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Encyclopedia of Microtonal Music Theory

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[Joe Monzo]

The interval-vector is a vector whose elements list in succession the number of occurrences of each interval in an equal-temperament or one of its subsets, the elements ordered according to interval size from smallest to largest.

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The diagram below represents 12-edo as a circle-of-degrees, with pink lines connecting each degree to form the circumference of the circle, and with other color-coded lines within the circle representing the interval-classes which can be found in the C-major scale used as the example. Legend:

color ic standard interval names frequency
black ic 1minor-2nd / major-7th 2
violetic 2major-2nd / minor-7th 5
blue ic 3minor-3rd / major-6th 4
green ic 4major-3rd / minor-6th 3
yellowic 5perfect-4th / perfect-5th 6
orangeic 6augmented-4th / diminished-5th1

It is only necessary to count the lines of each color to see the frequency of occurrence of each interval-class in the 12-edo C-major scale. The result is shown in the interval vector <254361>.

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