(fl. second half of the first century CE), musical theory.
A musical theorist and grammarian, Didymus was author of a treatise called On the Difference between the Aristoxenians and the Pythagoreans (of which only few fragments survive, quoted by Porphyry of Tyre), and perhaps of a work On Pythagorean Philosophy mentioned by Clement of Alexandria. He is famous above all for his intervallic divisions of the Greek musical scale recorded by Ptolemy in his Harmonics, where he is called “the musician.” His biographical data are uncertain, but he seems to inclined to the Pythagorean musical tradition.
Despite his possible connections with some Alexandrian scholars (he is said to have been son of a certain Heraclides, perhaps the Heraclides Ponticus the Younger who studied in Alexandria), Didymus is almost certainly to be distinguished from the famous Didymus nicknamed Chalkenteros (Brazen-guts) for his indefatigable industry with regards to books, who lived in the first century BCE. It seems more probable that he was the one said by the Byzantine encyclopedia Suda (s.v. Didymus) to have lived in the time of Nero and to have been a grammarian and good musician, with a talent for singing.
Both Ptolemy and his commentator Porphyry quote his activity as musical theorist, the former with regard to some improvements tentatively introduced by him in the monochord (the Pythagorean device for measuring intervals between notes expressing them as mathematical ratios) and concerning the numbers that make up the division of the octave; the latter in a section that discusses the different schools of harmonic theory and their methodologies, and as the source—together with Archytas—for a passage that comments on Pythagoreans’ mistakes in computing musical concords (symphoniai). Furthermore, see the reference to a certain Didymus who described the rhythm (rhythmos) as “a configuration (schematismos) of a particular sound” in Bacchius’s Introduction to the Art of Music(p. 313, 9 f. Jan), which may reasonably allude to the same person.
Despite his criticism, Ptolemy’s recording of Didymus’s scalar divisions beside those of more famous musical theorists—such as Archytas, Aristoxenus of Tarentum, and Eratosthenes—shows that his work in harmonics (the science of the elements out of which melody is built) was regarded as something of considerable importance in antiquity. According to Ptolemy, Didymus failed to mathematically identify the intervals that make up the octave because he relied on the misleading help of the mono-chord, whose difficulties in making more accurate measurements were not solved by his correction (diorthosis) “in that he concentrated solely on making the bridge easier to manipulate, being unable to find any cure for the other more numerous and more serious defects” (Didymus, trans. Barker, 1989, p. 342). His procedure was the positioning of the bridge so that the opposite sides of the string could produce usable sounds. But this system, though helpful for demonstrating basic Pythagorean ratios (as the double, corresponding to the octave, the hemiolic, corresponding to the fifth, and the triple ratios, corresponding to the octave and a fifth) did not allow him to construct exactly the mathematical proportions of smaller intervals in the tetrachord (the basic scalar system of ancient Greek music, which spans a fourth). According to Ptolemy’s judgment, his divisions of the diatonic, chromatic, and enharmonic tetrachords (the three main genera of tetrachordal divisions) were calculated without considering beforehand the way in which they were used in practice (chresis), the only thing that makes it possible for them to be brought into conformity with the impressions of perception (aisthesis).
In Porphyry’s Commentary on the Harmonics of Ptolemy, Didymus is mentioned in the section that compares the various schools of harmonic theory by reference to the status assigned by each to perception (aisthesis) and reason (logos), together with Ptolemais of Cyrene. In his treatise, titled On the Difference between the Aristoxenians and the Pythagoreans (which was probably Porphyry’s source for the quotations of Ptolemais’s fragments), Didymus distinguished at least three main approaches to the theoretical musical inquiry. At one extreme are those who concentrated on perception alone, ignoring reason completely; on the other extreme those who esteemed reason as the highest judge, the Pythagoreans, attending to perception only to the extent that it suffices to give them a starting point for further theoretical investigations. Between these two extremes there is Aristoxenus, who gave an equal importance to both principles.
The empiricists were called by Didymus instrumentalists (organikoi) and vocal trainers (phonaskikoi), names that suggest that they were practical musicians who only occasionally devoted themselves to theory, depicted as people who offered no demonstration and no coherent theory on this topic. Their description is similar to some others offered by more ancient sources, such as Plato Republic book seven (530c–531c), where these theorists were characterized as “those worthy persons who bully the strings and interrogate them with torture” (Didymus, trans. Barker, 1989, p. 56), and the Hibeh Papyrus on music (1.13), in which they claim the theoretical branch to be their own special business although they spent their entire life on strings. As a matter of fact, these pieces of evidence suggest a quite old and lasting empirical tradition in the theoretical inquiry on music, which is still echoed in Didymus’s treatise. The Pythagoreans, instead, though deriving the catalyst of their investigation from perceptibles, constructed their theorems through reason on its own, dismissing perception when it bears witness against their conclusions.
Between these two approaches, as in Ptolemais’s fragments, is Aristoxenus, who treated both principles, perception and reason, as having equal power. According to him, these criteria have to be as accurate as possible, because “music … is perceptual (aistheton) and rational (logikon) at the same time” (Didymus, second extract, trans. Barker, 1989, p. 244). It has to be noticed that the description of the Aristoxenian procedure in Didymus’s fragments finds several echoes in what survives of genuine Aristoxenian works.
Furthermore, among those theorists whose approach to harmonics was based more on reason than perception, Didymus quoted Archestratos, who is mentioned also by Philodemus (first century BCE) as a devotee of musical theory who regarded the nature of sounds, notes, and intervals as philosophical aspects of music.
WORKS BY DIDYMUS
Porphyrios kommentar zur Harmonielehre des Ptolemaios. Edited by Ingemar Düring. Göteborg, Sweden: Elanders, 1932. Reprint, New York: Garland, 1980. This is the most recent critical edition of Porphyry’s Greek text that includes Didymus’s fragments.
Greek Musical Writings. Vol. 2: Harmonic and Acoustic Theory. Edited by Andrew Barker. Cambridge, U.K.: Cambridge University Press, 1989. It includes the English translation of Didymus’s fragments.
Barker, Andrew. “Greek Musicologists in the Roman Empire.” In The Sciences in Greco-Roman Society, edited by Timothy D. Barnes, 53–74. Edmonton, Canada: Academic Printing and Publishing, 1994.
———. “Didymus .” In The Oxford Classical Dictionary, edited by Simon Hornblower and Antony Spawforth. Oxford: Oxford University Press, 1996.
Cohn, Leopold. “Didymus .” Real-Enzyklopädie der klassischen Altertumswissenschaft5, no. 1 (1903): 473–474.
Düring, Ingemar. Die Harmonielehre des Klaudios Ptolemaios. Göteborg, Sweden: Elanders, 1930. Reprint, New York: Garland, 1980.
———. Ptolemaios uns Porphyrios über die Musik. Göteborg, Sweden: Elanders, 1934. Reprint, New York: Garland, 1980.
Jan, Karl von. Musici Scriptores Graeci. Aristoteles, Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat. Leipzig, Germany: Teubner, 1895. Reprint, Hildesheim, Germany: G. Olms, 1962.
Zaminer, Frieder. “Didymus  von Alexandreia B. Musiktheorie.” In Der Neue Pauly: Enzyclopadie der Antike 3, edited by von Hubert Cancik and Helmet Schneider. Stuttgart, Germany: Metzler, 1997.