Discussions on 12 Tone Music with Mark Gould Continue: A Composer’s Journal Entry: April 8, 2007

This Journal entry is Mark’s response to my last e-mail to him. I have also included my thoughts on what he has written. In my opinion, Mark writes very intelligently and beautifully on this subject of 12 tone music.

Mark: Hello Laurie,

Please forgive this long reply, but so often even the simplest things in music take many words of description (and perhaps is the reason for music in the first place).

So much of twelve-note 'theory' looks arcane but in reality is merely spotting patterns in the notes.

LC: Hello Mark! I absolutely agree, and well said.

Mark: If my grammar goes awry, it is because I'd like, as in counterpoint, to say several things at once, but writing isn't designed for this! Transpositions and modulations. This is an interesting question. If we take the row at its original pitch as the 'tonic' area, then relationships between the notes are tonic relationships. A transposition moves these relationships around - F was between A and E in the 'tonic' row, but in a transposed row, F is now between B- Flat and G. This is the essence of the twelve-note problem - is this method really a 'combinational' way of using the twelve notes or do in fact we hear only the intervals? I would rather think we hear only the intervals - the motives - in the row.

LC: Thank you for this fine discussion. I think how we hear the row depends almost entirely on how the row was initially set up, written: i.e. chordally or melodically. I know in my own writing I have done both, some rows set up chordally, others melodically. If the row has been structured on melody, then yes, I would agree - we will more hear the melodies, i.e. the intervals, the motives, and their transpositions. But even if the row is not built on more traditional chords, I think the repeating ‘harmonies’ - if we can call them harmonies - exist. And since they exist, on some level of our being we will recognize them. Even if several rows are played simultaneously, or fragmented.

Mark: I have used transpositions sequentially in my twelve-note music, but deriving them from the row. Let us look at an example. The row: F G E C-sharp C F-sharp B A B-flat D A-flat E-flat. The interval of an augmented fourth (tritone) occurs between notes 5 and 6 and between 10 and 11. Therefore, the second tritone could be construe d as being notes 5 and 6 of a transposition (upward by a major second). Hence we could form a sequence of rising (or falling if we used the retrograde or inversion) thematic fragments, formed out of the repetition of this segment, like so: (F G E C-sharp) C F-sharp B A B-flat (D A-flat E-flat) (G A F-sharp E-flat) D A-flat D-flat B C (E B-flat F) and so on. Of course, if a row has several repeats of different intervals, multiple sequential combinations are possible.

LC: Yes, I see what you are saying here - and thank you for your clear examples. We can extract motives or melodies or harmonies and sequence them by using the transpositions of the row. But in my view, the entire transposition is a modulation or a sequence of sorts. It’s own world, connected to other worlds in the universe of the music. Mark: I spoke in my earlier description of my techniques of a way in which to use the row: to extract a fixed row from a succession of rows, using the remaining notes (in order) to form secondary material. (It is possible to extract up to twelve rows from a succession of twelve rows, each note from the row in use contributing one note to each of the twelve lines, but a very special row is required and a lot of patience in working it all out. I usually only extract one or two lines simultaneously from a local row.) If we think in terms of tonality we might therefore restrict the row used to the 'tonic' row, and extract different row from it. Alternatively, we might extract the tonic row from a succession of different transformations. Either is a valid use of the row.

LC: Yes, I understand, and I have used similar techniques in bigger pieces with many lines or voices.

In a sense we are forming new rows, as you say - extracting a fixed row. And also writing new motives (and harmonies) with the remaining notes. In a sense, all of 12 tone is one big fixed and changing motive, both melodically and harmonically. By forming these new harmonies and motives from existing rows we are preserving a certain unity. Like trying to build a beautiful vase from innumerable fragments of various sizes and widths and colors: or we 12 tone composers are trying to put the vase back together; I suppose we could look at it either way ...

Mark: Interestingly, the discussion of tonality brings up Schoenberg's use of combinatoriality: presenting a row and its inversion as a pair, and devising the row such that the first six notes of the row and a specially selected inversion combine to form the twelve notes. Of course the second six notes of each also combine to form the twelve notes as well. Schoenberg often chose to form the interval of a perfect fifth between the first notes of the row and its inversion, such that the inversion began on the lower note. For example if the row began on D the inversion would begin on G.

LC: Well done and informative.

Mark: Schoenberg would then reserve the thematic (motivic) use of the inversion beginning on D for secondary sections (the B section of a ternary form, or the 'second subject' of a sonata form), and once again use the combining rule to obtain another series with which to form the rest of the musical fabric. If the inversion on D is used, then the combining row itself must start on the note A. Comparing this pairing of notes and the pairing of D and G, we can see that the whole set of relationships has been transposed upwards by a perfect fifth. An analogy with modulation to the dominant? It may be construe d that way, but with the twelve notes circulating in the music in a non-tonal manner, deliberately avoiding tonal chords or connections, such analogies seem to be ghosts, phantom reminiscences of old ways. In fact, combining rows in this manner can be formed an interval of an odd number of semitones between the paired first notes: minor seconds, minor thirds, perfect fourths and their inversions, so the use of a perfect fifth is entirely arbitrary.

LC: Yes, as you say, an analogy to modulation to the dominant only in a sense. This ‘modulation to the dominant’ would be true only within the special and complicated framework - or better stated, terminology, reference point - of 12 tone music. But if we take the repeating harmonies of the row (or its inversions and retrogrades) as a whole, as an entity - then I think we could call it modulation or sequencing. Not tonic to dominant - I would more say "up a perfect fifth", if you see my meaning.

I found your statement: "It may be construe d that way, but with the twelve notes circulating in the music in a non-tonal manner, deliberately avoiding tonal chords or connections, such analogies seem to be ghosts, phantom reminiscences of old ways."very poetic and almost a breathtaking image. Yes, the old ways of tonality are left behind. But in 12 tone music there still exist repeating intervals and relationships between pitches and motives, melodies and harmonies. And as I have written to you, as I get older - I do often construct the row on tonal chords, which in a way sets up an inner and subtle chaconne or passacaglia.

I am not quite clear on what you mean by: "so the use of a perfect fifth is entirely arbitrary." Could you explain? In a sense all choice is arbitrary, that is almost the definition of choice. But as a composer I have always had reasons for every choice I made, even if other possibilities seemed equally valuable.

Mark: Reminiscences of tonality do occur in my own music, but I take delight in their unplanned nature, just as one takes delight in the unexpected beauty of light playing on water reflected onto a wall, or in the shafts of rainbow colours from sunlight striking a crystal.

LC: A beautiful image, well said.

Mark: In a chamber work of mine, from two to twelve transformations of the basic row are being presented simultaneously, broken into fragments and played like fleeting ornaments to notes that are themselves silent.

LC: Just beautiful.

Mark: The effect is of the wind in the leaves of trees and the calls of birds in those trees; a wash of sound full of momentary instants, uncoordinated. Within this seemingly random flow, notes combine unexpectedly, a tonal triad, a brief suggestion of a tonal progression, a hinted cadence, sonic dust motes caught in a shaft of acoustic light. But this does not go against what I have said earlier about choosing my notes carefully - the great delicacy I had to use when writing the fragments so as to avoid all obvious correspondences left only the subtle ones. And the greatest beauty is often to be found in the deepest subtlety. All the kindest regards for you and your music, Mark

LC: Again, just beautifully stated - and thank you for this discussion dear Mark.

I hope it continues.

Laurie