Odd limit: Difference between revisions
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== Definition == | == Definition == | ||
The '''odd limit''' is a metric that places an upper bound on (i.e. limits) the complexity of the | The '''odd limit''' is a metric that places an upper bound on (i.e. limits) the complexity of the harmonies used in a piece of music, and hence of the music itself. The term also refers to the metric itself, applied to individual ratios. Every ratio has an odd limit, and the q odd limit is the set of all ratios of odd limit of q or less. Integer limit and [[Prime limit|'''prime limit''']] are related concepts. | ||
To find the odd limit of a ratio: If either the numerator or the denominator is even, divide it by two until it is odd. The larger of the two numbers is the odd limit. Example: 12/7 becomes 3/7, and 7 > 3, thus the odd limit is 7. | To find the odd limit of a ratio: If either the numerator or the denominator is even, divide it by two until it is odd. The larger of the two numbers is the odd limit. Example: 12/7 becomes 3/7, and 7 > 3, thus the odd limit is 7. | ||