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In discussing his 1978 work Why Patterns? Morton Feldman said:
"The most interesting aspect for me, composing exclusively with patterns, is that there is not one organizational procedure more advantageous than another, perhaps because no one pattern ever takes precedence over the others. The compositional concentration is solely on which pattern should be reiterated and for how long ..."Such preoccupation with patterns can be seen in other works from Feldman's later output (e.g. Triadic memories, 1981; Palais de Mari, 1986), of which Piano and string quartet (1985) is one.
During our investigation we shall discuss some patterns found in Piano and string quartet (henceforth referred to as PSQ).
From the '70s onwards, Feldman began to 'glue' pitches together to form melodies. Such compositional interest manifests itself in PSQ, where we observe five melodies in the 'cello part, as shown in Ex. 1a.
If we transposed the second, third, fourth, and fifth melody so that the first note of each matched that of the first melody, we would find that the five melodies are virtually identical - see Ex. 1b. Then we may treat them as one same melody, in spite of the first and last bearing a time signature (9/8) which differs from that of the middle three (3/2).
There seems to be no underlying set of rules for such melodic patterns: each note follows the previous one without change in duration, dynamics, mode of attack, and the intervallic structure seems to be shaped by inexplicably subjective choices. What is, if any, the guiding principle of these melodies?
If we transcribed the first of the 'cello melodies to form a chromatic scale as shown in Ex. 1c, we would accept readily that the interval of a minor second, or semitone, is an element of vital importance.
It would be tempting to include certain piano figures in the 'melodic patterns' group, namely those shown in Ex. 2.
Yet are these 'melodies'? 'Broken chords' seems a better definition. Are these patterns? The 'cello pattern consisted of the repetition of the same element (the first melody of Ex. 1a). This element appeared in transpositions and in different time signatures, thus never recurred twice as wholly identical. Yet on the whole, an overall intervallic and durational outline was kept unchanged.
None of these piano figures appear in such groups as to constitute a pattern: whenever there is an identifiable group of such figures, as in bb. 245-251, for instance, this will not reappear except considerably different. So much so, that we are left to ask the question of whether perhaps it were more suitable considering each piano figure as a pattern itself. We could look at the piano figures and try to find repeated elements within each of them: intervals between tones, duration of tones, anything. What we find is that within each piano figure there are different intervals and different durations, as well as different direction of the motion from each tone to the next (upwards/downwards): in short, there are no repeated elements.
Before we set aside these piano figures, we may take a second look at them and observe how most of them offer three notes which could be re-arranged as chromatic scales. This would provide a link to the 'cello pattern of melodies where we saw how important the minor second interval was. Also, there is perhaps another link provided by the piano figures, which transports us to the quartet parts at the opening of the work. There we find a strong semitone structure in the overall chords played by the string quartet. This occurs at bb.1-9 to begin with, and then elsewhere.
What is interesting about these opening quartet chords is not that they are unique in their semitonal structure: it is that the pitches found therein, namely B/C/Db/D, are the very same ones as in most of the piano figures discussed. Seeing how these quartet chords occur several more times through the work, it would be tempting to ask ourselves whether these particular pitches may offer a pattern of some kind.
It will suffice to point out that in spite of the pitch-correspondence we identified, it is obvious that the intervallic structure of the B/C/Db/D group is what matters: the semitone between notes within individual groups is found elsewhere, and we begin to notice how much of PSQ as a whole is based (harmonically speaking) on the interval of a second.
Let us quote Feldman, as he spoke in 1982 at a lecture in Toronto, Canada:
"I've been living with the minor second all my life and I finally found a way to handle it ..."Looking at other compositions from the 1980s, we notice how PSQ is no isolated instance of Feldman's adoption of the minor second as a pivotal interval. For example, in the 1981 Bass Clarinet and Percussion we notice such trend right from the start of the piece, and persistently throughout the entire work. Similarly, the 1983 String Quartet II opens and ends with four pitches a semitone apart. Yet more evident is the minor second in the opening pages of For Bunita Marcus, written in the same year as PSQ, where only three pitches a semitone apart are used.
This impressionistic approach becomes evident as we look through the score. Perhaps it is best to look at the two quartet chords at Ex. 3. These are the basis for a chordal pattern that begins at b.519 and carries on uninterrupted until b.806, viz. 287 bars later.
With the piece ending at b. 810, it is already obvious that this is an important pattern. Also, these two chords occur earlier in the piece, i.e. at bb. 160-1 and 164-5 (in reverse order), then at 201, 458, 479, 483/5, 509-11.
To understand how the chords are changed in shape through their repetitions, look at the thirty-seven permutations at Ex. 4, which concern the second chord from Ex. 3. The list following the permutations gives the bar numbers for every one of them.
|Chord||Bar nos.||Chord||Bar nos.||Chord||Bar nos.|
|1||160, 161, 164, 165, 201||14||564, 580, 590, 788, 798||27||644, 728|
|2||458, 565, 566, 578, 579, 588, 594, 784, 790, 799, 800||15||567, 577, 591, 787, 801||28||648, 724|
|3||479, 483, 485, 509, 510, 511, 519, 520, 521, 522, 523, 524, 530, 533, 538, 543, 550, 551, 552, 555, 587, 791||16||568, 569, 571, 574, 575, 596, 597, 600, 602, 603, 775, 776, 778, 781, 782, 803, 804||29||649, 651, 653, 655, 658, 660, 662, 664, 670, 672, 676, 678, 680, 697, 699, 700, 701, 704, 707, 709, 711, 713, 716, 718, 719, 721, 723|
|4||477||17||570, 601, 777||30||650, 652, 654, 656, 657, 659, 661, 663, 665, 666, 668, 669, 673, 674, 675, 677, 694, 695, 696, 698, 702, 703, 706, 708, 710, 712, 714, 715, 717, 720, 722|
|5||487, 561, 583, 589, 789, 795||18||575, 573, 576, 595, 598, 599, 779, 780, 783, 802, 805, 806||31||679, 705|
|6||525, 534, 537, 547, 548, 549, 558||19||604, 615, 623, 637, 735, 749, 753, 763, 773||32||682|
|7||526, 531, 539, 544, 545, 546, 559, 585, 592, 786, 793||20||605, 614, 627, 639, 647, 725, 745, 751, 764, 774||33||683, 685, 687|
|8||527, 535, 541, 554, 557||21||606, 613, 622, 636, 642, 730, 736, 750, 765, 772||34||684, 686, 688, 689, 690|
|9||528, 532, 540, 556||22||607, 621, 626, 635, 646, 726, 737, 746, 757||35||691, 692, 693|
|10||529, 536, 542, 553||23||608, 620, 630, 638, 643, 729, 734, 742, 758, 770||36||733|
|11||560, 584, 586, 792, 794||24||610, 618, 629, 632, 640, 732, 740, 743, 755, 760, 768||37||752|
|12||562, 582, 593, 785, 796||25||611, 617, 624, 633, 645, 727, 739, 748, 761, 767||38||771|
|13||563, 581, 797||26||612, 616, 628, 631, 741, 744, 756, 762, 766|
This impressive display of inversions is typical of Feldman's late pieces. The aforementioned For Bunita Marcus is another exquisite example of such inventiveness. Feldman put it this way:
"Actually I just try to repeat the same chord. I'm reiterating the same chord in inversions."Truly enough, the chords of Ex.3 have an inner tension and an almost cadential feel. Yet after a few reiterations, we realise there is no resolution of discords, no cadence, and ultimately no directionality. During these repetitions time stretches to a different level, and we realise that the music has no past or future, but only a present, which consists of the particular permutation being played at a particular point in time. As Feldman explained, the permutations are "... a conscious attempt at "formalizing" a disorientation of memory."
"... there is a suggestion that what we hear is functional and directional, but we soon realize that this is an illusion ..."
The intervallic make-up of the Ex.3 chords becomes clearer if we re-write them in a scalic form, thus:
|= B/C#/D /E;|
It is obvious that the interval of a minor second, which we have encountered in the melodic pattern of the 'cello, is present here too, together with the major second. Such interval is observed in another quartet pattern of two chords (Ex.5).
Re-written in a scalic form, these chords would give us the following:
These two chords are found at bb. 204, 217, 233, 265, 318, 331, 500-2.
One-chord patterns are also found in the quartet parts. Of these, the most prominent is the one found at bb.122-7, 280-8, 298-306. Its pitches, re-arranged scalically, are as follows:
This one-chord pattern is interesting because it involves pitches all a minor second apart.
Let us now turn back to the chords of Ex.3. These two chords are found also in the piano part, permutated, at bb. 208-9, 319-20, 332-3, 456-7, 507-8 (in reverse order). The only difference with the quartet chords is that instead of being within one bar, the piano ones are spread across two bars, so that there is one chord in each bar. Such two piano chords, then, form a pattern, as they are repeated several times.
Other two-chord patterns can be found in the piano part, as listed in Ex.6.
There are also one-chord patterns in the piano part, of which the most obvious example is the opening chord at b.1 (Ex.7a), repeated unchanged at bb.3, 5, 7, 9, 11/3/5/7/9, then permutated at bb.21/3/5/7/9 (Ex.7b).
Afterwards the chord loses its identity as a pattern and is repeated intermittently, for example at b.37 in its original form, then as its first permutation at bb. 47/9, 51/3, 60, after which it is the original chord again at b.72, and then a second permutation (Ex.7c) occurs at bb. 79, 97, followed by its first permutation at b. 107, and by the original chord at bb.115/7. The chord is last seen at bb.443/5/7 (first permutation) and at b.449 (original form).
This chord, in the original and permutated forms, has the highest number of appearances in the piano part, with a percentage of 10%.
By comparison, the most recurring chords of the quartet parts (as given in Ex.3) are repeated much more insistently, with respectively 32% and 33.3% of the total number of bars for the first and second chord.
NB - The piano part 'fills in' between repetitions with its resonances, thanks to the sustaining pedal, so the percentages do not really tell the whole story here.
As far as the intervallic content of the first piano chord is concerned, it is worthwhile taking note that here we find minor and major seconds, once more, as becomes clear by re-writing the chord scalically, thus:
"... The reason my music is notated is I wanted to keep control of the silence ... when you hear it, you have no idea rhythmically how complicated that is on paper. It's floating. On paper it looks as though it's rhythm. It's not. It's duration."Indeed, PSQ is very 'complicated' when it comes to durations. Such complexity derives from Feldman's attitude, in his late works, to keep notated music free and 'floating', rhythmically speaking, as if it were a written transcription of an improvisation. Cage remarked once that Feldman's late works were Feldman playing his early graph pieces.
The 'free-floating' feel of PSQ is achieved, as Feldman said, through a complex and painstaking notation of the intended sound-images. This involves, among other factors, continuous small adjustments of the time-frame, and that is to say, of the time-signatures. It is precisely by looking at the time-signatures themselves that we find how they alternate and repeat to form several patterns, which are listed here:
bb.523-36, 537-43, 544-53, 558-65, 567-77, 579-648.
Bear in mind that these bar numbers do not take into account repeat bars. For instance the last example, if it included all repeated bars, would actually give ninety-four bars. The string of examples shown above is of further interest when we consider that the longest repetitions of the same time-signature occur in coincidence with the quartet parts' 287-bars-long two-chord pattern - which, as we saw earlier on, starts at b.519.
Notably, the aforementioned 94-bars-long example bears the time-signature of 5/4; such time-signature was found to be used about 23% of the times through the score, and that is more than any other time-signature present therein.
Another duration pattern found in the score is of a visual nature, concerning the notational sphere of PSQ rather than its acoustic one. If we look at the first page of the score, for instance, we see how a 'notated' bar alternates with an 'empty' one regularly: this creates a visual pattern of full and empty bars, which in a way is detached from the acoustic reality of the music - if anything because in performance the 'empty' bars would contain sound from the piano's resonances.
Feldman gives confirmation when he says that
"Though these patterns exist in rhythmic shapes articulated by instrumental sounds, they are also in part notational images that do not make a direct impact on the ear as we listen."We know that PSQ was no isolated instance of the visual use of alternating notated and empty bars. It will suffice to take a look at the 1986 piano piece Palais de Mari to notice how there too there is a visual use of 'black' and 'white' bars in alternation.
It is impossible not to mention Turkish rugs when writing about Feldman's late music, and especially with regard to the visual aspect of his scores. At Ex.8 and Ex.9 we have a visual rendition of the whole piece, with the first and second of these examples taking into consideration the outlook of the piano and quartet parts respectively.
Just by looking at these examples, we can begin to see how the 'weaving' of the durational layer of PSQ seems to follow the alternating squares on rugs of Turkish origin. Interesting also, is the similarity between the look of the piano part and of the quartet part up until b.122: thenceforth, there is a discordance between the parts, which begin to show individual patterns of 'black' and 'white' measures. Such disagreement becomes dramatic - at least visually - between b.519 and the end of the piece: while the piano presents the usual alternation of 'black' and 'white' bars, as well as strings of 'white' bars only, the string quartet presents a total predominance of 'black' measures, due to the uninterrupted 287-bar two-chord pattern.
We assume it is for no reason at all, for we must acknowledge Feldman's lack of interest in pitches per se, as he told one of his pupils:
"Timbre and range are the same problem, and both are more important than pitches. When one knows exactly the sound he wants, there are only a few notes in any instrument that will suffice. Choosing actual pitches then becomes almost like editing, filling in detail, finishing things off."Explaining the patterns as we did, focussing away from pitch-theories, would still leave room for other alternative approaches to PSQ. Until then, Feldman holds the key to the modus componendi of this piece.
© Frank Sani 2000
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