Subgroup monzos and vals: Difference between revisions

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Given a [[just intonation subgroup]], we can find a canonical form for its [[generator]]s by means of the [[Normal lists #Normal interval list|normal interval list]] which may be computed from any finite set of generators. In the case of the full ''p''-limit group for any prime ''p'', this consists of the primes from 2 to ''p'' in ascending order. This is precisely the ordered list used to define [[Vals and tuning space|vals]] and [[Monzos and interval space|monzos]], and we may generalize the notation simply by using any normal interval list in place of the ascending primes to ''p''. This generalization we may call the '''subgroup monzos''' and '''subgroup vals''', or '''smonzos''' and '''svals''' for short.

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			{{Legacy\|Smonzos_and_svals}}
	Given a [[just intonation subgroup]], we can find a canonical form for its [[generator]]s by means of the [[Normal lists #Normal interval list\|normal interval list]] which may be computed from any finite set of generators. In the case of the full ''p''-limit group for any prime ''p'', this consists of the primes from 2 to ''p'' in ascending order. This is precisely the ordered list used to define [[Vals and tuning space\|vals]] and [[Monzos and interval space\|monzos]], and we may generalize the notation simply by using any normal interval list in place of the ascending primes to ''p''. This generalization we may call the '''subgroup monzos''' and '''subgroup vals''', or '''smonzos''' and '''svals''' for short.		Given a [[just intonation subgroup]], we can find a canonical form for its [[generator]]s by means of the [[Normal lists #Normal interval list\|normal interval list]] which may be computed from any finite set of generators. In the case of the full ''p''-limit group for any prime ''p'', this consists of the primes from 2 to ''p'' in ascending order. This is precisely the ordered list used to define [[Vals and tuning space\|vals]] and [[Monzos and interval space\|monzos]], and we may generalize the notation simply by using any normal interval list in place of the ascending primes to ''p''. This generalization we may call the '''subgroup monzos''' and '''subgroup vals''', or '''smonzos''' and '''svals''' for short.