Morton Feldman once said that composers make plans and music laughs.
On another occasion, “My definition of composition is: the right note in the right place with the right instrument.”
With these two statements, Feldman infers a unique personal position in recent music—the experimental composer who values empiricism over methodology, and one who prioritizes traditional musical parameters (pitch, timing, and orchestration) over dynamic extremes or extended playing techniques, without denying them.
Perhaps the most continually striking aspect of Feldman’s music is its concentration—its focus on the sonority itself (like Varèse) and its awareness of the phenomenological experience of sound-time, which is mapped with complete precision and logic. In his use of notation, visual analogies and paradoxical relationships are continually exploited to suggest expressive inflections of the sound. Seemingly identical rhythms may be notated in various unorthodox ways. For example: an early piano piece consists entirely of dotted quarter notes instead of simply quarters, somehow implying a different dynamic shape, an inner division into three parts.
In his responses to harmony, Feldman poetically acknowledges the concerns of his time as a struggle between the abstract chromatic series of equal temperament and the tendency of tones to establish a chromatic field with gravitational polarities based on harmonic forces (tonality). His use of transformations applied to chromatic pitch-sets echoes the work of Schoenberg and Webern without relying on the systems of postwar serialism.
“…this could be an element of the aural plane, where I’m trying to balance, a kind of coexistence between the chromatic field and those notes selected from the chromatic field that are not in the chromatic series.”
Between 1977 and the mid-1980s, Feldman composed many pieces in which the spellings of the written pitches, especially for string instruments, evoke distinctly enharmonic variations. Tones, successive and simultaneous, are written in unorthodox ways, occurring as double-flats, flats, naturals, sharps, double-sharps. As in his notations of rhythm, Feldman here exploits the inherently paradoxical possibilities of visually distinct notations that sound ‘the same’, suggesting that they might imply shadings of difference in the sound.
What, then, is meant by Feldman’s use of the pitches Bb and B#, G# and Gbb, all in the first bar of his fragment Composition for violin (1984)? Before answering this question, let me backtrack for one moment to explain how these pieces ended up being performed at all.
Several years ago, Walter Zimmermann drew my attention to Sebastian Claren’s research about Morton Feldman. In his book Neither, Claren mentions two unpublished solo violin manuscripts in the collection of the Paul Sacher Stiftung, Basel. Around the same time, I was invited to prepare a concert program for the series Ars Nova presented by Armin Koehler. I had already been in contact with the Feldman Estate to obtain photocopies of the manuscripts and permission to perform the music. (Special thanks again to the Trustees of the Morton Feldman Estate and to Universal Edition, Wien, for allowing my annotated versions of the score to be published along with this text.)
Some months later, I received an envelope with three photocopied pages. One was the completed, dated and titled score For Aaron Copland (1981), a concise monophonic composition consisting entirely of diatonic white notes (no sharps or flats). It was the other two pages, however, that really aroused my interest—an untitled fragment dated 1984, possibly the beginning of a larger solo violin work for Paul Zukofsky which had been abandoned in favor of Violin and String Quartet. The intriguing texture of this piece consists almost entirely of double-stops grouped in pairs, forming progressions which are always immediately repeated. These structures recur unsystematically throughout the score in various constellations. Immediately remarkable are the extremely unorthodox pitch-spellings—among ‘normal’ intervals like perfect fifths and major thirds are strange triple-diminished fourths and double-augmented thirds.
At this stage in his work, Feldman had recently completed major pieces for violin, including Spring of Chosroes (1977) and the 75-minute piano-violin duo For John Cage (1982) written for Cage’s 70th birthday concert and premiered by Paul Zukofsky and Aki Takahashi as Symphony Space, New York. No doubt his conversations with Zukofsky and his familiarity with John Cage’s contemporaneous use of enharmonic spelling in Cheap Imitation (1977) would have inspired Feldman to compose shadings of intonation ‘on the edge’ of the tempered chromatic intervals. But exactly how did Feldman expect this notation to be interpreted?
Feldman was certainly aware of violinists’ expressive use of intonation, referring on one occasion to Heifetz’s “Jewish octave”. In conversation, Zukofsky has related to me his own model of intonation in practice, which loosely describes equal temperament “in the middle,” Pythagorean tuning based on acoustically just fifths “on one side” and Meantone tuning based on acoustically just thirds “on the other side.” With his legendary precision, Zukofsky was able to flexibly articulate intervals in pure tuning as well as micro-subdivisions of the tempered scale.
Roughly speaking, his Meantone model is similar to Leopold Mozart’s advice that in ensemble playing one should “take the flats higher and the sharps lower” to achieve harmonious intonation, without necessarily detuning the open strings to produce narrow Meantone fifths (tempered by 1/4 Syntonic Comma). Pythagorean intonation (which many violinists know as melodic “expressive” intonation) is based on the opposite principle: raised leading tones, narrow semitones, high sharps, low flats. This paradoxical situation between melodic and harmonic tuning led some 20th-century violinists (including Rudolf Kolisch and members of the LaSalle Quartet) as well as Arnold Schoenberg to respond with an unequivocal advocacy of Equal Temperament as the “modern solution.”
Given Feldman’s close relationship to the piano, the most “naturally” equal tempered of instruments (for which he occasionally notated double-flats and double-sharps as well) one might consider interpreting his accidentals as expressive inflections which can be realized without altering the pitch. This is certainly possible. An examination of For John Cage, however, reveals a far more liberal and specific use of enharmonic notation in the violin part. There are several examples of a phrase undergoing immediate repetitions with variations of spelling. This indicates to me that he felt a violinist would be able to interpret such signs and vary the intonational shadings.
Assuming, then, that the accidentals can be read as variations from the tempered chromatic field, how can a player interpret these in the absence of any specific directions? Clearly, the two concrete starting points would be Zukofsky’s models which Feldman must have known about. But which one? Zukofsky suggests that Feldman’s intention was Meantone while Claren has argued for a Pythagorean interpretation.
In the violin version of Cage’s Cheap Imitation, the Pythagorean Tuning is specified. It adds piquancy to the chance-derived modal transpositions and melodic structures taken from Satie’s Socrate, which are largely based on tetrachords (perfect fourths divided into whole-tones and semi-tones). Playing instructions suggest that the tuning should not necessarily be realized precisely, rather at times exaggerated for expressive effect, to delineate and microtonally inflect the melodies. In general, it is a good choice for melodic music in which the acoustical purity of the perfect fourth, fifth, and whole-tone are most important and an expressive distinction between lowered flats and raised sharps is desired.
In music where many double-stops are notated, a completely different logic must come into play. Simultaneous tones are acoustically drawn into special relationships which do not always conform with Pythagorean intervals or tempered tunings, instead depending primarily on how closely the ratio of the sounding frequencies approaches a simple rational number (i.e. a frequency ratio of 2:1 produces an octave). These special relationships are the basis of Just Intonation (JI), which is a term to describe the infinite micro-variations of tuning which the ear can perceive as harmonic relations between different tones.
Aspects of JI have formed part of the theory and practice of various world musics. Ancient Greek, Indian, Arabic, Chinese as well as European music have all considered how we hear tuned pitches forming melodic and harmonic relationships. For example, the melodic practice of Indian ragas is largely based on a set of 22 tones tuned above a drone in various JI ratios produced between the first ten pitches of the overtone series and their octave transpositions.
In Europe, Helmholtz’ publication of Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (1863) and its translation into English by Alexander Ellis (1875) inspired serious experimentation with JI amongst interpreters, instrument-builders, and composers. The initial musical research focused on pure tunings of the traditional chords based on the first six overtones, using prime partials 2, 3, and 5, and sometimes called 5-limit Tuning. In the 20th century, various composers (notably Harry Partch, Ben Johnston, La Monte Young, James Tenney, among others) have expanded this model to include new tuned sounds generated by higher prime partials, inventing the concept of Extended Just Intonation.
However, up until now, two main obstacles have slowed theoretical advances in this area. The first is notational: to date there has been no generally accepted method of reconciling conventional staff notation with the infinite variations of tunings. Standard European notation has been based on ignoring comma-sized differences of tuning, assuming that instruments of flexible pitch would make “appropriate” corrections anyway, while any successful system of JI notation would have to explicitly differentiate them. For example, consider the notes C and E played as open strings which have been tuned in a series of perfect fifths C-G-D-A-E. The interval produced between them is a comma larger than the pure major third, also written C-E.
The second obstacle has been a conceptual one: a mistaken idea that just intonation cannot “work” musically. In spite of music’s willing embrace of complexity in the parameters of instrumental timbre and rhythmic timing, a similar rigor has been avoided in the dimension of pitch and harmony. It is important to note that untempered tuning in no way restricts modulation. In fact, as in tempered tuning, any tone can be taken in any one of many harmonic contexts, and there are many tones which are enharmonic near-equivalents. What Extended JI offers is a wider palette of precisely-tuned and focused sonorities, consonant and dissonant, ranging from simple to extremely complex.
In my recent musical work, I have attempted to consider and address the practical development of intonation. (see Intonation and Microtonality) Together with Wolfgang von Schweinitz, I have co-developed The Extended Helmholtz-Ellis JI Pitch Notation, a system of accidental signs which allows pitch relationships to be written precisely using standard five-line staff notation. (This notation also allows for accurately-written tempered and irrational pitch relationships by incorporating Alexander Ellis’ notion of dividing the octave into 1200 tiny micro-intervals called “cents”). For a legend of this notation, a text describing it in detail, and various charts of pitches, see www.plainsound.org under the heading “research”.
For each interval in Feldman’s Composition for violin (1984), I interpreted his spelling by choosing a tuning in Extended JI. Since each bar repeats immediately, and then recurs later in the piece, it seemed to me more beautiful (and enjoyable) to notate a tuning for each pattern, rather than finding approximate shadings on the fly. For the most unusually spelled intervals, this meant finding “new” tuned sounds which I could reproduce reliably. At the same time, I often chose complex intervals which (in practice) would be subject to interpretative variation, as I believe Feldman would have preferred to any fixed solution.
As a starting point, I assumed that traditionally-spelled intervals would be tuned in the simplest way possible: a fifth would be a pure fifth (like the open strings) and a third would be a pure major or minor third, based on how violinists retune chords naturally. I avoided the exclusive use of any particular system (Meantone or Pythagorean), allowing context to dictate an “interesting” tuned sonority. First, I considered the size of the written interval, preferring a quasi-Meantone understanding of the accidentals which assumes sharps are relatively lower than flats. Then, I looked for nearby overtone-series based relationships from the prime partials 3, 5, 7, 11, and 13, choosing ratios which produced complex intervals that can be tuned by ear.
As I began the process of practicing to play these intervals, I realized that I would have to compose new pieces for myself to learn to accurately construct and hear the unconventional intervals I had notated. I thought of writing music in which the process of tuning would somehow become a subject in itself: a series of intonation studies, not unlike Feldman’s own early piano pieces, or perhaps Nancarrow’s player-piano studies, mapping out small corners of the new and unfamiliar terrain.
In particular, I became interested in discovering the enharmonic possibilities for modulation between different fundamentals—tuned tones which were identical or nearly identical to tones with completely different harmonic derivations. Such constructions enabled me to produce the more unusual sonorities, especially the quarter-tone and third-tone intervals involving prime partials 11 and 13. This project has developed into a book of music in just intonation for violin, containing solos and also duos with other instruments, titled Les Duresses.
Marc Sabat is a Canadian composer and violinist living in Berlin since 1999. He has written concert music for various ensembles including acoustic instruments, live computer and electronics, as well as making recorded projects involving sound and video (installation, DVD, and internet). He has recently developed The Extended Helmholtz-Ellis JI Pitch Notation and is currently teaching a course in acoustics and experimental intonation at the Universität der Künste Berlin. Sabat also performs chamber music and solo concerts and has recorded music on various labels including mode records, World Edition, and HatArt. Marc Sabat studied at the University of Toronto and the Juilliard School of Music in New York.
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