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

TL;DR

This paper compares various musical temperaments numerically, demonstrating that the 53-tone system offers the closest approximation to the Pythagorean scale, and proposes a three-manual keyboard design for versatile temperament implementation.

Contribution

It introduces a numerical comparison of temperaments, establishing the 53-tone system as the most advanced, and proposes a multi-temperament keyboard scheme adaptable to various systems.

Findings

53-tone temperament best approximates Pythagorean scale

Proposed keyboard schemes support multiple temperaments

Numerical data on overtone approximation

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.