Re: Historical vocal intonations and variations

Hello, there, and recently Joe Monzo offered some comments on
historical vocal intonations in theory and practice which suggest to
me a few observations. Here I focus mainly on just intonation (JI)
systems, because they are often presented in theory as ideal models
for the inevitably fluid reality of vocal intonation.

---------------------------------------------
1. "Mental limitation" or artistic selection?
---------------------------------------------

From a certain point of view, _any_ historical system can be presented
as a case of confining "mental limitations" when compared to some
later system permitting new concordant sonorities or tunings.

Thus neither medieval 3-limit nor Renaissance-Romantic 5-limit systems
can do justice (intonational or otherwise) to 20th-century musics
based on concordant sonorities including minor sevenths tuned at or
around 7:4.

In my view, each system has its own "limitations" -- and unique
artistic possibilities. When an interval such as the major third or
minor seventh is treated as a stable concord, this means that it no
longer can carry an unambiguous message of tension or of "more to
come."

Of course, there is no way of "proving" that singers of organum around
900, of complex motets around 1300, or of Monteverdi's madrigals
around 1600 did not "naturally" follow 7-limit JI and "sing those
minor sevenths _in tune_ at 7:4," regardless of the compositional
style or the intonational side-effects.

In fact, the recognition that harmonic and intonational systems select
a small subset of all possible sonorities and ratios (integer-based or
otherwise) is a very useful one. However, with musical styles as with
natural languages, such selectivity need not be treated as an
_unnatural_ limitation.

Gothic, Renaissance, and Romantic music all richly realize different
artstic possibilities. Intonational styles such as medieval 3-limit
and Renaissance 5-limit JI both reflect and enhance the unique musical
values of these eras.

--------------------------------------
2. Ideal systems and artful deviations
--------------------------------------

To say that a model such as 3-limit or 5-limit JI aptly represents the
intonational ideal of a given period is not to say that there is no
room for variations. Hypotheses as to such variations should be placed
in the context of a given musical style.

For example, one hypothesis might propose that singers tend to
"simplify" high odd-limit ratios to relatively lower ones. Thus a
singer around 1300 might "shade" an 81:64 major third toward either
5:4 or 9:7, both "simpler" ratios. This same singer might likewise
shade a 16:9 minor seventh toward 7:4, or possibly 9:5, in cases where
this would not compromise a vertical fourth.

At the same time, the theoretically standard 81:64 and 16:9 have a
certain attraction also: the first is a pure ditone resulting from two
pure 9:8 whole-tones, while the second results from two pure fourths
at 4:3.

With a keyboard, as Mark Lindley and others have noted, 3-limit is a
natural solution; in fact, it is arguably the one historical JI system
ideally suited to a fixed-pitch instrument. For singers, the classic
3-limit intervals may be taken as general guides, but with much room
for "artful deviations" in either a 5-limit or a 7-limit direction.

Then, again, it is easy enough on a meantone keyboard to suggest some
"artful deviations" which _might_ have happened around 1600 in the
intonation of minor sevenths. Consider, for example, this
transposition of a famous (and to me delightful) Monteverdian cadence,
which I show with continuo figures identifying the dissonances:

1 2 & | 1

C#4 C4 D4
Bb3 A3 Bb3
Eb3 F3 Bb2

7 5 -
5 4 3

As Dave Hill has demonstrated with 20th-century Blues pieces on his
meantone piano, the augmented sixth Eb3-C#4 in 1/4-comma meantone is
almost identical to a 7:4 minor seventh, while the augmented second
Bb3-C#4 is very close to a 7:6 minor third.

On such a keyboard, of course, it is easy to show that such intervals
are the exception, with the usual more "dissonant" minor sevenths at
around 1007 cents fitting both the actual notes in compositions of
this epoch, and the theoretical role of the minor seventh as a
dissonance, albeit one now much relished in bold treatments.

A 7-limit purist might argue that regardless of theories or keyboard
tunings, singers would "naturally" seek the maximum concord of 7:4,
rather than an alternative "a full sixth-tone or more out of tune."

From another viewpoint, however, we might consider the possibilities
of such an "artful variation" and the possible consequences for the
rest of the intonational system.

-------------
3. Conclusion
-------------

While it may hardly be the going fashion here to praise 12-tone equal
temperament (12-tet), I would like to credit this tuning system with
at least one important achievement.

The way that modern singers reportedly often tend to approximate 12-tet
intonation even when unaccompanied may suggest that "natural" vocal
intonation may be largely a matter of custom and training.

This is not to say that 12-tet has a privileged position, any more
than 3-limit or 5-limit or 7-limit. However, from one point of view,
it marks a very reasonable compromise between the vertical urge for
stable major thirds somewhere near 5:4, and the melodic urge for broad
whole-tones somewhere near 9:8 and narrow semitones not too far from
256:243.

In medieval music where stable major thirds are not a constraint,
singers may lean in polyphony as in chant to a pure ditone (81:64); in
Renaissance music where euphonious thirds are of supreme importance,
singers may lean strongly toward 5:4. It's an interesting question as
to how singers of the "well-tempered" era (18th-19th century) may have
been influenced by key color schemes on keyboards in shading their
thirds.

All in all, music history presents a kind of paradox. Any historical
JI system may seem either "dreadfully limited" by comparison with some
higher-limit system, or "amazingly rich and full" by its own standards
as realized in actual compositions. I prefer to take the latter
viewpoint when considering actual historical musics (medieval and
otherwise), and the former when _any_ system is proposed as a uniquely
"natural" or universal alternative.

Most respectfully,

Margo Schulter
mschulter@value.net