Bronxisma

Interval information

Ratio	10472/10469
Factorization	23 × 7 × 11 × 17 × 19-2 × 29-1
Monzo	[3 0 0 1 1 0 1 -2 0 -1⟩
Size in cents	0.4960319¢
Name	bronxisma
Color name	29u19uu17o1oz1 twenununusolozo unison
FJS name	[math]\text{P1}^{7,11,17}_{19,19,29}[/math]
Special properties	reduced
Tenney height (log2 nd)	26.7081
Weil height (log2 max(n, d))	26.7085
Wilson height (sopfr(nd))	108
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20052 bits
Comma size	unnoticeable
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10472/10469, the bronxisma, is a 29-limit unnoticeable comma of about 0.50 cents. It is the amount of a stack of two 22/19s and one 42/29 surpassing 33/17.

Commatic relationships

This comma factors into the commas 3510/3509 and 633556/633555.

Temperaments

Tempering out this comma in the full 29-limit leads to the rank-9 temperament bronxismic. Using the 2.7.11.17.19.29 subgroup leads to the rank-5 temperament bronxic.

Bronxismic

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 10472/10469

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955, ~5/4 = 386.314, ~7/4 = 968.796, ~11/8 = 551.273, ~13/8 = 840.528, ~17/16 = 104.893, ~19/16 = 297.648, ~23/16 = 628.274

Optimal ET sequence: 7deefghiiijj, 7deefghijj, 7dghi, 7, 9gij, 9, 11cdeefghijj, 12e, 12fij, 14cf, 15g, 18ehij, 19eghi, 23deffgghiij, 24ij, 24d, 26ei, 27e, 27egj, 27egij, 29gj, 31j, 34dh, 38dfij, 39dfgij, 41g, 43, 46j, 50, 58ghi, 62, 72ij, 77, 80, 94, 99ef, 111, 113, 118, 130, 145j, 152fgj, 161, 190gjj, 193, 217, 243e, 270, 311, 422, 472, 535, 540, 554e, 581j, 624j, 653, 692i, 742i, 814, 908, 1041, 1046dghj, 1125, 1164fi, 1178, 1282, 1357efhij, 1395, 1600, 2029, 2072, 2087h, 2460, 4060j, 4277h, 4547hj, 4631hj, 4874h, 5455hj, 6737hj

Bronxic

Subgroup: 2.7.11.17.19.29

Comma list: 10472/10469

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~7/4 = 968.796, ~11/8 = 551.273, ~17/16 = 104.893, ~19/16 = 297.648

Optimal ET sequence: 4, 5, 9gj, 9, 11, 14, 18dg, 20, 25, 32j, 37, 43, 52, 57, 100, 118, 156, 161, 218, 374, 379, 572, 592, 753, 810, 903, 1064, 1121, 1282, 1874, 2403, 2995, 4277h

Etymology

The name bronxisma was named by Francium in 2024. It refers to the postal code of Bronx, New York.

See also

• Unnoticeable comma