12L 12s: Difference between revisions

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=== Intervals ===

While 12L 12s can be treated as a 24-form system due to the scale containing 24 notes, it can also sense as two rings of 12edo that differ by a small step. For example, in compton, the small step represents the [[81/80]] comma, ~~which can be used to achieve~~ accurate 5-limit ~~harmony~~. In catler, the small step represents [[64/63]] and [[36/35]], and inflecting a 12edo minor seventh down by this step gives a more accurate ~[[7/4]], while 5-limit ~~intervals~~ are represented as in 12edo.

While 12L 12s can be treated as a 24-form system due to the scale containing 24 notes, it can also make sense as two rings of 12edo that differ by a small step. For example, in compton, the small step represents the [[81/80]] comma, and inflecting 12edo intervals by this step produces more accurate approximations of 5-limit intervals. In catler, the small step represents [[64/63]] and [[36/35]], and inflecting a 12edo minor seventh down by this step gives a more accurate ~7/4, with other ratios involving harmonic 7 also improved, while intervals within the 5-limit are represented as in 12edo.

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== Scale tree ==

Softer tunings of 12L 12s are closer to an unequal derivative of [[24edo]], while harder tunings are closer to two rings of 12edo a comma step apart.

{{MOS tuning spectrum

| 3/2 = [[Duodecim]]

| 3/1 = [[Catler]]

| 5/2 = [[Catler]]

| 5/1 = [[Compton]]

| 6/1 = [[Compton]]

}}

@@ Line 10: / Line 10: @@
 === Intervals ===
-While 12L 12s can be treated as a 24-form system due to the scale containing 24 notes, it can also sense as two rings of 12edo that differ by a small step. For example, in compton, the small step represents the [[81/80]] comma, which can be used to achieve accurate 5-limit harmony. In catler, the small step represents [[64/63]] and [[36/35]], and inflecting a 12edo minor seventh down by this step gives a more accurate ~[[7/4]], while 5-limit intervals are represented as in 12edo.
+While 12L 12s can be treated as a 24-form system due to the scale containing 24 notes, it can also make sense as two rings of 12edo that differ by a small step. For example, in compton, the small step represents the [[81/80]] comma, and inflecting 12edo intervals by this step produces more accurate approximations of 5-limit intervals. In catler, the small step represents [[64/63]] and [[36/35]], and inflecting a 12edo minor seventh down by this step gives a more accurate ~7/4, with other ratios involving harmonic 7 also improved, while intervals within the 5-limit are represented as in 12edo.
 {{MOS intervals}}
@@ Line 18: / Line 18: @@
 == Scale tree ==
+Softer tunings of 12L 12s are closer to an unequal derivative of [[24edo]], while harder tunings are closer to two rings of 12edo a comma step apart.
 {{MOS tuning spectrum
 | 3/2 = [[Duodecim]]
-| 3/1 = [[Catler]]
+| 5/2 = [[Catler]]
-| 5/1 = [[Compton]]
+| 6/1 = [[Compton]]
 }}