Glossary of scale properties: Difference between revisions

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A simplified explanation of the various properties of [[periodic scale]]s.

A simplified explanation of the various properties of [[periodic scale]]s. Also check the main [[Glossary]].

{{TOC Horizontal

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=== C ===

; [[chirality]]

: A scale is chiral if reversing the order of the steps results in a different scale up to rotation.

; [[constant structure]] (CS)

: A scale is a constant structure if all intervals of the same size are also within the same generic interval class. A single interval cannot be a part of two classes. The 12-tone diatonic scale does not have this property, since tritones can either be augmented fourths or diminished fifths. This is referred to as the ''partitioning property'' in most academic literature.

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=== D ===

; [[distributional evenness]] (DE)

: A scale with two step sizes is ''distributionally even'' if it has its two step sizes distributed as evenly as possible

: A scale with two step sizes is ''distributionally even'' if it has its two step sizes distributed as evenly as possible.

=== E ===

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: A [[#P|periodic]] [[#B|binary]] scale is maximally even with respect to an [[equal-step tuning]] if it is the result of rounding a smaller equal tuning to the nearest notes of the parent equal tuning with the same equave.

; ~~Myhill's property and~~ MOS

; [[maximum variety]] (MV)

* A scale ~~has ''Myhill's property''~~ if there are ''~~exactly~~'' two interval sizes for each ~~(reduced)~~ interval class not including the equave. A ~~scale is~~ a ~~[[MOS~~ scale]] if there are ''~~no more than~~'' two interval sizes for each ~~generic~~ interval class not including the equave. ~~This is equivalent to~~ a scale ~~being Myhill~~ with ~~a smaller equave.~~ Myhill's property is ~~sometimes~~ called "strict ~~MOS"~~.

: The maximum [[interval variety]] from all interval classes of a [[#P|periodic scale]].

; MOS

* A scale is a [[mos scale]] if there are ''no more than'' two interval sizes for each generic interval class not including the equave. A.k.a. maximum variety 2.

; Myhill's property

* A scale has ''Myhill's property'' if there are ''exactly'' two interval sizes for each interval class not including the equave. A.k.a. strict variety 2. A scale with Myhill's property is called a ''strict mos''.

=== N ===

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=== S ===

; [[strict variety]] (SV)

: The [[interval variety]] of all interval classes of a [[#P|periodic scale]], when all interval classes have the same interval variety.

; symmetry

: A scale is symmetrical if at least one mode of the scale is symmetrical. Therefore, every interval of that mode must have an inverse. These scales will always have an odd number of notes ''per period''. They may not always have an odd number of notes ''per octave'', however. The diatonic scale is symmetrical, but so is 12edo.

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; trivalence property

: Same as Myhill's property, but replace "two interval sizes" with "three interval sizes." The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.

: Same as [[#M|Myhill's property]], but replace "two interval sizes" with "three interval sizes". A.k.a. strict variety 3. The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.

=== U ===

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-A simplified explanation of the various properties of [[periodic scale]]s.
+A simplified explanation of the various properties of [[periodic scale]]s. Also check the main [[Glossary]].
 {{TOC Horizontal
@@ Line 35: / Line 35: @@
 === C ===
+; [[chirality]]
+: A scale is chiral if reversing the order of the steps results in a different scale up to rotation.
 ; [[constant structure]] (CS)
 : A scale is a constant structure if all intervals of the same size are also within the same generic interval class. A single interval cannot be a part of two classes. The 12-tone diatonic scale does not have this property, since tritones can either be augmented fourths or diminished fifths. This is referred to as the ''partitioning property'' in most academic literature.
@@ Line 43: / Line 46: @@
 === D ===
 ; [[distributional evenness]] (DE)
-: A scale with two step sizes is ''distributionally even'' if it has its two step sizes distributed as evenly as possible
+: A scale with two step sizes is ''distributionally even'' if it has its two step sizes distributed as evenly as possible.
 === E ===
@@ Line 67: / Line 70: @@
 : A [[#P|periodic]] [[#B|binary]] scale is maximally even with respect to an [[equal-step tuning]] if it is the result of rounding a smaller equal tuning to the nearest notes of the parent equal tuning with the same equave.
-; Myhill's property and MOS
+; [[maximum variety]] (MV)
-* A scale has ''Myhill's property'' if there are ''exactly'' two interval sizes for each (reduced) interval class not including the equave. A scale is a [[MOS scale]] if there are ''no more than'' two interval sizes for each generic interval class not including the equave. This is equivalent to a scale being Myhill with a smaller equave. Myhill's property is sometimes called "strict MOS".
+: The maximum [[interval variety]] from all interval classes of a [[#P|periodic scale]].
+; MOS
+* A scale is a [[mos scale]] if there are ''no more than'' two interval sizes for each generic interval class not including the equave. A.k.a. maximum variety 2.
+; Myhill's property
+* A scale has ''Myhill's property'' if there are ''exactly'' two interval sizes for each interval class not including the equave. A.k.a. strict variety 2. A scale with Myhill's property is called a ''strict mos''.
 === N ===
@@ Line 92: / Line 101: @@
 === S ===
+; [[strict variety]] (SV)
+: The [[interval variety]] of all interval classes of a [[#P|periodic scale]], when all interval classes have the same interval variety.
 ; symmetry
 : A scale is symmetrical if at least one mode of the scale is symmetrical. Therefore, every interval of that mode must have an inverse. These scales will always have an odd number of notes ''per period''. They may not always have an odd number of notes ''per octave'', however. The diatonic scale is symmetrical, but so is 12edo.
@@ Line 100: / Line 112: @@
 ; trivalence property
-: Same as Myhill's property, but replace "two interval sizes" with "three interval sizes." The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.
+: Same as [[#M|Myhill's property]], but replace "two interval sizes" with "three interval sizes". A.k.a. strict variety 3. The scale formed from the notes of a dominant 7th chord (e.g. C-E-G-Bb-C) is an example of a trivalent scale.
 === U ===