I just read Schoenberg’s rather scathing attack on the ‘linear contrapuntalists’ (in which he includes Krenek and Hindemith) in his article ‘Linear Counterpoint’ (from the late 1920s I believe) published in Style and Idea. It’s a very polemical article and Schoenberg admits that he hasn’t even read Curth’s book which proposed the theory of linear counterpoint… To the extent where he even misspells the author’s name as ‘Kurth’.
Basically Schoenberg calls the idea ‘nonsense’ since the term ‘counterpoint’ implies some kind of vertical relation. Moreover Schoenberg in particular is scathing of those who use this linear contrapuntal conception in an inconsistent and eclectic fashion in drawing upon older ‘models’, choosing “ruins as their foundations” (p. 292). Not only is the theory of linear counterpoint nonsensical, the composers who ostensibly draw upon it are not even consistent with their principles. In fact, Schoenberg puts forward a very interesting suggestion of what actual linear counterpoint would have to mean:
So: linear—one must not regard independence of the parts as meaning merely that, so far as their horizontal flow is concerned, they do not depend on one another—which means that parts:
1. (a) never move (carry out) in parallel for long;
(b) do not have to work with the same motive;
(c) if they work with the same motive, develop it differently;
(d) are independent rhythmically, in fact ought to contradict each other;
(e) ought to have different dynamics, performing indications, climaxes, cadences;
but must take it to mean also that parts ought to be independent of each other even in their harmonic relationship. This means:
2. (a) that in sounding together they need not be related to a common harmony;
(b) that no sort of ‘registerable’ harmony has to result from the way they sound together;
(c) that if possible they should produce dissonances when they sound together (to show how little they are worried);
(d) that there need be no attempt to produce harmonic progressions (‘registerable’) ones, such as cadences or any other identifiable fundamental-progressions, and that such progressions are no criterion of the parts’ function;
(e) that so far as possible one should avoid any articulation such as can arise from the coincidence of parts in articulating ‘steps’.
So by ‘linear’ one can imagine a number of parts, each of which has its own development, and none of which worries in any way about the others. (pp. 292-293)
Ok. It appears that this is just a thought experiment from Arnold, one which he seems to dismiss as impossible or undesirable in advance. But there’s something useful in it. The most interesting aspect of this passage is the tension between on the one hand, a fully determinate and thoroughgoing non-relation between lines, which would have to be carefully planned and represent a kind of totalisation in itself (as Adorno would call ‘total counterpoint’), and on the other, a kind of non-relation that might produce accidental relations since, by being determined independently, lines may produce (for instance) consonant intervals, etc. In the former, the lines do indeed ‘worry’ about one another, insofar as they must keep their distance (creating a negative totalisation), in the latter, the lines in a very real sense, do not ‘worry’ about one another. This is a useful distinction to keep in mind.
In any case, Schoenberg is opposed to both a compromised form of this ‘linear counterpoint’, and to the idea of its genuine realisation.
With regard to his own idea of counterpoint ‘proper’, Schoenberg argues for necessary contrapuntal relations. The idea is that there must be some kind of vertical relation between ‘points’ which is essential for the existence of the ‘idea’: “counterpoint means an ‘opposing point’ whose combination with the original point is needed if the idea is to exist” (p. 289).
It wouldn’t be difficult to read an Hegelian logic at play here: that counterpoint presupposes that a line by itself remains abstract and in need of an ‘opposing point’ or negation in order for it to become determinate.
It is not that the two lines are equal partners. It is not that the idea is the two together, the idea is not the texture itself. One is clearly called the ‘original point’, to which another is added.
But what is this matter of ‘priority’? This idea of ‘priority’ bundles up a number of different dimensions: 1) priority in the production (counterpoint as compositional method); 2) priority in the logic (‘cantus firmus’ or ‘theme’ that is the ‘essence’ or ‘kernel’ of the work); 3) priority in formal presentation (the fugue, for instance, where the opening bars present the subject).
For Schoenberg, these three are essentially the same, and all are related to the ‘theme’. Adorno notes that what Schoenberg learnt from Bach was ‘figures that accompany themselves’. Schoenberg puts it this way:
Anyway, whatever one’s views about the pleasure that can lie in conducting each part in polyphony independently, melodiously and meaningfully, there is a higher level, and it is at this level that one finds the question which needs answering in order to arrive at the postulate: ‘Whatever happens in a piece of music is nothing but the endless reshaping of a basic shape.’ Or, in other words, there is nothing in a piece of music but what comes from the theme, springs from it and can be traced back to it; to put it still more severely, nothing but the theme itself. Or, all the shapes appearing in a piece of music are foreseen in the ‘theme’. (I say a piece of music is a picture-book consisting of a series of shapes, which for all their variety still (a) always cohere with one another, (b) are presented as variations (in keeping with the idea) of a basic shape, the various characters and forms arising from the fact that variation is carried out in a number of different ways; the method of presentation used can either ‘unfold’ or ‘develop’.) (p. 290)
It should by now be clear that from this point of view linear counterpoint is nonsense, or at least a distortion of sense. (p. 290)
So, while tonal or modal harmony, with its clear rules for dissonance treatment, was no longer at play in Schoenberg’s counterpoint, for him at least, the essence remained the same: counterpoint was based on a necessary relation between original line and added line, which is now given a Hegelian slant of a determinate negation.
This is totally predicated on thematism. Thematism, as Nicolas has noted, represents a figure of self-consciousness (Traversée du sérialisme). A figure that broke down in the post-1945 world of new music, and that could hardly be reinstated today in any simple sense (although Hannah reminded me that Enno Poppe may be a good example of a renewed approach).
Can the term counterpoint have any meaning in the wake of the dissipation of this logic?
With regard to the three levels of priority, how does my approach relate?
1) Concerning priority in production (method), in my approach lines get added one after another over a small sequence of bars before moving on to the next (is it possible to do otherwise?). All lines are precompositionally constituted abstractly and mathematically with an intuitive feel for how they will relate (a general division of labour, division of space, etc). When I come to compose on the score itself, there is certainly a priority and a sequence putting in one line and then the next. This often means that the line that is written first has the most freedom to be deployed according to its own logic, whereas the second is somewhat more constrained, and the third and fourth still more constrained. Of course, as I add one line, I may change the previous line if I feel it is more important that the new line preserve its precompositional constitution. Thus there is an ongoing compromise between the needs of the various lines. This is most evident when writing piano music, where the span of the hands, and so on needs to be taken into consideration (even if risking going too far), but it is also the case in music for more than one instrument, since certain relations may be introduced between lines that are undesirable: one line may obscure too much another line, or may introduce unwanted harmonic or rhythmic relations, and thus one of the two will need to be changed.
2) So while there is, by necessity, a weak and changing priority in the compositional process, this is not rooted in any logical priority: no line assumes the role of ‘theme’ in the Schoenbergian sense of a ‘basic shape’ from which everything ‘springs’. Lines are often conceived of in their relation to each other, prior to being written down, and according to a
3) Without a logical priority, that is, without a ‘theme’ there is therefore no chance of a priority in formal presentation. Any priority in formal presentation results from compositional or precompositional choices that have everything to do with forming a contrapuntal discourse over time, and little to do with staging a dialectical process of deriving the many from the one.
To me, this dialectic is much too idealist and essentialist. It certainly feels as such today. My music is predicated on the materialist tenet that the multiplicity of matter is pre-existent and ultimately irreducible. As Badiou states, multiplicity is simply ‘what is’, the point is to create the ‘same’ out of the multiplicity (what this ‘same’ in music could be and how one could approach it, is another question entirely), not the other way around. So, while I don’t agree with the ‘linear counterpoint’ idea (there must be some consciously developed vertical relations), I do, however, feel that linear heterogeneity is an essential starting point, so I can’t agree with Schoenberg’s model.
Some scrappy thoughts…
(Here’s a thought: find the logic of the various phases of contrapuntal music: from the Notre Dame school through Ars Nova to Palestrina to Bach to Beethoven (?) to Schoenberg to Boulez to Ferneyhough… Of course there is no sense that this should necessarily be a narrative or necessary development… Maybe its worth finding some stimulating logics throughout history, rather than a catalogue or history of logics.)
(Hypothesis, if there is to be a general narrative development: the history of counterpoint moves from contingent addition of new voices to the original since this emerged from a more spontaneous, functional and occasional practice, to a ‘necessary’ one where all lines were derived from the initial line and nothing was unnecessary, to something more contingent again, though not through a reclamation of the functional or spontaneous. This is a very broad and perhaps impossible or unhelpful thesis…)
A few final quotes from Schoenberg from his article ‘Linear counterpoint: Linear polyphony’:
As opposition to this Riemann, who teaches counterpoint by adding ‘ornaments’—passing notes and suspensions— to harmonic textures, one could even approve of a formulation like ‘linear counterpoint’! But only then. (p. 297)
But now it is clear that linear counterpoint is a contradiction in terms. For counterpoint signifies, even in the view of school masters and historians, who lack any feeling for word-play, the relationship of one ‘point’ (note) to (or against—‘contra’) another point—that is to say, relationship in a direction other than that of the line. Here let me also set down what I have probably set down elsewhere—that I believe ‘counterpoint’ to be a play on words (I lack the philological equipment to explain this fully) and gather from it the following: the art of counterpoint, of ‘against-notes’, those notes or note-progressions which can be set in opposition and magically possess a relationship to each other that fulfils the principle of cohesive contrast. (p. 296; bold added)
This is revealing: the ‘against-notes’ carries the Hegelian idea of negation, and ‘the principle of cohesive contrast’ is nothing but a re-writing of the discordia concors doctrine of the Ars Nova period.
Interesting thoughts re harmony, though:
My earlier works did not yet come within the scope of my remark, ‘The harmony (or “the total sound”—but that was wide of the mark) is not under discussion’; it applied only to those from the time of twelve-tone composition. It can easily be shown that in the earlier works the chords are designed to have at least an accentual, articulating and colouring effect, and that their mutual conduct is full of regard for the relationships of the parts as they move. However, what is even here not under discussion—not, at least, in the way found in the Harmonielehre—is the harmonic progression. This, however, was never under discussion in counterpoint; but still one must pay a certain amount of attention to chordal progression, insofar as there is a prevalent tendency to avoid tone repetition as much as possible, or to disguise it. However, in twelve-tone composition harmony is no longer in any sense under discussion, nor even is progression, since both are subordinate to a different law. (pp. 295-296)
And finally, from his article ‘Fugue’:
Fugue is a composition with maximum self-sufficiency of content. (p. 297)
In its highest form, which may perhaps be a merely theoretical construction, nothing would claim a place in a fugue unless it were derived, at least indirectly, from the theme. (p. 297)
But the theme’s everchanging ‘way of accompanying’—through other parts, through transposition of invertible combinations, through the various types of canon, and also through harmonic re-interpretation—all this, too, is best regarded as variation. (p. 297)