[Smt-talk] Fetis and Harmonic Functions

Mon Feb 13 18:53:41 PST 2012

Dear Dimitar and the List,

discussion of tonal-harmonic functions is important. It is not a well-studied area, despite the fact that for centuries great theorists have been working in it. It is true that it makes sense to analyze tonal function of the dominant without having the leading tone in front of us, e.g., in the case of v. In general, voice leading is the effect, harmony is the cause. Often, voice leading does not follow the schoolbook rules but the flow of harmony saves the progression. Fetis suggests that the two chords have tonal harmonic functions independently of modifications and of the context of other chords. There is natural relationship of attraction; tonic represents rest and completion: dominant seventh--motion and attraction.

Example 1. Bach, Brandenburg Concerto no 6, slow movement, a theme:  Bb4-C5-D4-Eb4 etc.  In this phrase, the nucleus of a theme of a fugue, the scale steps are 5-6-7-1, with a leap down from C5 to D4. The only way Schenkerian dogma of Urlinie can connect these to notes is by interpreting them as "a chordal skip." However, the C5 is harmonized with Subdominant and D4--with the Dominant. There is no chordal skip here. It is truly a broken melody. Moreover, it does not fit into a clichee of descending fifth progression and tonic is approached not from above (scst2) but from below. I do not believe that 2-1 is "the most general case." Most trivial--probably. The most beautiful and musical soprano for D-T resolution is leading tone to tonic. So, what unites this ultimately broken and disorganized melodic line (voice leading nearing a disaster) is the smooth and logical progression of tonal functions T-S-D-Tp, which moves firmly as an oceanic wave and
 supports random notes of the melody.

Example 2. Beethoven, Appassionata, slow movement, a theme of variations. Again, melody is the worst ever: Ab4-Bb4-Ab4-Bb4-Ab4-Ab4-Ab4//Db5-Db5-Db5-Db5-Db5-C5-Db5! If any of your students will write a figured bass realization with a melody like that, I am sure it will deserve the D. However, Beethoven probably did this on purpose: we are listening to melody and often disregard harmony. In this case, we have no other choice than to focus on harmony and--truly--we discover noble beauty of these simple triads, T-S-T; S-D-T. Here, voice leading in soprano is poor, the functional flow of harmony is excellent.

Example 3. Rachmaninoff, Etude-tableau op 39, no 6, Little Red Riding Hood. The theme opens with a simple standard gesture, resolution of the Dominant into Tonic, just as we expected. Upon closer examination, we notice that Dominant is expressed here, in the key of A minor,  as a strange sonority, D#-A-B. It moves into Tonic, represented by the i6/4. The "Dominant" has two "leading tones," D# to E and B to C, but the Leading Tone proper, the G#, is missing! Dimitar mentioned Prokofiev's dominant (a B major triad in C major). This one is even more uncommon: the B seventh chord in first inversion with missing fifth, resolving into A minor six-four chord. No standard voice leading (and Schenker would be correct to say that), but plenty of harmony.

Example 4. Chopin, Scherzo No 1, three opening chords: ii4/3, V5/6 (two octaves lower!) and i5/3/. This progression can humiliate any voice-leading lover. There is simply no voice leading here: not only that the first two chords are separated by two octaves, but the choice of inversions, ii4/3 leading into V6/5 is horrible! Yet, every good musician immediately recognizes three main functions: S - D- T. Their flow is the most important: it is the opening gesture of a magnificent composition, like providing an initial count, One, Two, Three...

This is what I meant when I insisted on primary role of harmony in music.

Best,

Ildar Khannanov
Peabody Conservatory
Johns Hopkins University
solfeggio7 at yahoo.com

________________________________
From: "Ninov, Dimitar N" dn16 at txstate.edu
To: "smt-talk at lists.societymusictheory.org" <smt-talk at lists.societymusictheory.org> 
Sent: Monday, February 13, 2012 8:35 PM
Subject: [Smt-talk] Fetis and Harmonic Functions

Dear Ildar,

I read carefully the excerpt by Fétis, and one important detail impressed me in his deliberations. I was about to oppose the statement that two triads can express fully a tonality (here I do not include a well developed melody) when I realized that he does not speak of two triads, but of one triad and one seventh chord. This makes a lot of difference, of course, for by connecting the triads built on C and G you cannto tell whether you deal with a tonic and dominant or with a subdominant and tonic. But the arrival of a fourth tone over G – the “F” note – drastically changes the picture. On the one hand it creates two dissonances that need to be resolved, and on the other hand it represents a subdominant element within the dominant structure; a tone which stands a fifth below the tonic, and has an importan role in countering the tendency of the dominant to become a tonic on its own. 

Fetis suggests that all the other chords are obtained form the tonic and the dominant seventh chord. As long as we have the three elements (T, D, and S) within two chords, we may believe in that. But Fétis refers to a period which came after the sense of tonal center has been developed. 

Let me elaborate a little on these three elements, using triads alone, no leading tone, and no dissonance. In a certain sense, I am looking in retrospect to the Rennaissance, where the sharp tonal relationships such as between V7 and I have not been deliberately used as harmonic verticals, but perhaps as sparse incidental connections based on contrapuntal motion.

When we play in any order three different triads (major or minor, not diminished) built on ascending or descending successive perfect fifths, as a central chord naturally emerges the chord which stands right in the middle of the series of fifths. For example if we play Dm-Am-Em in any order, we will realize that we will begin to perceive Am as a central chord, which most successfully provides a sense of rest and somehow places the other two chords under its influence. You may say that this is modal harmony. Let is be so; modal and tonal have never been separated by a wall.

If, within modal harmony, we may have a tonal center, this means that the dominant-tonic relationship is older than the leading tone. The D-T relationship is not created by the presence of a leading tone but it is only enhanced and sharpened by the leading tone. We receive another natural proof of this notion in the overtone series where the third harmonic is found a fifth plus an octave over the fundamental. The fundamental is a center of gravity, and the third harmonic exemplifies the necessity of a tone to resolve down by a leap of fifth. No leading tone is necessary to support this tendency.

The above reflections are also addressed to those teachers who keep telling their students that the minor V chord does not have a dominant function per se. Play to them “Take Five” by David Brubeck and ask them to repeat their statement. Of course, “Take Five” is not in the style of Haydn or Wagner, but is has a lot to do with the common practice period, for it mixes devises from both natural and harmonic minor, and has familiar sequences.

Having said all of that, I do not mean that we should use minor V instead of the harmonic dominant in minor. On the other hand, teachers who tell their students that minor V and major VII should be permanently replaced by major V and vii diminished simply do not what they are talking about.

One of the funniest test questions is: list all the diatonic triads in minor. The answer to this question is that these are the seven triads from natural minor, period. But the teacher usually has a wrong expectation –  he/she expects the students to list all the triads from harmonic minor only, not knowing that the harmonic minor is not a diatonic scale. The question should be: list the most typical chords found in a minor key. A key deals with multiple scales. But even this is not good enough, for minor V and major VII are purely diatonic chords, and as such they cannot be thrown out of the system, no matter how frequently they occur. Perhaps the best formulated test question would be: besides the purely diatonic triads in natural minor, what other chords do we use more or less frequently in minor.

I am sorry for the deviation. Another time we may discuss what is purely diatonic, relatively altered and really altered.

Best regards,

Dimitar 

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
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