Rank 3 scale: Difference between revisions

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MOS scales can be generated by stacking a single generator modulo a period. Not all generated scales are MOS.

MOS scales with odd ~~number~~ of steps are ~~[[Scale properties simplified|~~symmetric]], ~~and those~~ with even ~~number~~ of steps ~~are not~~.

MOS scales with odd numbers of steps (odd ''cardinality'') are symmetric. ''Symmetric'' scales are the scales that have a ''symmetric mode'', wherein the inverse of each interval (about the period) also exists in the mode. The ''step arrangement'' of the scale in such a mode is a palindrome - e.g., the diatonic scale in Dorian mode has step pattern LsLLLsL. scales with even numbers of steps. The inverse of each mode of a symmetric scale is also a mode of the symmetric scale - where the inverse of the symmetric mode of such a scale is itself. Scales with even cardinality cannot be symmetric, however, MOS scales of even cardinality share this property, though there is no symmetric mode which is an inverse of itself: The axis of symmetry is half-way between two notes of the scale. We will call such scales ''even-symmetric'' (unless anyone, include myself, suggests a better name or knows one that already exists). Even-symmetric scales can be written in a mode for which the inverse of every interval in the scale about the largest interval of the scale bar the period also exists in the mode. The step pattern of such a mode is a palindrome, followed by a single step size. For example, Magic[10] in the ''even-symmetric mode'' has step pattern sLssLssLss. I'd like to propose that we change the definition of symmetric scales to include the 'even-symmetric scales'.

MOS scales and can be uniquely defined by their ''MOS signature'', i.e. the diatonic scale by 5L 2s.

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== 3-SN scales ==

The scales a...ba...c and abacaba are [[SN scales]], which are symmetric, and can be uniquely defined by a signature.

The scales a...ba...c and abacaba are [[SN scales]], which are symmetric or even-symmetric, and can be uniquely defined by a signature.

SN scales are generated iteratively by placing an instance of a new or the existing smallest step at the top or bottom of every larger step.

@@ Line 12: / Line 12: @@
 MOS scales can be generated by stacking a single generator modulo a period. Not all generated scales are MOS.
-MOS scales with odd number of steps are [[Scale properties simplified|symmetric]], and those with even number of steps are not.
+MOS scales with odd numbers of steps (odd ''cardinality'') are symmetric. ''Symmetric'' scales are the scales that have a ''symmetric mode'', wherein the inverse of each interval (about the period) also exists in the mode. The ''step arrangement'' of the scale in such a mode is a palindrome - e.g., the diatonic scale in Dorian mode has step pattern LsLLLsL. scales with even numbers of steps. The inverse of each mode of a symmetric scale is also a mode of the symmetric scale - where the inverse of the symmetric mode of such a scale is itself. Scales with even cardinality cannot be symmetric, however, MOS scales of even cardinality share this property, though there is no symmetric mode which is an inverse of itself: The axis of symmetry is half-way between two notes of the scale. We will call such scales ''even-symmetric'' (unless anyone, include myself, suggests a better name or knows one that already exists). Even-symmetric scales can be written in a mode for which the inverse of every interval in the scale about the largest interval of the scale bar the period also exists in the mode. The step pattern of such a mode is a palindrome, followed by a single step size. For example, Magic[10] in the ''even-symmetric mode'' has step pattern sLssLssLss. I'd like to propose that we change the definition of symmetric scales to include the 'even-symmetric scales'.
 MOS scales and can be uniquely defined by their ''MOS signature'', i.e. the diatonic scale by 5L 2s.
@@ Line 73: / Line 73: @@
 == 3-SN scales ==
-The scales a...ba...c and abacaba are [[SN scales]], which are symmetric, and can be uniquely defined by a signature.
+The scales a...ba...c and abacaba are [[SN scales]], which are symmetric or even-symmetric, and can be uniquely defined by a signature.
 SN scales are generated iteratively by placing an instance of a new or the existing smallest step at the top or bottom of every larger step.