Re: [tuning] tritone

hi Jerry,

> From: Gerald Eskelin <stg3music@earthlink.net>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, February 13, 2002 1:31 PM
> Subject: [tuning] tritone (was: Digest Number 1891)
>
>
> Me:
>
> > It's the ambiguous *keyboard* "tritone"
> > that prompted its "three whole steps" nickname.
> >
> Monz:
> >
> > no it's not, Gerry.
> >
> > we've been thru this before, and my responses then
> > were addressed directly to you.
>
> That doesn't mean the info stuck, Monz. Had I remembered
> I would have added appropriate qualifiers.

ok . . . upon reading my response to you again now,
it seems a little harsh. hope you didn't take it that way.

> > now of course i must acknowledge that the word "tritone"
> > is used generically to mean *both* the "augmented 4th"
> > *and* the "diminished 5th" -- and T H I S is probably
> > more likely the result of keyboard-based thinking.
>
> You got it! *That's* the one I was talking about. The term
> is handy when referring to either (or both) "inversions" as
> they function (usually as dominant in common practice) in
> musical contexts .

ok . . . but it seems like you were describing the 12edo tritone
(with the double meaning of aug4/dim5) as something special.

i want to point out that in 12edo it's no more special than
the double enharmonically-equivalent meanings of any of the
other intervals. i.e., the aug1/min2, aug2/min3, maj3/dim4
and their respective complements dim8/maj7, min7/aug6, min6/aug5.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Hello, there, Jerry, and thank you for such a gracious as well as
enthusiastic response to my comments on the tritone.

First, please me warmly agree that I am fascinated by these "time
machine" scenarios, with the musical world of Perotin around 1200 as
one of my favorites.

Also, one thing I'd emphasize is that we are fortunate to have some
actual music from these eras, as well as theoretical treatises, both
of which invite careful and joyful appreciation.

Describing music in words is not easy, but the treatises often say
fascinating things to those who listen -- not a substitute, of course,
for listening to the music itself, but a valuable supplement.

For example, writing maybe sometime around 1240, Johannes de Garlandia
(at least in one version of his treatise) tells us that "every
discord" when resolved to a stable concord is equivalent to that
concord -- the "equivalent" or "equipollent" here possibly indicating
that the unstable interval should receive the same rhythmic value as
its following resolution, often giving it extra emphasis.

While the exact interpretation might be a topic for lots of scholarly
exchanges, I'd say that it sure fits the style of someone like Perotin
with lots of major sevenths and minor seconds as well as tritones --
often getting dramatic resolutions, and sometimes treated more
freely. There's lots of sophisticated concord/discord theory in this
era: Jacobus of Liege regards 4:6:9 as relatively concordant (two
fifths forming an outer major ninth), and composers like Perotin and
Machaut use it in practice in a way that could illustrate this theory.

Anyway, some of this dialogue suggests to me that we might both share
certain ground regarding what I call "cadential streamlining," tuning
certain unstable cadential sonorities so that they are at once
sonorous in their smooth effect and efficient in their directed
resolutions.

Right now I'm largely occupied, as George Secor mentioned, in writing
an article about the "17-tone well-temperament revolution" we're both
involved in, so maybe I should save a longer exposition of this for a
bit, although I'm done some articles here on neo-Gothic progressions
which touch on some of the concepts. For the moment, I might mention
one article inspired by a classic paper of Paul Erlich:

/tuning/topicId_25376.html#25376

Mainly I want promptly and enthusiastically to thank you for your
friendly response, and look forward to more dialogue.

Most appreciatively,

Margo Schulter
mschulter@value.net