SN scale: Difference between revisions

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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.
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, but the period of a SN scale is arbitrary.
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.
 
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.