Totziensisma

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Interval information
Ratio 19251/19250
Factorization 2-1 × 33 × 5-3 × 7-1 × 11-1 × 23 × 31
Monzo [-1 3 -3 -1 -1 0 0 0 1 0 1
Size in cents 0.0899319¢
Name totziensisma
Color name 31o23o1urg31,
thiwotwetholurutrigu unison
FJS name [math]\text{m}{-2}^{23,31}_{5,5,5,7,11}[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 28.4652
Weil height (log2 max(n, d)) 28.4653
Wilson height (sopfr(nd)) 98
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.19989 bits
Comma size unnoticeable
open this interval in xen-calc

19251/19250, the totziensisma, is a 31-limit superparticular comma of about 0.09 cents.

Commatic relationships

This comma can be multiplied into the following superparticular commas:

Temperaments

Tempering out this comma in the full 31-limit leads to the rank-10 temperament totziensismic. Using the 2.3.5.7.11.23.31 subgroup leads to the rank-6 temperament totziensmic.

Totziensismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 19251/19250

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.950, ~5/4 = 386.324, ~7/4 = 968.831, ~11/8 = 551.326, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.261, ~29/16 = 1029.577

Optimal ET sequence5g, 5gj, 5eghjkk, 7deefghijjkkk, 7dfghijjk, 8di, 9, 10jk, 10k, 12deh, 12de, 12fijk, 15f, 15, 19eghi, 19, 22i, 24, 26i, 27egij, 31, 34dhk, 34dhjk, 38dfij, 39dfgijk, 41g, 41, 46, 58hik, 68ej, 72k, 77k, 80k, 94jk, 99ek, 99efk, 103h, 125f, 137, 140hk, 140k, 145jk, 149, 152fgj, 159k, 183, 190g, 217, 243ek, 270, 323, 342f, 354i, 373g, 383ij, 388, 422, 525, 566gj, 571, 624jk, 639hj, 718, 742i, 863efgjk, 908, 954hj, 1205g, 1289, 1308, 1395, 1578, 1920, 2311, 2460j, 2460, 2684, 2742k, 2901, 3323, 3638i, 3696, 3809k, 3889, 3992, 4038j, 4460, 4619, 4901, 4946gij, 5144, 5395, 5809, 6349, 6893, 7315, 7361, 7847jk, 8893, 9281, 10589, 10729k

Totziensmic

Subgroup: 2.3.5.7.11.23.31

Comma list: 19251/19250

Mapping:

[⟨ 1 0 0 0 0 0 1 ],
0 1 0 0 0 0 -3 ],
0 0 1 0 0 0 3 ],
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 = 701.950, ~5/4 = 386.324, ~7/4 = 968.831, ~11/8 = 551.326, ~23/16 = 628.261

Optimal ET sequence5, 7dik, 8di, 10k, 12de, 12ik, 15, 19ei, 19, 22i, 27ei, 31, 41, 46, 58ik, 72k, 80k, 94k, 99ek, 118k, 125, 140k, 144, 152, 183, 190, 224, 270, 342, 612, 764, 954, 1106, 1354, 1547, 1578, 1730, 1920, 2118, 2684, 4038, 5243, 5585, 8269

Etymology

The name totziensisma was named by Francium in 2024. It refers to 19251 Totziens, the asteroid. The asteroid was named such because it was Dutch for 'Au revoir'; the discovery was made shortly after the 1994 IAU meeting in The Hague.

See also