The organization of a three-manual keyboard for 53-tone tempered and other tempered systems
This addresses the challenge of optimizing musical scale organization for composers and performers, offering an incremental improvement in temperament design and keyboard implementation.
The paper tackles the problem of comparing musical temperaments by numerically evaluating their approximation to the Pythagorean scale, finding that the 53-tone tempered system is the most advanced, with specific numerical data on overtone approximation. It also proposes a three-manual keyboard design to implement this and other temperaments, enabling practical use if technical means are available.
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.