Friesachisma

Interval information

Ratio	9361/9360
Factorization	2-4 × 3-2 × 5-1 × 11 × 13-1 × 23 × 37
Monzo	[-4 -2 -1 0 1 -1 0 0 1 0 0 1⟩
Size in cents	0.184951¢
Name	friesachisma
Color name	37o23o3u1og2 thisotwethothulogu 2nd
FJS name	[math]\text{m}{-2}^{11,23,37}_{5,13}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	26.3847
Weil height (log2 max(n, d))	26.3849
Wilson height (sopfr(nd))	103
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19854 bits
Comma size	unnoticeable
open this interval in xen-calc

9361/9360, the friesachisma, is a 37-limit superparticular comma of about 0.18 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 253/252 and 260/259
• 391/390 and 408/407
• 3381/3380 and 5292/5291

It can be factored into the following superparticular intervals:

• 9801/9800 and 208495/208494
• 10241/10240 and 108928/108927
• 10557/10556 and 82621/82620
• 10626/10625 and 78625/78624
• 10648/10647 and 77441/77440
• 10693/10692 and 75141/75140
• 11914/11913 and 43681/43680
• 12673/12672 and 35816/35815
• 14652/14651 and 25921/25920
• 16576/16575 and 21505/21504
• 18241/18240 and 19228/19227

Temperaments

Tempering out this comma leads to the rank-11 temperament friesachismic. Using the 2.3.5.11.13.23.37 subgroup leads to the rank-6 temperament friesachic.

Friesachismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 9361/9360

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	4	],
⟨	0	1	0	0	0	0	0	0	0	0	0	2	],
⟨	0	0	1	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	1	0	0	0	0	0	0	-1	],
⟨	0	0	0	0	0	1	0	0	0	0	0	1	],
⟨	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	-1	],
⟨	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 = 701.965, ~5/4 = 386.325, ~7/4 = 968.826, ~11/8 = 551.293, ~13/8 = 840.556, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.232, ~29/16 = 1029.577, ~31/16 = 1145.036

Optimal ET sequence: 5cfik, 5egj, 5eghj, 6fhijl, 7dfghijjk, 8di, 9gijk, 10jk, 10k, 10, 10h, 12l, 12fk, 12fjk, 14cfjjkkl, 14cfjjl, 15gkl, 16j, 17cgk, 17cghk, 19egh, 21, 22i, 22fh, 24, 26ik, 29gjk, 29gk, 31fghjk, 31l, 34dhk, 38dfij, 39dfgijkl, 46, 50jk, 50k, 53, 53j, 58hik, 62, 65d, 68jl, 72hijk, 72ijk, 80, 80k, 94, 99efk, 103hl, 125f, 130j, 145jkl, 149, 152fgj, 159k, 181, 183k, 183, 198gl, 212ghj, 212gh, 217, 224, 239, 243e, 248h, 270, 311k, 311, 422l, 487, 525, 566gjl, 571, 597ik, 631, 639hj, 692ik, 718, 764j, 764hj, 814k, 814, 863efgjk, 882, 908, 1012, 1106, 1164fi, …

Friesachic

Subgroup: 2.3.5.11.13.23.37

Comma list: 9361/9360

Mapping:

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

Optimal tuning (CTE): ~2=1\1, ~3/2 = 701.965, ~5/4 = 386.325, ~11/8 = 551.293, ~13/8 = 840.556, ~23/16 = 628.232

Optimal ET sequence: 5e, 7fi, 7, 8i, 10, 12l, 12f, 14cfl, 15l, 19e, 22i, 22f, 24, 29, 34, 46, 50, 53, 65, 79l, 80, 87, 96, 118, 125f, 130, 152f, 159, 183, 224, 277, 357, 407, 684, 764, 988, 1012, 1171, 1448, 1696, 1855l, 2000, 2277, 2684, 5144, 6132, 7828l, 8816il, 9828il, 10512eil

Etymology

The friesachisma was named by Francium in 2024, referencing the postal code of Friesach, Austria.

See also

• Unnoticeable comma
• List of superparticular intervals