Incomposite interval

An incomposite interval (Ancient Greek: διάστημα ἀσύνθετον ; German: ungeteilte Intervall, einfache Intervall) is a concept in the Ancient Greek theory of music concerning melodic musical intervals (Ancient Greek: διαστημάτων) between neighbouring notes in a tetrachord or scale which, for that reason, do not encompass smaller intervals. (Ancient Greek: ἀσύνθετος means "uncompounded".)Aristoxenus (fl. 335 BCE) defines melodically incomposite intervals in the following context:

Let us assume that given a systēma, whether pyknon or non-pyknon, no interval less than the remainder of the first concord can be placed next above it, and no interval less than a tone next below it. Let us also assume that each of the notes which are melodically successive in each genus will either form with the fourth note in order from it the concord of a fourth, or will form with the fifth note from it in order the concord of a fifth, or both, and that any note of which none of these things is true is unmelodic relative to those with which it forms no concord. Let us further assume that given that there are four intervals in the fifth, of which two are usually equal (those constituting the pyknon) and two unequal (the remainder of the first concord, and the amount by which the fifth exceeds the fourth), the unequal ones are placed next to the equal ones in the opposite order above and below. Let us assume that notes standing at the same concordant interval from successive notes are in succession with one another. Let us assume that in each genus an interval is melodically incomposite if the voice, in singing a melody, cannot divide it into intervals.

In another place, Aristoxenus clarifies that

the mere discrimination of magnitudes by the senses is no part of a complete understanding of the subject. … For through the magnitudes as such, no knowledge is forthcoming of the functions of either the tetrachords or the notes, or of the distinctions between the genera, or, to put it briefly, of the distinctions between the composite and the incomposite, of the simple and the modulating, of the styles of melodic composition, or, in a word, of anything else at all.

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