copyright © 2003 by Larry J Solomon
Beethoven's C minor Variations as a Model for Recurrent Chords and Nonharmonic Notes
To postulate a method for determining RCs ( recurring chords) with a tonal model, consider an example from Beethoven's Variations in C Minor, WoO 80 (1806):
This is the Theme from a set of variations. The RC may be postulated from the locations where notes are verticalized, especially on long notes and notes on strong beats. These would include the chords on the first beats of the first six measures and the long notes on the second beat of measure 6. The hypothetical RC represented are all tertian: major, minor, a dominant seventh, and a German augmented-sixth chord. Thus, a tertian model of these trichords and tetrachords may be postulated. Nonharmonic notes, or NHTs, are circled.
For a Linear Analysis (quasi-Schenkerian) of the Theme and Variation 1 click here. The soprano line ascends from I (C) to VI (Ab), while the bass descends from I to V, both then plunging back to I. This frames a powerful contrapuntal structure in contrary motion..
The same chords occur in Variation 1, with the exception of an Eo7 replacing the C7. This chord type is then added to the list, whose members are easily confirmed to be a RC. (The Eo7 is maximally similar to the dominant seventh and is a subset of the Vb9, which also occurs in subsequent variations.)
The chord classes and their significant subsets may be abstracted from these chords, which include any major, minor, diminished, dominant sevenths, and German-sixth chords. Analysis of the following variations confirms the RC group. We may also postulate a regular harmonic rhythm of one chord per measure, with a shift to 1+2 beats in measure 6, and to 2+1 beats in measure 7. Using these parameters, the nonharmonic notes (NHTs) of the Theme and first variation may be located. These notes are circled in the Theme. They are all passing tones. There are no NHTs in Variation 1.
Var II also contains no NHTs, but there are chord substitutions in measure 3, a Eo7 instead of C7, and in measure 6, a V instead of I. Var III also contains no NHTs, but has chord substitutions: a Gb-Neapolitan of IV in measure 3, and measures 6-7 has a Bo7 following a V and preceding the cadence.
Var IV has Neighbor notes, which are circled here. The two chord substitutions are in the rectangles.
Var V uses appoggiaturas (circled), except for measure 8, where Ab and F# make up a cambiata. Chord substitutes are in rectangles. Var VI has no NHTs. The chord substitutes are all standard so far. Var VII contains mostly passing tones doubled in octaves.
Var IX contains Neighbor notes trilling off the beat. These are circled only in the first two measures, but they continue throughout the variation. Meanwhile there are incomplete neighbors in the soprano line starting in measure 3. However, the soprano G in measure 6 is a passing note, and the Ab in in 7 is an ornamented suspension.
Var XII is in C major with few NHTs but with several chord substitutions. The circled notes are passing tones, except the E in measure 4, which is an appoggiatura.
Var XIII has several NHTs, mostly passing and neighbors. The C in measure 7 is an appoggiatura. There are several chord substitutions as well (in rectangles).
This should be enough of the variations to analyze for NHTs and chord substitutions.
Some general observations on form: