Monzo: Difference between revisions
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⟨2: 13, 9: 41, 5: 30][2: -4, 9: 2, 5: -1⟩ = 13*-4 + 41*2 + 30*-1 = 0. | ⟨2: 13, 9: 41, 5: 30][2: -4, 9: 2, 5: -1⟩ = 13*-4 + 41*2 + 30*-1 = 0. | ||
== Monzos in temperaments == | == Monzos in regular temperaments == | ||
We write a tempered interval (an interval in a [[regular temperament]]) by taking a set of [[generator]]s (for rank-2 temperaments, this will be the period and the generator), then writing what JI ratio each generator approximates (distinguished from pure JI intervals by putting a tilde before it), followed by the number of that specified generator that the interval has. For example, the major third in [[meantone]] temperament can be written as {{monzo|~2: ‐2, ~3/2: 4}}, meaning "4 perfect fifths minus 2 octaves". | We write a tempered interval (an interval in a [[regular temperament]]) by taking a set of [[generator]]s (for rank-2 temperaments, this will be the period and the generator), then writing what JI ratio each generator approximates (distinguished from pure JI intervals by putting a tilde before it), followed by the number of that specified generator that the interval has. For example, the major third in [[meantone]] temperament can be written as {{monzo|~2: ‐2, ~3/2: 4}}, meaning "4 perfect fifths minus 2 octaves". | ||