Rank 3 scale: Difference between revisions

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'.  

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