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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=== 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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=== H ===

=== I ===

~~; [[interval variety]]~~

~~: The number of different interval qualities available for an interval class in a [[#P|periodic scale]].~~

=== J ===

=== K ===

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; [[maximum variety]] (MV)

: The maximum [[~~#I|~~interval variety]] from all interval classes of a [[#P|periodic 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 ~~and MOS~~

; Myhill's property

* 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"~~.

* 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 [[~~#I|~~interval variety]] of all interval classes of a [[#P|periodic scale]], when all interval classes have the same interval variety.

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

; symmetry

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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 ===

@@ Line 1: / Line 1: @@
-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 46: / 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 63: / Line 63: @@
 === H ===
 === I ===
-; [[interval variety]]
-: The number of different interval qualities available for an interval class in a [[#P|periodic scale]].
 === J ===
 === K ===
@@ Line 74: / Line 71: @@
 ; [[maximum variety]] (MV)
-: The maximum [[#I|interval variety]] from all interval classes of a [[#P|periodic 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 and MOS
+; Myhill's property
-* 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".
+* 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 102: / Line 102: @@
 === S ===
 ; [[strict variety]] (SV)
-: The [[#I|interval variety]] of all interval classes of a [[#P|periodic scale]], when all interval classes have the same interval variety.
+: The [[interval variety]] of all interval classes of a [[#P|periodic scale]], when all interval classes have the same interval variety.
 ; symmetry
@@ Line 112: / 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 ===