The Elements of Harmony by Aristoxenus of Tarentum: commentary and translation

Author(s)

Nataly Ianicelli Cruzeiro

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Faculdade de Filosofia, Letras e Ciências Humanas (FFLCH/SBD)
• Defense date: 2021-02-15

Examining board members

Paula da Cunha Correa; Lucas Angioni; Fernando Maciel Gazoni; Marcos Martinho dos Santos

• Advisor: Paula da Cunha Correa

Abstract

The Elements of Harmonics is a treatise written by the Peripatetic philosopher Aristoxenus of Tarentum (ca. 360-300). It is the earliest surviving and the best-preserved writing dedicated to the study of music structures known before the Hellenistic Period. Aristoxenus establishes that melodies should be subject of a science that deals exclusively with the analysis of musical elements: harmonics. This discipline is subordinated to a more comprehensive science, that of mousike, whose parts also include the study of rhythm, metrics and organology (41.10-12 [Da Rios]). According to Aristoxenus, the goal of harmonics is not to describe the physical movements of sounds in the air or its relationship with the cosmos or ethics, but to analyse the elements used in melodies - notes, intervals, scales, tonalities, genres, modulation and melopoiia (34.30ss [Da Rios]) - and to identify the combinations (syntheseis) of these structures in accordance to the following criteria: sounds should be executable (melōidoumenoi), harmonised (hērmosmenoi) and melodic (emmeloi) (51.1-4 [Da Rios]). Therefore, he defends the priority of sense-perception for the observation of sounds and the establishment of principles, rejecting both the arithmetic approach taken by the Pythagoreans and the empiricist one taken by the so-called \"harmonicists\" and practical musicians. The treatise is divided into three books that present, in books I and II, the general principles that guide harmonised melodies, discussions about the motion of the voice between low- and high-pitched sounds, the difference between singing and speaking, and philosophical questions about music. The third book presents the demonstrations (elements) of harmonics in 28 theorems. This dissertation comprises a translation of the Harm. with exegetical and critical commentaries, and an introduction that aims to place the Aristoxenian thinking among that of his predecessors and other music theorists. (AU)

• FAPESP's process: 18/26392-6 - The Elements of Harmony of Aristoxenus: translation, notes, and an essay on comprehension and judgement of music
• Grantee: Nataly Ianicelli Cruzeiro
• Support Opportunities: Scholarships in Brazil - Master