4L 3s: Difference between revisions

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=== Orgone ===

[[Orgone]] tunings (with generator a minor third sharper than 4\15 and flatter than 3\11) have step ratios between 2/1 and 3/1. It nominally approximates the 2.7.11 subgroup, on which the [[26edo]] tuning is pretty much optimal. The large step approximates [[8/7]], and the major smifourth (2 large steps + 1 small step) approximates [[11/8]].

[[Orgone]] tunings (with generator a minor third sharper than 4\15 and flatter than 3\11) have step ratios between 2/1 and 3/1. It nominally approximates the 2.7.11 subgroup, on which the [[26edo]] tuning is very accurate and pretty much optimal. The large step approximates [[8/7]], and the major smifourth (2 large steps + 1 small step) approximates [[11/8]].

EDOs that support orgone include [[11edo]], [[15edo]], [[26edo]], and [[37edo]].

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| 128/121, (16/15)

|}

=== Kleismic ===

[[Kleismic]] (aka hanson or keemun) tunings (with generator a minor third sharper than 5\19 and flatter than 4\15) have step ratios between 3/1 and 4/1. Kleismic is a [[5-limit]] microtemperament that tempers out the [[kleisma]] 15625/15552. The generator is close to a pure [[6/5]] minor third, and 6 minor thirds are used to reach [[3/2]]. The 7-note MOS only has one perfect fifth, so bigger MOSes, such as the [[4L 7s]] 11-note MOS, are suggested for getting 5-limit harmony.

@@ Line 514: / Line 514: @@
 === Orgone ===
-[[Orgone]] tunings (with generator a minor third sharper than 4\15 and flatter than 3\11) have step ratios between 2/1 and 3/1. It nominally approximates the 2.7.11 subgroup, on which the [[26edo]] tuning is pretty much optimal. The large step approximates [[8/7]], and the major smifourth (2 large steps + 1 small step) approximates [[11/8]].
+[[Orgone]] tunings (with generator a minor third sharper than 4\15 and flatter than 3\11) have step ratios between 2/1 and 3/1. It nominally approximates the 2.7.11 subgroup, on which the [[26edo]] tuning is very accurate and pretty much optimal. The large step approximates [[8/7]], and the major smifourth (2 large steps + 1 small step) approximates [[11/8]].
 EDOs that support orgone include [[11edo]], [[15edo]], [[26edo]], and [[37edo]].
@@ Line 544: / Line 544: @@
 | 128/121, (16/15)
 |}
 === Kleismic ===
 [[Kleismic]] (aka hanson or keemun) tunings (with generator a minor third sharper than 5\19 and flatter than 4\15) have step ratios between 3/1 and 4/1. Kleismic is a [[5-limit]] microtemperament that tempers out the [[kleisma]] 15625/15552. The generator is close to a pure [[6/5]] minor third, and 6 minor thirds are used to reach [[3/2]]. The 7-note MOS only has one perfect fifth, so bigger MOSes, such as the [[4L 7s]] 11-note MOS, are suggested for getting 5-limit harmony.