561/560
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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]\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
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.28854 bits
Comma size
unnoticeable
S-expression
S33 × S34
Open this interval in xen-calc
| Interval information |
solorugu unison,
Solorugu comma
reduced
(Shannon, [math]\sqrt{nd}[/math])
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
| [⟨ | 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
- 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*
Etymology
This comma was named by Scott Dakota in 2023 after the Monarda scale, a 12-tone scale of tannic, where this is one of the commas being tempered out.