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Feldman's "Durations I": a discussion

by Frank Sani

During the course of this essay, we shall be analysing Feldman's 1960 piece Durations I, by means of an inquiry into its overall harmonic and tonal make-up, and by means of observations about its time surface.

The first step is to look at the score. There we see how there is no tempo, and no time signature. There are no bar lines either. The instructions at the back of the score read:

"The duration of each sound is chosen by the performer."

This process of duration independence between parts was already used by Feldman in the 1957 Piece for Four Pianos, and can also be seen in the 1961 piece Intervals. One of two extracts from the latter piece appears in Boguslaw Schaffer's Introduction to Composition tome (Krakow, 1976) and is described as 'asynchronous temporal process'. Such definition applies equally well to Durations I.

In a way, the Durations pieces represent a transition between the improvisational phase of, say, the 1950-1 Projections, and that of later pieces such as the 1981 Triadic Memories where the notational content becomes very specific - especially in respect of rhythm. This implies that in the Durations period, Feldman was experimenting with specific harmonic content, whilst retaining the rhythmic freedom of his early graph pieces.

The temporal independence of each part brings about pitch aleatorism: we cannot predict what harmonies will ensue from the combining of the parts. On the other hand, Frank Denyer tells us (in the sleeve note to the Durations I recording in the Barton Workshop compact discs - see Discography) how

"... in performing Durations Feldman was anxious that individual players should never get too far ahead or behind each other."

In other words, the piece is intended to create specific harmonies or sonorities in spite of the "asynchronous temporal process", and it does so by means of a pitch-specific content.

However, we should bear in mind that Feldman valued orchestration more than precise harmonic content, and saw pitches as mere 'editing'. Such interest in instrumental colour beyond pitch-content, is already evident in the Durations pieces. Here, the pitch content is very specific yet it has no function in itself: it is a means to create instrumental colour .

We ought to mention that another poignant factor in the making of the piece was Feldman's intention to erase the aural memory of the listener, and that is, to confuse the listener's musical awareness of what had come before. It is worth pointing out how such wilful obliteration of reference points became one of the major preoccupations of Feldman's late output - especially in the longer pieces such as String Quartet II of 1983, and Piano and String Quartet of 1985. How can such disorientation of the ear be achieved harmonically? If we were presented with sound clusters of high density, the ear would then register them as sound-shapes rather than chords of specific pitch content. What sort of clusters would be necessary to create non-specific harmonic texture in Durations I ?

Dense clusters would seem the obvious choice, and the denser the better. The densest cluster imaginable would be made wholly of juxtaposed minor seconds. Indeed, if we look at Fig.1 we shall see how ten randomly chosen chords from Durations I - one from every system - can be transposed to form scales of which some present us with mostly minor seconds, others with a combination of a minor second and a wider interval, and only one with no minor second.

Fig.1 Durations I: Overall chords of 10 randomly chosen bars

Comparing the opening chords of the piece - as shown in Fig.2 - with such findings, we realise that the recurrence of the minor second in our randomly chosen chords is neither an isolated feature nor one that occurs simply as a result of transposition to scale format. Take for instance the very first overall chord of the piece: we can observe that from the lowest note up there are five consecutive minor seconds.

Fig.2 Durations I: Overall chords of first 10 bars

More significantly still, the minor second is found also through the horizontal dimension of the piece, and that is to say, along each individual part, albeit this becomes more readily evident only after transposing each part into scalic patterns.

In Fig.3 we find some such scalic transpositions of all the melodic parts (viz. alto flute, violin, 'cello). The piano part is omitted, as it is mostly chordal. The original phrases in the example are on the staves with circled clefs; below each one of them, are the transposed phrases, on staves with uncircled clefs.

Fig.3 Durations I: Scalic transposition of melodic parts

It becomes apparent how of all the recurring intervals, the aforementioned one of a minor second can be said to be most prominent. The alto flute part in Fig.3 gives also the names of the intervals in the original part. By looking at them we understand how difficult it is to detect the minor-second fabric simply through listening: the part leaps up and down disjointedly, in an attempt to elude the listener's intervallic awareness. Like the alto part, the other melodic parts too have such disjointed character.

Another important factor is the following. In order to confuse the aural consciousness of the listener further, each part has a different number of notes in each phrase. For instance, the alto flute part has 3/5/4 notes in the first, second and third phrase respectively, while the violin has 1/6/5, and the 'cello has 7/4/6. This is illustrated in Fig.4, which also shows how the phrase direction (upward/downward) is different in every part and follows no apparent pattern within each phrase. So we see how the non-periodicity of harmonic structures is not the only means employed to create a certain vagueness about the piece, but is helped considerably by the strongly individual outline of each melodic part.

Alto flute phrases
Violin phrases
'Cello phrases

Fig.4 Durations I: First 12 phrases of melodic parts

Thus far we have neglected the piano part. What do we make of it? At first it is easy to assume that it may have the function of reinforcing the melodic instruments, say, by means of chords containing all the pitches of the melodic parts at that moment. Unfortunately, this is not the case, as we can see from the very first chord in the score. What is, then, the function of the piano? Does it simply contribute to the overall texture or colour of the piece, or does it rather have a more pivotal role? The answer seems to be that it has no pivotal role, at least from a harmonic point of view, although it adds greatly to overall texture. It would not be surprising to find that Feldman may have included the piano in Durations I out of sheer force of habit: it will suffice to say, that the composer's early introduction to music came in the form of piano lessons, and that the piano features more or less consistently throughout his oeuvre - from Illusions of 1948 down to Piano, Violin, Viola, Cello of 1987. So even if the piano plays no dominating role in Durations I, we can see how Feldman almost could not do without its textural possibilities and its wide timbric palette.

Let us now concentrate on another aspect of the piece, and that is to say, to what extent repetition is used to determine the overall harmonic outcome in performance.

If we look at the score, we see how every system has a set of vertical structures or, shall we say, chords. There are one hundred and fifty-six such chords. In Fig.2 we can see the first ten transposed onto two staves. This will reveal a tendency observed throughout the piece, against exact repetition: no one chord is identical to the previous one.

It is interesting to notice how later in his career, Feldman became concerned with using several permutations (e.g. inversions, transpositions, &c.) and repetitions of the same harmonic material throughout a piece. Opposed to this view are earlier pieces such as Durations, where Feldman wilfully changes the harmonic content of neighbouring chords to further ensure non-recurrence of identifiable reference points. If Durations I is truly in antagonism with repetition, then there should be no recurring patterns. Yet in Fig.5 (third and fourth systems from the score), we can observe an unvaried repetition of individual tones in certain melodic instruments: in the fourth system, the flute has eight consecutive G sharps, and the violin has seven consecutive F sharps. This is not the only instance: take the repeated D sharps in the violin between fourth and fifth systems, or the Gs in the alto flute in the ninth system.

Edition Peters No. 6901
© assigned 1962 to C F Peters Corporation, New York
Reproduced by kind permission of the Publishers
Fig.5 Durations I: Third and fourth systems from the score

The function of these pedals seems to ensure that whatever the individual pace of the parts, certain harmonies will be heard. If we only think of the pedals in Fig.5, we can see how the F#/G# chord is secured.

The 'cello and the piano parts seem oblivious to the use of such one-note pedals, albeit they present us with patterns of more than one note. In the fourth system, the piano part gives the pattern E/G (see Fig.5). Another example is the piano's three-chord pattern at the end of the first system, repeated early in the second system.

The 'cello too has some such patterns, as the twelfth, thirteenth, fourteenth, and fifteenth notes of the first system (C/F/Db/C), repeated at the beginning of the second system - on different octaves. Another 'cello pattern is in the seventh system, second and third notes (A/G#), repeated three times in that system. In that same system is a three-note pattern in the alto flute part, A/A#/B (second, third, fourth notes), repeated twice and subsequently echoed by a two-note B/A# pattern - all in the same system.

There are many other such instances of pattern repetition throughout the score, which may induce us to re-consider the pedals in the flute and violin parts as 'one-note patterns', so as to view them not as isolated instances but as part of a larger-scale design of pattern repetition.

With the understanding that the pattern repetition in Durations I is a means of ensuring the presence of pre-established harmonic combinations through the piece, it would seem appropriate to investigate (statistically) whether such repetitions would generate certain intervals more frequently than others, once set against the notes of the neighbouring parts.

However appealing, this seems a rather vacuous task. For example, if we applied statistical pitch-analysis to the pitches of each melodic part, we would find that:

  1. in the alto flute part, the most recurring pitch - including grace notes - is A#/Bb (approximately 17.19% out of the total number of pitches in the part);

  2. in the violin part, the most recurring pitch - including grace notes - is D#/Eb (approximately 16.27% out of the total number of pitches in the part);

  3. in the 'cello part, the most recurring pitches - including grace notes - are A and C (approximately 12.39% out of the total number of pitches in the part).

Do such findings tell us anything revealing about the parts? Not really. For instance, the aforementioned one-note patterns in the flute part (eight consecutive G sharps) and in the violin parts (seven consecutive F# sharps) are entirely unaccounted for by a statistical approach. Yet in any performance of Durations I, said patterns would be unmistakably prominent. The same observation could extend to the many-note patterns, as for instance those in the 'cello and piano mentioned on page seven. So we see how unhelpful a statistical approach would be.

Let us now consider Feldman's own directing of Durations I, as found on the Time Records vinyl (see Discography / NB - the recording date is unknown). We are told that Feldman was offered only one side of the record for ALL of his Durations pieces. The performance is 8'20" long, from first to last note. The last 50" have David Tudor (piano) playing alone. Was this what Feldman really intended, and that is, a rushed performance with a relatively long piano postlude? This we cannot tell.

By timing each melodic part individually, it was possible to observe the time each player took on each system of the score. This enabled us to calculate an average pulse or ictus for the whole performance.

It was interesting to notice that:

  1. the 'cello, which has the shortest part in the score, has a TPT (i.e. Total Performing Time) of 7'30". On the other hand, the flute came second after the 'cello with 7'16", in spite of having a longer part. The violin has the shortest TPT of all with 6'28", in spite of having a part longer than the 'cello's;

  2. although there are discrepancies between part length and performance length, the three players never stray too far from one another. As it was said earlier, Feldman was anxious that the players should never be too far ahead or behind of one another. The following timings of the Time Records performance speak for themselves, and prove that Feldman's careful direction succeeded in avoiding the unwanted excessive time-lag between players:

    System no.Alto fluteViolin'Cello
    (TPT for each system)

With regard to the aforementioned issue of the overall pulse/ictus of the performance, it was found that by dividing the TPT of each part - including the piano's - by ten and then adding the four results together, we could obtain an average timing-per-system of 46". Subsequently, such result could be divided by sixteen (i.e. number of chords in every system except the last one - which has only twelve), to give the average speed of performance over each chord. The result obtained was 2.8".

It seems sufficient to say that every performance of Durations I should follow nothing else but Feldman's instructions, which imply both unspecificity of the performance tempo, and absence of a set pulse/ictus. Let us remind ourselves of what the notes said: "The duration of each sound is chosen by the performer." Also, further on, they read thus: "All beats are slow".

We could argue that the James Fulkerson recording (see Discography) is more effective than the composer's own, for it allows more space, with an overall duration of 12'30", and an overall average pulse-per-chord of 4.6". In the sleeve notes to the Fulkerson recording, Denyer suggests a maximum lag between players of between 30" and 45". Theoretically, we could argue that as long as the players kept within an agreed maximum distance from each other, musically speaking, a performance of Durations I could be stretched to any length. Perhaps a much longer performance would enable us to look into the piece as though through a magnifying glass, and to discover new intervallic inter-relationships between parts ...

We are now at the end of this essay, and we should summarise the main points discussed hitherto, thus:

  1. we understand that Durations I is a work which combines non-specificity of time-surface, with specificity of pitch content;

  2. the combining of pre-determined and variable elements in the piece is tell-tale of a transitory phase in the composer's output, between improvisational (graph-)pieces and notationally detailed ones;

  3. we also understand how the asynchrony of pacing from part to part generates an unpredictable wealth of possibilities with regard to the intervallic relationship between parts;

  4. such intervallic relationships ought not to be reduced to predictable patterns by means of statistical analysis, for the simple reason that the latter is immediately proven fallible as we apply it to the pitch content of the individual melodic parts;

  5. we learn from the discovery of repeated patterns, how Feldman intended not to introduce recurring motifs but simply to ensure that certain intervallic relationships take place whatever the individual pace of each player;

  6. there is no certainty as to what such intended relationships might be, although we established the importance of the interval of a minor second both harmonically and (especially) melodically;

  7. we agree that there ought to be an optimal time-lag between players, and that it should not be exceeded, and yet we cannot establish exactly its quantifiable measure for lack of tempo indications - unless we consider the two average pulses, obtained mathematically from the recordings, as viable models.

Finally, we conclude by observing that the piece as a whole may be described as a memory-defying succession of instrumental brush-strokes, which leave a series of diversely-coloured patterns across a time-canvas of static quality. Such sound-patterns appear to contain a thoughtful inner logic which, ultimately, remain inexplicable (save for the recurrence in disguise of the minor second interval).

Truly, the enigmatic quality found in Durations I - a mixture of logical and illogical - is also present in many other works by the same composer, and it is quintessentially Feldmanesque. Let us end with this quote from Feldman's Essays (Epilogue, page 229 - see Bibliography), where Zimmermann, in an interview with the composer, concludes that:

"Your pieces seem ... very enigmatic in a certain sense. If one tries to find out, he won't find out. You really don't know how MORTON FELDMAN composes."


I - Articles

II - Recordings

© Frank Sani 2000

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