User:Nick Vuci/Moments of Symmetry: Difference between revisions

(11 intermediate revisions by the same user not shown)

Line 1:

WORK-IN-PROGRESS AS OF ~~27 MAY~~ 2025

WORK-IN-PROGRESS AS OF 25 OCT 2025

'''Moments of Symmetry (MOS)''' are scales created by a simple procedure that generates the common [[2L 3s|pentatonic]] and [[5L 2s|diatonic]] scales, but also a wide range of novel xenharmonic scales that share ~~the same~~ melodic coherence and structural balance. First described by [[Erv Wilson]] in the 1970's, the concept shares fundamental similarities and is often thought of as synonymous with the concept of Well-Formed scales, as well as the more generalized concept of [[Maximum variety|MV2 scales]]. Over time, MOS have become a fundamental concept in xenharmonic theory, inspiring a wide range of musical uses, analytical approaches, and derivative concepts such as [[MODMOS]], multi-MOS, and [[MOS rhythm|MOS-based rhythm]].

'''Moments of Symmetry (MOS)''' are scales created by a simple procedure that generates the common [[2L 3s|pentatonic]] and [[5L 2s|diatonic]] scales, but also a wide range of novel xenharmonic scales that share similar melodic coherence and structural balance. First described by [[Erv Wilson]] in the 1970's, the concept shares fundamental similarities and is often thought of as synonymous with the concept of Well-Formed scales, as well as the more generalized concept of [[Maximum variety|MV2 scales]]. Over time, MOS have become a fundamental concept in xenharmonic theory, inspiring a wide range of musical uses, analytical approaches, and derivative concepts such as [[MODMOS]], multi-MOS, and [[MOS rhythm|MOS-based rhythm]].

MOS are commonly notated with either a [[Step pattern|scale signature or a step pattern]]. For example, the common major scale of 12-EDO would be notated:

As a concrete step pattern: 2 2 1 2 2 2 1

As an abstract step pattern: L L s L L L s

As a scale signature: 5L 2s

== Construction ==

Line 18:

Line 26:

To find the equal tuning that supports a given MOS pattern at a particular hardness, simply multiply the number of each step type by its relative size and sum the results. For example, for the 5L 2s pattern at a hardness of 2:1, calculate 5×2+2×1=12, showing that 12-EDO supports this pattern.

Line 28:

Line 35:

== Spectrum of MOS ==

[[File:~~MOStest~~.gif|~~right~~|~~frameless]]~~.

As a generator moves through all possible positions within a fixed period, MOS emerge in specified ranges bounded by equal divisions. This spectrum is symmetric and mirrored at the midpoint of the period, with generators larger than half the period produce the same MOS as their complements.<gallery mode="slideshow" widths="200" heights="200">

File:MOS Spectrum.gif|The entire MOS spectrum at 6-levels

.

File:MOS Spectrum mirror.gif|Showing the mirror-like symmetry of the half period. The same patterns repeat from 0-600 cents and 1200-600 cents.

File:MOS Spectrum Level2.gif

.

File:MOS Spectrum Level3.gif

</gallery>

.

== Formal definitions and conditions of MOS ==

@@ Line 1: / Line 1: @@
-  WORK-IN-PROGRESS AS OF 27 MAY 2025
+  WORK-IN-PROGRESS AS OF 25 OCT 2025
-'''Moments of Symmetry (MOS)''' are scales created by a simple procedure that generates the common [[2L 3s|pentatonic]] and [[5L 2s|diatonic]] scales, but also a wide range of novel xenharmonic scales that share the same melodic coherence and structural balance. First described by [[Erv Wilson]] in the 1970's, the concept shares fundamental similarities and is often thought of as synonymous with the concept of Well-Formed scales, as well as the more generalized concept of [[Maximum variety|MV2 scales]]. Over time, MOS have become a fundamental concept in xenharmonic theory, inspiring a wide range of musical uses, analytical approaches, and derivative concepts such as [[MODMOS]], multi-MOS, and [[MOS rhythm|MOS-based rhythm]].
+'''Moments of Symmetry (MOS)''' are scales created by a simple procedure that generates the common [[2L 3s|pentatonic]] and [[5L 2s|diatonic]] scales, but also a wide range of novel xenharmonic scales that share similar melodic coherence and structural balance. First described by [[Erv Wilson]] in the 1970's, the concept shares fundamental similarities and is often thought of as synonymous with the concept of Well-Formed scales, as well as the more generalized concept of [[Maximum variety|MV2 scales]]. Over time, MOS have become a fundamental concept in xenharmonic theory, inspiring a wide range of musical uses, analytical approaches, and derivative concepts such as [[MODMOS]], multi-MOS, and [[MOS rhythm|MOS-based rhythm]].
+MOS are commonly notated with either a [[Step pattern|scale signature or a step pattern]]. For example, the common major scale of 12-EDO would be notated:
+As a concrete step pattern: 2 2 1 2 2 2 1
+As an abstract step pattern: L L s L L L s
+As a scale signature: 5L 2s
 == Construction ==
@@ Line 18: / Line 26: @@
 To find the equal tuning that supports a given MOS pattern at a particular hardness, simply multiply the number of each step type by its relative size and sum the results. For example, for the 5L 2s pattern at a hardness of 2:1, calculate 5×2+2×1=12, showing that 12-EDO supports this pattern.
@@ Line 28: / Line 35: @@
 == Spectrum of MOS ==
-[[File:MOStest.gif|right|frameless]].
+As a generator moves through all possible positions within a fixed period, MOS emerge in specified ranges bounded by equal divisions. This spectrum is symmetric and mirrored at the midpoint of the period, with generators larger than half the period produce the same MOS as their complements.<gallery mode="slideshow" widths="200" heights="200">
+File:MOS Spectrum.gif|The entire MOS spectrum at 6-levels
-.
+File:MOS Spectrum mirror.gif|Showing the mirror-like symmetry of the half period. The same patterns repeat from 0-600 cents and 1200-600 cents.
+File:MOS Spectrum Level2.gif
-.
+File:MOS Spectrum Level3.gif
+</gallery>
-.
-.
 == Formal definitions and conditions of MOS ==