MOS substitution: Difference between revisions

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'''MOS substitution''' is a procedure for obtaining a ternary scale with arbitrary scale signature <math>a\mathbf{L}b\mathbf{m}c\mathbf{s}</math>. Originally developed by Inthar for the purpose of adding aberrisma steps in an orderly manner to a MOS pattern <math>a\mathbf{L}b\mathbf{m}</math> (which we write in place of <math>a\mathbf{L}b\mathbf{s}</math> for convenience's sake, since <math>\mathbf{s}</math> denotes the new aberrisma steps added to the MOS) in the context of groundfault's aberrismic theory, MOS substitution is intended to take advantage of extra potential symmetry when <math>a, c</math> or <math>b, c</math> is not a coprime pair and generalize the congruence substitution procedure for building [[balanced]] words to obtain non-balanced but still more "even" scales with simple [[generator sequence]] expressions (in the sense of using only two distinct generators).

'''MOS substitution''' is a procedure for obtaining a [[arity|ternary]] scale with arbitrary scale signature <math>a\mathbf{L}b\mathbf{m}c\mathbf{s}</math>. Originally developed by Inthar for the purpose of adding aberrisma steps in an orderly manner to a MOS pattern <math>a\mathbf{L}b\mathbf{m}</math> (which we write in place of <math>a\mathbf{L}b\mathbf{s}</math> for convenience's sake, since <math>\mathbf{s}</math> denotes the new aberrisma steps added to the MOS) in the context of groundfault's aberrismic theory, MOS substitution is intended to take advantage of extra potential symmetry when <math>a, c</math> or <math>b, c</math> is not a coprime pair and generalize the congruence substitution procedure for building [[balanced]] words to obtain non-balanced but still more "even" scales with simple [[generator sequence]] expressions (in the sense of using only two distinct generators).

(Note: This article bolds steps <math>\mathbf{L}, \mathbf{m}, \mathbf{s}, \mathbf{x}.</math> For integers <math>m, n, \ (m, n) := \gcd(m, n).</math>)

Revision as of 02:34, 25 January 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,668 edits mNo edit summary ← Older edit		Revision as of 02:34, 25 January 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,668 edits mNo edit summary Newer edit →
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	'''MOS substitution''' is a procedure for obtaining a ternary scale with arbitrary scale signature <math>a\mathbf{L}b\mathbf{m}c\mathbf{s}</math>. Originally developed by Inthar for the purpose of adding aberrisma steps in an orderly manner to a MOS pattern <math>a\mathbf{L}b\mathbf{m}</math> (which we write in place of <math>a\mathbf{L}b\mathbf{s}</math> for convenience's sake, since <math>\mathbf{s}</math> denotes the new aberrisma steps added to the MOS) in the context of groundfault's aberrismic theory, MOS substitution is intended to take advantage of extra potential symmetry when <math>a, c</math> or <math>b, c</math> is not a coprime pair and generalize the congruence substitution procedure for building [[balanced]] words to obtain non-balanced but still more "even" scales with simple [[generator sequence]] expressions (in the sense of using only two distinct generators).		'''MOS substitution''' is a procedure for obtaining a [[arity\|ternary]] scale with arbitrary scale signature <math>a\mathbf{L}b\mathbf{m}c\mathbf{s}</math>. Originally developed by Inthar for the purpose of adding aberrisma steps in an orderly manner to a MOS pattern <math>a\mathbf{L}b\mathbf{m}</math> (which we write in place of <math>a\mathbf{L}b\mathbf{s}</math> for convenience's sake, since <math>\mathbf{s}</math> denotes the new aberrisma steps added to the MOS) in the context of groundfault's aberrismic theory, MOS substitution is intended to take advantage of extra potential symmetry when <math>a, c</math> or <math>b, c</math> is not a coprime pair and generalize the congruence substitution procedure for building [[balanced]] words to obtain non-balanced but still more "even" scales with simple [[generator sequence]] expressions (in the sense of using only two distinct generators).

	(Note: This article bolds steps <math>\mathbf{L}, \mathbf{m}, \mathbf{s}, \mathbf{x}.</math> For integers <math>m, n, \ (m, n) := \gcd(m, n).</math>)		(Note: This article bolds steps <math>\mathbf{L}, \mathbf{m}, \mathbf{s}, \mathbf{x}.</math> For integers <math>m, n, \ (m, n) := \gcd(m, n).</math>)