The Treatment of Random Pitches in Frank Zappa’s 'Approximate'


Richard Hemmings (aka Evil Dick)

paper addressed to ICE-Z (International Conference of Esemplastic Zappology) 16 January 2004 at Theatro Technis, Crowndale Road, Camden Town, London


This paper begins with a general overview of the randomising techniques deployed by Frank Zappa, one of the few composers to experiment with randomness and contribute genuinely new approaches to its use in popular music. Zappa’s use of randomness was inspired as much by the Dada movement of the early twentieth century, as the avant-garde New York composers of the 1950s. It played a part in his assault on the limitations of the Top 40 song format and the steadfast rules of formula pop. The final section of this paper contains an analysis of 'Approximate', discussing how Zappa went about notating random pitches, and aspects of its performance. Prior to this, as comparative material, and to provide an historical perspective, three avant-garde compositions from the twentieth century will be briefly explained: two pieces by Marcel Duchamp, both called Erratum Musical (1912/1913), and Intersection I (1951) by Morton Feldman. These compositions are relevant because, like 'Approximate', they are concerned with the randomisation of pitch as a means of breaking from tradition.


Frank 'Random' Zappa

The motto of Zappa’s 1988 tour band, 'Anything, Anytime, Anywhere – For No Reason At All', is also a summary of the way he deployed randomising strategies in live performances and recordings throughout his career. In concerts, the purpose of embracing chance occurrences, indeterminacy, improvisation and audience participation, was to forge a unique experience in contrast to the fully composed sections. It is no coincidence that Zappa appeared on the John Cage tribute CD, A Chance Operation (1993).

Without Cage, Zappa said, much of what takes place in modern music and art 'would not be possible'. [1]

In the late-1960s, Zappa pointed to Cage as the inspiration behind an indeterminate piece of music theatre in which Mothers’ saxophonist, Motorhead Sherwood, talked banally about working in an aeroplane factory, suping-up cars, and his various girlfriends [2]. That Zappa was using Cage’s strategies within popular music made them especially resonant since in this context they found a new audience.

Understanding the excitement unpredictable forms of behaviour could bring to a live event, Zappa encouraged concert audiences to get involved. This often resulted in some form of unplanned mayhem. During a concert at the Royal Albert Hall in 1968, a member of the audience climbed on stage with a trumpet. Possibly making the mistake that free jazz was easy to play, the interloper was left flailing behind when the band joined in. Zappa captured the incident on tape and released it on Uncle Meat (1969) [3]. Recordings of live events also caught the occasional audience outburst. The unsettled fan, heard shouting from the back of the concert hall at the end of Burnt Weeny Sandwich (1970), was a forerunner of the rioting Italian audience Zappa dealt with at the end of the 1982 tour [4]. Unrehearsed, unplanned moments offered performances of the older repertoire a new identity. Before going on tour, Zappa would spend months rehearsing his group to the point of perfection, inserting and removing eyebrows as he saw fit. But when it came to live albums, Zappa was only too happy to include the version with the unexpected 'humour-something', the reveller, the tear gas grenade, the 'fucked-up' lick.

'Approximate' is essentially indeterminate; that is to say, some of the decisions regarding its performance are left to the musicians. In some respects, all notated music is indeterminate to a degree; the fact that scores leave room for interpretation is a mark of this. However, scores that utilise regular notation do not aim to sound completely different at each performance, whereas indeterminate works usually do. Although indeterminacy in music can be traced back as far as C.P.E Bach, it did not really penetrate the art form until the 1950s, when Cage and fellow composers, Morton Feldman, Earle Brown and Christian Wolff began investigating ways of incorporating chance. The idea of allowing pitches to be decided by the performers is also common to jazz. At around the same time, Charles Mingus is known to have created scores that allowed musicians to choose harmonising pitches from a selection. The aim here was to diminish repetition [5]. The initial seeds, however, were sown some thirty years earlier in Switzerland.


Erratum Musical

In his book Dada: Art and Anti-art (first published in 1964) Hans Richter tells the story of how Dada painter and collagist Hans Arp supposedly first came to use chance techniques. Dissatisfied with a drawing he had been working on for some time, he ripped it up, allowing the torn pieces of paper to fall to the floor. Later, he noticed that the pattern they formed on the floor seemed to express what he had initially been aiming for [6]. Richter states:

Chance appeared to us as a magical procedure by which one could transcend the barriers of causality and of conscious volition, and by which the inner eye and ear became more acute, so that new sequences of thoughts and experiences made their appearance. [7]

With regards to the development of compositional techniques that incorporate chance, the Dadaist Marcel Duchamp is important. Although he only composed two pieces of music, calling them both Erratum Musical, they contain the origins of the principles later adopted by Cage, and in turn, Zappa. In the first:

[…] Three people pull notes out of a hat and place them in order on music paper. Each note is sung slowly – the singers follow the same tempo. The text for these random harmonies is the dictionary definition of the verb to print (imprimer): 'Faire une empreinte marquer des traits une figure sur une surface imprimer un sceau sur cire' (To make an imprint mark with lines a figure on a surface impress a seal on wax). [8]

The piece allows for some interpretational leeway; if pitches turn up outside the singer’s range they maybe performed approximately. The score of the second Erratum Musical exists as a description of how the piece should be carried out. It can be performed on virtually any instrument. In addition, some peculiar bits of equipment are required: a large funnel, five toy train wagons (open and connected) and numbered balls, one for each timbre or pitch the instruments can produce. The performer assigns a time period to each of the five wagons. The balls are then poured into the funnel and allowed to fall at random into the wagons as they are pulled underneath. Balls that fall outside the wagons are discounted. Upon completion of this task, balls are removed from each wagon, at a rate proportional to the time period allocated to the wagon. Dynamics are left to the performer to decide. The final result is a piece of music in five sections, however, Duchamp allows the process to be repeated any number of times, making it essentially unfinishable.


Intersection I

Duchamp’s attempt to create random music produced, in his own words, 'a very useless performance in any case', but his influence on Cage and associates was profound. In both Erratum Musicaux pitches are chosen using a chance procedure to prevent performers controlling the order they are played. In contrast, Feldman’s Intersection I places the note choices in the hands of the performers; not a single pitch is defined. Whereas Duchamp was strict about each pitch being heard only once, Feldman opens up the possibilities by allowing note repetition, so that the chance of two identical performances becomes even more unlikely. Scored for large orchestra, the piece only contains four parts: one for wind instruments, one for the brass instruments, one for violins and violas, and one for cellos and basses. Each part indicates three ranges of pitch high, middle and low, the limits of which are determined by the performers. The simplistic look of the score, free of dynamic markings and fixed durations, belies the difficulty of a successful interpretation, which depends heavily on the skill and imagination of the performers.

Although Feldman provides instructions to play high, middle and low pitches (providing all the information required to generate simple melodic shapes), the piece is essentially an investigation of abstract sound rather than chance melodies. This is of particular relevance to the next section, where Feldman’s use of pitch ranges can be compared to Zappa’s treatment of pitch in 'Approximate'.



The first public performance of 'Approximate' took place on 10 September 1972 at the Hollywood Bowl, home of the easy listening 101 Strings Orchestra. Third on the set list, Zappa described it as the most 'far-out' [9] piece performed. Four parts are shared between twenty musicians, generating an arrangement in much the same way as Feldmen’s Intersection I. Zappa explained the process to his audience:

There is one page that is for all instruments in C and F, including percussion. There's another page for all the instruments in E flat and B flat and elsewhere and then there's a bass part and a drum set part, which combine the rhythms of the other two. The only thing that is indicated in the score is the exact rhythm […] that is supposed to happen for most of the piece and all players get to choose their own pitches that they play. So... it randomizes a certain bit. [10]

Subsequent versions of 'Approximate', performed by various incarnations of Zappa’s rock band, have since been released, with one on Zappa In New York (1977) and two others in the You Can't Do That On Stage Anymore series Vols. 2 & 4 (1988). There is also a version on the video release Dub Room Special [11]. The score, the majority of which omits pitch information, contains the type of rhythms Zappa went on to perfect in pieces like The Black Page. By removing the importance of pitch, the score is open to interpretation by any instrument, allowing an unusual type of flexibility when generating arrangements. Here, a comparison with Duchamp’s Erratum Musical for toy wagons and numbered balls is relevant. In the Stage II version, Zappa turns 'Approximate' into movement theatre, his band performing the score with their feet. There is also a version for voice, in which singing the most stomach-warming [12] dissonances would seem to be the prerequisite.

With musicians able to make different pitch choices each time, there exists a greater degree of freedom to explore harmonic possibilities. In later versions, the randomness of 'Approximate' seems to become less of a feature. The speed of the 1974 Mothers’ rendition indicates that initial random note choices, possibly decided upon during rehearsals, had become fixed parts of the score, there being less noticeable variations between different performances. Arthur Barrow, Zappa’s eighties bass player, contests this:

Like most of his music, Frank was always experimenting and changing things. Perhaps some players picked random notes they stayed with, but I think they mostly stayed random. [13]

My initial investigations conducted without a score involved comparing the Stage 2 version with the Stage 4 version to differentiate between random and composed pitches. This proved problematic, with both versions structurally at odds and performed at dramatically different speeds. Close listening revealed a number of mutual characteristics. Both versions share an introductory three-and-a-half bar long, reiterated B-flat motif, which instantly establishes itself as the tonal centre. Zappa stated that the fixed pitches were deployed 'for the sake of contrast' [14], but the effect they have is much greater, since they contain some of the longest durations in the piece [15]. The majority of the random pitches occur in jittery groups of semiquaver tuplets, which move too fast to establish any tonal stability. Despite this, there are moments in both versions that sound distinctly like descending sequences [16]; the Stage 2 version even sounds like it contains repeated phrases.

When Zappa told his audience that the piece was randomised a 'certain bit', he was talking about the degree of randomness: the dichotomy between the pitches with a designated register and those left to chance. Upon analysis of the score, the randomising process becomes clearer. Using a traditional staff, a series of markers (shown as crosses, instead of dots) indicate a predetermined, melodic contour.

These are markers that show, by their positions, the approximate register for each instrument. [17]

Compared to Feldman’s use of high, middle and low pitch ranges in Intersection I, 'Approximate' places greater control over the melodic shape. With the approximate shape of the melody given, the musicians simply follow its undulations. This provides a possible explanation why the listener can perceive sequences and repetitions; musicians often play melodic shapes on their instruments, and these can easily be transposed at random intervals. In larger ensembles, such features would be less obvious due to the increased timbral density. Interpretation of the score becomes interesting during moments where the melodic contour levels out. These flat sections give the impression that a random pitch ought to be repeated, and this is what happens in both Stage versions. However, there are no instructions in the score to suggest this is the case, leading one to conclude that in fact, it merely implies the same degree of randomness as elsewhere in the score.

(NB: The next section, on conceptual continuity as a pseudorandom process, was not presented at ICE-Z because it is slightly off topic. But since it utilises 'Approximate' to make its point, the decision was made to include it here as a kind of 'bonus track'. )


Pseudorandomness, Conceptual Continuity and 'Approximate'

The randomness of conceptual continuity is a matter of perception. Strictly speaking, it is the type of pseudorandomness described in cryptography as obscure complexity. All the clues are present but the patterns are so complex and intricate that the end result is one of perceived randomness. For example, in the 1982 live version of 'Approximate', members of the group replaced parts of the score with the following vocal lines:

(1) Heinz, Heinz…

(2) Make food.

(3) Ah-Oh-Eh-Ah…(Ieee!)

(4) Dagmar, Din-din!

(5) Stayin’ alive - Ah, ah, ah, ah

(6) There’s a ‘39 Buick blocking the driveway.

To the occasional listener of Zappa’s music, this most likely reads as six lines of postmodern, deconstructed irrelevance, when in truth, each line is packed with cross-references and themes relevant elsewhere. Watson makes a valid argument for Zappa the modernist by raising this point.

Conceptual continuity may well serve as a term for an underlying substratum of associations that anyone uses over the years in order to express themselves – the network of meanings revealed, say, in Samuel Taylor Coleridge’s notebooks, which show irrational attachment to words that appear at key points in his poems – but what makes Zappa’s use of it modernist is that he brings this substratum to consciousness. [18]

It is difficult to assess the spontaneity of the vocal lines without comparison to other performances from around the same time, none of which are currently available. Later versions of 'Approximate' sound increasingly 'fixed' so as to accelerate performance tempo. It is tempting to assume that the same applies to these lyrics. This theory is backed up by a copy of the score provided by Barrow, showing in his own handwriting, the word 'cornhole' written in pencil, above the music. However, changing the words to songs was extremely common at live concerts.

But Zappa was not simply fixing the infinite; he was applying the principal of cryptography, aiming to disguise a message behind a screen of gibberish. Each line of lyric acts as a conceptual trigger. Bottles of Heinz Tomato Ketchup conspicuously made their way onto the front of two albums in 1984, Them or Us and The Perfect Stranger by way of Donald Roller Wilson’s artwork. The word 'Ketchup' can be traced to 'San Ber’dino' and 'When The Lie’s So Big'. The theme of making/preparing food is common in Zappa, but unusual in popular music, some examples occur in 200 Motels (1971) 'Sealed Tuna Sandwich' ('This town is just a sealed tuna sandwich with the wrapper loose'), Joe’s Garage (1979) 'Crew Slut' ('add water, makes its own sauce'), Broadway the Hardway (1988) 'Why don’t you like me'('Make me a sandwich!'). 'Dagmar' appears for the first time on Sheik Yerbouti as the drag queen at The Grape nightclub in 'Broken Hearts Are For Assholes'. By 1982, 'Stayin’ Alive' by the Bee Gees was assimilated into 'Approximate'; the inclusion of a line from such a rhythmically simple song, in such a rhythmically complicated one, emanates Zappa humour. The final line is most likely inspired by an uncharacteristically, banal moment during a Mothers of Invention concert in 1969, when Zappa announced to the audience that a Chevrolet, parked outside, needing moving. It is also the most obscure line.

Then, suddenly…

Today, with new pop acts under pressure to enter the charts or be dropped, performances are carefully worked out in advance, effectively ruling out the possibility of unplanned events. But apart from computerised dance music, it is difficult to remove them all, since musicians are never 100% accurate. Wrong notes notwithstanding, musicians always make subtle tempo and dynamic variations. Since Zappa’s death, other methods of randomising music have evolved in the form of sound manipulation software packages and plug-ins with randomisation facilities [19]. But these are rarely used in ways that might challenge listeners, especially in chart-orientated pop [20]. This is not surprising since popular music is designed to be instantly catchy, a quality depending on repetition and structural conformity. A pop song, which changes each time it is performed, would soon be under pressure from the powers that be, the record executives and other dip-shits, to become fixed in the form of a definitive version. But somehow Frank Zappa managed to do things his way, and for that we should all eat our greens and things that look like meat.



[1] Los Angeles Times, 1 October 1992. Interview with Frank Zappa,

[2] Courrier, Kevin, Dangerous Kitchen: The Subversive World of Zappa, EWC Press, Toronto, 2002, p. 131. This piece was eventually released on Lumpy Gravy (1968).

[3] Frank Zappa, 'Louie Louie', Uncle Meat, 1969.

[4] Frank Zappa, 'Cocaine Decisions', You Can’t Do That On Stage Anymore, Vol. 3., 1988.

[5] '[…] (The musicians) are given different rows of notes to use against each chord but they choose their own notes and play them in their own style […]', Diane Dorr-Dorynek citing Mingus in the liner notes to Charles Mingus, Mingus Ah Um, 1959.

[6] Richter, Hans, Dada: Art and Anti-art, Thames and Hudson, London, 1997, p. 51.

[7] Ibid., p. 57.

[8] Landy, Leigh, 'Duchamp Dada Composer and his Vast Influence on Post-World War II Avant-garde Music'.

[9] Review from Oor magazine, 27 September 1972, translated from Dutch by Jillis Stada (edited by Charles Ulrich).

[10] This comes from a bootleg recording of Zappa at the Hollywood Bowl, 10th September, 1972.

[11] Frank Zappa, Dub Room Special, Honker Home Video, 1982.

[12] As opposed to 'heart -turning', Out To Lunch’s description of Evil Dick and the Banned Members.

[13] Arthur Barrow on 'Approximate' in correspondence with the author, 6 December 2002. Arthur kindly answered my questions and provided me with a scan of Approximate (for study purposes only!) upon which many of these new revelations are founded. Cheers Arty!

[14] Chevalier, Dominique, Viva Zappa, Omnibus Press, London, 1986, p. 113. Citing The Grand Wazoo’s tour programme, 1972.

[15] The experiments of Lantz and Cuddy conclude that the duration, rather than the rate of recurrence of a pitch, plays a more crucial role in establishing the tonal centre. Lantz, M.E. and Cuddy, L.L., 'The Effects of Surface Cues in the Perception of Pitch Structure; Frequency of Occurrence and Duration', ICMPC proceedings (1996), pp. 281-286.

[16] Occurring from 18 sec. to 21 sec. in the Stage 2 version and from 33 sec. to 37 sec. in the Stage 4 version (times measured from first notes of each piece).

[17] Chevalier, Dominique, Viva Zappa, Omnibus Press, London, 1986, p. 113.

[18] Watson, Ben, Frank Zappa: The Negative Dialectics of Poodle Play, Quartet Books, London, 1993, p. 229.

[19] Typical exponents of such technologies are the group Mouse on Mars.

[20] Unless, of course, you are listening to Rock ‘n’ Random (2002) by Evil Dick and the Banned Members.


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