029/1000 |
| Factorization | 2-3 × 3 × 5-3 × 73 |
| Monzo | [-3 1 -3 3⟩ |
| Size in cents | 49.491579¢ |
| 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 | |
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].