First Aristoxenus Memorial Conference for the Spectrographic Investigation of Musical Praxis,
hosted by Dante Rosati.
(That's a wonderfully ostentatious title for a study of how far off key people sing, don't you think?!)
This site is part of a discussion about whether unaccompanied singers tend to tune diatonic scales in 3-, 5-, or 7-limit JI (just intonation), or some other simple tuning, or tunings too dynamic to be described in relatively simple terms. Involved in the question is whether a long reverberation time in the acoustical environment increases the tendency toward tuning intervals according to higher harmonics. I estimate the RT-60 (standard measure of reverb time) for the recording here in question at just under 3 seconds.
The data in the table below were gathered from a spectrographic analysis of a monophonic chant; namely, "O gloriosa domina," the opening track from the CD The Lily and the Lamb by Anonymous 4, a wonderful collection of medieval English chant and polyphony. It has a simple and beautiful modal melody, and consists of 4 verses of 4 phrases each. The whole piece was analyzed so that verses may be compared to each other in addition to the whole set of adjacent-note intervalic analyses. Characteristically of English chant, intervals of a third are used here and there, and it could easily be harmonized triadically.
As an interesting aside, there are several layers of meticulous organization beneath the 4 groups of 4. For example, all together there are 99 intervals between distinctly pitched notes: 25 in each of the four verses, less 1 for the first note which has no previous one with which to form an interval. And I don't wanna hear no existential-math crap about that statement! ;-) The 25 are organized by phrase as 4 + 8 + 6 + 7 -- could that possibly be an accident?! Those wacky medieval composers, I tell ya! It's a thing of beauty, and no mistake.
It's probably in Dorian mode, or maybe Aolean Plagal? It's hard for me to tell without a 6th degree (the piece uses only 6 different tones). The perfect 5th A to D between the first and last notes of each verse indicates to me that D should be considered the 1/1 for purposes of a JI analysis. At first blush then, C would seem to need to be at 9/5. But since in the context it sounds like the 1/1 of a temporary Ionian mode (sort of the medieval equivalent of false modulation?), it's consistently sung nearer 16/9; that's confirmed by the fact that C to E is consistently sung as 81/64 or wider (!)
Since the overall pitch of a cappella music nearly always drifts somewhat over the course of a piece, 1/1 cannot be tied to an absolute frequency. For now I've chosen probably the simplest solution to this dilemma: consider only the intervals between immediately adjacent tones. This, of course, is overly simplistic but it's a place to start. For instance, once a tone goes "wide" the successive ones often stay "wide" for 3 or 4 in a row, indicating that the pitch before that string of "wide" ones is still being held in memory as the primary point of reference.
UPDATE! To my great delight, I received on June 25, 1999 an email from Susan Hellauer of Anonymous 4 giving their view of tuning in brief:
The first verse's spectrograph, and technical details of how the data were gathered, can be opened in a separate browser window for quick reference between the chart and the graph.
|Tuning analysis of Anonymous 4 "O gloriosa" Chart 1|
Out of a total of 99 intervals between adjacent distinct note names, I count
An aside: anyone see fractal patterns in these supposed deviations from Just tuning?
Further analysis to come!
FOOTNOTE: "Any and all 5-limit intervals" as I use the term in this context
[Back to "How to interpret the chart"]
Written by David J. Finnamore June 11-27, 1999
I look forward to reading your comments, corrections, and suggestions!
You may email me at firstname.lastname@example.org
or the whole Tuning List, on which this discussion is being held, at email@example.com
Need a break? See my bio page! Or if you're interested in J. R. R. Tolkien's Middle-earth literature, peruse an early draft of my newest site, An Essay on the development of music for Middle-earth. It includes some microtonal references, charts, and MIDI and Real Audio files.