MOS substitution: Difference between revisions

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

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

Note: This article bolds steps '''L''', '''m''', '''s''', and '''X'''.

Revision as of 23:02, 24 January 2024 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,668 edits mNo edit summary ← Older edit		Revision as of 23:02, 24 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 a'''L'''b'''m'''c'''s'''. Originally developed by Inthar for the purpose of adding aberrisma steps in an orderly manner to a MOS pattern a'''L'''b'''m''' (which we write in place of a'''L'''b'''s''' for convenience's sake, since s denotes the new steps added to the MOS) in the context of groundfault's aberrismic theory, MOS substitution is intended to take advantage of extra symmetry when a, c or b, c is not a coprime pair and generalize the congruence substitution procedure for building [[balanced]] words to obtain non-balanced but still more "even" scales and simple generator sequence expressions (in the sense of using only two distinct generators) for them.		'''MOS substitution''' is a procedure for obtaining a ternary scale with arbitrary scale signature a'''L'''b'''m'''c'''s'''. Originally developed by Inthar for the purpose of adding aberrisma steps in an orderly manner to a MOS pattern a'''L'''b'''m''' (which we write in place of a'''L'''b'''s''' for convenience's sake, since '''s''' denotes the new steps added to the MOS) in the context of groundfault's aberrismic theory, MOS substitution is intended to take advantage of extra symmetry when a, c or b, c is not a coprime pair and generalize the congruence substitution procedure for building [[balanced]] words to obtain non-balanced but still more "even" scales and simple generator sequence expressions (in the sense of using only two distinct generators) for them.

	Note: This article bolds steps '''L''', '''m''', '''s''', and '''X'''.		Note: This article bolds steps '''L''', '''m''', '''s''', and '''X'''.