Composing with Tone Rows

Row, row, row your boat...

Hello and welcome or welcome back to Composing Phrase by Phr... No, wait. That's not quite right. I want the next Composing Phrase by Phrase composition to be 12-tone. That's a couple steps more complicated than the last composition (which was already pretty complicated, mind) and I'm not as familiar with using tone rows for composition as I am with triadic, quasi-tonal harmony. So, instead, I'm going to do a number of little piano preludes to help demonstrate different ways of using tone rows for composition, both to prep the readers and to prep myself.

To begin with, what is a tone row? There are twelve pitches in Western music (more or less, I'm not going to debate that right now). A tone row takes those twelve pitches and arranges them into a collection where each pitch is repeated exactly once. The resulting construct is then used as the basis for generating melody and harmony in a composition. Here's what one looks like.

1.1 Tone Row Example

And here's another

1.2 Tone Row Example 2

As you can imagine, there are many, many ways to arrange twelve distinct pitches. 12! number of ways, in fact. That's some 479,000,000 and change. Luckily, many of these tone rows are actually "the same," so there are "only" 9,985,920 unique tone rows. This is, in part, a big reason why composing with tone rows can be so difficult - the number of possibilities to even start from is overwhelmingly large. Composers have found a variety of ways to combat that fact. Mine is to use a random number generator.

A quick note before proceeding. This approach to composition was invented by Arnold Schoenberg. When he invented it, he created a set of rules which were intended to avoid any semblance of tonality. The historical and personal reasons for doing so aren't what this post is about, but I bring it up only to say - I don't really care? Avoiding tonality isn't a particular goal of mine. Neither is the creation of aggregates (see: Babbitt). The only "rule" I'll hew closely to will be the "use the whole row" rule. That's kind of the point, after all.

Beyond that, there are a host of fairly complicated techniques developed by 12-tone forebears. I will, as much as possible, try not to reinvent the wheel. That I will inevitably develop idiosyncratic approaches to using tone rows is not only inevitable, it is (to me) desireable.

Now. To quote a famous British comedy troupe: Get on with it!

The very most basic thing one can do with a tone row is to take the notes of the row, slap some rhythm on it, and BAM! You've got yourself a theme. Here is a possible theme using the first of the tone rows above:

1.3 Using a tone row as a theme

Considering the "use the whole row" constraint, rhythmic motives and phrasing are among the primary means of composing with tone rows. This particular phrase is six measures and can be understood as four bars with a two bar "pickup" gesture, as follows:

1.4 Theme 1 phrase

Things get more difficult when creating harmony. Starting with the most basic thing I could think of, the easiest approach would be to create dyads, triads, and tetrads with consecutive pitches of the row.

1.5 Row dyads, triads, and tetrads starting from 0

There's nothing stopping a composer from using pentads or hexads or whatever. It just happens the 2, 3, and 4 divide the row neatly. Usings 5s or 7s would create some interesting possibilities where the harmonies would cycle through the row multiple times before returning to the first cluster. I'd say it would be tricky to make things sound unique, the more notes added to the harmonic stack, because you get closer and closer to sounding all twelve chromatic notes at once. These are chords which can really only be differentiated by voicing.

In any case, a composer is not limited to always starting the row from the first pitch of the row. By starting the harmonies from a different point, we get a new set of intervals and harmonic colors.

1.6 Row dyads, triads, and tetrads starting from 1

The approach I used to harmonize the above melody was to make dyads builts starting from pitch 1 of the row and place them underneath the melody. Because the harmonies are made from a row independent of the melody, I had a good deal more freedom in harmonizing the theme.

1.7 Theme with Harmonization

In this case, I chose to harmonize in a way that gave a sense of extended tonal harmony. It is true that the row also lent itself to that usage, though. Here are the triadic chords suggested by the harmony and melody acting together:

1.8 Chord Symbol analysis

As you can see, this isn't a particularly satisfying analysis of the harmony. A theorist approaching this phrase only with the tools of extended tonal analysis will quickly find themselves frustrated by the many elements that don't really fit and from the fact that there's not really a clear function to the progression. It's... planing thirds, I suppose. But the rest of the melody doesn't follow that plan. From a 12-tone perspective, however, the construction is relatively simple (ha! simple...).

1.9 Tone Row Analysis

There are two layers: the melody layer and the harmony layer. The melody, as stated above, is just the tone row with rhythm. The harmony is built from the exact same tone row, same transposition and all, except it's starting from the "second" note of the row rather than the first. In addition, there are three dyads at the end which are repeated: [7,8] ; [9,10] ; and [0,11]. This was to give the end of the phrase more of a sense of conclusion, which can be tricky to do when working with tone rows. Is this an unorthodox compositional choice? I suppose. Do I care? Not particularly.

So, that gets us started on a new composition with tone rows! These are going to be very short, probably four phrases, max. I'm also trying to figure out the best way to include audio. For now, I think I'll include a YouTube link of the full thing at the end of each, with time stamps for the example phrase. Thanks for reading!