Re: Response to Pierre Lamothe

Hello, there, Pierre Lamothe and everyone.

Please let me begin by thanking you for directing me to your
fascinating Web site and graphical diagram of "constitutive"
sonorities.

May I warmly assure you also that your English is much better than my
French, for which your Web page provides a welcome exercise.
Incidentally, I much admire the French musical tradition for keeping
Guido's solmization syllable _ut_.

Possibly the question of language is an especially apt metaphor here,
for we may be speaking different musical languages, and different
theoretical languages to explain this music. Communnication can be a
delicate process -- and a precious one, which I wish to treat with a
care to match your courtesy and hospitality.

Before deciding whether "constitutive" sonorities or "extensions" are
concepts which might apply to medieval and Renaissance European music,
I need better to understand these concepts.

Your Web site provides illustrations tied to a key system like that of
Rameau, by which I mean, for example:

(1) Sonorities are built are mainly in thirds, and are organized into
major and minor keys (your examples being in C major and A minor);

(2) The text of your Web page focuses specifically on Rameau's
dominant seventh and its resolution; and

(3) Notes of vertical sonorities are derived as overtones of a tonic.

Are these assumptions inherent in the "constitutive" and "extension"
concepts, or is 18th-century tonality here used as one possible
illustration of what may be wider concepts applying to other musics
also?

Possibly we may need to engage in a bit of dialogue in order to answer
these questions, and I feel that the best first step is for me seek a
further explanation of "constitutive" and "extension," and to listen
very carefully to what you say.

Please let me emphasize that I practice and analyze mainly European
styles from around 1200 to 1600 or a bit later, or roughly from
Perotin to Monteverdi, and may not be the best person to evaluate your
proposals regarding key-based music of the 18th century and later.

Where I might be able best to help, for example, is on such points as
distinguishing Zarlino's approach from the very different approach of
Rameau. While Zarlino's gamut was regarded by an 18th-century theorist
such as Kirnberger (1771) as the usual "modern" gamut, and so is very
rightly mentioned on your Web page, Zarlino's 16th-century musical
world was often greatly misunderstood.

Above all, I am moved by your interest in historical questions very
important to me, and hope to speak always in a spirit of friendship.

Concerning your Web page, I find that you raise one question about
18th-century music which may be of special interest from the viewpoint
of tuning and the theory of consonance/dissonance. Given the
18th-century setting, I shall feel free to use 18th-century terms.

This question is which "chord of four tones" (not including octaves)
is "the most consonant" in a style like that of Rameau.

If asked this question, I might propose Rameau's "added sixth," for
example F3-A3-C4-D4 (or f-a-c'-d'), which might be tuned 12:15:18:20.
The only dissonant interval in this chord is the major second between
the highest two voices, here tuned at 20:18 or 10:9. The other five
intervals are all consonances: (M6 + 5 + 4 + M3 + m3 + M2).

Rameau interestingly comments that most musicians go wrong, because
they regard the added sixth chord as a consonance, not taking account
of the major second between two of the upper voices. Possibly the fact
that all of the upper voices form consonances with the bass may help
to explain the rather gentle effect of this sonority.

In contrast, Rameau's dominant seventh chord has two dissonances: the
minor seventh above the bass, and the tritone between the voices at the
major third and minor seventh above the bass. Here the six intervals
are: (m7 + 5 + d5 + M3 + m3 + m3).

There are various just tunings for this latter sonority: 20:25:30:36;
or 36:45:54:64; or 4:5:6:7. In a meantone or well-temperament of
Rameau's era, something between the first and second tunings seems to
me much more likely than the third.

Whatever the tunings, I suspect that the added sixth chord would be
judged milder or "more consonant" than the dominant seventh chord in
an 18th-century setting.

I would be curious to see how people more familiar with 18th-century
style might approach this question.

Most appreciatively,

Margo Schulter
mschulter@value.net

>There are various just tunings for this latter sonority: 20:25:30:36;
>or 36:45:54:64; or 4:5:6:7. In a meantone or well-temperament of
>Rameau's era, something between the first and second tunings seems to
>me much more likely than the third.

Sorry but some of your messages I have saved but not read yet, because
these days I have little free time. Just a short remark, only to show
everybody that I am a true defender of utonality. The utonal fine
tuning of the above sonority is 1/9:1/7:1/6:1/5. I would call
that tuning "just", though not in the sense of the 5-limit JI.

In an earlier message I replied to Joseph's comments but I forgot to
ask him about Wolf'es experiments -- any URL, files, ...? Please!

Best Regards,
- George K.