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 | {{TOC Horizontal | ||
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=== C === | === C === | ||
; [[chirality]] | |||
: A scale is chiral if reversing the order of the steps results in a different scale up to rotation. | |||
; [[constant structure]] (CS) | ; [[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. | : 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. | ||
; [[ | ; [[convex scale|convexity]] | ||
: A scale in a [[regular temperament]] is convex if its representation on a [[harmonic lattice diagram]] forms a convex polygon. | : A scale in a [[regular temperament]] is convex if its representation on a [[harmonic lattice diagram]] forms a convex polygon. | ||
=== D === | === D === | ||
; [[distributional evenness]] (DE) | ; [[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 === | === E === | ||
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=== L === | === L === | ||
=== M === | === M === | ||
; [[ | ; [[maximal evenness]] | ||
: 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. | : 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. | ||
; | ; [[maximum variety]] (MV) | ||
* A scale | : 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 === | === N === | ||
=== O === | === O === | ||
=== P === | === P === | ||
; [[ | ; [[periodic scale|periodicity]] | ||
: A scale is periodic if its [[step pattern]] repeats after a certain [[#I|interval]]. | : A scale is periodic if its [[step pattern]] repeats after a certain [[#I|interval]]. | ||
; [[ | ; [[pepper ambiguity]] | ||
: The Pepper ambiguity of an [[interval]] in an [[equal-step tuning]] is the ratio of the best approximation to the second best approximation. | : The Pepper ambiguity of an [[interval]] in an [[equal-step tuning]] is the ratio of the best approximation to the second best approximation. | ||
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=== S === | === 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 | ; 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. | : 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 | ; trivalence property | ||
: Same as Myhill's property, but replace "two interval sizes" with "three interval sizes. | : 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 === | === U === | ||
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== Examples == | == Examples == | ||
The | The [[5L 2s|diatonic scale]] in 12edo has Myhill's property, and is also distributionally even. | ||
The diminished scale is | The [[diminished scale]] is a mos with a 1/4-octave period. Because there is only one interval size at the period, it does not have exactly two interval sizes per interval class. Therefore, it is a mos, but does not have Myhill's property. | ||
An | An edo is a kind of degenerate mos, in that it is distributionally even. It does not have Myhill's property. In other words, it has no more than two interval sizes for each generic interval class, but does not have exactly two interval sizes. | ||
== See also == | == See also == | ||
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[[Category:Terms| ]] | [[Category:Terms| ]] | ||
[[Category:Scale]] | [[Category:Scale]] | ||
{{Todo| add illustration }} | |||