From: roger@crux.Princeton.EDU (Roger Lustig)
Subject: Re: tonal value of chords and harmonic series [?]
Originator: news@nimaster
Reply-To: roger@astro.princeton.edu (Roger Lustig)
Organization: Princeton University
Date: Wed, 27 Jan 1993 15:49:50 GMT

In article <1993Jan27.075738.23548@news.cs.brandeis.edu> jacob@max.cc.brandeis.edu ( ) writes:
>using the harmonic series (or "resonance" as some say) to determine
>the tonal value of a chord (the degree on which it sits, as it were)
>consists of two assumptions (maybe verified in actual perception or
>not, that is irrelevant to my point here, although i'm interested to
>hear about experiments testing their validity, and especially the precise
>domain in which they are valid)

The journals Music Perception (category error in the title, folks!)
and Journal of Perception: Human Performance (this title is mangled)
have tons of articles.  

>one assumption is that the brain will try to interpret a chord as a
>complex sound 

Yes.  Key problem: how much is perception, how much cognition and
training and the like?

>and the second that it will give it a tonal value
>corresponding to the pitch class of the sound it has reconstructed as
>a fundamental.

A real toughie, that one -- especially when you examine a minor triad.
A c minor triad has an A flat as its fundamental.  Does anyone hear it
that way?

>this hypothesis was rameau's basic discovery along with the "naturalistic"
>model that "justifies" or "explains" much of tonal harmony.

Well, it doesn't actually explain much -- and I'm not sure that Rameau 
discovered it, either.  He put a new spin on it, if you will.

>now in describing how this reconstruction of the fundamental is actually
>peformed, rameau's model involved complicated and arbitrary assumptions
>(equivalence of octaves, layering of thirds)

Right -- and layering of thirds doesn't have much to do with the harmonic
series, in general.

>worse, it failed to account for some important facts of the harmony
>of his time, such as that the tonal value of the minor triad
>is the same as the pitch (class) of its bass, 

Bingo.  

>and it fails even more
>completely, ex post facto, with chords used later: for example
>according to rameau's model the chord
>C-E-G-A, i.e. a major triad with an added 6th should be a VI chord,
>lying on A whereas everbody knows it is a tonic chord lying on C

Depends on its function.  Even in first inversion, one can resolve that 
to an F or Dm7 in accordance with its a-minor-triad quality.

>now my question is: is it true that people have all but stopped trying to
>justify the tonal value of the minor triad based on "resonance" arguments,
>even when they've kept the harmonic series to justify other parts of the
>system?

Well, most have.  There are probably a few nuts still out there.  
Psychologists, mainly...8-)...but most music theorists of today don't
spend too much time on what Milton Babbitt calls the Overtone Follies.

Note that all the centuries of harmonic-series-mucking-about hasn't 
given us any rules at all about which chord follows which.

>i'm asking this because, i believe that i have got a way to justify the
>minor triad and the major triad with added 6th using a very simple
>extension of rameau's idea. i'm just curious if somebody has seen anything
>like that anywhere, that made any sense? (as i think my idea makes sense :-)
>i'm of course not interested in hearing
>about negative harmonics and "additive" principle)

Well, we won't be able to judge your ideas until we see them!  But no,
people aren't spending a lot of time "justifying" triads by psycho-
acoustical means these days, unless they simply wish to bash Arnold
Schoenberg.

>anyway, my impression was that people have long ago stopped trying to use
>the harmonic series, at all, to justify harmonic facts, let alone to
>deal with minor triads. but (as usual) i might be wrong...

It's still out there.  See the journals mentioned above; also, see
Christopher Longuet-Higgins' work on music.

>i'd be grateful if anyone could indicate to me somesuch attempt, and
>incidentally, i'd like to hear of psychology experiments testing
>the assumptions on which rameau's idea is based.

Some of the articles in thos journals are experimental.  Once you find
them, scan hte bibliographies for more goodies.  Be prepared for disappointment.

Roger
Newsgroups: rec.music.classical