SN scale: Difference between revisions
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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.--> | 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. [[ | 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. [[Equal division]]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. | ||
SN scales are [[chirality|mirror-symmetric]], and may be uniquely defined by a ''step signature'' - a generalization of the MOS signature into arbitrary rank. | SN scales are [[chirality|mirror-symmetric]], and may be uniquely defined by a ''step signature'' - a generalization of the MOS signature into arbitrary rank. | ||