Kite's thoughts on negative intervals: Difference between revisions

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Negative minor 2nds are possible but rare. For example, [[1728/1715]] = [6 3 -1 -3⟩ = 13¢ is equal to ([[8/5]])/([[7/6]])<sup>3</sup>, a minor 6th minus three minor 3rds.

~~== Reentrant scales ==~~

A '''reentrant scale''' has at least one negative interval, going backwards relative to the general direction of the scale. Although a reentrant scale is not strictly ascending or descending, its ascending and descending forms are determined by its general direction.

Reentrant scales are mostly relevant when applying extreme tunings to abstract scales, causing some steps to have a negative size in order to preserve the abstract scale's usual structure. For example, if you try to generate a [[MOS scale]] with a [[generator]] whose size falls outside of the generator range of all possible MOS patterns with the same given number of notes, you will obtain a MOS scale with a negative [[step ratio]]. A 7-tone scale with a 295{{cent}} generator is just outside of the range for [[4L 3s]], and can be interpreted as a 4L 3s scale with 315{{cent}} large steps and -20{{cent}} (negative) small steps, whereas considering the scale's pitches in ascending order leads to a [[ternary]], [[Maximum variety|MV4]] scale interpretation.

== See also ==

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 Negative minor 2nds are possible but rare. For example, [[1728/1715]] = [6 3 -1 -3⟩ = 13¢ is equal to ([[8/5]])/([[7/6]])<sup>3</sup>, a minor 6th minus three minor 3rds.
-== Reentrant scales ==
-A '''reentrant scale''' has at least one negative interval, going backwards relative to the general direction of the scale. Although a reentrant scale is not strictly ascending or descending, its ascending and descending forms are determined by its general direction.
-Reentrant scales are mostly relevant when applying extreme tunings to abstract scales, causing some steps to have a negative size in order to preserve the abstract scale's usual structure. For example, if you try to generate a [[MOS scale]] with a [[generator]] whose size falls outside of the generator range of all possible MOS patterns with the same given number of notes, you will obtain a MOS scale with a negative [[step ratio]]. A 7-tone scale with a 295{{cent}} generator is just outside of the range for [[4L 3s]], and can be interpreted as a 4L 3s scale with 315{{cent}} large steps and -20{{cent}} (negative) small steps, whereas considering the scale's pitches in ascending order leads to a [[ternary]], [[Maximum variety|MV4]] scale interpretation.
 == See also ==