SN scale: Difference between revisions

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== Further definition ==

~~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.

The above scales all have a period of an octave - and therefore a) first introduces the interval of an octave, however, the period of an SN scale, as with 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.

SN scales are based on epi-Christoffel words form combinatorics, which generalize finite Sturmian words. Finite sturmian words are equivalent to well-formed scales, and equivalently equivalent to MOS scales that are not ''Multi-MOS'' scales, wich are MOS scales of more than one period, typically with a period that divides the octave evenly. The algorithm for generating SN scales introduced above is equivalent to the two episturmian morphisms that generate epi-Christoffel words.

Though for rank-2, any possible step signature corresponds to an SN scale, for higher ranks only a small portion of possible step signatures correspond to SN scales. For a step signature to correspond to an SN scale, there must be at least as many incidences of each step size as there are incidences of all less highly incident step sizes. The step signature (2, 2, 3), for example, does not correspond to an SN scale, as there are more incidences of less highly incident step sizes than there are of the most highly incident step size (2+2>3).

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 == Further definition ==
-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.
+The above scales all have a period of an octave - and therefore a) first introduces the interval of an octave, however, the period of an SN scale, as with 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.
+SN scales are based on epi-Christoffel words form combinatorics, which generalize finite Sturmian words. Finite sturmian words are equivalent to well-formed scales, and equivalently equivalent to MOS scales that are not ''Multi-MOS'' scales, wich are MOS scales of more than one period, typically with a period that divides the octave evenly. The algorithm for generating SN scales introduced above is equivalent to the two episturmian morphisms that generate epi-Christoffel words.
+Though for rank-2, any possible step signature corresponds to an SN scale, for higher ranks only a small portion of possible step signatures correspond to SN scales. For a step signature to correspond to an SN scale, there must be at least as many incidences of each step size as there are incidences of all less highly incident step sizes. The step signature (2, 2, 3), for example, does not correspond to an SN scale, as there are more incidences of less highly incident step sizes than there are of the most highly incident step size (2+2>3).