IX. Twelve-Tone Music
Composing with Twelve Tones
Mark Gotham
Key Takeaways
So far, we’ve seen some rows and serial properties in the abstract, and their usage in some existing pieces. Now let’s complement that by writing a new piece. It’s worth reiterating that (like any other musical style or technique) there are infinitely many ways of approaching composition with twelve-tone rows, and so this can only be an example and not representative—indeed no more than a single analysis can be. All the same, an example of writing with rows will be a helpful illustration of how we can navigate between theory and practice. We can aspire to something like Béla Bartók’s marvelous Mikrokosmos collection: short pieces with a clear compositional “brief” that are also rather interesting as “real” pieces.
Here, we’ll start by choosing and examining rows, then go on to write at least the start of some passages that vary in how they approach the same material, especially in terms of how relatively “free” or “strict” they are in their use of serial processes.
Choosing Rows
Let’s start by choosing some rows to work with. Among the many possible motivations for choosing rows, I’m inclined to seek out those that:
- Have “interesting” internal properties …
- … that are suggestive of some compositional strategies
- And have been relatively under-explored in previous pieces.
For me, the “all-trichord” rows are a great fit for these criteria. Alan Marsden (2012, 162) defines these as “12-note series which, when treated as circular, [contain] in the 12 sets of 3 consecutive pitch classes all the 12 possible classes of trichord.”[1]
Marsden has demonstrated that there are exactly four distinct forms of this row:
- [0, 2, 6, 10, 5, 3, 8, 9, 11, 7, 4, 1],
- [0, 2, 6, 10, 11, 9, 8, 3, 5, 1, 4, 7],
- [0, 2, 6, 10, 7, 4, 11, 9, 8, 3, 5, 1],
- [0, 2, 6, 10, 1, 4, 5, 3, 8, 9, 11, 7]
Here they are as twelve-tone rows starting on C, and also with the corresponding trichords given and labeled below:
All-trichord rows by FourScoreAndMore
Given that all standard tone rows feature all twelve pitches and the “all-interval” rows featuring all eleven intervals are also familiar and common, you could view the all-trichord rows as a logical extension of these familiar row properties. They are certainly useful insofar as our goal in composing with twelve tones is to pursue maximal variance.
Perhaps most compellingly of all, Marsden concludes that he “never did find a convincing way to make use of this in composition” (2012, 163). To some composers, that kind of comment is irresistible.
Example Compositions
Following are several example compositions and discussions of how a row can be used to generate the pitch material for a musical composition.
A (relatively) free fantasia
Let’s begin with the least strict approach. Here we’ll consider the use of these rows and the emphasis on overlapping trichords as enough of a constraint, leaving to free creative choice all other matters including:
- Repet