A Pedagogical Piece Proceeding from Paganini (Part IV)

I have metaphorically described the opening of my Paganini variation as flitting between the southern part of the United States and the northern part of South America. (Last month’s post will hopefully clarify this statement if it makes no sense.) For example, the first progression in my variation from an A-minor triad to an E-major triad could be compared to a flight from Caracas to New Orleans. (In Paganini’s variation, the first eight measures travel back and forth like a dual homeowner or commercial pilot between these two harmonic coastal cities, whereas I (discontentedly?) journey to different but nearby ports of call.) Musically, this means that these initial chords are just a semitone (or two, with some of my chords) away from the augmented triad C-E-G#, which is represented in my geographic analogy by the Caribbean Sea plus the Gulf of Mexico. For example, both the A-minor triad and the E-major triad require only a single semitone of change to transform into this augmented triad.

In both the first eight measures of both Paganini’s original caprice and my variation on these measures, the augmented triad does not appear as a harmony, even as a waystation from consonant triad to consonant triad. (Augmented triads assume this function to some extent later in my variation.) Likewise, a typical flight from Caracas to New Orleans goes over the Caribbean Sea and the Gulf of Mexico without stopping there: most planes aren’t equipped to land on water, and most people don’t live on water. And yet it is reasonable to represent such a flight as a Caribbean flight. Likewise, Richard Cohn encourages his readers to think of the C- E-G# augmented triad as an absentee emblem for progressions like the first eight measures of either Paganini’s caprice or my variation.

Perhaps it is not completely absent, if a broader category expands our notion of what “it” is. The photo below shows how the C-E-G# augmented triad tilts the four-pan scale. All three notes are in the same pan, so the scale unsurprisingly tips straight toward that single pan.

There are exactly two other ways to put three notes on the four-pan scale so that it tilts in the same direction as C-E-G#, although these ways may not tilt the scale with the same magnitude. (By design, my scale does not measure magnitude: either it tips one way, touching a side to the table, or it does not.) These two ways are shown below.

 

Each of these first two motives in Paganini’s caprice—consisting of three different notes each, octaves and repetitions aside—tilts in each of these two ways, that is, in the same direction as the C- E-G# augmented triad. My chromatic variants of these two motives (in my mm. 5-6) do the same, but the two ways are swapped between the motives. All four tilts are shown below. Thus, on the four-pan scale, Paganini’s motives and my variations of these motives are in the same watery region of the musical globe as the patch of less hospitable harmony that both Paganini and I repeatedly fly over during our first eight measures.