User:Nick Vuci/Moments of Symmetry: Difference between revisions
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WORK-IN-PROGRESS AS OF 27 MAY 2025 | WORK-IN-PROGRESS AS OF 27 MAY 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 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]]. | '''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 == | == Construction == | ||
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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. | 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. | ||
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== Spectrum of MOS == | == Spectrum of MOS == | ||
[[File: | [[File:MOS Spectrum.gif|thumb]] | ||
The '''MOS spectrum''' is the sequence of MOS that appear as a generator moves through all possible positions within a fixed period. Each point in this sweep defines a generator–period pair that yields an MOS, producing a full map of where two-step structures occur. | |||
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=== Core properties === | |||
. | * The spectrum is bounded by the equal divisions that mark the range of distinct L/s pattern formation. | ||
* It is symmetric (mirrored) around the midpoint of the period, because generators larger than half the period produce the same MOS as their complements (period − generator). | |||
== Formal definitions and conditions of MOS == | == Formal definitions and conditions of MOS == | ||