Etampesisma
| 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 | 0.16689006¢ |
| 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
| [⟨ | 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
| [⟨ | 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.