Nuno Trocado

(012) Trichords and Turning Ornaments into Harmony



Voicing (012) trichords

Continuing with the exploration of three-pitch sets, it's now time for the very special (012) trichord.

Let's take a C, a C# and a D. We can put the three notes in the same octave, a cluster of pitches as compact as possible. Or we can move each of the notes to another octave, up or down. Now, how many ways are there to voice a chord consisting of just those three notes? Let's use an additional constraint: no intervals larger than an octave between consecutive notes. Starting from a middle C, we can write the six possible combinations like this:

Combinations of the (012) trichord class

These are all instances of the (012) trichord class.

This expresses in a very particular way the sonority of the twelve-tone equal temperament, focusing on the smallest available intervals and its inversional equivalents.


The (012) trichord is also found in a simple ornamental technique: surrounding a target note with its chromatic neighbors above and below. Some people call this an enclosure, in the context of the analysis of bebop melodies and solos. The idea then is to perceive the target note and its neighbors as a single entity, and play all three pitches simultaneously. This is a form of integrating ornaments into harmony, a transformation that - we can speculate - is prevalent in the historical development of western music, e.g. leading tones being incorporated into chords. Why not take this idea further and promote the chromatic neighbors to the same harmonic hierarchy of chord tones?

For a Cmaj7 chord with the 9th, #11th and 13th1, this yields:

C major seventh chord and its chromatic ornaments

This is what I'm practicing in the video.

While I go through the harmonization of the target notes - C E G B D F# A and back - I also cycle through the all possible voicing types seen before, changing the octave of individual pitches.

That's it. In a way, for me these are all possible voicings for a C major chord, although offering a particularly striking sonic effect.



Instead of a traditional harmonic entity like a major 7th chord, the sequence can also be seen, more abstractly, as intertwined cycles of alternating major and minor thirds, (012) trichords, and a series of all possible distribution of pitches along neighboring octaves.