[Smt-talk] Fetis and Harmonic Functions

[Ninov, Dimitar N]

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