Realization 3: extract bass from table No. 1a
for any bass instrument
Realization 3: extract bass from table No. 1a is a part of a great planned cycle under the general title Euler’s Book. As a starting point for this project served a treatise An attempt at a new theory of music, exposed in all clearness according to the most well-founded principles of harmony (lat. – Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae) created in 1739 by famous mathematician Leonhard Euler. In this treatise Euler operates with such aesthetic categories as pleasant/unpleasant, perfect/imperfect and connects with them a number of propositions of consonance and dissonance.
In the Chapter XI “About harmonies of diatonic-chromatic genus” he demonstrates a table with chain of harmonies divided into species and arranged according to their acceptability for hearing. (The fragment of Euler’s table is reproduced as an addendum at the end of score).