111th-octave temperaments: Difference between revisions
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{{Fractional-octave navigation|111}} | {{Fractional-octave navigation|111}} | ||
==Roentgenium== | ==Roentgenium== | ||
Roentgenium is defined as 4884 & 8103 in the 19-limit and is named after the 111th element. 111 is 37 x 3, and what's particularly remarkable about this temperament is that it still preserves the relationship of 11/8 to 37edo in EDOs the size of thousands. Developed for a musical composition in [[8103edo]] by Eliora. | Roentgenium is the [[Fractional-octave temperaments|fractional-octave temperament]] defined as 4884 & 8103 in the [[19-limit]] and is named after the 111th element. 111 is 37 x 3, and what's particularly remarkable about this temperament is that it still preserves the relationship of 11/8 to [[37edo]] in EDOs the size of thousands. Developed for a musical composition in [[8103edo]] by [[Eliora]]. | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
Comma list: {{monzo|-25 -12 -3 12 5}}, {{monzo|-27 27 0 3 -7}}, {{monzo|26 -8 -2 8 -9}} | [[Comma list]]: {{monzo|-25 -12 -3 12 5}}, {{monzo|-27 27 0 3 -7}}, {{monzo|26 -8 -2 8 -9}} | ||
Mapping: [{{val|111 111 2855 896 384}}, {{val|0 1 -40 -9 0}}] | [[Mapping]]: [{{val|111 111 2855 896 384}}, {{val|0 1 -40 -9 0}}] | ||
Optimal tuning (CTE): ~3/2 = 701.964 | [[Optimal tuning]] (CTE): ~3/2 = 701.964 | ||
====19-limit==== | ====19-limit==== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
Revision as of 08:06, 8 September 2023
Template:Fractional-octave navigation
Roentgenium
Roentgenium is the fractional-octave temperament defined as 4884 & 8103 in the 19-limit and is named after the 111th element. 111 is 37 x 3, and what's particularly remarkable about this temperament is that it still preserves the relationship of 11/8 to 37edo in EDOs the size of thousands. Developed for a musical composition in 8103edo by Eliora.
Subgroup: 2.3.5.7.11
Comma list: [-25 -12 -3 12 5⟩, [-27 27 0 3 -7⟩, [26 -8 -2 8 -9⟩
Mapping: [⟨111 111 2855 896 384], ⟨0 1 -40 -9 0]]
Optimal tuning (CTE): ~3/2 = 701.964
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 31213/31212, 486400/486387, 633556/633555, 653429/653400, 1037232/1037153, 9714446/9713275, 24764600/24762387
Mapping: [⟨111 111 2855 896 384 410 452 472], ⟨0 1 -40 -9 0 -11 -25 7]]
Optimal tuning (CTE): ~3/2 = 701.9...
Optimal ET sequence: 3219c, 4884, 8103, 12987, ...