Pyknon

Pyknon, Greek: πυκνόν, sometimes also transliterated as pycnon (from Greek: πυκνός close, close-packed, crowded, condensed; Latin: spissus) in the music theory of Antiquity is a structural property of any tetrachord in which a composite of two smaller intervals is less than the remaining (incomposite) interval. The makeup of the pyknon serves to identify the melodic genus (also called "genus of a tetrachord") and the octave species made by compounding two such tetrachords, and the rules governing the ways in which such compounds may be made centre on the relationships of the two pykna involved.

The pyknon was an important criterion in the classification of melodic genera (Greek: γένη τῶν μελῳδουμένων). The Greek word πυκνόν is an adjective meaning "close", "compact", "close-packed", or "crowded" (Liddell and Scott 1996). In Ancient Greek music theory, this term is used to describe a pair of intervals within a tetrachord, the sum of which is less than the remainder of the tetrachord (Levin 2007, 413). Although in modern usage, a tetrachord may be any four-note segment of a scale, or indeed any (unordered) collection of four pitch classes, in ancient Greek music theory a tetrachord consists of a four-note segment of the Greater and Lesser Perfect Systems bounded by the interval of a perfect fourth, the outer notes of which remain fixed in all genera and therefore are called "standing notes" (Greek: ἑστῶτες φθόγγοι). The positions of the inner notes vary from one genus to another, for which reason they are called "movable notes" (Mathiesen 1999, 301, 312, 322, 344, 350, et passim; from Greek: κινούμενοι φθόγγοι). In its basic theoretical form, the largest internal of a tetrachord is at the top, and the smallest at the bottom. The existence of a pyknon therefore depends on the uppermost interval being larger than half of a perfect fourth, which occurs only in the chromatic and enharmonic genera. Because the diatonic genus consists of two whole tones and one semitone, no single interval is larger than the other two combined, and so there is no pyknon (Barbera 1984, 229). For this reason, the enharmonic and chromatic genera are sometimes called the "pyknic genera", in order to distinguish them from the diatonic (Solomon 1984, 246).

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