Kaguyisma

Interval information

Ratio	10880/10879
Subgroup monzo	2.5.11.17.23.43 [7 1 -1 1 -1 -1⟩
Size in cents	0.1591281¢
Name	kaguyisma
Color name	43u23u17o1uy1 fothutwethusoluyo unison
FJS name	[math]\text{m2}^{5,17}_{11,23,43}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	26.8186
Weil height (log2 max(n, d))	26.8188
Wilson height (sopfr(nd))	113
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19845 bits
Comma size	unnoticeable
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10880/10879, the kaguyisma, is a 43-limit superparticular comma of about 0.16 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 990/989 and 1089/1088
• 3312/3311 and 4761/4760
• 5376/5375 and 10626/10625

It can be factored into the following superparticular commas:

• 11271/11270 and 313600/313599
• 11340/11339 and 268192/268191
• 11662/11661 and 162240/162239
• 12376/12375 and 90000/89999
• 14400/14399 and 44506/44505
• 14535/14534 and 43264/43263
• 18792/18791 and 25840/25839

Temperaments

Tempering out this comma in the full 43-limit leads to the rank-13 temperament kaguyismic. Using the 2.5.11.17.23.43 subgroup leads to the rank-5 temperament kaguyic.

Kayugismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43

Comma list: 10880/10879

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	5	5	6	],
⟨	0	1	0	0	0	0	0	0	0	0	0	0	0	0	],
⟨	0	0	1	0	0	0	0	0	0	0	0	0	0	1	],
⟨	0	0	0	1	0	0	0	0	0	0	0	0	0	0	],
⟨	0	0	0	0	1	0	0	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	0	0	1	0	0	0	0	0	0	1	],
⟨	0	0	0	0	0	0	0	1	0	0	0	0	0	0	],
⟨	0	0	0	0	0	0	0	0	1	0	0	0	0	-1	],
⟨	0	0	0	0	0	0	0	0	0	1	0	0	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	0	0	1	0	0	],
⟨	0	0	0	0	0	0	0	0	0	0	0	0	1	0	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955, ~5/4 = 386.303, ~7/4 = 968.826, ~11/8 = 551.341, ~13/8 = 840.528, ~17/16 = 104.924, ~19/16 = 297.513, ~23/16 = 628.313, ~29/16 = 1029.577, ~31/16 = 1145.036, ~37/32 = 251.344, ~41/32 = 429.062

Kaguyic

Subgroup: 2.5.11.17.23.43

Comma list: 10880/10879

Mapping:

[⟨	1	2	3	4	4	6	],
⟨	0	1	0	0	0	1	],
⟨	0	0	1	0	0	-1	],
⟨	0	0	0	1	0	1	],
⟨	0	0	0	0	1	-1	]]

Optimal tuning (CTE): ~2 = 1\1, ~5/4 = 386.303, ~11/8 = 551.341, ~17/16 = 104.924, ~23/16 = 628.313

Optimal ET sequence: 4n, 5eg, 6gn, 6, 9, 13n, 15, 16, 19, 21, 28g, 29g, 30, 35, 37, 44, 46, 50, 59, 115, 124, 298, 422, 516, 640, 699, 814, 938, 1637, 1715, 1839, 2137, 2777, 2836, 4973, 5613, 8449, 8573in

Etymology

The kaguyisma was named by Francium in 2024. It refers to 10880 Kaguya, the asteroid. Which was in turn named after the princess from Japanese folklore.

See also

• Unnoticeable comma
• List of superparticular intervals