User:VectorGraphics/Monzo notation: Difference between revisions

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In tuning theory, intervals within tuning systems (whether just intonation, EDOs, or regular temperaments) are often thought of as being composed by stacking different types of basic intervals, called "generators" or "basis elements" (which for reference make up the "basis"), and it is useful to be able to write an interval directly in terms of the number of generators of each type it contains. This can be seen as a "formula" for the interval.

== Monzos in the diatonic scale ==

== Example: Monzos in the diatonic scale ==

For example, to reach a minor third in diatonic, you can go up two diatonic semitones (m2) and one chromatic semitone (A1). So, to write this information, you start with the kinds of intervals you're stacking, separated by a period (so ''m2.A1''), and then write the number of intervals of each type included in the target interval's "formula", separated by spaces and enclosed in square brackets (so ''[2 1]''). The completed formula, ''m2.A1 [2 1]'', is called a "monzo" (more specifically, this one is a tmonzo), and it essentially tells you how to get to the interval you want by only stepping up or down by the intervals on the left.

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 In tuning theory, intervals within tuning systems (whether just intonation, EDOs, or regular temperaments) are often thought of as being composed by stacking different types of basic intervals, called "generators" or "basis elements" (which for reference make up the "basis"), and it is useful to be able to write an interval directly in terms of the number of generators of each type it contains. This can be seen as a "formula" for the interval.
-== Monzos in the diatonic scale ==
+== Example: Monzos in the diatonic scale ==
 For example, to reach a minor third in diatonic, you can go up two diatonic semitones (m2) and one chromatic semitone (A1). So, to write this information, you start with the kinds of intervals you're stacking, separated by a period (so ''m2.A1''), and then write the number of intervals of each type included in the target interval's "formula", separated by spaces and enclosed in square brackets (so ''[2 1]''). The completed formula, ''m2.A1 [2 1]'', is called a "monzo" (more specifically, this one is a tmonzo), and it essentially tells you how to get to the interval you want by only stepping up or down by the intervals on the left.