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Encyclopedia of Microtonal Music Theory

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[John Chalmers, Divisions of the Tetrachord]

The structural module or motif of ancient Greek [musical] scales consisted of four notes spanning a Perfect Fourth. These four notes divided the Fourth into three intervals, the largest of which, the C.I., determined the genus as Diatonic, Chromatic or Enharmonic.

Tetrachordally derived scales are still prominent in the music of India, the European cultural area, and the Islamic countries.

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[Joe Monzo]

An example tetrachord may be diagrammed schematically thus:

          /   D
         /       > tone
        /     C
perfect-4th      > semitone
        \     B
         \       > tone
          \   A

In the ancient Greek theory, the two bounding notes ("A" and "D" in this example) were fixed in pitch, which the two inner notes were variable in pitch, and the various tunings of those two notes determined the genus and shade.

See Monzo, Tutorial on Ancient Greek Tetrachord-theory for more info.

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