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The interval of the fourth has an important structural role in the music of many peoples, particularly in certain geographical zones: Scotland and Ireland, eastern and south-eastern Europe, northern Africa, southern Asia as far east as Indonesia, and Indian North America.3 Here and there melodies can be found based wholly on two notes a fourth apart with no (or only occasional) intermediate notes to bridge the gap.4 More usually there is at least one 'infix', an additional note dividing the fourth into smaller steps. The steps are always unequal, the larger one being anything between a minor and a major third, and the smaller one accordingly something between a tone and a semitone. |
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In this case, where there is just one infix in the fourth, we have a scale of the type called pentatonic, because in an octave constructed in this way there will be just five steps, for example, A c d e g a, or e f a b c' e'. Pentatonic systems are found in the folk music of many parts of the world, including these islands; many Scottish melodies in particular are pentatonic. |
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Now, Aristoxenus (and other, unspecified experts before him) believed that the Greek enharmonic tetrachord ( ) had evolved from a simpler, pentatonic trichord, e f a, by division of the semitone e-f into two quarter-tones. The evidence adduced was a traditional aulos tune played at libations and attributed to the semi-legendary piper Olympus. In Aristoxenus' time it was generally played with the divided semitone, but, he said, if you listen to someone playing it in the old-fashioned way, you can see that the semitone is meant to be undivided. In other compositionsdeemed to be later onesOlympus did divide the semitone and so invented the enharmonic genus.5 Whether Olympus was really the author of the various traditional airs ascribed to him, we cannot tell. But the important fact is that there was an 'old-fashioned' way of playing at least one of them without dividing the semitone. Aristoxenus drew the right inference: that the enharmonic type of scale evolved from one in which the fourth was divided by a single infix into semitone and major third. |
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3 Sachs, WM 63, 163, cf. The Musical Quarterly 29 (1943), 381-404. By contrast, according to the same authority, the third is the important interval in black Africa, most of Europe, and northern Asia. |
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4 Sachs, WM 62. One passing reference in Aristoxenus implies the existence of melodies composed entirely from 'standing' notes, i.e using empty fourths (Harm. 2. 44, amplified in Cleon. Harm. p. 189. 9-15). |
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5 Aristox. fr. 83 ap. ps.-Plut. De mus. 1134f-1135b. cf. Thrasyllus ap. Theon. Smyrn. p. 93 1 (Barker, GMW ii. 229 with n. 91). |
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