Even-regular MV3 scale: Difference between revisions
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* Even-regular MV3 scales always satisfy all 3 of the [[monotone-MOS scale|monotone-MOS]] conditions. | * Even-regular MV3 scales always satisfy all 3 of the [[monotone-MOS scale|monotone-MOS]] conditions. | ||
* Another characterization of even-regular MV3 scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One even-regular MV3 scale is the achiral variant of [[diachrome]]. | * Another characterization of even-regular MV3 scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One even-regular MV3 scale is the achiral variant of [[diachrome]]. | ||
* Even-regular MV3 scales are MV3 | * Even-regular MV3 scales are [[maximum variety]] 3 (MV3) but not [[strict variety]] 3 (SV3), and by the [[ternary scale theorems|MV3 classification theorem]] a balanced single-period MV3 scale that has an even number of notes is always even-regular MV3 and has [[step signature]] aXaYbZ where a is odd and b is even. | ||
* Even-regular MV3 scales are [[chirality|achiral]]. There is only one even-regular MV3 scale pattern for a given scale signature if it exists. | * Even-regular MV3 scales are [[chirality|achiral]]. There is only one even-regular MV3 scale pattern for a given scale signature if it exists. | ||
Revision as of 09:51, 6 January 2025
An even-regular MV3 scale is a type of ternary scale with an even number of notes per period. An even-regular MV3 scale consists of two identical generator chains, where all generators are identical and subtend the same step class. The two chains are offset by an interval that subtends k steps in a 2k-note even-regular MV3 scale.
Notable even-regular MV3 scales
Properties
- Even-regular MV3 scales always satisfy all 3 of the monotone-MOS conditions.
- Another characterization of even-regular MV3 scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One even-regular MV3 scale is the achiral variant of diachrome.
- Even-regular MV3 scales are maximum variety 3 (MV3) but not strict variety 3 (SV3), and by the MV3 classification theorem a balanced single-period MV3 scale that has an even number of notes is always even-regular MV3 and has step signature aXaYbZ where a is odd and b is even.
- Even-regular MV3 scales are achiral. There is only one even-regular MV3 scale pattern for a given scale signature if it exists.
Terminology
The term even-regular MV3 has been coined by Inthar.