Step variety: Difference between revisions

Line 10:

* Certain chroma-altered MOS scales, which are contained in the group generated by the period and the generator of the unaltered MOS are ternary. An example is harmonic minor in any non-edo diatonic tuning, a chroma-alteration of the diatonic MOS with step pattern msmmsLs.

The term ''n-ary'' disregards the rank of the group generated by the step sizes, although an ''n''-ary scale is still ''generically'' rank-''n'' (the group generated by the ''n'' step sizes X<sub>''i''</sub> > 0, ''i'' = 1, ..., ''n'', has rank ''n'', not lower, for ''almost all'' choices of X<sub>''i''</sub>, in the same sense that almost all real numbers between 0 and 1 are irrational).

== List of named ternary scales ==

The following is a list of (temperament-agnostic) names that have been given to 3-step scales.

=== 7 notes ===

* [[nicetone]] (3L 2M 2S)

* [[omnidiatonic]] (2L 3M 2S)

* [[smicot]] (3L 1M 3S)

=== 8 notes ===

* [[porcusmine]] (4L 3M 1S)

* [[pinedye]] (5L 2M 1S)

=== 9 notes ===

* [[diasem]] (5L 2M 2S)

* [[armozan]] (2L 5M 2S)

* [[balgram]] (2L 2M 5S)

=== 10 notes ===

* [[blackdye]] (5L 2M 3S)

* [[blackville]] (2L 5M 3S)

=== 11 notes ===

* [[diamech]] (5L 2M 4S)

* [[semion]] (5L 3M 3S)

=== 12 notes ===

* [[diachromedye]] (5L 2M 5S)

=== 14 notes ===

* [[whitedye]] (5L 2M 7S)

[[Category:Terms]][[Category:Scale]]

@@ Line 10: / Line 10: @@
 * Certain chroma-altered MOS scales, which are contained in the group generated by the period and the generator of the unaltered MOS are ternary. An example is harmonic minor in any non-edo diatonic tuning, a chroma-alteration of the diatonic MOS with step pattern msmmsLs.
 The term ''n-ary'' disregards the rank of the group generated by the step sizes, although an ''n''-ary scale is still ''generically'' rank-''n'' (the group generated by the ''n'' step sizes X<sub>''i''</sub> > 0, ''i'' = 1, ..., ''n'', has rank ''n'', not lower, for ''almost all'' choices of X<sub>''i''</sub>, in the same sense that almost all real numbers between 0 and 1 are irrational).
+== List of named ternary scales ==
+The following is a list of (temperament-agnostic) names that have been given to 3-step scales.
+=== 7 notes ===
+* [[nicetone]] (3L 2M 2S)
+* [[omnidiatonic]] (2L 3M 2S)
+* [[smicot]] (3L 1M 3S)
+=== 8 notes ===
+* [[porcusmine]] (4L 3M 1S)
+* [[pinedye]] (5L 2M 1S)
+=== 9 notes ===
+* [[diasem]] (5L 2M 2S)
+* [[armozan]] (2L 5M 2S)
+* [[balgram]] (2L 2M 5S)
+=== 10 notes ===
+* [[blackdye]] (5L 2M 3S)
+* [[blackville]] (2L 5M 3S)
+=== 11 notes ===
+* [[diamech]] (5L 2M 4S)
+* [[semion]] (5L 3M 3S)
+=== 12 notes ===
+* [[diachromedye]] (5L 2M 5S)
+=== 14 notes ===
+* [[whitedye]] (5L 2M 7S)
 [[Category:Terms]][[Category:Scale]]