Ancient Greek music was purely or predominantly melodic; and in such music subtleties of intonation count for much. If our sources of information about the intervals used in Greek music are not always easy to interpret, they are at any rate fairly voluminous. On the one hand we have Aristoxenus, by whom musical intervals were regarded spatially and combined and subdivided by the processes of addition and subtraction; for him the octave consisted of six tones, and the tone was exactly (...) divisible into fractions such as the half and quarter, so that the fourth was equal to two tones and a half, the fifth to three tones and a half, and so on. On the other hand we have preserved for us in Ptolemy's Harmonics the computations of a number of mathematicians, who realized correctly that intervals could only be expressed as ratios , that the octave was less than the sum of six whole tones and that this tone could not be divided into equal parts. These authorities are Archytas, the Pythagorean of the early fourth century, Eratosthenes , Didymus and Ptolemy himself . To these we must add the scale of Plato's Timaeus and, closely related to it, the computations of the pseudo-Philolaus and of Boethius himself . Aristoxenus is less easy to understand than the mathematicians because of the unscientific nature of his postulates. His importance, however, is very great, not only from his comparatively early date but because he claims to champion the direct musical consciousness against the scientific approach of some of his predecessors and contemporaries. (shrink)

Our information about the early stages of Greek music is so slight that these references of Aristides Quintilianus to an the Pseudo-Plutarch to a scale employed by the legendary figure Olympus take on an immense value for us. The dialogue itself is an unskilful patchwork, but the author's sources are often good. These particular passages are almost certainly both derived with small alteration from Aristoxenus, in whose time the traditional music ascribed to Olympus was still in use. For the elucidation (...) of the scale's history and structure we have three1 pieces of evidence to help us. There is the first passage mentioned above, which deals with the discovery of the enharmonic genus by Olympus, which is connected, at first sight obscurely, with the Spondeion scale; and the second passage, which discusses the scalar limitations of theσφoνδειξων τρόφoς with especial reference to an elementary polyphony. There are also the ancient scales quoted by Aristides Quintilianus. (shrink)