Milne/Wolf 4-5-6-7-8 and Gr Aug6th/Fr Aug6th chords

Andrew Milne quoted and commented:

>Daniel Wolf wrote:
>
>> These features are enhancements of
>> the dominant/tonic voice leading relationship: root movement by fifth, and
>> stepwise ''resolution'' in the remaining voices.

>Root movement by a fifth is certainly a powerful and satisfying
>resolution of the dominant 7th chord, but it is not the only acceptable
>resolution. V7 resolves well to vi (minor) as well (i.e. up a major
>second), and the augmented sixth chord (e.g. g - b - d - e#) - which is
>another chord that I think would be incorrectly represented by a 4-5-6-7
>tuning - resolves most effectively to a major or minor chord a *minor
>second* below.
>
>The stepwise resolution of the intervals making up the tritone in both
>these chords is, I believe, the *critical* factor which determines their
>resolution.
>For these reasons, and the arguments above, I really think that using
>4-5-6-7 in common-practice tonal music is not appropriate.
>
>Using this ratio in a xenharmonic music is of course a different matter!

I would like to bring to light another augmented sixth chord that may or
may not be appropriate to the 4-5-6-7-8 topic, but maybe a new one. Im
thinking about the "French Augmented 6th chord". It came up in today's
music class (De Anza College / Dr. Paul Setziol) while discussing
Schubert's _Der_Doppelganger_ C. 957 song. The b minor piece basically
ambiguously toys with the b minor and f# major sonorities. In mm 32-33 the
chord is C E F# A#, the Fr6. My teacher describes it as a non-tertian
sonority. Its intruiging placement in the music is that is resolves to b
minor, and not to e minor, which is the traditional progression. He also
talks about the roles of each within the voice-leading context, and
delegates the acoustical context to claiming it's "non-tertian", not based
on a acoustic triad like the 4-5-6 relationship.
What is the acoustical basis for this chord / unique sonority? What is
the tuning implications of using a non-tertian sonority as a dominant or
penultimate or half-cadence function? Id like to tie in the traditional
music theory with something more responsible to current
paradigms/controversies.... etc etc

Richard E Barber.



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I think that Johnny R's most recent series of thoughts regarding
(partly) choosing pitch relationships giided by scientific principles,
natural phenomena, or mysticism, had some very valuable thinking behind it.
Thanks Johnny!

I think that microtonal exporation can learn a lot, as music over time
has, from the history and methods of scientific exploration. Scientific
exploration has shown clearly two very bad attitudes:
1. Saying that something apparently unrelated to the topic of interest
cannot possibly
have any bearing on that topic. (I realize that I recently - well, up
to a point
anyway - reacted this way to somebody's proposal.)
2. Asserting that something apparently unrelated to the topic of interest
really is
related based upon no clearly-observable reason.

So let's suppose, for example, that somebody builds a tuning system
based upon the orbital periods of the moons of Jupiter. The history of
science has showed us clearly that there are two very bad ways to approach
this idea:

The first is to closed-mindedly reject the idea that the orbital periods
of the moons of Jupiter could possibly have any meaning to our ears, and
refuse to even listen to music generated in that manner. A far greater
mistake is to listen to it with a predisposition against it.

The second big mistake is to construct such a tuning, play with it for a
moment, and say, "yeah! Wow! That really DOES sound good" and claim a
major musical discovery.

A major musical discovery must be thrown open to such questions as
these:
1. Does a fair number of others also react positively to it, or is it just
you?
2. How confident are you that the tuning is what they're reacting to,
rather than the
rhythms you happened to choose for that particular composition, for
example?
3. All in all, do you and others react less positively, or at least
differently, to
fairly similar music built upon a different tuning?
4. Have you composed enough music in this tuning, and in enough variety of
styles,
orchestration, texture, and so forth, to be confident that you, much
less your
audience, REALLY understand this tuning?
5. If you can't explain any sort of reason, based upon well-known
principles, to
believe that a tuning SHOULD sound great, can you at least describe
what it is
about how the tuning touches you that makes it seem so meaningful? Can
you for
example, say something like, "wow, everytime I hear that interval, it
just blows
me away", or are you merely reduced to aspecific nebulocities like, "it
just sounds
so right!"
6. Does it seem to lose whatever quality it seems to have when you
slightly detune its
pitches from the orbits of the Jovian moons? Do many others feel a
similar sense of
loss regardless of factors like, for example, the order in which you
present the
two examples?
7. Again, regarding original and slightly-detuned versions of the same
composition,
using some random means of playing one or the other, can or others you
consistently
tell one from the other?
8. Ask yourself truthfully (and more importantly answer yourself
truthfully!) what are
the chances that you're reacting positively to it simply because you
have something
invested - even financially - in it?

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