13L 2s (3/1-equivalent): Difference between revisions
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This MOS scale pattern is most notable for corresponding to the 15-note [[3.5 subgroup]] scale generated by a just [[5/3]], which has an L:s ratio of approximately 1.57. In this case, the large step represents [[27/25]] and the small step represents [[1220703125/1162261467]]. It is the smallest MOS generated by the [[3.5 subgroup]] which does not have 2 large steps, and the smallest in which the entire range of generators can reasonably be taken as an approximation of [[5/3]]. | This MOS scale pattern is most notable for corresponding to the 15-note [[3.5 subgroup]] scale generated by a just [[5/3]], which has an L:s ratio of approximately 1.57. In this case, the large step represents [[27/25]] and the small step represents [[1220703125/1162261467]]. It is the smallest MOS generated by the [[3.5 subgroup]] which does not have 2 large steps, and the smallest in which the entire range of generators can reasonably be taken as an approximation of [[5/3]]. | ||
Tritave-equivalent temperaments | Tritave-equivalent temperaments generated by a near-just or slightly flat [[5/3]] will also produce this MOS scale. The [[3.5.11 subgroup]] [[microtemperament]] [[delta centauri]] (which is generated by a near-just ~5/3 such that 9 generators stacked represent ~[[11/9]]) has this as its 15-note MOS scale. Interestingly, the chroma (L-s) represents [[125/121]] in this case. If you want the high accuracy offered by this temperament then a ~5/3 generator between [[28edt|15\28edt]] and [[43edt|23\43edt]] is best (corresponding to L:s between 3:2 and 2:1). | ||
The most optimized tunings of [[Arcturus]] temperament have the ~5/3 slightly sharper than in [[13edt]] and thus generate this MOS, but Arcturus has a quite wide range of reasonable generators so it is not a given that it will generate this MOS. | The most optimized tunings of [[Arcturus]] temperament have the ~5/3 slightly sharper than in [[13edt]] and thus generate this MOS, but Arcturus has a quite wide range of reasonable generators so it is not a given that it will generate this MOS. | ||
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== Scale tree == | == Scale tree == | ||
{{MOS tuning spectrum|11/7=Just-[[5/3]] | {{MOS tuning spectrum|11/7=Just-[[5/3]] a.k.a. [[Trithagorean]] tuning (884.359{{c}})|12/7=[[CWE]]-optimized [[Delta centauri]] (883.901{{c}})|1/0=[[CWE]]-optimized [[Arcturus]] (878.291{{c}})}} | ||
{{stub}} | {{stub}} | ||