User:Nick Vuci/Moments of Symmetry - Revision history

Nick Vuci: /* Spectrum of MOS */

2025-10-27T00:36:16Z

Spectrum of MOS

← Older revision		Revision as of 00:36, 27 October 2025
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	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">		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.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 Level2.gif
	File:MOS Spectrum Level3.gif		File:MOS Spectrum Level3.gif

Nick Vuci: /* Spectrum of MOS */

2025-10-27T00:32:05Z

Spectrum of MOS

← Older revision		Revision as of 00:32, 27 October 2025
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	== Spectrum of MOS ==		== Spectrum of MOS ==
	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">		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		File:MOS Spectrum.gif\|The entire MOS spectrum at 6-levels
	File:MOS Spectrum Level2.gif		File:MOS Spectrum Level2.gif
	File:MOS Spectrum Level3.gif		File:MOS Spectrum Level3.gif

Nick Vuci: /* Spectrum of MOS */

2025-10-25T17:54:19Z

Spectrum of MOS

← Older revision		Revision as of 17:54, 25 October 2025
Line 35:		Line 35:

	== Spectrum of MOS ==		== Spectrum of MOS ==
	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="~~nolines~~" widths="200" heights="200">		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		File:MOS Spectrum.gif
	File:MOS Spectrum Level2.gif		File:MOS Spectrum Level2.gif

Nick Vuci: /* Step Ratios */

2025-10-25T17:53:54Z

Step Ratios

← Older revision		Revision as of 17:53, 25 October 2025
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	== Spectrum of MOS ==		== Spectrum of MOS ==
	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="nolines" widths="~~300~~" heights="~~300~~">		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="nolines" widths="200" heights="200">
	File:MOS Spectrum.gif		File:MOS Spectrum.gif
	File:MOS Spectrum Level2.gif		File:MOS Spectrum Level2.gif

Nick Vuci: /* Spectrum of MOS */

2025-10-25T17:36:41Z

Spectrum of MOS

← Older revision		Revision as of 17:36, 25 October 2025
Line 37:		Line 37:
	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="nolines" widths="300" heights="300">		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="nolines" widths="300" heights="300">
	File:MOS Spectrum.gif		File:MOS Spectrum.gif
	~~File:MOS Spectrum Level1.gif~~
	File:MOS Spectrum Level2.gif		File:MOS Spectrum Level2.gif
	File:MOS Spectrum Level3.gif		File:MOS Spectrum Level3.gif

Nick Vuci at 17:36, 25 October 2025

2025-10-25T17:36:10Z

← Older revision		Revision as of 17:36, 25 October 2025
Line 35:		Line 35:

	== Spectrum of MOS ==		== Spectrum of MOS ==
	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="nolines">		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="nolines" widths="300" heights="300">
	File:MOS Spectrum.gif~~\|The complete~~ MOS ~~spectrum for the 6-level horogram~~.		File:MOS Spectrum.gif
	File:MOS Spectrum ~~Level3~~.gif		File:MOS Spectrum Level1.gif
			File:MOS Spectrum Level2.gif
	File:MOS Spectrum Level3.gif		File:MOS Spectrum Level3.gif
	</gallery>		</gallery>








	== Formal definitions and conditions of MOS ==		== Formal definitions and conditions of MOS ==

Nick Vuci: added spectrum gifs

2025-10-25T17:30:24Z

added spectrum gifs

← Older revision		Revision as of 17:30, 25 October 2025
Line 35:		Line 35:

	== Spectrum of MOS ==		== Spectrum of MOS ==
	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>		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="nolines">
	File:MOS Spectrum.gif\|The complete MOS spectrum for the 6-level horogram.		File:MOS Spectrum.gif\|The complete MOS spectrum for the 6-level horogram.
			File:MOS Spectrum Level3.gif
			File:MOS Spectrum Level3.gif
	</gallery>		</gallery>

Nick Vuci at 17:24, 25 October 2025

2025-10-25T17:24:53Z

← Older revision		Revision as of 17:24, 25 October 2025
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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\|The complete MOS spectrum for a 6-level horogram.]]~~		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>
	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.		File:MOS Spectrum.gif\|The complete MOS spectrum for the 6-level horogram.
			</gallery>

Nick Vuci: /* Spectrum of MOS */

2025-10-25T06:37:13Z

Spectrum of MOS

← Older revision		Revision as of 06:37, 25 October 2025
Line 36:		Line 36:
	== Spectrum of MOS ==		== Spectrum of MOS ==
	[[File:MOS Spectrum.gif\|thumb\|The complete MOS spectrum for a 6-level horogram.]]		[[File:MOS Spectrum.gif\|thumb\|The complete MOS spectrum for a 6-level horogram.]]
	As a generator moves through all possible positions within a fixed period, MOS emerge as 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.		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.

Nick Vuci: /* Spectrum of MOS */

2025-10-25T06:36:45Z

Spectrum of MOS

← Older revision		Revision as of 06:36, 25 October 2025
Line 35:		Line 35:

	== Spectrum of MOS ==		== Spectrum of MOS ==
	[[File:MOS Spectrum.gif\|thumb]]		[[File:MOS Spectrum.gif\|thumb\|The complete MOS spectrum for a 6-level horogram.]]
	~~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~~.		As a generator moves through all possible positions within a fixed period, MOS emerge as 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.







	~~=== 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 ==