117649/117128: Difference between revisions

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'''117649/117128''' is a small comma in the 2.7.11 subgroup. It is the amount by which the [[cloudy comma]] 2/(8/7)<sup>5</sup> exceeds the [[8/7]] wholetone lowered by two [[128/121]] semitones.
'''117649/117128''' is a small comma in the 2.7.11 subgroup. It is the amount by which ([[49/44]])<sup>3</sup> exceeds [[11/8]]. It is also the amount by which six [[8/7]] wholetones [[octave reduction|octave-reduced]] (equivalently 8/7 lowered by the [[cloudy comma]]) fall short of two [[128/121]] semitones.
 
Some edos that temper it out are [[20edo]], [[26edo]], [[46edo]], [[58edo]], [[72edo]], [[84edo]], and [[98edo]]. 26edo in particular is quite accurate in the 2.7.11 subgroup, especially for its size.

Latest revision as of 01:55, 21 February 2026

Interval information
Ratio 117649/117128
Factorization 2-3 × 76 × 11-4
Monzo [-3 0 0 6 -4
Size in cents 7.683669¢
Name Bilulutrizo
Color name 1u4z64, bilulutrizo 4th
FJS name [math]\displaystyle{ \text{d4}^{7,7,7,7,7,7}_{11,11,11,11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 33.6819
Weil norm (log2 max(n, d)) 33.6883
Wilson norm (sopfr(nd)) 92
Comma size small
Open this interval in xen-calc

117649/117128 is a small comma in the 2.7.11 subgroup. It is the amount by which (49/44)3 exceeds 11/8. It is also the amount by which six 8/7 wholetones octave-reduced (equivalently 8/7 lowered by the cloudy comma) fall short of two 128/121 semitones.

Some edos that temper it out are 20edo, 26edo, 46edo, 58edo, 72edo, 84edo, and 98edo. 26edo in particular is quite accurate in the 2.7.11 subgroup, especially for its size.