SN scale: Difference between revisions

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== Definition ==

A Step-nested scale, or SN scale (or SNS) is a scale generated through iteratively ~~placing an instance of~~

A Step-nested scale, or SN scale (or SNS) is a scale generated through iteratively performing the following two moves:

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

a) Add 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 '''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.

b) Add 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.

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 == Definition ==
-A Step-nested scale, or SN scale (or SNS) is a scale generated through iteratively placing an instance of
+A Step-nested scale, or SN scale (or SNS) is a scale generated through iteratively performing the following two moves:
-a) A new smaller step at the top or bottom of every existing step, or
+a) Add 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 '''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.
+b) Add 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. <!-- 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.-->