Re: Concords/dual-purpose sonorities/discords

Hello, there, John deLaubenfels, Paul Erlich, and everyone.

When I read your description of 4:5:6:7 as at once blending but
calling for a resolution, John, I said to myself, "Isn't this an ideal
illustration of Ludmila Ulehla's concept of a dual-purpose sonority?"
Ulehla, in her _Contemporary Harmony_, defines such a "dual-purpose"
sonority as one which combines some of the characteristics of
"concord" and "discord," so that she proposes a three-category scheme
of "concord/dual-purpose/discord."

Typically I use the term "dual-purpose sonority" somewhat more
specifically to describe a sonority perceived in a given a style as
"relatively blending but unstable." A 4:5:6:7 seventh sonority in many
tertian contexts where it is regarded as independently euphonious but
in need of resolution might provide an ideal example either of
Ulehla's general concept or of my typical usage.

In Gothic music, interestingly, some theorists of the 13th and early
14th century describe five or six categories of "concord/discord"
ranging from the purely blending unison or octave to the most acute
discords (e.g. m2, M7, A4, d5). An interval or sonority may be at once
relatively "concordant" but unstable, i.e. a "dual-purpose sonority"
as I might also describe it.

An example, maybe analogous to the 4:5:6:7 in the music you are
describing, John, would be the _quinta fissa_ or fifth "split" by the
middle voice of sonority into two thirds, e.g. F3-A3-C4 (64:81:96);
and also the major ninth "split" into two fifths, e.g. F3-C4-G4
(4:6:9). Both sonorities are relatively blending, but definitely
unstable, inviting resolution either to a complete 3-limit trine
(2:3:4), e.g. E3-B3-E4 for the first sonority and F3-C4-F4 for the
second, or to the trine's choicest interval of the fifth.

Paul, your comments about 4:5:6:7 as a stable tetrad in decatonic
music nicely illustrate how some terms routinely used to describe
sonorities can carry implications about stability/instability which
may fit one style of music but not another.

Thus the term "triad" fits the 4:5:6 sonority in Renaissance-Romantic
style, tending to imply that this is the richest stable concord. In a
Gothic setting, the term _quinta fissa_ (or its English translation
"split fifth") describes the mildly unstable 64:81:96, which has the
same intervals (5 + M3 + m3) but a different role.

Similarly the term "dominant seventh" fits 20:25:30:36 or 4:5:6:7 in
various tonal styles where triads are the most complex stable
sonorities, while "complete tetrad" fits 4:5:6:7 in a decatonic style.

One metaphor I sometimes use to express the relationship between
stable concords and dual-purpose sonorities is that of "saturation"
and "supersaturation." In a Gothic style, a 2:3:4 trine marks the
point of saturation or complete stable concord; in tonal music, a
4:5:6 triad. A Gothic 64:81:96 or 4:6:9, or a tonal 4:5:6:7, is
alluringly blending but "supersaturated," somehow too complex to
be stable.

Most respectfully,

Margo Schulter
mschulter@value.net

Thanks, Margo, for your comments. The analogies you mention seem very
on-target. The only quibble I might have is with your statement that
a 64:81:96 chord is "relatively blending". To my ear the Pythagorean
thirds are discordant in and of themselves. Certainly that sensation
reinforces your assertion that resolution is needed! As for the 4:6:9
chord, I agree that it is both smooth and in need of resolution.

In discussing dominant 7ths, you give two tuning possibilities,
20:25:30:36 and 4:5:6:7. The first of these puts the 7th degree at
9/10 of the root above, the second puts it at 7/8. What about the
intermediate tuning, 8/9? To my ear this last is discordant but
tolerable, where the 9/10 is VERY high. Is 9/10 more "historical"?

JdL