During October 2004 the National and University Library in Zagreb (Croatia) was venue for an event called a musical measure of the triangle-Trianglemetre. This was a musical measure formed on the basis of the   dimensions of a right-angled triangle, the creation of Croatian composer Antun Toni Blažinović.

The triangle-meter was established by the alternation of several (two or three) different measures, in the manner of a horizontal polymeter in which changes of measures came one after another (in the ratio of each dimension of the triangle): a/n + b/n + c/n. The sides of the triangle (a, b, c) determine the number of beats in a bar and are written in the numerator, and in the denominator the kind of the beat (n). Each side of the triangle represents a single bar. The sides of the triangle can be aggregated and set up as the measure for a single bar.

In those triangles in which the dimension of the hypotenuse is not a whole number, he has determined the beat by computer programming and arrived at a smaller deviation than with the live conducting of some of the standard musical measures. Everything has been done on a computer, and accordingly the problem of the division of the measure into the smallest musical units – beats – did not constitute a problem, since with a computer it is possible to define beats of less than 1/64, for example, 1/128 or 1/512 and so on.
This measure can be classified as a mechanical measure attained with the use of technical devices, but there is also the triangle with 3-4-5 dimensions, which are whole numbers, and live performances thus become relatively easy. In live performance of the musical measures of triangles that are not integers, Blažinović mentions the use of monitors on which animation can be used to keep up with the adjustment of the measure per side.

Blažinović’s intention is to announce to the musical and cultural world his composing techniques and the musical measures that he has established according to the dimensions of the triangle. ©

Music genre: electronic/ minimalism/ contemporary

TRIANGLEMETRE by ANTUN TONI BLAZINOVIC

THE MUSICAL MEASURE OF THE TRIANGLE-TRIANGLEMETRE