8281/8192

Interval information

Ratio	8281/8192
Factorization	2-13 × 72 × 132
Monzo	[-13 0 0 2 0 2⟩
Size in cents	18.70714¢
Name	diahuntmisma
Color name	L3oozz2, labithozo 2nd, Labithozo comma
FJS name	[math]\displaystyle{ \text{d2}^{7,7,13,13} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	26.0156
Weil height (log2 max(n, d))	26.0312
Wilson height (sopfr(nd))	66
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~3.5785 bits
Comma size	small
Open this interval in xen-calc

8281/8192, the diahuntmisma is a 13-limit interval measuring about 18.7¢. It forms the difference between two 91/64s and an octave.

Temperaments

Tempering out this comma leads to the diahuntmismic temperament, which splits the octave into two equal parts, each representing 91/64 (large huntmic tritone) and its octave complement, 128/91 (small huntmic tritone). Odd-numbered EDOs cannot temper it out.

2.7.13 diahuntmismic

Subgroup: 2.7.13

Comma list: 8281/8192

Mapping: [⟨2 0 13], ⟨0 1 -1]]

Mapping generators: ~91/64, ~7

Optimal tuning (POTE): ~91/64 = 1＼2, ~8/7 = 235.0003

Optimal ET sequence: 10, 26, 36, 46

Badness: 0.001183

See also

• Small comma