Etampesisma

Interval information

Ratio	10374/10373
Factorization	2 × 3 × 7 × 11-1 × 13 × 19 × 23-1 × 41-1
Monzo	[1 1 0 1 -1 1 0 1 -1 0 0 0 -1⟩
Size in cents	0.1668901¢
Name	etampesisma
Color name	41u23u19o3o1uz2 fowutwethunotholuzo 2nd
FJS name	[math]\text{dd3}^{7,13,19}_{11,23,41}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	26.6812
Weil height (log2 max(n, d))	26.6814
Wilson height (sopfr(nd))	119
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.19848 bits
Comma size	unnoticeable
open this interval in xen-calc

10374/10373, the etampesisma, is a 41-limit superparticular comma of about 0.17 cents.

Commatic relations

This comma can be factored in following superparticular ratios:

• 11271/11270 and 130340/130339
• 11340/11339 and 121771/121770
• 12168/12167 and 70357/70356
• 12376/12375 and 64125/64124
• 13377/13376 and 46208/46207
• 17836/17835 and 24795/24794
• 19551/19550 and 22100/22099
• 19845/19844 and 21736/21735

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament etampesismic. Using the 2.3.7.11.13.19.23.41 subgroup leads to the rank-7 temperament etampesic.

Etampesismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41

Comma list: 10374/10373

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.951, ~5/4 = 386.314, ~7/4 = 968.813, ~11/8 = 551.337, ~13/8 = 840.506, ~17/16 = 104.955, ~19/16 = 297.484, ~23/16 = 628.307, ~29/16 = 1029.577, ~31/16 = 1145.036, ~37/32 = 251.344

Optimal ET sequence: 5, 5g, 5eghj, 5eghjl, 6fhijlm, 7dfghijjkllmmm, 7dghijjkm, 7dghikm, 7l, 8di, 9gijkl, 10jkm, 10h, 12del, 12l, 12fkm, 12fjkm, 14cfggjjkklmm, 14cfjjkklmm, 14cfjjlmm, 15m, 15km, 15gkm, 15gklm, 17cg, 17cgk, 17cghkm, 18ehijkm, 19eghlm, 19eghm, 21m, 22il, 22i, 22h, 24d, 26ik, 29gjk, 29gk, 34dhkm, 34dhjkm, 34dhjklm, 38dfijkklm, 38dfijlm, 39dfgijklmm, 41, 43, 46l, 46, 50jkm, 50km, 53gk, 53k, 53, 53j, 58hik, 58hikl, 60ehl, 62, 72hijkllm, 72hijkm, 77, 80, 80k, 99efkm, , 121hhiklm, 130j, 137, 140hk, 145jkl, 149, 166gl, 181, 183k, 183, 190gl, 193, 193l, 198l, 198gl, 224h, 236dghi, 239, 243e, 248h, 270, 282, 311k, 311, 388, 431, 436, 472, 486gjklm, 487, 525, 540, 566gjl, 624jk, 639hjm, 653, 692ikm, 718, 764, 764j, 814k, 814, 863efgjk, 954hjl, 1012, 1147i, 1164fim, 1178, …

Etampesic

Subgroup: 2.3.7.11.13.19.23.41

Comma list: 10374/10373

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.951, ~7/4 = 968.813, ~11/8 = 551.337, ~13/8 = 840.506, ~19/16 = 297.484, ~23/16 = 628.307

Optimal ET sequence: 5fi, 5, 7dhim, 7, 8dhhimm, 9i, 14fmm, 15m, 17, 26i, 29, 36e, 41, 46, 53, 55fhim, 58hi, 63, 80, 94, 104i, 113, 152fm, 166, 207, 265, 311, 373, 431, 477m, 494h, 518, 540, 549f, 566, 581, 684hm, 701, 747, 1012, 1759, 2383, 2477, 2590, 3602, 6079, 7951, 8669, 9681m

Etymology

The name etampesisma was named by Francium in 2024. It refers to 10374 Etampes, the asteroid. Which was in turn named after a location near Paris, France.

See also

• Unnoticeable comma
• List of superparticular intervals