SN scale: Difference between revisions

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a) A new smaller step at the top or bottom of every existing step, or

b) The existing smallest step at the top or bottom of every larger step: i.e. replacing '''x''' with '''sx''' for every occurrence of any step '''x''' such that '''x''' > '''s''' at the current stage, where '''s''' is the current smallest step.

b) The existing smallest step at the top or bottom of every larger step: i.e. replacing '''x''' with '''xs''' or '''sx''' for every occurrence of any step '''x''' such that '''x''' > '''s''' at the current stage, where '''s''' is the current smallest step.

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

Each iteration of a) increases 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. [[ET]]<nowiki/>s 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.

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 a) A new smaller step at the top or bottom of every existing step, or
-b) The existing smallest step at the top or bottom of every larger step: i.e. replacing '''x''' with '''sx''' for every occurrence of any step '''x''' such that '''x''' > '''s''' at the current stage, where '''s''' is the current smallest step.
+b) The existing smallest step at the top or bottom of every larger step: i.e. replacing '''x''' with '''xs''' or '''sx''' for every occurrence of any step '''x''' such that '''x''' > '''s''' at the current stage, where '''s''' is the current smallest step.
-Each iteration of a) increases the rank of the scale by 1.
+Each iteration of a) increases the rank of the scale by 1. <!-- In any of the steps, "bottom" may be replaced with "top", but the choice of "bottom" and "top" must be consistent. Todo: Prove this or find relevant literature on episturmian words to clarify this.-->
 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. [[ET]]<nowiki/>s 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.