Boethius (EN)

Boethius, Boetius Anicius Manlius Severinus, *ca. 480 Rome, †23 October 524 Calvenzano (?) near Milan, Roman politician, philosopher, mathematician and music theorist. He was related to the noble Anicius family, which produced two emperors (Petronius Maximus and Olibrius) and two popes (Felix III and Gregory the Great). Boethius’ father was consul in 487. After his father’s death, he was raised and educated in the home of the Roman patrician Quintus Aurelius Memmius Symmachus. He married his daughter. 

Following in his father’s footsteps, Boethius devoted himself to a political career and worked at the court of the Emperor, Theodoric, where he also gained recognition as a musician; in 510, he became consul, and in 522, he took up the office of magister officiorum. At the end of 522 or the beginning of 523, Boethius was involved in the trial of Senator Albinus. Accused of participating in a conspiracy against Theodoric, he was sentenced to exile and death. Symmachus died with him. He was probably imprisoned in Ticinum (now Pavia) and then in Calvenzano near Milan. His most famous work, De consolatione philosophiae (‘on the consolation of philosophy’), dates from this period.

Boethius is the author of writings on arithmetic, geometry, astronomy, logic, theology and philosophy. He devoted a treatise entitled De institutione musica libri V (‘on the fundamentals of music in five books’) to music. This treatise, like De institutione arithmetica libri II (‘on the principles of arithmetic in two books’), belongs to a series of his works on the quadrivium (a concept created by Boethius), of which the other two, on astronomy (based on the views of Ptolemy) and geometry (based on the views of Euclid), have been lost (the authorship of the preserved fragments of the geometric treatise is questionable). These works are estimated to have been written between 500 and 507.

In his treatise De institutione musica, Boethius discussed issues of harmony and acoustics. The structure of the treatise was probably dictated by didactic considerations: book 1 contains remarks on the ethical and therapeutic function of music, reflections on the classification of music and the concept of “musicus,” as well as elementary issues of acoustics and the theory of consonance; books 2 and 3 contain arithmetic calculations concerning the proportions of intervals, as well as a discussion of the views of the two main Greek theoretical schools, the Pythagoreans and the followers of Aristoxenus; book 4 deals with the division of the monochord, the most important consonances and notation; book 5 (not preserved in its entirety) presents the problems of harmony as conceived by Ptolemy. The question of the sources on which Boethius drew has not been definitively researched, although it is assumed that he based his work on a lost textbook by Nicomachus of Gerasa. The author himself mentions Plato, Aristotle, Albinus, and quotes Nicomachus of Gerasa, Archytas, Philolaus and Ptolemy. In his views, Boethius mainly referred to Pythagorean concepts, while he was critical of the school of Aristoxenus. He was a supporter of the superiority of intellectual knowledge over empirical knowledge; he treated auditory experience as the first stage of cognition, the results of which must be verified by the mind. In his view, neither composers, whom Boethius considered guided solely by instinct, nor instrumentalists, who served merely as tools, were true musicians; only those who based their musical knowledge on rational premises could be considered such. Music, according to Boethius, was mathematical knowledge, but it was connected not only with speculation, but also with morality. He regarded music, following Plato, as closely connected with the soul of the world (anima mundi) and influential on human character and the practices of the state. He agreed with Plato, that only simple music should be practised: diversity, complexity and the mixing of genres deprive music of its seriousness and thus have a negative impact on human character. Boethius’ division of music into musica mundana, humana and musica in quibusdam instrumentis derives from Neopythagoreanism and Neoplatonism. Boethius considered the harmony of the spheres to be a phenomenon that sounds real but is elusive to the senses. 

Boethius’ views on acoustics are also in line with Pythagorean thought. He understood sound, like Nicomachus of Gerasa, as a phenomenon resulting from repeated impacts of air, perceived by the ear as a unified whole. He recognised the relationship between the frequency of these impacts (vibrations) and the pitch of the sound. He distinguished between sounds of a specific (sonus incontinuus) and an indefinite pitch (sonus continuus). He defined an interval as the difference between a high and a low sound. He understood consonance in empirical terms as a combination of high and low sounds that reach the ear in a sweet and uniform manner. Boethius considered numerical proportion to be the ultimate criterion of consonance: consonance is created by the proportions multiplices “xn : n” and superparticulares “(n+1) : n.”  Following the example of the Pythagoreans, he included the octave, twelfth, double octave, fifth and fourth among the consonances. He did not consider the eleventh, which Ptolemy allowed, or the triple octave to be consonant. He defined further intervals (ditonus – major third, semiditonus – minor third, apotome – major semitone, limma – minor semitone consisting of 2 diesis) using the Pythagorean formula as sums or differences of already defined intervals. Precise calculations related to the division of individual tetrachords in the Systema teleion in all three types (diatonic, chromatic and enharmonic) are contained in book 4. It has been disputed whether Boethius, in his accounts of octave species and Greek modes, was drawing on Ptolemy. Boethius used the term ‘modus’ for octave species. He listed eight modi, which he named Hypodorian, Hypophrygian, Hypolydian, Dorian, Phrygian, Lydian, Mixolydian, and Hypermixolydian (a repetition of Hypodorian an octave higher). 

Boethius’ writings were the most influential source of Platonic philosophy in the early Middle Ages. His views, especially his classification of music and theory of consonance, played a fundamental role in music theory up to and including the 16th century. His calculations of intervals were used, among others, by Johannes de Muris (Musica speculativa). Boethius’ treatise was one of the most frequently copied works. Boethius was widely regarded by medieval theorists as one of the “inventors of music.” During the Renaissance, De institutione musica was the main source of knowledge about ancient Greek music. It was used by Gafurius and Glareanus, among others, and in Poland by Jerzy Liban of Legnica (De musicae laudibus oratio). The treatise De consolatione philosophiae also played a significant role in the history of European music. The poetic works contained in it were set to music as early as the Carolingian era; in the 16th century, they were sometimes arranged in the style of the so-called Horatian ode (e.g. in Poland). 

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