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 are ''mirror-symmetric'', wherein the scale is symmetric about a point. In mirror-symmetric scales of odd cardinality, the axis of symmetric lies on a note of the scale, and so the scale has 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. For mirror-symmetric scales of even cardinality, the axis of symmetric lies exactly half-way between two notes of the scale, and no such mode exists. Mirror-symmetric scales of odd cardinality are symmetric about a note, and mirror-symmetric scales of even cardinality are symmetric about an interval. Mirror-symmetric scales of even cardinality 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. We will call such a mode the ''even-symmetric 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. Mirror-symmetric scales may alternatively be defined as scales for which the inverse of every mode is also a mode of the scale. Clearly the symmetric mode is an inverse of itself.

MOS scales are ''mirror-symmetric'', or ''achiral'', wherein the scale is symmetric about a point. In mirror-symmetric scales of odd cardinality, the axis of symmetric lies on a note of the scale, and so the scale has 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. For mirror-symmetric scales of even cardinality, the axis of symmetric lies exactly half-way between two notes of the scale, and no such mode exists. Mirror-symmetric scales of odd cardinality are symmetric about a note, and mirror-symmetric scales of even cardinality are symmetric about an interval. Mirror-symmetric scales of even cardinality 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. We will call such a mode the ''even-symmetric 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. Mirror-symmetric scales may alternatively be defined as scales for which the inverse of every mode is also a mode of the scale. Clearly the symmetric mode is an inverse of itself.

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

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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 are ''mirror-symmetric'', wherein the scale is symmetric about a point. In mirror-symmetric scales of odd cardinality, the axis of symmetric lies on a note of the scale, and so the scale has 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. For mirror-symmetric scales of even cardinality, the axis of symmetric lies exactly half-way between two notes of the scale, and no such mode exists. Mirror-symmetric scales of odd cardinality are symmetric about a note, and mirror-symmetric scales of even cardinality are symmetric about an interval. Mirror-symmetric scales of even cardinality 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. We will call such a mode the ''even-symmetric 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. Mirror-symmetric scales may alternatively be defined as scales for which the inverse of every mode is also a mode of the scale. Clearly the symmetric mode is an inverse of itself.
+MOS scales are ''mirror-symmetric'', or ''achiral'', wherein the scale is symmetric about a point. In mirror-symmetric scales of odd cardinality, the axis of symmetric lies on a note of the scale, and so the scale has 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. For mirror-symmetric scales of even cardinality, the axis of symmetric lies exactly half-way between two notes of the scale, and no such mode exists. Mirror-symmetric scales of odd cardinality are symmetric about a note, and mirror-symmetric scales of even cardinality are symmetric about an interval. Mirror-symmetric scales of even cardinality 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. We will call such a mode the ''even-symmetric 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. Mirror-symmetric scales may alternatively be defined as scales for which the inverse of every mode is also a mode of the scale. Clearly the symmetric mode is an inverse of itself.
 MOS scales and can be uniquely defined by their ''MOS signature'', i.e. the diatonic scale by 5L 2s.