Joe vs. Joe?? Oh no!

Thanks to Joe Monzo for clarifying his description of the Riemann
"functional harmony" theory as appeared originally (at least to me) in TD
523:6, and then recently was elaborated in TD 526:8.

I must confess it was not clear to me from the original TD 523:6 post that
the Reimann theory was like a gigantic "gravitational" field with the
entire span of dominant Pythagorean fifths implied by the formula
3^(-1,0,1).

Isn't it amazing how a little formula like that can, with a few brush
strokes, be so global, so all-encompassing, so CLEAR?? ( ;-), :-) )

For me, it looked like, Joe, you were just "labeling" diatonic triads with
I, IV or V in a "gross" over- symplification.

Also, even if you did have the "global pull" in mind and the overall "force
field" of Pythagorean fifths in mind and were labeling according to this,
some of the labels were wrong!

For example, you quote again from our Forte exchange in TD 526:8:

> [Forte, quoted by Joe Pehrson]
> Functionally, however, the supertonic triad has little
> relationship to the tonic triad. By virtue of the 5th
> relationship II always functions as a dominant
preparation.

> [monz referring to Riemann]
> II Subdominant (sometimes Dominant, I think)

Here you have the II supertonic "classified" as a "subdominant" [well, OK,
SOMETIMES, dominant], which it clearly is not. It is, of course, your most
basic V of V relationship.

The II is clearly on the V "side."

BTW, I think terming these "force fields" as "sides" or "elaborations" is
better than saying that anything is being "replaced," since it isn't. In
the simple chord progression I-vi-ii-V-I, it's meaningless to say that the
V is being "replaced" all the time. If so, why not just go I-V-V-V-I.
This would not lead to the most interesting of musics...

You state in TD 526:8:
> The whole point of having the new qualifier 'functional' added to
'harmony' is to explain the >secondary chord-roots as 'substitutes' for the
three primary functions.

I guess it all depends on what a person means by the term "substitutes."
Why not go "all the way" and say that the V is a "substitute" for the I?
In this case you could ultimately create a piece with only ONE CHORD, or
maybe even only ONE NOTE! (Tom Johnson has done it already...)

Additionally, your historical research may be accurate, and Riemann may
have been the very first to come out with the term "functional harmony,"
but I can assure you the limited definition you give to this term (as
contrasted with "traditional harmony") is NOT the way this term in used in
the major music conservatories of this country. [I know since I've been in
some...] "Functional harmony" as it is taught today, IS "traditional
harmony," at least as it's taught in the schools. Perhaps, yes, the term
has been bastardized and does not have it's original Riemann meaning, but
terms CHANGE over time.

Let's continue with the "analysis":

> [Forte, quoted and edited by Joe Pehrson]
> It is important to notice that III does NOT serve as a
> dominant preparation. On the contrary, it occurs as a
SUFFIX
> to V. [Joey P's caps] it also occurs as a suffix to I.

> [monz referring to Riemann]
>III Tonic or Dominant

> Note that V (dominant) and I (tonic) are precisely the
> functions I specified.

OK, so you have the same triads listed here, but Fortes ENTIRE IDEA was
that the III Mediant chord was NOT immediately related or "substituting"
[to use the dreaded word] for EITHER IV OR V.

Again, from my quotations in TD 525:20 from Forte:

>"III (Mediant) in the Major Mode" [don't forget that "key" term,
literally] "It is important to notice >that III does NOT serve as a
dominant preparation. On the contrary, it occurs as a SUFFIX to V. >[Joey
P's caps] it also occurs as a suffix to I. THUS III IS QUITE DISTANT FROM
BOTH >ELEMENTS OF THE HARMONIC AXIS, AND IS RELATED TO THEM ONLY THROUGH
VI."

I note that in your recent post of 526:8 you "conveniently" leave out the
final capitalized sentence, which is the meaning Forte wished to convey in
the ENTIRE PARAGRAPH.

So now, how we gonna classify III? Tonic, subdominant, or dominant?? Does
that really mean anything. No. Only in relation to VI, which is on the "V
force field" side. The important part in traditional harmony -- and, as I
say, this is called "functional harmony" today, perhaps erroneously, but
that's what it's called -- is that the III is so INDEPENDENT. It's an
AC-DC kind of chord. (Oh my!)

Frankly, Joe, I don't think you like traditional theory or harmonic
analysis very much, and this is why you're glossing over this stuff so
cursorily.

More errors:

I note that you "conveniently" avoided mentioning the submedient VI in your
recent rejoinder. Maybe that was because the original classification was
so wrong in the first place.

Here was your "original" post of 523:6
> VII Dominant or Subdominant
> VI Tonic or Subdominant
> V Dominant
> IV Subdominant
> III Tonic or Dominant
> II Subdominant (sometimes Dominant, I think)
> I Tonic

> So typically, in an analysis, every chord is marked either
> 'T', 'S', or 'D'.

Note that you have VI as the "Tonic or Subdominant." VI is you most simple
V of V of V... and it would MOST CERTAINLY be on the V side of the "force
field" NOT on the subdominant.

From my TD 525:20 post:
>again from Forte. (Don't trust ME for a minute...):

>We have seen that VI SERVES AS A DOMINANT PREPARATION BOTH IN MAJOR AND
IN >MINOR. [NB, NB!] Often it follows I immediately, providing the first
cue to progression toward V."

So even if we go with the acceptance that your nice little formula
3^(-1,0,1) explains everything there is to know about tonal music, the
"assignments" to the basic force fields were incorrect.

I agree with you that theory needs to evolve and some of the older methods
need further elaboration with mathematics and, certainly, with microtonal
implications. However, I firmly believe that the traditional methods of
realizing figured bass and, especially, four part writing are what
separates the "sheep from the goats" as far as composers are concerned.
You can tell right away the people who have never had this "basic training"
as composers. There are more than enough of them out there... [BTW Allen
Forte has EXCELLENT exercises in figured bass and 4-part harmonization in
_Tonal Harmony in Concept and Practice_ and I have to admit, I managed to
do most of them...]

One of the limitations of the conventional, _Stufen_ - theory, although I
must in my defense state that I am not mired in it... is the fact that it
doesn't do a very good job describing the process of MODULATION...
Everything is described with a chord symbol, but the overall
"gravitational" implications are not always made clear. A good resource is
Elie Siegmeister's _Harmony and Melody_ which is still available from
Wadsworth Publishing Company of Belmont, CA. Elie does a great job
describing modulation, and the conditions required before one is _really_
in a new key. It's more complex than one might imagine, and is determined
by a number of factors, one of which is, most reasonably, the length of the
section in the new key. His four conditions of modulation are "1.)
Establishment of the home key, 2.)Use of a pivot chord 3.) Entry into the
new key and 4.) Establishment of the new key." I have to admit that the
"step by step" old fashioned roman numeral chord labeling didn't handle
these concepts adequately. [Elie also happened to be a friend of mine...
but enough of 'name dropping' at the moment]

Regarding Schenker... yes he was a strange one. However, unless you have
done countless Schenkerian analyses, as some of us have, you most probably
will not fully realize the implications of his approach. As an active
composer, I am fully aware of the importance of pitch level to the contour
of a piece of music, especially regarding points of arrival in the matrix
of 3^(1-,0,1) [see, it's catching on!]. I think Schenker really remedied
some of the shortfalls of the old-stock _stuffers_, and he has made lots of
people look at tonal analysis in a new way...

Bye Joe!: Smiles and we're "having fun" (hopefully!)

Joseph Pehrson

Joseph Pehrson wrote,

> [monz referring to Riemann]
>> II Subdominant (sometimes Dominant, I think)

>Here you have the II supertonic "classified" as a "subdominant" [well, OK,
>SOMETIMES, dominant], which it clearly is not. It is, of course, your most
>basic V of V relationship.

I don't agree. The diatonic II triad is often in first inversion and
functionally interchangeable with the diatonic IV triad. In a major key, I
once mistook the II triad in first inversion for an IV triad, the only
mistake I ever made in Roman numeral dictation in my college ear-training
class. To me, that's sure evidence of a commonality in function.

>Perhaps, yes, the term
>has been bastardized and does not have it's original Riemann meaning, but
>terms CHANGE over time.

I doubt Riemann invented that term. Riemann was a very idiosyncratic
theorist -- a dualist for much of his life (dualism means a belief in total
parity between otonal and utonal).

>III is so INDEPENDENT. It's an
>AC-DC kind of chord. (Oh my!)

Huh? I would have said Barry Manilow.

>Maybe that was because the original classification was
>so wrong in the first place.

>Here was your "original" post of 523:6
> > VII Dominant or Subdominant
> > VI Tonic or Subdominant
> > V Dominant
> > IV Subdominant
> > III Tonic or Dominant
> > II Subdominant (sometimes Dominant, I think)
> > I Tonic

> > So typically, in an analysis, every chord is marked either
> > 'T', 'S', or 'D'.

>Note that you have VI as the "Tonic or Subdominant." VI is you most simple
>V of V of V... and it would MOST CERTAINLY be on the V side of the "force
>field" NOT on the subdominant.

Joey, I don't think Monz' post was so wrong. One teacher I had (with whom we
used Forte) did the same kind of thing, emphasizing that the "subdominant"
function is one of "dominant preparation" -- my best recollection (in
reference to major or harmonic minor):

VII Dominant
VI Tonic or Subdominant
V Dominant
IV Subdominant
III in minor, a rare augmented triad; in major, Subdominant preparation
II Subdominant
I Tonic

The idea here is that any chord labelled "subdominant" usually leads to a
chord labeled "dominant", though not always immediately; any chord labelled
"dominant" tends to resolve usually immediately, to a chord labeled "tonic";
and any chord labeled "tonic" can do whatever it wants.

To Joe Pehrson:

Rather than address your latest points [TD 528.9], I'd say
that Paul Erlich [TD 528.10] did a pretty good job of providing
the answers I would have.

I like the way you called the 3^(-1,0,1) paradigm a 'gravitational
force' - that's a pretty good way to characterize what Riemann
was saying.

While reading that part of your post, I was struck by how
Partch's 'Three Observations' [see _Genesis_ 2nd ed., p 181-183],
seem to be an expansion of this idea into the other prime
dimensions.

Daniel Wolf pointed out [TD 527.3]:

> Perhaps the most critical question for us in the tuning
> community is whether the Riemannian traditions deals adequately
> with mediant tonal relations, that is, harmonies related to the
> fixed functional harmonies by thirds.

Indeed, I think some of the controversy between Joe and myself
centers around this point. Riemann categorized the 'secondary'
triads (II, III, and VI) in either of two categories precisely
*because* of their mediant-relationships with the primary
triads I, IV, V. (The VII quite unproblematically represents
an incomplete V.) Thus, the explanation of III, for example,
as representing either I or V, depending on context. The same
idea holds for II and VI.

Much of the recent elaboration on Riemann to which I alluded
(Journal of Music Theory) has to do with analyzing mediant-
relationships.

> [Daniel Wolf]
> Already with such scholars as Tanaka (before the turn of the
> 20th century), tonal space was represented two dimensionally,
> in triangulated lattices.

In fact, Riemann's own _Tonnetz_ *was* a 2-D triangular lattice.
I don't know if he got the idea from Tanaka (Riemann's _Tonnetz_
appeared while Tanaka was living in Germany), or for that matter
from someone else. There's a dissertation available on microfilm
(which I haven't been able to find but would *love* to read)
by someone named Mooney, which covers the history of lattice
diagrams in music, IIRC, or perhaps it's just the history of
the development of the _Tonnetz_.

Anyway, I was under the impression that 'functional harmony'
had the specific meanings applied by Riemann and his followers,
and didn't realize that so many people use it to simply be
synonymous with 'common-practice harmony'.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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