Scale: Difference between revisions

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In practice, considering that there are physical limitations to the accuracy of an instrument's tuning, especially in the context of acoustic instruments, a tolerance should be allowed to avoid labelling as abstract what would otherwise be concrete scales. Similarly, playing out of tune with relation to a given concrete scale would correspond to playing outside of that tolerance. The concept of [[just-noticeable difference]] (JND) may be helpful to determine a reasonable tolerance.

Analogous definitions exist for [[tuning system]]s.

== Scale properties ==

== Relation to tuning systems and chords ==

A [[tuning system]] defines the set of discrete pitches used ~~to tune~~ an [[instrument]] in ~~a composition~~. A scale can be built by taking a subset of pitches from a given tuning system. Furthermore, a [[chord]] can be built by taking a subset of pitches from a given scale.

A [[tuning system]] defines the set of discrete pitches to be used in a composition e.g. the set of pitches on an [[instrument]] or loaded in [[software]]. A scale can be built by taking a subset of pitches from a given tuning system. Furthermore, a [[chord]] can be built by taking a subset of pitches from a given scale.

Scales are generally treated with a greater focus on melody, while chords are generally treated with a greater focus on harmony. That said, the boundary between the two is fuzzy, and some musicians use the term ''scale-chord'' to refer to a set of pitches that is treated both as a scale and as a chord.

== Reentrant scales ==

A '''reentrant scale''' features at least one '''negative step''', 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.

A '''reentrant scale''' features at least one '''[[Kite's thoughts on negative intervals|negative step]]''', 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.

This concept is 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 should obtain a negative MOS scale. 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.

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 In practice, considering that there are physical limitations to the accuracy of an instrument's tuning, especially in the context of acoustic instruments, a tolerance should be allowed to avoid labelling as abstract what would otherwise be concrete scales. Similarly, playing out of tune with relation to a given concrete scale would correspond to playing outside of that tolerance. The concept of [[just-noticeable difference]] (JND) may be helpful to determine a reasonable tolerance.
+Analogous definitions exist for [[tuning system]]s.
 == Scale properties ==
-{{Main|Scale properties simplified}}
+{{Main|Glossary of scale properties}}
 == Relation to tuning systems and chords ==
-A [[tuning system]] defines the set of discrete pitches used to tune an [[instrument]] in a composition. A scale can be built by taking a subset of pitches from a given tuning system. Furthermore, a [[chord]] can be built by taking a subset of pitches from a given scale.
+A [[tuning system]] defines the set of discrete pitches to be used in a composition e.g. the set of pitches on an [[instrument]] or loaded in [[software]]. A scale can be built by taking a subset of pitches from a given tuning system. Furthermore, a [[chord]] can be built by taking a subset of pitches from a given scale.
 Scales are generally treated with a greater focus on melody, while chords are generally treated with a greater focus on harmony. That said, the boundary between the two is fuzzy, and some musicians use the term ''scale-chord'' to refer to a set of pitches that is treated both as a scale and as a chord.
 == Reentrant scales ==
-A '''reentrant scale''' features at least one '''negative step''', 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.
+A '''reentrant scale''' features at least one '''[[Kite's thoughts on negative intervals|negative step]]''', 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.
 This concept is 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 should obtain a negative MOS scale. 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.