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Page 160
6
Scales and Modes
Before we come to melody itself we must investigate the rails on which it ran: the scales that provided a framework of discipline by limiting the infinity of possible notes and intervals to an ordered set, and the varieties of their structures and associations that make it appropriate and conventional to speak of modes.
Our information is, of course, far from complete. But Aristoxenus and other theoreticians formulate general principles which are supposed to govern the structure of scales, and they specify the sizes of intervals between successive degrees of the scale in various different tuning systems. There are some records of actual scales used in the Classical period, and numerous references to the names and characters of different modes. The surviving fragments of musical texts give us glimpses of scale systems in use.
The anatomy of the octave
The ancient writers attach great importance to the distinction between 'concordant' and 'discordant' intervals (symphona, diaphona). By concordant intervals they mean those at which two notes, sounded either simultaneously or successively, go well together or seem to blend harmoniously. The intervals which they regard as concordant are the fourth, the fifth, and the octave (or larger intervals compounded from these, octave + fourth, etc.). All other intervals were classed as discordant, though considered perfectly acceptable in melody provided that they arose between notes of a properly constituted scale.
The higher status Of the recognized concords was reflected in the structure of scales. All scales (according to Greek theory) are built up from 'tetrachords', that is, from systems of four notes spanning the interval of a fourth. Successive tetrachords were either 'conjunct', that is, with a shared note (for example, d-g-c'), or 'disjunct', separated by a tone (for example, d-g: a-d'). Since a fourth plus a tone equals a fifth, a pair of disjunct tetrachords is in effect a fourth

 
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