A Technique of Inversion in Polyphonic Theory and Practice of the latter half of the 16th–18th centuries: syllables and tones

Abstract
The paper concerns the typology of melodic inversions in the polyphonic music of the second half of the 16th–18th centuries. The focus is on the hexachordal inversions — one of the least studied subjects of the theory and practice of counterpoint. The hexachordal principle of inversion is based on the symmetry of the solmization syllables which are equidistant from the axis mi–fa. According to the offered typology the inversion is produced by using the symmetrical syllables within 1) one hexachord, 2) the hexachords of the relation of fifth or 3) major second. The article contains a number of examples from the treatises and polyphonic pieces of the 16th–18th centuries.

Keywords
Hexachordal and nonhexachordal inversions, solmization syllables, the axis of symmetry, polyphony of the music of the 16th–18th centuries