Monzo: Difference between revisions
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== Monzos in JI subgroups == | == Monzos in JI subgroups == | ||
To write a JI ratio as a (generalized) monzo in a [[JI subgroup]], we choose a basis for the subgroup and factor an interval into the basis elements as we factor an interval in the ''p''-limit into primes at most ''p''. Then we write the monzo so as to explicitly state what basis elements we factor the intervals into and how many of each basis element the interval has in the factorization. For example, we can write [[81/80]] = 9<sup>2</sup>/(2<sup>4</sup> 5<sup>1</sup>) in the 2.9.5 subgroup as {{monzo|2: -4, 9: 2, 5: -1}}. | To write a JI ratio as a (generalized) monzo in a [[JI subgroup]], we choose a [[basis]] for the subgroup and factor an interval into the basis elements as we factor an interval in the ''p''-limit into primes at most ''p''. Then we write the monzo so as to explicitly state what basis elements we factor the intervals into and how many of each basis element the interval has in the factorization. For example, we can write [[81/80]] = 9<sup>2</sup>/(2<sup>4</sup> 5<sup>1</sup>) in the 2.9.5 subgroup as {{monzo|2: -4, 9: 2, 5: -1}}. | ||
== Monzos in temperaments == | == Monzos in temperaments == |