Lifthrasirsma: Difference between revisions
mNo edit summary |
Update data |
||
| Line 6: | Line 6: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''lifthrasirsma''' ({{monzo|legend=1| 29 -11 -2 0 -2 }}, [[ratio]]: 536870912/535869675) is an [[ | The '''lifthrasirsma''' ({{monzo|legend=1| 29 -11 -2 0 -2 }}, [[ratio]]: 536870912/535869675) is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (also [[2.3.5.11 subgroup|2.3.5.11-]][[subgroup]]) [[comma]] measuring about 3.23 [[cent]]s. It marks the difference between the [[rastma]] and a stack of two [[schisma]]s. | ||
== Temperaments == | == Temperaments == | ||
| Line 18: | Line 18: | ||
Comma list: 536870912/535869675 | Comma list: 536870912/535869675 | ||
Subgroup-val mapping: {{mapping| 1 1 0 9 | 0 2 0 -11 | 0 0 1 -1 }} | |||
Optimal | Optimal tunings: | ||
* WE: ~2 = 1199.9228{{c}}, ~16384/13365 = 351.0529{{c}}, ~5/4 = 386.4968{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~16384/13365 = 351.0805{{c}}, ~5/4 = 386.4947{{c}} | |||
{{Optimal ET sequence|legend=0| 17, 24, 41, 65, 205, 270, 335, 581, 605, 646, 916, 981, 2878e, 3859bcee }} | |||
Badness: | Badness (Sintel): 4.48 | ||
==== 2.3.5.11.19 subgroup ==== | ==== 2.3.5.11.19 subgroup ==== | ||
| Line 31: | Line 33: | ||
Comma list: 1216/1215, 131072/131043 | Comma list: 1216/1215, 131072/131043 | ||
Subgroup-val mapping: {{mapping| 1 1 0 9 -1 | 0 2 0 -11 10 | 0 0 1 -1 1 }} | |||
Optimal | Optimal tunings: | ||
* WE: ~2 = 1199.9494{{c}}, ~256/209 = 351.0800{{c}}, ~5/4 = 386.4828{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~256/209 = 351.0960{{c}}, ~5/4 = 386.4831{{c}} | |||
{{Optimal ET sequence|legend=0| 17, 24, 41, 65, 181, 205, 270, 581, 646, 851, 916, 1186, 2102 }} | |||
Badness: 0. | Badness (Sintel): 0.581 | ||
== Etymology == | == Etymology == | ||
Latest revision as of 15:07, 11 February 2026
| Interval information |
reduced subharmonic
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
Subgroup-val mapping: [⟨1 1 0 9], ⟨0 2 0 -11], ⟨0 0 1 -1]]
Optimal tunings:
- WE: ~2 = 1199.9228 ¢, ~16384/13365 = 351.0529 ¢, ~5/4 = 386.4968 ¢
- CWE: ~2 = 1200.0000 ¢, ~16384/13365 = 351.0805 ¢, ~5/4 = 386.4947 ¢
Optimal ET sequence: 17, 24, 41, 65, 205, 270, 335, 581, 605, 646, 916, 981, 2878e, 3859bcee
Badness (Sintel): 4.48
2.3.5.11.19 subgroup
Subgroup: 2.3.5.11.19
Comma list: 1216/1215, 131072/131043
Subgroup-val mapping: [⟨1 1 0 9 -1], ⟨0 2 0 -11 10], ⟨0 0 1 -1 1]]
Optimal tunings:
- WE: ~2 = 1199.9494 ¢, ~256/209 = 351.0800 ¢, ~5/4 = 386.4828 ¢
- CWE: ~2 = 1200.0000 ¢, ~256/209 = 351.0960 ¢, ~5/4 = 386.4831 ¢
Optimal ET sequence: 17, 24, 41, 65, 181, 205, 270, 581, 646, 851, 916, 1186, 2102
Badness (Sintel): 0.581
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.