A Companion to Hildegard of Bingen

180 leigh-choate, flynn, and fassler
to the joints of the fijingers. John’s treatise, which helped transmit the
Guidonian gamut to South Germany, includes a chapter on improvised
polyphony and recommends the use of the hand as a mnemonic replacement
for the monochord: “Indeed, one should avidly practice playing
upon the joints of one’s hand, so that after a while, whenever one wishes,
one may become accomplished in using it instead of a monochord, and
may test, correct, and compose chant on it.”59
The range of O vos angeli is only the most prominent feature reflecting
South German theory. Recent studies of Hildegard’s music underscore the
ways in which the modal theory developed by Bern of Reichenau and transmitted
to the Hirsau network of music theorists by his student, Hermannus
Contractus, emphasizes the structural pitches of fijinal, fijifth, and octave, and
note that Hermannus’s own music reflects his theoretical teaching.60 O vos
angeli clearly fijits into this general context by employing these important
pitches to structure its modal space. According to Hermannus’s theory, it
would be classifijied as being in deuterus mode with its fijinal on E. The E mode
is called deuterus since its fijinal note is the second note of the “tetrachord of
the fijinals” (D-E-F-G). According to the theory, the authentic range of deuterus
mode emphasizes not only the fijinal E but also h (the second note of
the “tetrachord of the superiores”) and e (the second note of the “tetrachord
of the excellentes”). The plagal form of the mode uses B (the second note of
the “tetrachord of the graves”) while cadencing on E or h. Each of the primary
consonances (diatessaron, perfect fourth; diapente, perfect fijifth; and
diapason, the octave) occurs in a series of species that reflects the arrangement
of tones and semitones characterizing the mode. In deuterus mode,
each of these primary intervals, when fijilled in, must start with the semi-tone
above: thus the diatessera are B-C-D-E, E-F-G-a, h-c-d-e, and e-f-g-aa; the
only regular diapente runs from E-F-G-a-h, and the diapasons are B-C-D-E-
F-G-a-h and E-F-G-a-h-c-d-e. South German theorists tended to characterize
the overall range as mirroring the nature of the modes, and explained the
octave species that produced authentic and plagal forms as being derived
59 Johannes Afffligemensis (Cotto), De Musica cum Tonario, ed. Joseph Smits van Waesberghe,
Corpus Scriptorum de Musica 1 (Rome, 1950), p. 50: “In manus etiam articulis
modulari sedulus assuescat, ut ea postmodum quotiens voluerit pro monochordo potiatur
et in ea cantum probet, corrigat et componat.” The section “De diaphonia, id est organo,”
pp. 157–63, treats improvised polyphony.
60 See Bain, “Hildegard, Hermannus, and Late Chant Style,” and “Hooked on Ecstasy”;
Pfau and Morent, Klang des Himmels, pp. 293–309; and David Hiley, “Das Wolfgang-
Offfijizium des Hermannus Contractus—Zum Wechselspiel von Modustheorie und Gesangspraxis
in der Mitte des XI. Jahrhunderts,” in Die Offfijizien des Mittelalters: Dichtung und
Musik, eds. Walter Berschin and David Hiley (Tutzing, 1999), pp. 129–42.