12L 12s: Difference between revisions

(3 intermediate revisions by the same user not shown)

Line 10:

=== Intervals ===

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.

~~=== Generator chain ===~~

~~{{MOS genchain}}~~

=== Modes ===

Since 12L 12s has only one large step and one small step per period, there are only two modes, which can be called major and minor. In compton, catler, and duodecim, the major mode favors otonalities above the root, while the minor mode favors utonalities above the root. This is because [[5/4]], [[7/4]], and [[11/8]] are all closer to the 12edo step above it than the step below it.

Since 12L 12s has only one large step and one small step per period, there are only two modes, which can be called the major and minor modes. In compton, catler, and duodecim, the major mode favors otonalities above the root, while the minor mode favors utonalities above the root. This is because [[5/4]], [[7/4]], and [[11/8]] are all closer to the 12edo step above it than the step below it.

== 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 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}}
-=== Generator chain ===
-{{MOS genchain}}
 === Modes ===
-Since 12L 12s has only one large step and one small step per period, there are only two modes, which can be called major and minor. In compton, catler, and duodecim, the major mode favors otonalities above the root, while the minor mode favors utonalities above the root. This is because [[5/4]], [[7/4]], and [[11/8]] are all closer to the 12edo step above it than the step below it.
+Since 12L 12s has only one large step and one small step per period, there are only two modes, which can be called the major and minor modes. In compton, catler, and duodecim, the major mode favors otonalities above the root, while the minor mode favors utonalities above the root. This is because [[5/4]], [[7/4]], and [[11/8]] are all closer to the 12edo step above it than the step below it.
 {{MOS mode degrees}}
 == 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]]
 }}