925/924

Interval information

Ratio	925/924
Subgroup monzo	2.3.5.7.11.37 [-2 -1 2 -1 -1 1⟩
Size in cents	1.872617¢
Name	alphonsinisma
Color name	37o1uryy1 thisoluruyoyo unison
FJS name	[math]\text{d}{-2}^{5,5,37}_{7,11}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	19.7051
Weil height (log2 max(n, d))	19.7066
Wilson height (sopfr(nd))	72
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.23182 bits
Comma size	unnoticeable
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925/924, the alphonsinisma, is a 37-limit superparticular comma of about 1.9 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 100/99 and 112/111
• 111/110 and 126/125
• 148/147 and 176/175
• 155/154 and 186/185
• 225/224 and 297/296
• 400/399 and 704/703

It can be factored into the following superparticular intervals:

• 931/930 and 143375/143374
• 936/935 and 78625/78624
• 969/968 and 20350/20349
• 1036/1035 and 8625/8624
• 1156/1155 and 4625/4624
• 1184/1183 and 4225/4224
• 1225/1224 and 3774/3773
• 1275/1274 and 3367/3366
• 1332/1331 and 3025/3024
• 1369/1368 and 2850/2849
• 1450/1449 and 2553/2552
• 1480/1479 and 2465/2464
• 1625/1624 and 2146/2145
• 1665/1664 and 2080/2079
• 1702/1701 and 2025/2024

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament alphonsinismic. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament alphonsinic.

Alphonsinismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 925/924

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

Alphonsinic

Subgroup: 2.3.5.7.11.37

Comma list: 925/924

Mapping:

[⟨	1	1	2	2	3	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, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633

Optimal ET sequence: 7d, 8d, 9l, 10e, 12el, 12, 15, 19el, 19, 22, 27e, 31, 41, 50, 53, 60el, 72, 130, 152, 224, 311, 342l, 463, 494, 566l, 805l, 877l

Etymology

This comma was named by Francium in 2025. It refers to 925 Alphonsina, the asteroid, which in turn was named after two Spanish kings.

See also

• Unnoticeable comma
• List of superparticular intervals