The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachords, or divisions of the perfect fourth, into several complex systems encompassing tetrachords and octaves, as well as octave scales divided into seven to thirteen intervals. Any discussion of the music of ancient Greece, theoretical, philosophical or aesthetic, is fraught with two problems: there are few examples of written music, and there are many, sometimes fragmentary, theoretical and philosophical accounts. The empirical research of scholars like Richard Crocker, C. André Barbera, and John Chalmers has made it possible to look at the ancient Greek systems as a whole without regard to the tastes of any one ancient theorist. The primary genera they examine are those of Pythagoras and the Pythagorean school, Archytas, Aristoxenos, and Ptolemy (including his versions of the genera of Didymos and Eratosthenes).
Overview of the first complete tone system As an initial introduction to the principal names and divisions of the Ancient Greek tone system this article will give a depiction of the "perfect system" or systema teleion, which was elaborated in its entirety by about the turn of the 5th to 4th century BCE. The diagram at the right reproduces information from Chalmers (1993). It shows the common ancient harmoniai, the tonoi in all genera, and the system as a whole in one complete map. (Half-sharp and double-sharp notes not used with the depicted notes are omitted.)
The central three columns of the diagram show, first the modern note-names, then the two systems of symbols used in ancient Greece: the vocal symbols (favoured by singers) and instrumental symbols (favoured by instrument players). The modern note-names are given in the Helmholtz pitch notation, and the Greek note symbols are as given in the work of Egert Pöhlmann. The pitches of the notes in modern notation are conventional, going back to the time of a publication by Johann Friedrich Bellermann in 1840; in practice the pitches would have been somewhat lower. The section spanned by a blue brace is the range of the central octave. The range is approximately what is now depicted on a modern music staff and is given in the graphic below, left. Note that Greek theorists described scales as descending from higher pitch to lower, which is the opposite of modern practice and caused considerable confusion among Renaissance interpreters of ancient musicological texts.
The earliest Greek scales were organized in tetrachords, which were series of four descending tones, with the top and bottom tones being separated by an interval of a fourth, in modern terms. The sub-intervals of the tetrachord were unequal, with the largest intervals always at the top, and the smallest at the bottom. The 'characteristic interval' of a tetrachord is its largest one. The Greater Perfect System (systema teleion meizon) was composed of four stacked tetrachords called (from lowest to highest) the Hypaton, Meson, Diezeugmenon and Hyperbolaion tetrachords. These are shown on the right hand side of the diagram. Octaves were composed from two stacked tetrachords connected by one common tone, the synaphe. At the position of the paramese, the continuity of the system encounters a boundary (at b-flat, b). To retain the logic of the internal divisions of the tetrachords and avoid the Meson being forced into three whole tone steps (b–a–g–f), an interstitial note, the diazeuxis ('dividing'), was introduced between the paramese and mese. This procedure gives its name to the tetrachord diezeugmenon, which means the 'divided'. To bridge the inconsistency of the diazeuxis, the system allowed moving the nete one step up, permitting the construction of the Synemmenon ('conjunct') tetrachord, shown at the far left of the diagram. The use of the Synemmenon tetrachord effected a modulation of the system, hence the name systema metabolon, the modulating system, also called the Lesser Perfect System. This was considered apart, built of three stacked tetrachords—the Hypaton, Meson and Synemmenon. The first two of these are the same as the first two tetrachords of the Greater Perfect System, with a third tetrachord placed above the Meson. When all these are considered together, with the Synemmenon tetrachord placed between the Meson and Diezeugmenon tetrachords, they make up the Immutable (or Unmodulating) System (systema ametabolon). The lowest tone does not belong to the system of tetrachords, as is reflected in its name, the Proslambanomenos, the adjoined. In sum, it is clear that the Ancient Greeks conceived of a unified system with the tetrachord as the basic structure, but the octave as the principle of unification. Below is an elaboration of the mathematics that led to the logic of the system of tetrachords just described.
The Pythagoreans
… excerpt ends here. Continue reading the full article.
