Aristoxenus

Greek philosopher and music theorist

• Born: 375-360 b.c.e.
• Birthplace: Tarentum (now Taranto, Italy)
• Died: Unknown
• Place of death: Probably Athens, Greece

The theoretical writings on music by Aristoxenus established a foundation on which modern music theory is based.

Early Life

Aristoxenus (ar-ihs-TAWK-see-nuhs), born in Tarentum, was a Greek philosopher and music theorist who flourished during the fourth century b.c.e. He received his earliest musical training at the hands of his father, Spintharus, who enjoyed some reputation as a musician. He later studied with Lamprus of Erythrae, of whom little is known. In time Aristoxenus moved to Athens, where he studied with the Pythagorean Xenophilus—important in view of the position he was to take in his theoretical treatises. He also studied at the Lyceum with Aristotle. Because Aristoxenus later competed, although unsuccessfully, with Theophrastus, a colleague, for headship of the Lyceum around 322, it may be assumed that Aristoxenus was a superior student and respected in scholarly circles.

Life’s Work

Aristoxenus was apparently a prolific writer, with one source attributing more than 450 works to him, although only a few Aristoxenus fragments have survived. The writings, which cover a variety of topics, including works on music, biography, history, and philosophy, reflect the diversity of his studies. All the fragments are of interest, but the most important of the extant fragments pertain to music: Aristoxenus made his truly original contribution as he challenged the way that theorists, past and contemporary with him, had studied and written about music. So great was his influence that theorists and philosophers on music who followed him were compelled to address his arguments.

Numbering among the music fragments that survive are parts of three books titled Harmonika stoicheia (The Harmonics, 1902), the contents of which are believed to have been derived from Aristoxenus’s earlier writings on the subject. Much of what is known about ancient Greek theory comes from his writings and those of later writers, such as Plutarch, Cleonides, and Aristides, who expounded on Aristoxenus’s principles.

In addition to The Harmonics, there is a fragment on rhythm, consisting of approximately 250 lines, which was treated by Aristides several centuries later. While Aristoxenus’s work reveals a man who could be rather pompous and contentious, his writings are clearly the product of a first-rate mind.

Aristoxenian theory was about melody and articulated a system that addressed the issues of pitch, intervals, genera, systems, modes, and modulation as they applied to melody. The smallest consonant interval recognized in his system was a perfect fourth, which also formed the fixed outer boundary of a four-note unit called a tetrachord. The tetrachord was a kind of building block, which, in combination with other tetrachords, formed larger structures. The tetrachord could belong to one of three types, or genera: diatonic, enharmonic, or chromatic. This system was determined according to the placement of the two inner notes that fell within the boundary of the fixed interval of the fourth, which was formed by the two outer notes of the tetrachord. The varied placements of the two inner notes of the tetrachord were known as shadings, or colors. Aristoxenus recognized two alternative positions of the inner notes in the diatonic genus and three in the chromatic, although he accepted that the variety of shadings was theoretically infinite.

The tetrachords could be combined, either sharing a common note and called conjunct, or, if a whole step separated the two tetrachords, called disjunct. The combining of the tetrachords produced three important larger theoretical structures known as the Greater Perfect System, the Lesser Perfect System, and the Immutable System.

The Greater Perfect System consisted of two pairs of conjunct tetrachords with an added note, or, in modern terminology, it can be seen in its diatonic form as a two-octave scale ranging from A to a′, as seen on the piano keyboard. The range most used for the writing of Greek melodies, however, appears to have been the octave e′ to e, and the Greater Perfect System was probably regarded as a central octave from e′ to e lying within the A to a′ range previously noted and with a conjunct tetrachord on each end and an added note on the bottom. The Greater Perfect System produced seven different species of the octave, because a different intervallic sequence would occur for the octave scale built on each of the seven different pitches represented in the system as it is brought within the central octave of e′ to e.

The Lesser Perfect System consisted of three conjunct tetrachords with an added note that, using the piano keyboard for purposes of illustration, had the range of A to d′. The Lesser Perfect System is believed to have assisted in the function of change, or modulation, from one species to another.

The Immutable System was a combination of the Lesser Perfect and Greater Perfect systems and could be performed at various pitch levels. Such a structure was called a tonos. Aristoxenus identified thirteen different tonoi. The term is not without ambiguity, and scholars are not exactly sure what the term meant to Aristoxenus. It is, however, generally believed that the octave species and the tonos were one and the same during the time of Aristoxenus.

Aristoxenus’s approach to the theory of music, conceived around 320 b.c.e., was unique for his time. A superior student of Aristotelian logic who was familiar with the “new math,” geometry, Aristoxenus turned both logic and geometry to his advantage as he defined the way subsequent theorists were to look at the discipline of music. His treatise was not simply an exercise in abstract logic. He elevated the musician’s “ear” to a level equal with the intellect. By doing so, he recognized the value and importance of the commonsense judgment of the practicing musician.

Aristoxenus’s writings clearly challenged both the teachings of Pythagoras, who flourished around 530 b.c.e. and whose reputation and writings were legendary by the time of Aristoxenus, and those of a group known as the Harmonists. The supporters of Pythagoras’s theories about music were scientists and mathematicians who were not interested in explanations or observations about the interplay of musical elements or about the science of music itself. They believed that understanding numbers was central to understanding the universe, and, therefore, it was quite logical to express musical intervals, of key importance to the Pythagoreans, in terms of mathematical ratios.

The Harmonists, criticized by Aristoxenus for failing to establish a rigorous system, were interested in the practical and empirical aspects of music theory but fell short of articulating an acceptable system. They were preoccupied with the identification and measurement of microintervals, which emphasized the study of certain scales to the exclusion of others.

A key factor in Aristoxenus’s approach was his description of sound as a continuum, or line, along which the pitch could come to rest at any point, permitting him the freedom to create intervals of varying sizes without regard to whether the interval could be expressed using rational numbers. While abstract mathematical expression of a musical interval had become most important to the Pythagoreans and the Harmonists, Aristoxenus focused instead on the development of a system that would afford him the freedom and flexibility to identify subtleties of scalar structure. He based his system on judgments made by the ear and then represented it through geometric application.

Significance

Aristoxenus was the earliest writer on music theory known to address practical musical concerns. When he took the unique position that the ear, along with the intellect, should be used in the study of music, he established a precedent that ultimately altered the course of music theory. In effect, he redefined what music theory was, taking it out of the hands of the scientists and mathematicians and creating a new discipline that focused only on the interrelationship of musical elements. His arguments, which owed much to Aristotelian influence and methodology, enabled him to produce a clearly defined and organized system of music theory.

Bibliography

Aristoxenus. Aristoxenou harmonika stoicheia = The Harmonics of Aristoxenus, edited by Henry Stewart Macran. New York: Olms, 1990. An English translation of Aristoxenus’s main work; also contains some commentary and some biographical material.

Barker, Andrew. “Music and Perception: A Study in Aristoxenus.” Journal of Hellenic Studies 98 (1978): 9-16. Examines Aristoxenus’s approach to music theory through an attempt to clarify the exact role the ear plays in relation to the intellect and also with respect to mathematics.

Crocker, Richard. “Aristoxenus and Greek Mathematics.” In Aspects of Medieval and Renaissance Music, edited by Jan LaRue. New York: Pendragon Press, 1978. An excellent article that discusses the key aspects of Aristoxenus’s theories on music. Compares and explains Pythagorean arithmetic with Aristoxenus’s use of geometric principles to illustrate and explain his new theories on music.

Henderson, Isobel. “Ancient Greek Music.” In Ancient and Oriental Music, edited by Egon Wellesz. Vol. 1 in The New Oxford History of Music. 2d ed. New York: Oxford University Press, 1990. An excellent study of ancient Greek music, with considerable treatment of Aristoxenus. There is a brief discussion of the Harmonists and the Pythagoreans. The history, issues, and elements of Greek music are all discussed.

Lippman, Edward. Musical Thought in Ancient Greece. New York: Da Capo Press, 1975. It is not necessary to be a practicing musician or theorist to appreciate or understand this book. There is an excellent treatment of Greek ethics, philosophy, and aesthetics of music.

Rowell, Lewis. “Aristoxenus on Rhythm.” Journal of Music Theory 23 (Spring, 1979): 63-79. Provides a translation of Aristoxenus’s fragment on rhythm. Rowell identifies the fragment as being in an Aristotelian format and discusses Aristoxenus’s concept of rhythm.

Winnington-Ingram, R. P. “Aristoxenus.” In New Grove Dictionary of Music and Musicians, edited by Stanley Sadie. 2d ed. New York: Grove’s Dictionaries, 2001. The article contains important biographical material. The author discusses the philosophical differences between Aristoxenus and the Pythagoreans. He also provides a summary of Aristoxenus’s contribution to theory. Includes bibliography.