5th-cent. theories about sound fall into two groups. Most though not all non-Pythagorean Presocratics were concerned primarily with the process of hearing (see especially Theophr. Sens.; cf. also Hippocr. De victu 1. 8 and 15 on hearing and voice). The Pythagoreans opened a musical perspective, beginning from observed correspondences between pitch-relations and the relative lengths of pipes or strings. They showed that the correspondences hold quite generally, through demonstrations using other sound-sources (see e.g. DK 18. 12, 13; texts attributing ‘experiments’ to Pythagoras himself are unreliable). The resulting hypothesis that pitch itself is a quantitative variable prompted deeper enquiries, beginning in the 4th cent., into the physical nature of sound, its causes, transmission, and attributes, as well as the process of hearing.
The Greeks did not recognise acoustics as a separate science; the issues were studied in other contexts, mainly by philosophers interested in sense-perception, by biologists and medical writers, and above all by harmonic theorists.
Archytas' essay (fr. 1) is the direct ancestor of most later discussions. Sound, he says, is always caused by an impact (later writers specify the immediate cause as an impact on the air). It moves through the air like a missile until it strikes the ear: more vigorous movements constitute louder and higher-pitched sounds. Probably in Plato (1), certainly in Aristotle and after, what travels is not a ‘missile’ but an impulse in a stationary medium, variously conceived: as a succession of collisions between adjacent portions of air (e.g. ps.-Arist. Pr. 11. 6), or as a progressive ‘tensing’ or compression of the medium (Ptol. Harm. 1. 3), or by Stoics (see stoicism) on the analogy with expanding circular ripples in water, but spreading ‘spherically’, in three dimensions (Diog. Laert. 7. 158). Aristotle's analysis, unlike Archytas', allowed for distinctions between the determinants of pitch (speed of transmission) and of volume (mass of air moved), each depending on relations between quantifiable features of the agent (esp. De an. 419b–421a, Gen. an. 786b–788b; cf. Pl. Ti. 67a–c). The correlation of pitch with speed (though Aristotle denies their strict identity) remained orthodox as late as Boethius, despite difficulties (e.g. Arist. Sens. 448a–b, Theophr. fr. 89) and alternative hypotheses, correlating pitch with degrees of aerial tension (Ptol. Harm. 1. 3) or with the rapidity of successions of impacts on the air (Euc. Sectio canonis 149. 18–20). The causation of apparently continuous sounds by successions of discrete impacts is discussed at ps.-Arist. De audibilibus 803b–804a, later by Heraclides (1) Ponticus (Porph. On Ptolemy's Harmonics 30. 1 ff.). The former passage is designed to explain the phenomenon of concord, another topic provoking much debate. Early treatments are Plato Ti. 79c–80b, Arist. Sens. 447a–b, and the proem to Euc. Sectio canonis: most later discussions are elaborations of these (there are traces of still earlier investigations at DK 47 A 17).
Despite Theophrastus' criticisms (fr. 89) of quantitative theories of pitch, later harmonic theorists drew freely on Platonic and Peripatetic views to justify their treatment of intervals as numerical ratios, to explain many properties of instruments (e.g. Nicom. Ench. 4), especially the monochord and related ‘scientific’ devices (carefully discussed by Ptolemy (4)), sometimes (as in Theon (2) and Aristides Quintilianus) to account for ‘musical’ attributes of the soul and the universe. Practical applications were found: Vitruvius discusses theatre design in the light of Stoic acoustics, explaining how hollow vessels, suitably pitched and placed, can improve an auditorium's resonance (De arch. 5. 3–5). Investigations of sound's pitch and transmission, and certain properties of sounding bodies, sometimes approached the scientific, though observations and experiments were never adequate to adjudicate conclusively between rival views. Discussions of other acoustic phenomena are usually uncoordinated and speculative (as in Pr. bk. 11): the fullest and most influential treatise, De audibilibus, is mainly a systematization of common sense, guided by the principle that a sound's qualities reflect those of its causes.