The organization of a three-manual keyboard for 53-tone tempered and other tempered systems

Abstract

The aim is to explore new opportunities of the pitch organization of the musical scale. Specifically, a numerical comparison of the different musical temperaments among themselves in the degree of approximation of the Pythagorean scale is provided, and thus it numerically substantiates the thesis that the 53-tone tempered system is the most advanced among possible others. We present numerical data on the approximation of overtones from first twenty by steps of the 53-tone temperament. Here were proposed some schemes of the three-manual keyboard for the implementation of 53-tone temperament, which are also implemented at the same time for 12 -, 17 -, 24 -, 29 - and 41-sounding system. If there are technical means then these schemes can be used to play music in any temperaments, based on said number of steps.