SN scale: Difference between revisions

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Each iteration of a) increasing the rank of the scale by 1.

An SN scale of rank 2, a 2-SN scale, is a [[MOS scale]]. Accordingly, SN scales are a generalization of MOS scales into arbitrary rank.

An SN scale of rank 2, a 2-SN scale, is a [[MOS scale]]. Accordingly, SN scales are a generalization of MOS scales into arbitrary rank. ETs can be considered to be 1-SN scales, which can be generated by applying a) once, introducing a step of a single degree of the ET.

SN scales are inversionally symmetric / invariant under reversal, and may be uniquely defined by a ''step signature'' - a generalisation of the MOS signature into arbitrary rank.

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The double harmonic scale can be generated by iterating a) three times, introducing first the octave, then the fifth, then the major third, leading to a major seven tetrad, and then applying b) once. It has step signature 2L 1M 4s, and in the symmetric mode, it has step arrangement sLsMsLs.

These scales all have a period of an octave - and therefore a) first introduces the interval of an octave~~. SN scales may have periods other than an octave -~~ the period, ~~along with~~ the ~~rest~~ of ~~the mapping~~, is arbitrary.

These scales all have a period of an octave - and therefore a) first introduces the interval of an octave, however, the period of a SN scale, and the mapping of any new smallest step introduced, is arbitrary.

SN scales are a subset of [[MOS Cradle Scales]].

SN scales are based on epi-Christoffel words form combinatorics, which generalize finite Sturmian words, which are equivalent to well-formed scales, and equivalently equivalent to MOS scales that are not ''Multi-MOS'' scales, MOS scales of more than one period, typically with a period that divides the octave evenly.

@@ Line 7: / Line 7: @@
 Each iteration of a) increasing the rank of the scale by 1.
-An SN scale of rank 2, a 2-SN scale, is a [[MOS scale]]. Accordingly, SN scales are a generalization of MOS scales into arbitrary rank.
+An SN scale of rank 2, a 2-SN scale, is a [[MOS scale]]. Accordingly, SN scales are a generalization of MOS scales into arbitrary rank. ETs can be considered to be 1-SN scales, which can be generated by applying a) once, introducing a step of a single degree of the ET.
 SN scales are inversionally symmetric / invariant under reversal, and may be uniquely defined by a ''step signature'' - a generalisation of the MOS signature into arbitrary rank.
@@ Line 18: / Line 18: @@
 The double harmonic scale can be generated by iterating a) three times, introducing first the octave, then the fifth, then the major third, leading to a major seven tetrad, and then applying b) once. It has step signature 2L 1M 4s, and in the symmetric mode, it has step arrangement sLsMsLs.
-These scales all have a period of an octave - and therefore a) first introduces the interval of an octave. SN scales may have periods other than an octave - the period, along with the rest of the mapping, is arbitrary.
+These scales all have a period of an octave - and therefore a) first introduces the interval of an octave, however, the period of a SN scale, and the mapping of any new smallest step introduced, is arbitrary.
 SN scales are a subset of [[MOS Cradle Scales]].
 SN scales are based on epi-Christoffel words form combinatorics, which generalize finite Sturmian words, which are equivalent to well-formed scales, and equivalently equivalent to MOS scales that are not ''Multi-MOS'' scales, MOS scales of more than one period, typically with a period that divides the octave evenly.