Lifthrasirsma

Interval information

Ratio	536870912/535869675
Factorization	229 × 3-11 × 5-2 × 11-2
Monzo	[29 -11 -2 0 -2⟩
Size in cents	3.231678¢
Name	lifthrasirsma
Color name	ss1uugg3, sasa-bilugu 3rd
FJS name	[math]\text{dd3}_{5,5,11,11}[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	57.9973
Weil height (log2 max(n, d))	58
Wilson height (sopfr(nd))	123
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.29683 bits
Comma size	unnoticeable
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The lifthrasirsma (monzo: [29 -11 -2 0 -2⟩, ratio: 536870912/535869675) is an unnoticeable 11-limit (also 2.3.5.11 subgroup) comma measuring about 3.23 cents. It marks the difference between the rastma and a stack of two schismas.

Temperaments

Tempering out this comma in the full 11-limit leads to the rank-4 lifthrasirsmic temperament, or in the 2.3.5.11 subgroup, the rank-3 lifthrasir temperament.

Lifthrasir can be extended to the 2.3.5.11.19 subgroup by tempering out 1216/1215. The second comma in the list, 131072/131043, has the effect of equating the undevicesimal schisma of 513/512 with the schisma. Lif is a notable weak extension of lifthrasir.

Lifthrasir

Subgroup: 2.3.5.11

Comma list: 536870912/535869675

Sval mapping: [⟨1 1 0 9], ⟨0 2 0 -11], ⟨0 0 1 -1]]

Optimal tuning (CTE): ~2 = 1\1, ~16384/13365 = 351.0971, ~5/4 = 386.4070

Optimal ET sequence: 17, 24, 41, 65, 205, 270, 335, 581, 605, 646, 916, 981, 2878e, 3859bcee

Badness: 0.542 × 10^-3

2.3.5.11.19 subgroup

Subgroup: 2.3.5.11.19

Comma list: 1216/1215, 131072/131043

Sval mapping: [⟨1 1 0 9 -1], ⟨0 2 0 -11 10], ⟨0 0 1 -1 1]]

Optimal tuning (CTE): ~2 = 1\1, ~256/209 = 351.1010, ~5/4 = 386.4125

Optimal ET sequence: 17, 24, 41, 65, 181, 205, 270, 581, 646, 851, 916, 1186, 2102

Badness: 0.260 × 10^-3

Etymology

This comma was named by Flora Canou in 2023 along with the corresponding temperaments, lif and lifthrasir, after the human survivors of Ragnarök in Norse mythology.