Enharmonic genus

Genus (Gr.: γένος [genos], pl. γένη [genē], lat. genus, pl. genera "type, kind") is a term used in the Ancient Greek and Roman theory of music to describe certain classes of intonations of the two movable notes within a tetrachord.

Aristoxenus (in his fragmentary treatise on rhythm) names 'genera' some patterns of rhythm. The tetrachordal concept is also found in the modal theory of Byzantine music and relates to the jins of Arabic music.

According to the system of Aristoxenus and his followers—Cleonides, Bacchius, Gaudentius, Alypius, Bryennius, and Aristides Quintilianus (Solomon 1980, vi)—the paradigmatic tetrachord was bounded by the fixed tones hypate and mese, which are a perfect fourth apart and do not vary from one genus to another. Between these are two movable notes, called parhypate and lichanos. The upper tone, lichanos, can vary over the range of a whole tone, whereas the lower note, parhypate, is restricted to the span of a quarter tone. However, their variation in position must always be proportional. This interval between the fixed hypate and movable parhypate cannot ever be larger than the interval between the two movable tones (Mathiesen 1999, 311–12, 326). When the composite of the two smaller intervals is less than the remaining (incomposite) interval, the three-note group is called pyknon (meaning "compressed"). The positioning of these two notes defined three genera: the diatonic, chromatic (also called chroma, "colour"), and enharmonic (also called ἁρμονία [harmonia]). The first two of these were subject to further variation, called shades—χρόαι (chroai)—or species—εἶδη (eidē). For Aristoxenus himself, these shades were dynamic: that is, they were not fixed in an ordered scale, and the shades were flexible along a continuum within certain limits. Instead, they described characteristic functional progressions of intervals, which he called "roads" (ὁδοί), possessing different ascending and descending patterns while nevertheless remaining recognisable. For his successors, however, the genera became fixed intervallic successions, and their shades became precisely defined subcategories (Mathiesen 2001a; Mathiesen 2001b). Furthermore, in sharp contrast to the Pythagoreans, Aristoxenos deliberately avoids numerical ratios. Instead, he defines a whole tone as the difference between a perfect fifth and a perfect fourth, and then divides that tone into semitones, third-tones, and quarter tones, to correspond to the diatonic, chromatic, and enharmonic genera, respectively (Mathiesen 1999, 310–11).

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