An Instance of "Anti-Composing-Out" in "The Alcotts"

One type of "composing out" is when the intervals within a group of notes correspond to transpositions among groups of notes. A simple and well-known example is in "Nacht" from Arnold Schoenberg's Pierrot Lunaire: E4-G4-Eb4 | G4-Bb4-Gb4 | Eb4-Gb4-D4. (The 4's mean that these notes are all in the octave above middle C.) The melodic intervals of minor-third-up and major-third-down between a note and the one that follows it within each three-note cell correspond to the transpositions between a cell and the one that follows it.

The second system of "The Alcotts," the third movement of Charles Ives's Piano Sonata "Concord," contains a single phrase that begins and ends with three-note chords that are transpositions of one another. A third transposition occurs soon after the phrase begins, using a duration that is longest of any three-note chord in this phrase before the end. These three chords are Ab4-F5-Bb5 | F4-D5-G5 | Bb3-G4-C5. The harmonic intervals of major sixth and perfect fourth between registrally adjacent notes within each chord correspond, but in inversion, to the minor-third and perfect-fifth transpositions between adjacent chords. Because of the inversion, I call this "anti-composing-out."