Duration: c. 11:00
Hildegard of Bingen (1098-1179) was a medieval abbess whose remarkable works as a poet, composer, naturalist, theologian, and visionary have been rediscovered to some justifiable fame in recent times. O viridissima virga is one of a series of sequences (a form of chant) attributed to her. As in many of her other works, the growth of Christian love and the Church is represented symbolically through nature in springtime, nurtured by the Earth, represented by Mary, the Earth mother. Hildegard felt a strong connection to nature, and, indeed, wrote a book on plant life and a compendium of folk remedies. In her mystical visions, green was often symbolic of the Church and of the nurturing spirit of women.
Like most medieval mystics, Hildegard paid special attention to the symbolism of numbers, and to their manifestation as musical pitches. I have used the ratios of the two most holy numbers, 3 and 7, to construct a series of interlocking scales through which this piece "grows." Therefore the choir is frequently singing pitches that are not at all close to those of twelve-tone equal temperament used in our time of practical standardization. The music also grows from chaos to order, much as God's creation of nature from the void is recapitulated every spring.
Computer accompaniment and tuning
This piece is sung with computer-generated tape or disc. The pitches the voices sing are in just intonation, which is to say, "in tune." In most cases they do not correspond to the tempered pitches found on a piano keyboard. The singers find their pitches from the tape, which prominently contains drones of all pitches in the score. Some special accidentals, shown below, are used to give the singers a rough idea of where their pitches lie in relation to conventional equally tempered pitches:
|somewhat sharp (~33 cents)|
|+||slightly sharp (~15 cents)|
|somewhat flat (~33 cents)|
These signs may be combined with conventional accidentals:
|somewhat sharp of a semitone (~133 cents)|
|somewhat flat of a semitone sharp (~67 cents)|
|somewhat sharp of a semitone flat (~67 cents)|
|somewhat flat of a semitone (~133 cents)|
However, singers should not try to overintellectualize this system, which is offered as a convenience. As always, good intonation means good listening and being in tune with the accompaniment. Just intonation means that, despite the unusual intervals, they should mostly seem to "lock in" and be in tune with each other. The tuning system with the exact pitches used is explained in an appendix, but it is not necessary to understand the tuning system in order to be in tune with the tape and with each other.
All accidentals remain in force throughout a measure, as normal, but in sections without bar lines, accidentals remain in force only on repeated pitches.
Score and recording
Click here for an excerpt from the score (pdf format).
Click here for another score excerpt (pdf format).
Click here for an excerpt of the performance by the Wa yne State University Chamber Choir (mp3 format 1.8MB). (Corresponds to the above score excerpts.)
Technical Notes on the Tuning
The following information is for those with a special interest in the details of the tuning for this piece and need not appear with the program notes for performance. While some may find it helpful, is not at all necessary to fully understand the following in order to effectively perform the piece.
O Viridissima Virga is in extended just intonation, that is, the pitches are related to one another by relatively simple numerical ratios. Because, unlike most acoustic instruments, the computer does not have to be locked to a fixed set of pitches, this piece freely modulates to five different tonal centers in six sections (the first and the last are the same). The singers tune to the computer accompaniment. Some pitches are held in common between adjacent keys, therefore the whole scheme may be represented by what tuning theorists call a lattice diagram.
In the tuning used in O Viridissima Virga, the pitches may be expressed in terms of ratios only having prime factors 2 (the octave), 3, and 7. In a lattice diagram, relations of 3 are shown by two pitches (represented by dots) being connected by a horizontal line -- the pitch to the right is a 3/2 (a pure perfect fifth) higher than the pitch to the left. Relationships of 7 are shown by diagonal lines. The upper pitch is a 7/4 (a somewhat flat minor seventh) higher than the lower.
With that in mind, here is the lattice diagram for O Viridissima Virga. Next to each dot is the ratio of that pitch relative to the original tonic (1/1, in this case Eb) as well as the letter name and accidental used in the notation. The circled pitches indicate the tonal centers of the different sections of the piece.
Back to my list of compositions
Updated on July 23, 2002 by Bill Alves (alves @hmc.edu).