Honeybrookisma

Interval information

Ratio	19344/19343
Factorization	24 × 3 × 13 × 23-1 × 29-2 × 31
Monzo	[4 1 0 0 0 1 0 0 -1 -2 1⟩
Size in cents	0.08949952¢
Name	honeybrookisma
Color name	31o29uu23u3o-2 thiwobitwenu-atwethutho negative 2nd
FJS name	[math]\text{P1}^{13,31}_{23,29,29}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	28.4791
Weil height (log2 max(n, d))	28.4792
Wilson height (sopfr(nd))	136
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19989 bits
Comma size	unnoticeable
open this interval in xen-calc

19344/19343, the honeybrookisma, is a 31-limit superparticular comma of about 0.089 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 2002/2001 and 2233/2232
• 4992/4991 and 6728/6727
• 5888/5887 and 8464/8463

It can be factored into following superparticular commas:

• 20736/20735 and 288145/288144
• 21736/21735 and 175770/175769

Temperaments

Tempering out this comma leads to the rank-10 temperament honeybrookismic. Using the 2.3.13.23.29.31 subgroup leads to the rank-5 temperament honeybrookic.

Honeybrookismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 19344/19343

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.954, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.318, ~13/8 = 840.520, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.286, ~29/16 = 1029.604

Optimal ET sequence: 5cfik, 5eghjkk, 6fhijkk, 7deefghijjkkk, 7dghik, 7, 8di, 9jk, 10, 10h, 12de, 12e, 14cfjjkk, 14c, 15, 17cgk, 17cghk, 18ehijk, 19eghikk, 19egh, 19, 22i, 22fh, 26ik, 31fghjk, 31, 38dfijkk, 39dfgijk, 41i, 49fghjkk, 50, 53k, 56, 58hik, 62, 77g, 77, 80k, 94, 103h, 121ik, 140k, 145jk, 152fgjk, 159k, 183, 190g, 217, 243ek, 270, 311, 388, 436, 472, 487, 532dfghik, 540, 552g, 554ek, 571, 653, 692ik, 718, 863efgjk, 882, 908, 997, 1041, 1106, 1164fi, …

Honeybrookic

Subgroup: 2.3.13.23.29.31

Comma list: 19344/19343

Mapping:

[⟨	1	1	3	4	4	4	],
⟨	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, ~3/2 = 701.954, ~13/8 = 840.520, ~23/16 = 628.286, ~29/16 = 1029.604

Optimal ET sequence: 5fik, 5f, 7ik, 7, 10, 12, 17k, 19, 29, 34, 39fijk, 41i, 43i, 51, 70, 94, 96k, 113, 135, 147, 241, 260, 311, 571, 718, 978, 1289, 1872, 2183, 2754, 3472, 5655, 7768, 8339, 10522

Etymology

The honeybrookisma was named by Francium in 2024. It refers to the postal code of Honey Brook, Pennsylvania.

See also

• Unnoticeable comma
• List of superparticular intervals