This chapter goes through the composition of some new twelve-tone music. It can be useful to follow someone else's process closely in this way. It is certainly useful to try something similar yourself.

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, in the 12 sets of 3 consecutive pitch classes all the 12 possible classes of trichord."Note that the term "all-trichord rings" is sometimes used for this topic, with "all-trichord row" referring instead to rows without wrapping around (and therefore omitting two of the trichords). See Robert Morris’s "Elementary Twelve-Tone Theory," for instance, and note the definition (after Babbitt) of an all-trichord row as "A ten-trichord row that excludes SC 3-10[036] and 3- 12[048]."

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:

Repetition of a note or a trichord (but perhaps not other groupings like dyads and tetrachords).

The specific rhythms and phrasings (as long as they typically emphasize grouping in threes).

Registral and timbral variety for expressive range.

That starting premise could be realized in any number of different ways. Here’s an example opening for solo viola that moves from the first trichord to the second (the two that are common to the start of all four rows as set out above):

Many composers—serial and otherwise—find it helpful to set initial constraints in this way, partly because it can give you license to approach the more detailed matters freely. The restrictions leave open a wide range of possibilities for how to proceed. For instance, we might like to create an overall contour that works up to a high point and then comes back down from there. Alternatively, we might prefer a static and demonstrably constrained passage. It’s wide open.

A process-driven "moto perpetuo"

We could also approach these overlapping trichords in a more vigorous, rhythmic way. For instance, we could have a kind of minimalist moto perpetuo style, insistently repeating each trichord numerous times before moving on to the next one. Let’s start with a continuous stream of notes, repeating our trichord in order (so with pitches 1-2-3-1-2-3- …). To move on to the next trichord, we can simply take the second pitch as the start of a new cycle for pitches 2-3-4. So if we’re repeating pitches 1-2-3-, then at some point we have a 1-2-3-1- and the following 2 marks the beginning of a 2-3-4- cycle.

We can make this change after completing any number of 3-note cycles plus 1 note: that is, after 4 notes (one cycle +1), or 7 (two cycles), 10, 13, 16, and so on. This should get us thinking about rhythm and meter. Say we put this predominantly 3-grouping pattern into a duple meter like \mathbf{^2_2}. That would lend the music an attractive and familiar 3-against-4 metrical dissonance. Whatever meter we choose, we’ll have to make adjustments for some of the cycle lengths: some will "fit" with the meter, and others will disrupt it. For instance, in our duple meter, the 4 cycle could be "one beat" (e.g., four eighth notes as one beat in \mathbf{^2_2}) and 16 could be 2 measures (4 x 4 beats). By contrast, the 10 cycle means breaking up the meter a bit (e.g., wi