Lifthrasirsma
Ratio | 536870912/535869675 |
Factorization | 2^{29} × 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 |
Tenney height (log_{2} nd) | 57.9973 |
Weil height (log_{2} max(n, d)) | 58 |
Wilson height (sopfr (nd)) | 123 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.44402 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.