4L 6s (5/1-equivalent): Difference between revisions
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{{MOS intro}} | {{MOS intro}} | ||
== Intervals == | == Intervals == | ||
{{MOS degrees|Step Ratio=2/1; 3/1; 3/2 | {{MOS degrees|Step Ratio=2/1; 3/1; 3/2}} | ||
== Theory == | == Theory == | ||
The primary no-twos-or-threes temperament interpretation of this scale is as the decatonic scale of the 5.7.11 temperament [[juggernaut]], in which the generator is [[7/5]] and the half-pentave period is [[11/5]]. This is a very good and low-badness temperament on the 5.7.11 subgroup, although it suffers from a somewhat high error because of the smeary 11/5 at 1393 cents. This MOS can be viewed as a pentave analog of [[5L 2s|diatonic]] or [[4L 5s (3/1-equivalent)|lambda]], since its basic tuning of [[14ed5]] is the smallest [[ed5]] that can seriously claim to represent no-twos-or-threes harmony. | The primary no-twos-or-threes temperament interpretation of this scale is as the decatonic scale of the 5.7.11 temperament [[juggernaut]], in which the generator is [[7/5]] and the half-pentave period is [[11/5]]. This is a very good and low-badness temperament on the 5.7.11 subgroup, although it suffers from a somewhat high error because of the smeary 11/5 at 1393 cents. This MOS can be viewed as a pentave analog of [[5L 2s|diatonic]] or [[4L 5s (3/1-equivalent)|lambda]], since its basic tuning of [[14ed5]] is the smallest [[ed5]] that can seriously claim to represent no-twos-or-threes harmony. | ||
== Scale tree == | == Scale tree == | ||
{{Scale tree|Comments=9/7:Optimal tridecimal juggernaut;11/7: Optimal juggernaut, bright generator is near-7/5;5/2: Dark generator is near-11/7}} | {{Scale tree|Comments=9/7:Optimal tridecimal juggernaut;11/7: Optimal juggernaut, bright generator is near-7/5;5/2: Dark generator is near-11/7}} | ||