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  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 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]].  


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== Spectrum of MOS ==
== Spectrum of MOS ==
[[File:MOS Spectrum.gif|thumb]]
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">
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.
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.
=== Core properties ===
File:MOS Spectrum Level2.gif
 
File:MOS Spectrum Level3.gif
* The spectrum is bounded by the equal divisions that mark the range of distinct L/s pattern formation.
</gallery>
* 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 ==
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