226/225

This page presents a topic of primarily mathematical interest.

While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Interval information

Ratio

226/225

Subgroup monzo

2.3.5.113 [1 -2 -2 1⟩

Size in cents

7.677325¢

Name

reversed marvel comma

Color name

113ogg2

FJS name

[math]\displaystyle{ \text{d2}^{113}_{5,5} }[/math]

Special properties

superparticular,
reduced

Tenney height (log₂ nd)

15.634

Weil height (log₂ max(n, d))

15.6404

Wilson height (sopfr(nd))

131

Comma size

small

Open this interval in xen-calc

226/225 is a 2.3.5.113 subgroup comma measuring 7.68 cents. It is the amount by which the octave-reduced 113th harmonic (113/64) exceeds the classic augmented sixth of 225/128, and differs from the marvel comma (225/224) by 50625/50624 (S225, ~0.0342¢). It is the parent comma for the reversed marvel temperaments.

Temperaments

In the 2.3.5.113 subgroup, tempering out this comma results in the reversed marvel temperament. By substituting the 7th harmonic out for the 113th harmonic in the marvel temperament, it results in sharper 3rd and 5th harmonics, rather than flatter.

226/225

Temperaments

See also