120/119

Interval information

Ratio	120/119
Factorization	23 × 3 × 5 × 7-1 × 17-1
Monzo	[3 1 1 -1 0 0 -1⟩
Size in cents	14.4874¢
Name	lynchisma
Color name	17ury-2, suruyo negative 2nd, Suruyo comma
FJS name	[math]\displaystyle{ \text{d}{-2}^{5}_{7,17} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	13.8017
Weil height (log2 max(n, d))	13.8138
Wilson height (sopfr(nd))	38
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~2.87488 bits
Comma size	small
S-expressions	S15 × S16, S18 × S19 × S20
Open this interval in xen-calc

120/119, the lynchisma is the 17-limit superparticular comma of about 14.49 cents. It is the difference between 20/17 and 7/6, 17/10 and 12/7, or 30/17 and 7/4. Tempering this comma allows you to assign 10:12:15:17 as the inverse of 4:5:6:7, a much simpler version of what would otherwise be 70:84:105:120. William Lynch calls this the minor tetrad, and so equating it with the inverse of the major tetrad is quite useful.

Temperaments

Tempering out this comma in the 17-limit leads to the rank-6 lynchismic temperament. In the 2.3.5.7.17 subgroup, tempering it out results in the rank-4 lynchic temperament.

Lynchismic

Subgroup: 2.3.5.7.11.13.17

Mapping:

[⟨	1	0	0	0	0	0	3	],
⟨	0	1	0	0	0	0	1	],
⟨	0	0	1	0	0	0	1	],
⟨	0	0	0	1	0	0	-1	],
⟨	0	0	0	0	1	0	0	],
⟨	0	0	0	0	0	1	0	]]

Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

Optimal tuning:

• TE: ~2 = 1198.953, ~3 = 1901.078, ~5 = 2784.431, ~7 = 3371.578
• CTE: ~2 = 1200.000 (1\1), ~3/2 = 700.835, ~5/4 = 383.910, ~7/4 = 972.340

Lynchic

Subgroup: 2.3.5.7.17

Mapping: [⟨1 0 0 0 3], ⟨0 1 0 0 1], ⟨0 0 1 0 1], ⟨0 0 0 1 -1]]

Mapping generators: ~2, ~3, ~5, ~7

Optimal tuning (CTE): ~2 = 1200.000 (1\1), ~3/2 = 700.835, ~5/4 = 383.910, ~7/4 = 972.340

Optimal ET sequence: 10, 12, 19, 22, 26, 31, 41, 53

See also

• Small comma
• List of superparticular intervals