2187/2185
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Ratio
2187/2185
Subgroup monzo
3.5.19.23 [7 -1 -1 -1⟩
Size in cents
1.583929¢
Name
vashegyitisma
Color name
L23u19ug-2
latwethunugu negative 2nd
FJS name
[math]\text{P1}_{5,19,23}[/math]
Special properties
reduced
Tenney height (log2 nd)
22.1882
Weil height (log2 max(n, d))
22.1895
Wilson height (sopfr(nd))
68
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.22168 bits
Comma size
unnoticeable
Open this interval in xen-calc
| Interval information |
latwethunugu negative 2nd
(Shannon, [math]\sqrt{nd}[/math])
2187/2185, the vashegyitisma, is a 23-limit (also 3.5.19.23 subgroup) unnoticeable comma of about 1.6 cents.
Commatic relationships
This comma is the difference between the following intervals:
- 96/95 and 736/729
- 729/722 and 115/114
- 162/161 and 190/189
- 324/323 and 460/459
- 59049/58880 and 513/512
- 23328/23275 and 736/735
It can be factored into the following ratios:
- 1197/1196 and 12636/12635
- 1521/1520 and 3888/3887
- 1701/1700 and 3060/3059
- 1863/1862 and 2646/2645
- 2025/2024 and 2376/2375
- 2277/2275 and 110565/110561
- 3520/3519 and 334611/334400
- 8075/8073 and 767637/767125
Temperaments
Tempering out this comma in the full 23-limit leads to the rank-8 temperament vashegyitismic. Using the 3.5.19.23 subgroup leads to the rank-3 temperament vashegyitic.
Vashegyitic
Subgroup: 3.5.19.23
Comma list: 2187/2185
| [⟨ | 1 | 1 | 2 | 4 | ], |
| ⟨ | 0 | 1 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 1 | -1 | ]] |
Optimal tuning (CTE): ~3 = 1\1, ~5/3 = 884.553, ~19/9 = 1294.254
Optimal ET sequence: b6, b9, b13, b28, b69, b97, b103, b116, b144, b172, b316, b673, b817, b845, b989, b1305, b2294hi, b3599chhii
Badness (Sintel): 0.020
Etymology
This comma was named by Francium in 2025. It refers to Vashegyite, the mineral.