1029/1024: Difference between revisions

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'''1029/1024''', the '''gamelisma''', is a [[7-limit]] (also 2.3.7 subgroup) [[small comma]] measuring about 8.4 cents. It is the amount by which a stack of three [[8/7]]s falls short of [[3/2]]. Tempering out this comma for the 2.3.7 subgroup leads to [[slendric]] temperament. In addition to that the perfect fifth is split into three equal parts, the [[256/243|Pythagorean limma (256/243)]] is also so split, one for [[64/63]]~[[49/48]] and two for [[28/27]]. It therefore provides the little interval known as [[quark]].
'''1029/1024''', the '''gamelisma''', is a [[7-limit]] (also 2.3.7 subgroup) [[small comma]] measuring about 8.4 cents. It is the amount by which a stack of three [[8/7]]s falls short of [[3/2]]. Tempering out this comma for the 2.3.7 subgroup leads to [[slendric]] temperament. In addition to the perfect fifth being split into three equal parts, the [[256/243|Pythagorean limma (256/243)]] is also split into three in the same way, one for [[64/63]]~[[49/48]] and two for [[28/27]]. It therefore provides the little interval known as [[quark]].


== See also ==
== See also ==

Revision as of 01:30, 25 December 2023

Interval information
Ratio 1029/1024
Factorization 2-10 × 3 × 73
Monzo [-10 1 0 3
Size in cents 8.43272¢
Names gamelisma,
gamelan residue
Color name Lz32, latrizo 2nd,
Latrizo comma
FJS name [math]\displaystyle{ \text{m2}^{7,7,7} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 20.007
Weil height (log2 max(n, d)) 20.0141
Wilson height (sopfr(nd)) 44
Comma size small
S-expression S7 / S8
Open this interval in xen-calc

1029/1024, the gamelisma, is a 7-limit (also 2.3.7 subgroup) small comma measuring about 8.4 cents. It is the amount by which a stack of three 8/7s falls short of 3/2. Tempering out this comma for the 2.3.7 subgroup leads to slendric temperament. In addition to the perfect fifth being split into three equal parts, the Pythagorean limma (256/243) is also split into three in the same way, one for 64/63~49/48 and two for 28/27. It therefore provides the little interval known as quark.

See also