Issue No. 12: How To Combine Traditional Seventh Chords Into Twelve-Tone Structures
Introduction
In the previous issue of The Theisen Journal, I outlined how we could combine traditional triads in ways that would complete twelve-tone aggregates. In this issue, I will explore merging two or more of the same traditional seventh chord type - fully-diminished, half-diminished, minor-minor, major-minor (dominant), and major-major seventh chords - into total chromatic structures.
As before, I acknowledge that none of this is groundbreaking, original research and that I am presenting these combinations through traditional hearing/nomenclature, but my purpose in this brief essay is to provide an easy-to-read resource for composers, arrangers, improvisors, and curious musicians in general (no PhD in theory required).
Three Fully-Diminished Seventh Chords (The Obvious)
An obvious, almost trivial method of combining traditional seventh chord types into a twelve-tone structure is to fuse three fully-diminished seventh chords whose roots are all separated by half step. Such arrays may be found in Lutoslawski’s earlier mature works, including Paroles tissées, Musique funèbre, and Symphony No. 2 (see: Charles Bodman Rae’s excellent book The Music of Lutoslawski).
Of course, combining any two fully-diminished seventh chords results in an octatonic set so this approach to creating twelve-tone structures through traditional seventh chords is useful if one wishes to navigate easily between aggregate and octatonic spaces.
Two Half-Diminished Seventh Chords
We may also combine two half-diminished seventh chords whose roots are separated by semitone plus a different chord type that I usually hear/consider as a “minor triad add sharp four.” The latter sonority will be a half-step higher than the highest root of the two half-diminished seventh chords.
Two Minor-Minor Seventh Chords
Oh, my friends, this is a personal favorite.
We may combine two minor-minor seventh chords whose roots are separated by a semitone plus another chord type - the “split-third major/minor triad.” This latter tetrachord will be a half-step higher than the highest root of the two minor-minor seventh chords.
Two Major-Minor (Dominant) Seventh Chords
It is possible to combine two major-minor (dominant) seventh chords whose roots are separated by a semitone plus another chord type - a “major triad add flat 2.” The latter sonority will be a half-step higher than the highest root of the two major-minor seventh chords.
Two Major-Major Seventh Chords
Combining two major-major seventh chords produces results unlike what we have witnessed so far.
If we write two major-major seventh chords whose roots are a tritone apart, the remaining tetrachord will be two perfect fourths separated by a semitone - prime form [0167] or what I regard as the “Bartok fourths”. (I call them this due to how frequently they appear in Bartok’s crunchier compositions.) The bottom note in this particular set of dissonant fourths will be the minor third in between the roots of the two major-major seventh chords (represented in the diagram with a dotted line).
We may also combine two major-major seventh chords whose roots are a whole step apart. If we take this approach, the tetrachord necessary to complete the aggregate will be a series of stacked perfect fourths or perfect fifths (depending, of course, on arrangement). As you may guess, I chose a particular transposition in my example to demonstrate how useful this particular combination could be when writing for string instruments.
Fusing major-major seventh chords was not favored by Lutoslawski the same way he did superimposing fully-diminished, half-diminished, minor-minor, and major-minor seventh chords because the complementary tetrachord introduced too many non-third interval types into the overall aggregate harmony. Lutoslawski, completely opposite of his contemporary Elliott Carter, generally preferred twelve-note formations that contained limited intervallic types; contrast this with Carter’s well-documented preference for all-interval twelve-note arrays as structurally significant sonorities. (See my dissertation for more information and a bibliography on this topic.)
Let me know what you think about this issue by leaving a comment below, commenting on social media posts, or shooting me a DM!
I would love to hear sonorities, twelve-tone rows, or improvisational patterns you create using the information in this issue.