[Smt-talk] Forward and backward root movements

Paul Siskind siskinpa at potsdam.edu
Sun May 6 05:56:34 PDT 2012

Hello Colleagues:  I'd like to raise a point that seems to be missing from
a lot of the recent interesting discussion about harmonic function....

There have been two debates underlying the discussion:  1) What terms most
appropriately define the harmonic function of certain chords; and 2) what
do those terms imply about the syntax of the harmonic language being
described.  The discussion began with point #1, but out of necessity,
evolved into point #2.

About point #2: Most of the comments seem to be rooted in the belief that
there is a single common practice that governs the syntax of chord usage. 
Indeed, much ink has been spilled throughout the history of music theory
to attempt to discern and explicate a singular set of natural principles
which govern the "true" or "correct" usage of chords.

I believe that this approach, while interesting from an intellectually
theoretical perspective, is misguided, and in fact does not really help us
(and our students) understand the variety of musical languages/styles that
have been used throughout the history of Western music, and in musics of
other cultures.

In other words, I believe that understanding and explicating (i.e.
analysis) the syntax of chord progressions is analogous to the syntaxes
spoken languages, in that they vary from culture to culture and therefore
must be understood within a specific cultural context.

For example:  In English prose, adjectives "normally" (i.e. are "supposed
to") come before nouns; in prose, we say "The red moon."  Conversely, in
other languages, adjectives "normally" come after nouns; e.g. in Spanish,
"La luna roja."

Similarly, in musical syntax, IV "normally comes before V" only in certain
musical styles, e.g. common-practice tonality.  But in the blues style,
the normative syntax is reversed, and "V usually comes before IV."

Thus, there is no singularly "correct" or even "normative" usage of IV
versus V (just as there is no universally correct linguistic grammar); the
normative usage is defined by the stylistic context.  Furthermore, the
decision of whether to use "predominant" versus "subdominant" for IV
therefore predicates a stylistically normative syntax, which might or
might not be appropriate per various examples.

I think that this issue has been muddied in the ongoing discussion,
because musical style (i.e. syntax) has changed over time; the syntax and
terminology that might apply satisfactorily to Haydn's harmonic grammar
might not be applicable to explicating Faure's.

Furthermore, the "normative" syntax of words in prose is often altered
when used in more poetic circumstances.  In every day parlance, we might
say: "The red moon looked ominous."  But in a poetic usage, we might
write: "The moon, red and ominous, appeared before me."  Suddenly, the
adjectives which "normally" come before nouns came afterwards; it's the
messing up of the normative grammar which turns the prose into poetry.  In
music, we have the same sorts of non-normative usages of chords; this
creates surprise, tension, humor, etc.

Thus, the whole point of defining a "normative" usage of chords is really
to understand how the exceptions to those expectations create the
particular affect of a specific passage, or how they create the different
styles of different composers, or how we define the different styles that
evolved over time.  But again, the whole wonderfully complex and messy
situation can only be understood by defining "normative" within a certain
stylistic context, rather than as a singular absolute truth or standard.

I believe that we, as a profession, often mistakenly use the normative
syntax of common-practice tonality as the "standard" when we teach harmony
to our students.  After all, most of the art music concert repertoire does
come from that style.  However, unless we keep reminding our students that
"What we are teaching you in Theory class is really just the syntax of one
particular style situated in one particular location and one particular
time period," we risk giving our students the impression that any other
syntaxes are "wrong" or "weird" or "backward."

(Personally, when I teach, I do use the terms "forward and backward" as
Bruce Grant describes below, which can be problematic; but I keep
reminding the students that the "forward and backward" only apply to
common-practice classical music, and that jazz or Machaut or Debussy have
a different set of principles of what defines forward/backwards, which
seems to help them contextualize what we're learning.  For example, in
Mozart's K. 284, in the Theme and Variations, when Mozart suddenly slips
in a series of "backwards" downward step progressions, I ask: "Why would
Mozart suddenly do something "wrong" like this?  We then discuss the
earlier tradition of fauxbourdon, which helps them understand that by
suddenly using an "anachronistic syntax," Mozart was being puckish.)

Sorry to be long-winded; but I hope this perspective might help in the
ongoing discussion.


> Dear colleagues,
>             The discussion about descending or advancing progressions can
> be
> resolved by observation of the fact that the notes of the dominant triad
> are
> the third, ninth, and fifteenth harmonics of any tonic. Therefore, a I > V
> root movement backs up, as does a IV > I movement, since the notes of the
> tonic triad are the third, ninth, and fifteenth harmonics of the
> subdominant. V > I and I > IV root movements go forward since the second
> chord introduces frequencies that are not to be found in the first chord.
>             Major third root movements are similar since III sounds the
> tenth, twelfth, and fifteenth harmonics of  the tonic as Dimitar Ninov
> reminds us in his May 3rd posting. I sounds the tenth, twelfth, and
> fifteenth harmonics of bVI if minor, and  the tenth, fifteenth, and
> twenty-fifth harmonics of bVI if major. Therefore, III functions as a
> dominant  and bVI as a subdominant, which is interesting as they are also
> the dominant of the relative minor and subdominant of the relative major.
>            The minor submediant is similar to the minor mediant because
> they
> share a major third with the degree a minor third above, VI with I, or
> below, bIII with Im. II, the subdominant of the relative minor, has long
> been recognized as a substitute for IV. So it is possible to combine
> Schenker’s « stufen » with the three functions of Riemann.
>             I teach my students that I, IV and V are the « primary »
> chords,
> tonic, subdominant and dominant. In the major mode, II, III, and VI are «
> secondary » chords, the subdominant, dominant and tonic of the relative
> minor. VII is an incomplete dominant since it represents the fifth, sixth
> and seventh harmonics of V. (If the seventh harmonic is modified in equal
> temperament, so are the other harmonics!) In the minor mode, bIII, bVI,
> and
> bVII are secondary: the tonic, subdominant and dominant of the relative
> major. The diminished triad on II is an inversion of the minor triad on IV
> with an added sixth, but without the fifth.
>             We can therefore chart the equivalences of the stufen and the
> functions as follows: I is tonic major or minor. II is subdominant of the
> relative minor or the incomplete minor subdominant with an added sixth.
> The
> bIII is tonic of the relative major. III is dominant of the relative
> minor.
> IV is subdominant major or minor. V is dominant major or minor. The bVI is
> subdominant of the relative major. VI is tonic of the relative minor. The
> bVII is dominant of the relative major. VII is an incomplete dominant
> seventh.
>             Dominant to tonic root movements go forward as do tonic to
> subdominant movements. The subdominants IV and bVI go forward to dominants
> by analogy to the II > V progression. The contrary root progressions back
> up. Root movements by perfect fifths and fourths, major thirds and  major
> or
> minor seconds change the function, but Root movements by minor thirds and
> diminished fifths stay within the same function. After backing up,
> stability
> is found by returning forwards, as in Schenker’s « ursatz »: TDT. TST is
> similar if contrary. TSDT progressions are more complete since they use
> all
> the notes of the diatonic scale and replace a back and forth movement with
> a
> circular one as Ildar Khannanov says in his May 1st posting. Stability is
> coming back home after a trip, rather than being left out on a limb, away
> from friends and family.
>             Thank you for your attention.
> Bruce Grant, DM, Indiana University
> Chef d’orchestre et chef des chœurs,
> Théâtre de l’opérette, Lyons, France
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Dr. Paul A. Siskind                        Home:
Professor of Composition and Theory        Sweet Child Music
The Crane School of Music, SUNY-Potsdam    69 N. Main Street
Potsdam, NY  13676                         Norwood, NY  13668
(315) 267-3241                             (315) 353-2389

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