37/22: Difference between revisions

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Theory: it is convergent
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{{Infobox Interval|Ratio=37/22}}
{{Infobox Interval
| Name = 37-limit major sixth, 37-limit 3/4-octave
}}


37/22, the '''37-limit major sixth''' or '''37-limit 3/4-octave''' is a 37-limit, (also 2.11.37 subgroup) interval.  
37/22, the '''37-limit major sixth''' or '''37-limit 3/4-octave''' is a 37-limit, (also 2.11.37 subgroup) interval.  

Revision as of 11:21, 6 July 2023

Interval information
Ratio 37/22
Subgroup monzo 2.11.37 [-1 -1 1
Size in cents 900.0261¢
Names 37-limit major sixth,
37-limit 3/4-octave
FJS name [math]\displaystyle{ \text{M6}^{37}_{11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.66888
Weil norm (log2 max(n, d)) 10.4189
Wilson norm (sopfr(nd)) 50
Open this interval in xen-calc

37/22, the 37-limit major sixth or 37-limit 3/4-octave is a 37-limit, (also 2.11.37 subgroup) interval.

Theory

In logarithmic division, it is extremely close to three quarters of the octave, being a convergent.

The 4320 & 5544 period-72 temperament in the 2.3.5.7.11.13.17.31.37 subgroup tunes both 11th and 37th harmonic to 25 generators down, thus tempering this interval to exact 3/4 of the octave.