Musica Enchiriadis (ca. 900), trans. 31
"...the same guiding principle that controls the concord of pitches
regulates the natures of mortals. Through these numerical relationships,
by which unlike sounds concord with each other, the eternal harmony of
life and of the conflicting elements of the whole world is united as
one with material things"
Scolica Enchiriadis (ca. 900), trans. 65
"Harmony is deemed the agreeable mixture of different pitches; music
is the theory [ratio] of that agreeableness. Just as music is bound
up in every respect with this theory of numbers, as are also the other
mathematical disciplines, so it is proper that they be understood
through numbers."
Guido, Micrologus (1026-28), Chapter 18 (trans., 77)
"Diaphony sounds as a separateness of [simultaneous] sounds, which we also call
organum, in which notes distinct from each other make dissonance harmoniously
and harmonize in their dissonance."
John (ca. 1100), trans. 159
Diaphony is the sounding of different but harmonious notes, which is
carried on by at least two singers, so that while one holds to the original
melody, another may range aptly among other tones, and at each
breathing point both may come together on the same note or at the
octave. This method of singing is popularly called "organum"....Diaphony
means "twofold sound" or "difference of sound."
Montpellier Organum Treatise (early 1100s)
Diaphony is two-part song; that is its definition.
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