A note to self on contingency in motet 3

My third motet, or (to alter a phrase by Klaas Coulembier):

Complexity1 as compound simplicity1; complexity2 as compound complexity1. Complexity2 can sometimes appear, contingently, as simplicity2.

So I’m part-way through writing the violin part at bars 16-17 of the third of my Mirror Motets. Here’s what it looks like (in all its unadorned glory):

Motet 3_emergent structure

I’ve just entered the rhythms and phrase structures and noticed an interesting emergent (unintended, contingent) simplicity that I wanted to relay.

Here’s the rhythmic sequence (the bolded bit is at play here):

1 1 1 1 1 1 5 1 1 1 4 1 1 1 1 1 6 1 1 3 1 1 1 1 7 1 2 1 1 1 1 1 7 3 1 1 1 1 6 1 1 1 4 1 1 1 5 1 1 4 1 1 1 1 6 1 3 1 1 1 7 2 1 1 6 1 1 1 3 1 1 1 5 1 1 4 1 1 5 1 3 1 6 2 0 7 1 1 3 1 1 1 6 1 4 1 1 5 0 4 1 6 1 3 0 7 0 2 1 1 1 7 0 3 1 1 6 0 4 1 5 0

Which is made up of two alternating processes.

  • The distribution of 1’s is according to its own alternating processes: a) 6 5 4 5 4 3 4 3 2 3 2 1 2 1 0 1 0 0 0 0 0; b) 3 2 1 0 3 2 1 0 3 2 1 0 etc. This gives 6 3 5 2 4 1 5 0 4 3 3 2 4 etc.
  • The longer note values (from 2-7) are on a repetitive symmetrical loop: 5 4 6 3 7 2 7 3 6 4 (repeat)

The other rhythmic dimensions are the phrase lengths (bold are the relevant bits here):

Result 9 10 7 8 5 12 9 10 7 8 11 12 8 8 6 12
Basic Process 9 8 7 6 5 10 9 8 7 6 11 10 9 8 7 12
Add 0 2 0 2 0 2 0 2 0 2 0 2 0 1 0 1
Sub 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

The top (result) row defines the number of rhythmic units from rhythmic sequence that are assigned pitches before three of them are assigned rests (was two in the previous section).

The long-range process (the process continues about 4 times this length) is much more interesting than this of course, since the addition and subtraction rows begin to interact in a more complex manner.

On top of this is the fact that this is at the beginning of section 2. While this is in a sense a simplifying factor, since it means that the rhythm starts on beat 1 of bar 1 of the section, it is the case that I had no idea at which point in the phrase length process I would be when the new rhythmic sequence took off. Nor did I, while creating the phrase length process (which was designed at the beginning for the whole piece) have any idea what I was going to do in the new rhythmic sequence section, and vice versa. (If you tried, and I might do this in my dissertation to demonstrate) applying the phrase length filter as though it was one later, starting at 6… you would get a very different result, entirely lacking this emergent clarity).

The result, from a compositional point of view, is then quite contingent, and since I notice this contingent emergence of simplicity on the rhythmic/phrase level before all of the parameters are set (pitch, articulation, etc), I can use these parameters to either highlight or obscure this contingent emergence of simplicity. Likewise the other voices, which enter a little later in rhythmic-mensural canon with this can either further emphasise this simplicity, or they can undermine it in various way. This is represents the composer’s ability to interpret and respond to the results of processes as they emerge.

I would hope also, from a listener’s perspective, that the emergence of this simplicity would sound contingent and obscure. (The fact that the first of these will be taken over by a harmonics tremolo cuts against the unity of the three phrases, but the simplicity of the moment should nonetheless be evident).

This also indicates a basic anti-motivic approach in my counterpoint. ‘Motivic’ sounding moments are contingent and not essential.



One goal I set for myself for my new motets was to develop some form of approach to pitch material.

In Si el clima, I generally focussed on controlling the long-range trajectory of lines, but did not have any structural approach to the specific pitch or intervallic content. What I did on that front was largely intuitive (with the exception of the chordal passage and a handful of passages in the middle section where I had a kind of extended-‘modal’ approach). In general I enjoy the aural results that came from this intuitive approach, but I decided I wanted to develop some kind of systematic way of dealing with harmony, in order to be able to use it for articulating formal development, contrast etc. The somewhat academic question was also in my mind: ‘what form of harmonic structure would suit a modern counterpoint?’

Now, the historical perspective implied by the term counterpoint is a potential trap, and it’s true that a part of my initial thoughts with regard to developing a harmonic approach was to find a way of re-founding the contradiction between harmony and line (the vertical and the horizontal) that in different ways was at the heart of counterpoint in earlier eras.

I am now quite happy to say that this is no longer the aim. I’m not interested in developing a new system of ‘dissonance treatment’ that would regulate the relations between lines (and against which they could push). This is an old logic of counterpoint, belonging to an age that can’t come back. Basically this means forsaking any pretence to a 1-to-1 relationship between composer and audience (or score and audience, or performers and audience). But this is both a good and unavoidable thing in any case: new music is an alienated medium, its alienation still carries great potential, but you have to face up to it first.

What I do want to do is develop an approach to pitch material that heightens my ability to control relations between lines. That is to say, it is part of an overall concept of ‘imitation’ that is increasingly at the basis of my approach to counterpoint.

So, what I decided to do in motets 1 and 3 of this set (motet 2 is a little different, though related), is to set up not one harmonic framework, nor just define certain interval or pitch structures for each line, but instead to lay out three different simultaneous harmonic fields running through the one piece.

This is not dissimilar to the old idea of polytonality or polymodality that people like Ives and Bartok developed over 100 years ago (which reminds me, I should go back and check them out a bit for the ol’ PhD). The differences being: 1) the harmonies are considerably more varied (coming from a variety of different approaches) and extended (including up to 8th-tone distinctions); 2) the control over these harmonies and their development is significantly rationalised (the computer helps here); 3) the harmonies are not generally associated to a rhythmic layer (even if they each have their own structure of harmonic rhythm); 4) their degree of differentiation is itself subject to control, since individual lines can partake of two or more harmonic layers at once. Those differences aside, I am definitely trying to draw in some of that striking cognitive dissonance between two identifiable harmonic layers that you can find in some of Ives’s work.

To be more concrete, in my first motet ‘Sappho/Matilde/Flora’ the three harmonies are laid out thus: 1) An abstract, atonal harmonic field across the entire possible range of the instruments, constructed by an intervallic sequence repeating every 10 semitones, and subject to transformations and transpositions; 2) A folkish layer in D-minor derived from a Spanish funeral march sung during the Civil War, this is microtonally distorted in a fairly random manner, as though the guitar that was playing these chords was going in and out of tune; 3)  A ‘spectral’ band taking every third partial between the 15th and 30th of Db3 (I put spectral in ‘scare-quotes’ because while I start with this spectral chord, I immediately treat the pitches in a more abstract manner, modulating the chord in different ways).

While the first layer covers the entire range of the instruments, the second and third are kept within their respective band-widths: the spectral layer goes from the middle to just above the treble staff, and the folkish layer goes from a low G below the staff to a D in on the second line from the top.

I worked out their various processes of modulation and change of harmonic rhythm in OpenMusic and then exported them into Finale to make a harmonic ‘plot’ of the piece. Here’s what it looks like:

Motet_1 plot

Ugly huh? The export to Finale never really comes off so well…

In general each layer was associated with an instrumental line (themselves representing a different text in the ‘triple motet’), at least initially: the clarinet, crossing a largish register, was the first, abstract field; the flute, weaving around the top of the staff, was the bottom, spectral harmony; and the violin alternated between the abstract layer and the middle, folkish layer.

Across the work, the lines make some forays into each others’ harmonic terrains, thus bringing them closer together in terms of their identity relation, but mostly stick to their own original field.

What this all means is that the resulting harmony is a kind of ‘meta-harmony’ whose verticality is not envisaged as a unified chord, but nor is it completely stratified, or at least not always – plenty of times there will be weird admixtures of the various harmonic layers fusing into something perceptually different.

One thing that these pieces will test is the discernibility of these layers. I’ve tried to make it so that the D-minor quality of the violin line stands out strongly at some points; and the contrast between the 12-tone clarinet and the very microtonal flute (often criss-crossing each other in register), should also be noticeable. But the overall effect of stratification? That remains to be seen. I’m also unsure how much I want it to be discernible. In any case, that’s the experiment at this point.

Three or four methods

Having practically completed the first of my three Mirror Motets (for flute, clarinet and violin) and in the process of writing the next two (all the basic planning done), it might be interesting to write up a few thoughts about the process and how it is all going and what I think about these pieces at this stage. This post I’ll just focus on the basic logic of each different motet, the next ones will deal with other more concrete issues.

Three (or four) methods. 

The first thing to say is that each of the three takes a different approach to the construction of the counterpoint, to test what this means for the listening (and the performing) experience. The initial inspiration was the motets of the late 13th century (‘Petronian’ motets) and those of the Ars Nova and ‘Ars Subtilior’ period, and in particular the double-texted motets (with three texts). I have not really taken any direct models, but tried to find inspiration from these earlier styles to help me define different approaches in my own pieces.

Motet 1.

The first motet is the most basically ‘cantus firmus’ in style of the three. The phrase structure of the flute gives the basic bar structure and tempi to the full ensemble texture. In general its also the slowest moving, as in medieval motets. The other two lines have their own autonomously conceived phrase structures (derived from the texts on which they are based) but these are mediated by (or made to agree with) the flute line. So while the work doesn’t start with a precomposed solo-line to which I add extra parts (as was the basic approach in the 14th century, though not always), nonetheless the basic logic of a hierarchy is there. (The plan remains to write a solo flute piece and then add an ensemble composition around it… but that’s for later). The hierarchy includes a basic tempo ratio between the lines (flute: slow; violin: faster; clarinet: fastest). As in the Ars Nova period, localised imitative procedures cut across this hierarchy…

Somebody who might have been Petrus de Cruce (famous for his 'Petronian' motets)

Somebody who might have been Petrus de Cruce (famous for his ‘Petronian’ motets)

Motet 3.

The third motet is something of the reverse, and perhaps resembles the polyphonic practices of the 15-16th century more closely. While there is still a basic tempo hierarchy, the structure of the work is founded on ‘points of imitation’. Rhythmic imitation is the main player here although other parameters will no doubt come in. At each major section a different line takes up the principle position, giving the metre and the tempo for the rest of the ensemble, and the other voices unfold as a tempo canon.

Motet 2.

The second is the combination of two methods. Firstly, most of the work has no common score. While I have worked out so that the three lines should technically take the same amount of time, they each proceed with a distinct tempo and a distinct metric structure and since the discourse is (well, will be…) quite complex and challenging, it’s unlikely that the performers will have the capacity or the desire to make sure they are ‘in sync’. My attempt will be to compose with as little memory of what I’ve written for each other line, to see what effect this may have (if any!) on the listening experience and the sense of ‘counterpoint’. I have already undertaken this experiment before but that was when I was writing in a much more intuitive and short-range manner. At that time I found that, because of this short-range thinking, the overall result was that things fit together very nicely as though I composed them all with reference to each other. My hypothesis is that there will be a different result this time, since I will have much more long-range planning in each line, and therefore perhaps far more palpable divergences between lines.

My point of reference for this non-synchronised approach is Finnissy’s great piece Nobody’s Jig for string quartet. However, against this, there are two sections during the piece where there will be a score. The logic for these sections will be the exact opposite: all the lines will clearly articulate the same metric structure, in fact it is a kind angry-chorale. Basically to make this work whichever performer reaches this section first sits on a fermata note until the others catch up (or jump immediately ahead as need be). They all hold the fermata chord and cue the next section together. The inspiration for this is the wild opening to ‘First take’ of the album Twins by Ornette Coleman’s Double Quartet.

So there’s kind of 4 basic logics of counterpoint here: 1) fixed hierarchy, 2) shifting hierarchy, 3) complete freedom, and 4) complete interdependency. In my view none are necessarily any less or more ‘contrapuntal’ than any others, since counterpoint is more a perspective and a manner of working than any particular techniques. But what will be interesting will be to see the differences in musical results generated by these different approaches.

Texture types and imitation

Still reading through Courtot’s book on Ferneyhough, which is a little slower going for me since it’s in French, but it nonetheless has a lot of interesting thoughts.

I came across this statement by Courtot the other day:

In Ferneyhough’s polyphonies, no impersonal fusion into a large whole is observable, no more than the inverse, the egocentric desire of the domination of the ego [moi]. For him, in brief, the degree of autonomy of each voice is more important than in Stockhausen: each participant contributes in equal part, and its own part is as refined as the others, up to the point of frenzy. (p. 101)

What is immediately evident is that this continues the long tradition of seeing counterpoint (or polyphony) in terms of a relation between part and whole in which neither is dominant over the other. As I have written numerous times on this blog, to me, this remains the basic ‘idea’ of counterpoint, which must be renewed in different times in different ways. I’m not entirely convinced that, on an aural level, Ferneyhough actually manages to achieve this balance very often, since the complex gestures that he creates in each part tend to fuse on a moment to moment level into gestalt (‘frenzied’) units (albeit internally nuanced). But it is nonetheless true that his constructive process, at least on an abstract level, does give each part its own specificity, while retaining a sense of how they fit together vertically in the texture.

With regard to the vertical dimension of Ferneyhough’s polyphony, Courtot makes an interesting suggestion that texture classes – a set of common parametric characteristics across the ensemble (for instance a particular playing technique) – correspond in a way to harmony in tonal counterpoint:

a class of textures could represent, in a synchronic fashion … different compatible superpositions of gestures inside a polyphony (polysemy). The class of textures corresponds then to a sort of morphological harmony, a vertical constraint applied to gestural, rather than ‘horizontal’, entities. (p. 99)

I think this is an important point. It is definitely true that this approach is a vertical operator which acts as a unifying element between lines, and brings their identities closer together. Yet it is not exactly the same as a harmony, since the tension between the syntax of the total harmonic units and the individual lines is one of the driving forces of the common practice contrapuntal universe. There is no corresponding tension in this idea of ‘morphological harmony’ between the syntax of the part and that of the whole, since there is no perceptible ‘morphological’ syntax in, say, the degree of presence of glissandi.

For me, instead, we should see these texture types in terms of ‘imitation’ rather than in terms of harmony.

In my next pieces Mirror Motets, I am deploying ‘imitation’ in a couple different ways.

In its most essential, imitation is the sharing of parametric structures between voices in a texture. I currently can think of three basic types of imitation: 1) Two or more lines are pre-compositionally assigned to particular vertical structures (presence of particular techniques, common gestural elements, common pitch or interval field), this corresponds roughly to the ‘texture types’ idea in Ferneyhough; 2) ‘Points of imitation’ where, at a moment during the discourse, a process of imitation in one or more parameters begins, starting from one voice to another (e.g. a canon); 3) ‘Hocket’ of whatever parameters, i.e. a single abstract line realised in two alternating voices in the texture.

Each of these are ways of bringing about and controlling the identity relations between the various voices in a texture.

What is missing in all this is the aspect of ‘tension’ between syntaxes. I don’t believe that it is possible, or desirable, to simply replace the old tonal harmonic syntactic system with a new one. Nor is such a pervasive dissonantial system necessary for counterpoint: I don’t feel that counterpoint without a pervasive vertical syntax is somehow less ‘counterpoint’. Instead, what I think should be done, what I am testing out in place in my new pieces, is the entrance of dissonantial relations on rhythmic, harmonic, or other levels, at various points in the work. Rather than a dissonantial system being prevalent the entire time, I would rather see these relations emerge and disappear throughout the work, fluctuate on the edge of presence for a time, and so on. Thus this ‘treatment of the dissonance’ on a broad scale is then but one operator in the overall contrapuntal approach. I’ll come back to this in a future post.


Beginning ‘Mirror Motets’: An initial mission statement

So, I’ve begun writing three short pieces for violin, flute, and clarinet (to be performed, if we can work out the logistics, by the great Sarah Saviet, Hannah Reardon-Smith, and Heather Roche). They’ll be called Mirror Motets: Songs for almost everyone, after the late Eduardo Galeano’s book Mirrors: Stories of almost everyone (which is so excellent I can’t even tell you… read it for yourself).

I will be taking inspiration from various approaches to the motet form (particularly of the late-13th and 14th centuries), which will have an impact both on the form and the method of construction of the pieces. I will talk more about that aspect in a later post, after a little more research into these historical examples. Certainly it will not be a matter of ‘translating’ or ‘updating’ the approach of the earlier styles into more contemporary language, but simply abstracting from these earlier approaches general concerns that might have an impact on our construction of a counterpoint for today.

For this post, I just want to write down a general set of aims for the work. A kind of ‘mission statement’ or ‘manifesto’, or, in the research world, these could if rephrased function as ‘research questions’.

The reflections on (anti-)motivicism and complexity come from engaging with Ferneyhough, via Courtot’s book. However, this is set against a renewed interest in the idea of periodicity, which I’m getting back into by looking at Enno Poppe’s Gelöschte Lieder with Hannah (and through this, remembering Grisey’s contributions). In addition, I’m now beginning to explore the idea of ‘dissonantial relationships’. In all this, one may begin to detect the begins of an influence of OpenMusic software on my thinking and general approach. More on that in future posts, for sure.

So here’s some points for a possible mission statement for Mirror Motets:

  • I want to thoroughly depose the motivic function. Rather than starting out from a basic object and moving to its variations, I want to move from variational techniques, without a discernible primary object, to the emergence of various objects, produced by particular local conditions. Polyphonic imitation should be, in the first place, the imitation of (parametric) development, and only secondarily the imitation of stable musical objects.
  • In this sense, on the level of the temporal flow of the work, I do not want to move, as the sonata or fugue does, from simplicity to complexity, nor its simple reverse, but to start in the middle of a state of complexity, in which realms of simplicity emerge, either with continuity or discontinuity. This formal level will be mirrored on the pre-compositional level: I intend that the process of pre-composition won’t, in general, be the derivation of variations from an initial material, but the planning of various parametric processes and structures that will define the constraints of each line at each section of the work.
  • (This is not to say that I won’t sometimes use a standard variational process, moving from simple to complex, or from original to varied or permuted – it just means that these aspects will not be the basic compositional logic, nor the prime ‘narrative’ aspect, of the work.)
  • A related issue is the contradiction between heterogeneity and homogeneity of the polyphonic relations. On the one hand, placing parametric process rather than parametric structure at the base of the compositional logic tends to suggest unstable linear identities and undermine the possibility of a strong heterogeneity and distinctness of lines in a texture.
  • On the other hand, the flipside of this is that to perceive lines as highly heterogeneous often means that the lines themselves has to be simplified. By this I mean that in order to be perceived as distinct, each line has to have a strongly formed identity, and thus must not have too much internal development or variation. In a three-voice texture, this degree of heterogeneity will likely be heard as a ‘simple’ texture.
  • So here’s the double-bind: complex and changing linear identities will deliver a ‘simple’ texture insofar as they will jumble into a gestural non-polyphony, whereas the most distinct and (in a certain sense) ‘complex’ texture (maximally distinct), will rely on relatively stabilised and simplified identities in the individual lines and will itself end up as a simple texture. It’s a classic case of identity of opposites.
  • My solution to this will be to spend most time in the in-between of these extremes, and structure the work according to the relative weighting of the two poles.
  • Yet this relative identity relations between lines, their parametric distinctness or closeness, their parametric imitation, is only part of the story. This could be achieved in a way that is purely abstract and contemplative. What is required, to achieve a total ‘contrapuntal feeling’ for the listener (at least from my experience as a listener), is the creation of dissonantial relations – ones which can be felt. I’m new to thinking in these terms, but what I imagine is required for this is two or more fairly well recognisable musical structures (processes or objects), which exhibit not maximum difference but certain similarities, a certain relation, set in close proximity to each other. What is important is a sense of ‘subversion’ of the one by the other. This requires the coordination of several parameters, for instance a certain ‘dissonant’ polyrhythm (or rhythmic structure like acceleration vs. stable rhythm) will only be felt if there are enough other similarities between the lines – for instance, though not necessarily, similar register, timbre, dynamic level, etc etc.
  • I don’t think that this type of dissonantial relationship is something that can (or that I would want to) be sustained for a whole work, but it should certainly form a part of it, and I aim to control relative degrees of dissonance in this sense.
  • One thing I do feel is necessary to bring about more dissonant relations between lines is the audibility of periodicity of lines. In recent pieces, I have created fairly elaborate metric structures, which, while having an impact on the construction of the work, do not necessarily deliver the feeling of metre to the listener. In this new piece I want to explore how to move in and out of a genuinely perceptible periodicity, which will help create local frames against which things can be heard as dissonant.
  • On the harmonic level I want to layer, juxtapose and link the following contradictory determinations:
    • Harmonic operators for the whole ensemble (perhaps even multiple, contradictory ensemble harmonic layers) vs. harmonic (or simply intervallic) structures for individual lines
    • Heterogeneous harmonic systems: spectrally-derived vs. intervallic (à la Carter) vs. referentially derived (e.g. Irish folk, etc) vs. instrumentally-derived (e.g. fingerings, etc)

In all of this the thought that comes increasingly to mind is that of ‘liminal’ composition, as Grisey was talking about in the last period of his composing. On a global scale, I’m interested in exploring the following (interpenetrating, though logically separate) contradictions in the work, by way of moving around the limits between each side of the binary (but reversing in priority of conception, the terms, so that what is normally seen as the negative, is placed first):

  • Aperiodicity <-> Periodicity
  • Parametric development <-> parametric stasis
  • Indistinction of lines (by way of information transfer or overload) <-> distinction of lines
  • Non-dissonantial relations (negative consonance, consonance as absence of dissonance) <-> dissonantial relations
    • Lines as independently conceived and then brought into relation <-> lines originally conceived together, in a complimentary manner (on one or more parametric levels)
  • Abstract materials <-> referent/socially concrete materials