Monzo: Difference between revisions

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== Monzos in JI subgroups ==

We can generalize the concept of monzos from the ''p''-limit to other [[JI subgroup]]s. This can be useful when considering different edo tunings of [[subgroup temperaments]].

We can generalize the concept of monzos and vals from the ''p''-limit to other [[JI subgroup]]s. This can be useful when considering different edo tunings of [[subgroup temperaments]].

To write a JI ratio as a 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]] = 92/(24 51) in the 2.9.5 subgroup as {{monzo|2: -4, 9: 2, 5: -1}}. (We reserve the notation {{monzo|a b c ...}} for the ''p''-limit.)

@@ Line 74: / Line 74: @@
 == Monzos in JI subgroups ==
-We can generalize the concept of monzos from the ''p''-limit to other [[JI subgroup]]s. This can be useful when considering different edo tunings of [[subgroup temperaments]].
+We can generalize the concept of monzos and vals from the ''p''-limit to other [[JI subgroup]]s. This can be useful when considering different edo tunings of [[subgroup temperaments]].
 To write a JI ratio as a 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}}. (We reserve the notation {{monzo|a b c ...}} for the ''p''-limit.)