Music from the Earliest Notations to the Sixteenth Century

EX. 5-1B    Diapente

EX. 5-1C    Diatessaron

EX. 5-1D    Composite

To “hear” (that is, aurally conceptualize) strict parallelism at the fifth without any sense of
“polytonal” contradiction, one must be able to imagine “fifth equivalency” on a par with the octave
equivalency we have all learned to take for granted as a listening norm. The author of the Musica
enchiriadis recognized as much and even constructed a scale that exhibits fifth equivalency as the basis
for “the symphonia of the diapente” (Ex. 5-2a). Instead of reproducing interval species at the octave, this
scale duplicates interval sequences at the fifth. Just as one encounters discrepancies in fifth-size (perfect
vs. diminished) when harmonizing within the “normal” diatonic scale, so in the Musica enchiriadis scale
there will be uniform fifths but discrepancies in octave-size (perfect vs. augmented).