A Dictionary of Music and Musicians/Diaphonia
DIAPHONIA (from δις, twice; and φωνέω, I sound. Lat. Discantus; from dis, twice, and cantus, a song. Inexact synonym, Organum). A term, applied, by Guido d'Arezzo, in his Micrologus, to a form of composition in which a second Part, called Organum, was added below a given Cantus firmus. Writers, of somewhat later date, while generally describing Diaphonia under its Latinized name, Discantus, have treated that word as the exact synonym of Organum. Guido, however, clearly restricts the term, Organum, to the Part added below the Cantus firmus; and not without good reason, since it is only to the union of the two Parts that the terms, Diaphonia, or Discantus, can be logically applied. In its oldest known form, the added Part moved in uninterrupted Fourths below the Cantus firmus. Guido disapproved of this, and recommended, as a more agreeable (mollis) method, that the Major Second, and the Major and Minor Third, should be used in alternation with the Fourth. When a third Part was added, by doubling the Organum in the Octave above, the form of composition was called Triphonia. Tetraphonia was produced by doubling both the Organum and the Cantus firmus, in the Octave above. Guido called the third Part, Organum duplicatum. In later times, it was called Triplum (= Treble), and the fourth Part, Quadruplum.
[ W. S. R. ]