2255/2254

Interval information

Ratio	2255/2254
Factorization	2-1 × 5 × 7-2 × 11 × 23-1 × 41
Monzo	[-1 0 1 -2 1 0 0 0 -1 0 0 0 1⟩
Size in cents	0.7679016¢
Name	qinghaisma
Color name	41o23u1orry-3 fowotwethuloruruyo negative 3rd
FJS name	[math]\text{m}{-2}^{5,11,41}_{7,7,23}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	22.2772
Weil height (log2 max(n, d))	22.2778
Wilson height (sopfr(nd))	96
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20532 bits
Comma size	unnoticeable
Open this interval in xen-calc

2255/2254, the qinghaisma, is a 41-limit superparticular comma of about 0.77 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 246/245 and 276/275
• 369/368 and 441/440
• 484/483 and 616/615
• 820/819 and 1288/1287

It can be factored into the following superparticular intervals:

• 2262/2261 and 728365/728364
• 2500/2499 and 23001/23000
• 2640/2639 and 15457/15456
• 3025/3024 and 8856/8855
• 3060/3059 and 8569/8568
• 3520/3519 and 6273/6272
• 3690/3689 and 5797/5796
• 4264/4263 and 4785/4784

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament qinghaismic. Using the 2.5.7.11.23.41 subgroup leads to the rank-5 temperament qinghaic.

Qinghaic

Subgroup: 2.5.7.11.23.41

Comma list: 2255/2254

Mapping:

[⟨	1	2	2	3	4	4	],
⟨	0	1	0	0	0	-1	],
⟨	0	0	1	0	0	2	],
⟨	0	0	0	1	0	-1	],
⟨	0	0	0	0	1	1	]]

Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.271, ~7/4 = 968.949, ~11/8 = 551.224, ~23/16 = 628.435

Optimal ET sequence: 4, 6, 9, 12im, 15, 20, 22i, 25, 29, 31, 43m, 58i, 66im, 74m, 78, 109, 233, 342, 618, 649, 727, 758, 764, 873, 1106, 1215, 1491, 1833, 2597m, 2706m, 3048m

Badness (Sintel): 0.047

Etymology

This comma was named by Francium in 2025. It refers to 2255 Qinghai, the asteroid, which in turn was named after a province in Northwestern China.

See also

• Unnoticeable comma
• List of superparticular intervals