2L 11s (3/1-equivalent): Difference between revisions

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This MOS scale pattern is most notable for corresponding to the 13-note [[Trithagorean]]/[[3.5 subgroup]] scale generated by a just [[5/3]], which has an L:s ratio of approximately 1.64. In this case, the large step represents [[48828125/43046721]] and the small step represents [[27/25]]. It is also the 13-note MOS of several tritave-equivalent temperaments generated by ~5/3 (similar to how the [[5L 2s]] diatonic scale is the 7-note MOS of chain-of-fifth temperaments). 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 13-note MOS scale. [[Arcturus]] temperament tunings with ~5/3 sharper than 6 steps of [[13edt]] will generate this MOS, but tunings with ~5/3 flatter than 6 steps of [[13edt]] will instead generate the sister MOS {{MOS scalesig|11L 2s<3/1>|link=1}}.

This MOS scale pattern is most notable for corresponding to the 13-note [[Trithagorean]]/[[3.5 subgroup]] scale generated by a just [[5/3]], which has an L:s ratio of approximately 1.64. In this case, the large step represents [[48828125/43046721]] and the small step represents [[27/25]]. It is also the 13-note MOS of several tritave-equivalent temperaments generated by ~5/3 (similar to how the [[5L 2s]] diatonic scale is the 7-note MOS of chain-of-fifth temperaments). 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 13-note MOS scale, although the 15-note {{MOS scalesig|13L 2s<3/1>|link=1}} scale may be preferred as it has a much greater abundance of 9:11:15 triads for only 2 more notes. [[Arcturus]] temperament tunings with ~5/3 sharper than 6 steps of [[13edt]] will generate this MOS, but tunings with ~5/3 flatter than 6 steps of [[13edt]] will instead generate the sister MOS {{MOS scalesig|11L 2s<3/1>|link=1}}.

In the moderately hard-of-basic region is the 3.5.11 subgroup [[Polaris]] temperament which, like Delta centauri, constructs an ~11/9 from stacking ~5/3 generators, but here ~5/3 is tuned quite sharp so that -6 5/3s stacked (or 6 [[9/5]]s stacked) tritave-reduced is ~11/9. If the L:s ratio is very high (starting at around 5:1), the generator becomes too sharp to approximate 5/3, and everything gets closer and closer to collapsing into [[2edt]].

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 {{MOS intro}}
-This MOS scale pattern is most notable for corresponding to the 13-note [[Trithagorean]]/[[3.5 subgroup]] scale generated by a just [[5/3]], which has an L:s ratio of approximately 1.64. In this case, the large step represents [[48828125/43046721]] and the small step represents [[27/25]]. It is also the 13-note MOS of several tritave-equivalent temperaments generated by ~5/3 (similar to how the [[5L 2s]] diatonic scale is the 7-note MOS of chain-of-fifth temperaments).  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 13-note MOS scale. [[Arcturus]] temperament tunings with ~5/3 sharper than 6 steps of [[13edt]] will generate this MOS, but tunings with ~5/3 flatter than 6 steps of [[13edt]] will instead generate the sister MOS {{MOS scalesig|11L 2s<3/1>|link=1}}.
+This MOS scale pattern is most notable for corresponding to the 13-note [[Trithagorean]]/[[3.5 subgroup]] scale generated by a just [[5/3]], which has an L:s ratio of approximately 1.64. In this case, the large step represents [[48828125/43046721]] and the small step represents [[27/25]]. It is also the 13-note MOS of several tritave-equivalent temperaments generated by ~5/3 (similar to how the [[5L 2s]] diatonic scale is the 7-note MOS of chain-of-fifth temperaments).  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 13-note MOS scale, although the 15-note {{MOS scalesig|13L 2s<3/1>|link=1}} scale may be preferred as it has a much greater abundance of 9:11:15 triads for only 2 more notes. [[Arcturus]] temperament tunings with ~5/3 sharper than 6 steps of [[13edt]] will generate this MOS, but tunings with ~5/3 flatter than 6 steps of [[13edt]] will instead generate the sister MOS {{MOS scalesig|11L 2s<3/1>|link=1}}.
 In the moderately hard-of-basic region is the 3.5.11 subgroup [[Polaris]] temperament which, like Delta centauri, constructs an ~11/9 from stacking ~5/3 generators, but here ~5/3 is tuned quite sharp so that -6 5/3s stacked (or 6 [[9/5]]s stacked) tritave-reduced is ~11/9. If the L:s ratio is very high (starting at around 5:1), the generator becomes too sharp to approximate 5/3, and everything gets closer and closer to collapsing into [[2edt]].

2L 11s (3/1-equivalent): Difference between revisions

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