Totziensisma

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]\displaystyle{ \text{m}{-2}^{23,31}_{5,5,5,7,11} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	28.4652
Weil norm (log2 max(n, d))	28.4653
Wilson norm (sopfr(nd))	98
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:

• 19344/19343 and 4004001/4004000
• 22816/22815 and 123201/123200

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 sequence: 5g, 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 sequence: 5, 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.

See also

• Unnoticeable comma
• List of superparticular intervals