XIX Elements of logic
for wind orchestra, by Jos Kunst and Jan Vriend (1972)

by Jos Kunst and Jan Vriend (1975)

Comments to the LP Composers' voice DAVS 7475/3.
With thanks to Jan Vriend for his permission to include this text.


The main reason for doing a composition together was due to the wish to objectify the production process, not so much in view of compositional techniques, but rather in view of the prominent and decisive part which has always been pfayed by intuition, even in the most rational compositional processes.

We trust intuition: it will not fail to stand scrutiny, and the myth that reason might lead to elimination or paralysis of (irrational) feeling, is no longer accepted, not even in psycho-analysis where once this trend was in vogue. On the contrary, we are convinced that it must be possible to bring about an operative contact between vital intuition and sound reason, being an advantage to both. For that reason we did not make any division of labour as far as musical decisions were concerned.

Our first concern was to find a system in which any decision was to be made in an atmosphere of criticism and control towards the results of the several methods of production.


The title 'Elements of Logic' suggests a textbook. It shows that 'musical thinking' will be brought up for discussion by the composition, and in addition that this will take place in an 'elementary' way.

Our starting-point was that in music ambiguities function as the main catalysts of thinking, that all activating musics live by them, and that our composition should entirely be concentrated upon the treatment of several ambiguities, upon the anticipation and the steering of the musical thinking of the audience in relation to the ambiguities at issue.

What is ambiguity? Not: vagueness. To give a very simple example: Think of an opposition-axis extending from high to low. A position somewhere in between high and low does not raise real ambiguity.

A position within two perspectives at the same time (high and low), however, does. For example: c' (at the keyhole of the piano) is high for a tuba and low for a flute. The two ways of understanding c' are both convincingly present, the one excluding the other. In such a case thinking is forced (or induced) to switch to a higher level in order to find a solution. Simple parameters are replaced by less simple ones, or few parameters are exchanged for more, i.e. new parameters are discovered (created). In our example it might be necessary to split our idea of pitch into more areas of reference, e.g. into the two widely diverging instrumental ranges.

(Another example: The pivotal chord of a modulation is first heard as pertaining to one key and later on to a new key as well, so to two keys at once.)


The 'Elements of Logic' are, as far as the concentration on ambiguities is concerned, a work dealing with musical logic. The first part of the title is suggested by their somewhat loose developments in form: they remain 'elementary'. In this respect the Elements of Logic make the impression of being a book of illustrations of the musical situations they deal with: the ambiguities. (By the way, illustrative books can be entertaining, and good ones are.) For that reason the overall form is, in its particular way, indeed effective, though less problematic, less 'peculiar' than might be expected because of the application of certain materials. The developments in tension are relatively normal, which yields the advantage that there is ample room for distinctly different treatments of ambiguity in various places in the composition.

Thus we find in the bars 106-130 a chain of short musics, each of them rendering, as clearly as possible, an ambiguity which is as elementary as possible, whereas, strictly speaking, there is not any specific follow-up. The (potentially) newly created rooms for thinking are not really made use of (compare the examples further down).

The polyphonic musics covering the bars 60-106 may be regarded as the antipole of this way of treatment. Here the starting-point is functionality, the results of ambiguity processes, and the very moments on which every individual listener hears his brains cracking do not exactly depend on any definite musical moment. We will come back to this in the following examination of the composition from the beginning to the end.


  1. Bar 1-13

    Main ingredient: a music of maximal energy which is produced by the brass instruments. Distinct courses are run among three levels of pitch (high, medium, low). In principle the courses are run straightly, without accidental curvings; length and tempo of the steps are dosed, however.

    By-ingredient: woodwinds (functioning as the overtones of the brass instruments) are gradually brought in from bar 6.

  2. Bar 13-30

    Main ingredient: blocks of instruments (immobile in themselves), yielding an outline of differently shaped triangles. The result, when connected with the main ingredient of A, is our first great ambiguity (immobility/mobility). The idea of movement, which has been realized in a primitive way in A, is now realized in a new, paradoxical way: though every instrument is immobile, a linear movement (compare A) is effected by the contour lines of the group. The idea of movement is shifted from individual to group.

    By-ingredient: long strata, developing crescendo, are constituted by the woodwinds from A. Crescendi are gradually alterated into decrescendi: a primitive transformation.

  3. Bar 31-42

    A contour music issuing from the by-ingredient of B, in which, contrary to the triangles of B, in horizontal perspective 'soloists' (see bassoon 1, bars 31-33) and in vertical perspective totally synchronized chord shiftings (see bar 38, final beat) are released or are not. (New possibility: something 'happens' without linear consequences. Also compare F.)

  4. Bar 42-60

    An elaborate statement concerning the ambiguity 'low/not low' is made in the weak musics for flute, which concentrate as much as possible on low pitches (bass flute! — pay attention to the vertical effect of the musics, realized e.g. by consonance); due to the extremely low position of the other instruments, however, they attain a kind of floating position — giving the impression of height — weightless as it were, like a vapour. This situation is combined with the relative tranquillity and slowness in the pseudo height (flutes) and the frantic micro-activities in the 'real' lowness. The big instruments behave like small ones, and reversely.

    From bar 52 interruptive, autonomous musics are introduced in order to prepare E.

  5. Bar 60-106

    In various respects this part may be regarded as the climax of the composition. It is also the most difficult part for the audience. The building-up (60-70) is succeeded by a constant 'polyphony of musics' (except bar 79-82); though their number had originally been stipulated to six by the 'bare machinery of the composition process' we would rather call them indeterminable for various reasons.

    The only way to 'follow' the music is to behave like a spider-monkey making its way through the jungle: the audience should swing from one grip to another. The polyphony has been organized in such a way that the participating musics provide various degrees of 'grip'. Thus, for example, three out of the ten parameters (see Fig.1), which have been chosen because of their elementary character and their unlimited qualities to effect mutual combinations, and which are to keep the six musics apart, affect the degree of presence of these musics in a decisive way.

    For example, a music containing 'many' instruments, 'synchronic' chords and 'periodical' rhythm, is incomparably more present than a music containing few instruments, which, in addition, play a-synchronically and a-periodically. Because in every parameter three out of the six musics invariably play towards one extreme (or away from it) and the three other musics to the other extreme, there will always be a number of musics showing a tendency to hide behind the others, to sneak round the back and to emerge on the other side. In such a context the audience are liable to get lost among the contrasts which are effected by the musics mutually on the one hand, and the contrasts among the ingredients of one music on the other hand; thus it might happen that the suddenly occurring monophony (= one music) in the bars 79-82 does not make an essentially different impression from the music in the preceding bars, which proves the audience's ambiguous orientation with regard to the polyphony of instrumental groups, which are 'closed/not closed'. (This situation is also promoted by the continuous instrumental alterations in them.)

    Another important factor is that the music, instead of altering gradually, may turn the other way round abruptly: in such a case it will convert to the opposite in all parameters, which is of course fatal for the following of the music in a traditional sense A definite music suddenly links up with various other musics: ambiguity.

    A final factor of importance is the tempo in which the musics (gradually) evolve. When bar 106 comes near, the tempo in one of the musics becomes slower and slower, whereas it is speeded up in the other five musics. On page 35 8 x 5 = 40 musics are realized within three bars, overlapping each other in five strata, the result being the global contrast between one slow music (crescendi in horns and saxophones) and the other 40 musics as an entity.

    However, the speed of the evolution that is now destroying polyphony has been attained gradually. Consequently every individual listener must have known a moment in the past that initiated his hearing five out of the six musics as an entity: a moment of ambiguity.

    Fig. 1 (if the table is unreadable, please use this version)
    Pitch high <------> low
    (consonance) dissonant <------> consonant
    narrow <------> broad
    Rhythm rapid <------> slow
    periodical <------> a-periodical
    synchronic <------> a-synchronic
    Instruments many <------> few
    homogeneous <------> heterogeneous
    Forms of articulation homogeneous <------> heterogeneous
    Dynamics homogeneous <------> heterogeneous
  6. Bar 106-130

    Main ingredient: a chain of short musics, mentioned above, in which the elementary parameter-oppositions, forming the basis of the polyphony in E, are affected and estranged one by one in definite musical situations. Numbering the musics according to the numbering in the score, we schedule F in the following way:

    Fig. 2 (if the table is unreadable, please use this version)
    AP 13 8 11 15 4 12 3 5 17 22 6 21 1 19 7 20
    high – low   x     x   x       x   x x x  
    dissonant – consonant               x     x          
    narrow – broad     x x x     x x x            
    rapid – slow         x x     x       x      
    periodical – a-periodical x             x               x
    synchronic – a-synchronic       x x       x   x x x x   x
    many – few (instruments)     x x       x x x     x     x
    homogeneous – heterogeneous (idem)     x x x   x   x x   x     x  
    homogeneous – heterogeneous (articulation)                   x         x x
    homogeneous – heterogeneous (dynamics)     x   x     x x     x       x

    The 'neutralized' parameter-oppositions of each music (AP in the score) are indicated.

    Remark. Generally speaking language (words) on the one hand and music on the other hand are badly co-ordinated. This might cause the audience to qualify the music of F, at first hearing, as 'peculiar'. Most probably the qualification will apply to the ordering effect of the short musics. The listener first has to perceive that some musics show a peculiarity in themselves, to make the consulting of Fig. 2 useful in order to check whether the mentioned parameters indeed bring about these effects.

    By means of the marked parameters an attempt has been made to indicate the ambiguity per music.

    When we take AP13 as an example, we find that periodicity (in each of the several winds: bass clarinet I, horn I and baritone saxophone I) and a-periodicity (by means of shifting = mutual interference) are both present (compare church-belIs).

  7. Bar 130-end

    In this fragment the independence of the applied parameters is brought about in a new way, namely by means of a-synchronic interactions: changes in every separate parameter are effected as a-simultaneously as possible. The mutual independence of the parameters is tested in the extreme: parameter-polyphony. Dynamics are 'frozen' on ppp.

    In a new context we are presented reduced, weakened and de-stabilized (see NB on page 44 in the score) versions of material we know (it occurred in E), constituting one stratum of fragments merging into each other. Everything we hear, we 'did/did not' hear before. The duration of the final quint chord is so long, but besides so well-prepared in the final bars, that is 'does/does not' seem to disengage itself entirely from the preceding, continuous, transformational music: a pseudo coda attached to the real one.