561/560

Interval information

Ratio	561/560
Factorization	2-4 × 3 × 5-1 × 7-1 × 11 × 17
Monzo	[-4 1 -1 -1 1 0 1⟩
Size in cents	3.088732¢
Name	monardisma
Color name	17o1org1, solorugu unison, Solorugu comma
FJS name	[math]\displaystyle{ \text{d1}^{11,17}_{5,7} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	18.2611
Weil height (log2 max(n, d))	18.2637
Wilson height (sopfr(nd))	51
Comma size	unnoticeable
S-expression	S33 × S34
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561/560, the monardisma is an unnoticeable 17-limit superparticular comma of about 3.1 cents. It is the difference between 33/32 and 35/34.

Temperaments

Tempering out this comma in the 2.3.5.7.11.17 subgroup results in the monardic temperament, or in the full 17-limit, the monardismic temperament, enabling monardismic chords.

Monardismic

Subgroup: 2.3.5.7.11.13.17

Mapping:

[⟨	1	0	0	0	0	0	4	],
⟨	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	-1	],
⟨	0	0	0	0	0	1	0	]]

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

Optimal tunings:

• CTE: ~2 = 1200.0000, ~3/2 = 701.7805, ~5/4 = 386.6883, ~7/4 = 969.3735, ~11/8 = 550.4865, ~13/8 = 840.5277
• CWE: ~2 = 1200.0000, ~3/2 = 701.6204, ~5/4 = 386.3575, ~7/4 = 968.9591, ~11/8 = 550.2059, ~13/8 = 840.0917

Optimal ET sequence: 12f, 14cf, 15, 17cg, 19g, 22, 26, 29g, 31, 38df, 41g, 43, 46, 58, 72, 103, 111, 130, 140, 183, 243e, 301, 373g, 886eefgg, 1362bdeeefgggg*

* optimal patent val: 484

See also

• List of superparticular intervals