3042/3025

Interval information

Ratio	3042/3025
Factorization	2 × 32 × 5-2 × 11-2 × 132
Monzo	[1 2 -2 0 -2 2⟩
Size in cents	9.702013¢
Name	diagassormisma
Color name	3oo1uugg2, bitholugu 2nd, Bitholugu comma
FJS name	[math]\text{d2}^{13,13}_{5,5,11,11}[/math]
Special properties	reduced
Tenney height (log2 nd)	23.1335
Weil height (log2 max(n, d))	23.1416
Wilson height (sopfr(nd))	66
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~2.03076 bits
Comma size	small
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3042/3025, the diagassormisma is a 13-limit interval measuring about 9.7¢. It forms the difference between two 55/39s and an octave.

Temperaments

Tempering out this comma leads to the diagassormismic temperament, which splits the octave into two equal parts, each representing 55/39 (small gassormic tritone) and its octave complement, 78/55 (large gassormic tritone). Odd-numbered EDOs cannot temper it out.

2.3.5.11.13 diagassormismic

Subgroup: 2.3.5.11.13

Comma list: 3042/3025

Mapping: [⟨2 0 0 0 -1], ⟨0 1 0 0 -1], ⟨0 0 1 0 1], ⟨0 0 0 1 1]]

Mapping generators: ~55/39, ~3, ~5, ~11

Optimal tuning (POTE): ~55/39 = 1＼2, ~3/2 = 701.7083, ~5/4 = 387.2538, ~11/8 = 553.2831

Optimal ET sequence: 8, 10, 12e, 12f, 14cf, 16, 22, 24, 34, 58, 72, 96, 130, 282f

See also

• Small comma