2.5 subgroup: Difference between revisions
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The 2.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 3. Its simplest [[expansion]] is the [[2.5.7 subgroup]], which adds prime [[7/1|7]]. | The 2.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 3. Its simplest [[expansion]] is the [[2.5.7 subgroup]], which adds prime [[7/1|7]]. | ||
== EDO approximation == | |||
[[EDO]]s which do relatively well at approximating 2.5 subgroup intervals can be found as the denominators of the convergents and semiconvergents of the {{w|continued fraction}} for the logarithm base 2 of 5. The sequence is equivalent to the numbers of notes per octave in the [[mos scale]]s generated by a pure 5/4 generator: {{EDOs| 2, 3, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 59, 87, 146, 205, 351, 497, 643, 789, 1432 … }} | |||
== MOS scales == | == MOS scales == | ||