# Lifthrasirsma

 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 $\text{dd3}_{5,5,11,11}$ 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, $\sqrt{nd}$) ~1.29683 bits Comma size unnoticeable open this interval in xen-calc

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.