15 – Sextets

Scripting issues for orchestral and large ensembles scores : the decline of the piano reduction reference score : the rise of the small mixed chamber ensemble : simultaneous composition and orchestration : timbre and texture-centred scores : practical scoring size for rough-prototyping : the mixed sextet : The Starting Point series with Pitch, Intervals and Chords: the scripting of silence – the problem of the pause : graphical representations of what plays and what is silent : rhythmic shortcuts : looping lengths and pitches : removing pitches with the ambitus function.

Although this section is titled Sextets, and will include examples of whole compositions for this number of instruments, it also contains guidance and strategies for composing music for orchestra and larger ensembles generally. Experiment has shown this composer that in using CAC systems for large ensemble and orchestral music there’s a practical limit in scripting effectively for more than ten instruments, although there are sure to be exceptions!

Let’s compare the opening bars of the  full orchestral score of the Second Symphony of Johannes Brahms with his own version for piano 4-hands:



When writing such a symphonic score today with a computer-aided composition system there’s no contest in what would be easier to code. Detailed orchestration in a large number of parts, though quite practical on the virtual staves of the  MIDI score writer,  does pose problems on a script-based programming system. There’s a tendency to create a short-score, not necessarily for piano duet, but for a group of instruments that can represent the principal sections of the orchestra.

In my experience, when writing with a CAC system a series of six concertos for orchestra, I found that a seven-layer short-score – was more than adequate from which to compose an entire work, to produce a rough prototype. Developing a robust strategy to do this took much preparation and the composition of a series of preliminary works before I gained the technique and confidence necessary. And in solving that problem for my personal needs, recognised a second issue: the way composers now tend invent and orchestrate simultaneously.

There are perhaps two quasi-historical issues to discuss here; one is the development in musical history of the expanded ensemble or orchestra; the second is a fundamental change in the way composers invent and orchestrate multi-instrument scores.

In the latter half of the 19th century, conductors and impresarios  encouraged composers to write for an expanded orchestra: think of the changes in size and instrumentation from Berlioz to Stravinsky, Mahler and Richard Strauss. An expanded orchestral palette encouraged composers to use complex musical layering. This is turn contributed to the move from composing in short-score to composing in full-score.  But practicality of representing such multi-layered orchestral scores became problematic on a keyboard score and went beyond the technique of amateur players who before the advent of sound recording had got to know the new orchestral works ‘at home’ at the piano. Though the major works for the ballet repertoire and opera have remained in reduced piano format, the 2-piano versions of all Mahler’s symphonies were amongst the last such reference ‘reductions’ made of the symphonic repertoire. Composers gradually began to think of orchestration as something synchronous with the composition itself, not as some extra to be dealt with after the piano-score or even a short-score had been completed.

The composer who firmly instituted this approach was probably Shostakovich, who from his First Symphony onwards wrote his symphonic work directly in full-score. But whilst Shostakovich wrote music that could easily have been realised in a reference score for piano, other composers of his time developed approaches to orchestral and large ensemble music that focused on timbre and texture,  making realisations in short or piano score not just difficult but redundant: the musical message moved from pitch and rhythm to instrumental colour and expression.

It was Schoenberg and Stravinsky who showed the way towards a richer palette in chamber ensemble music-making. Although works like Pierrot Lunaire and Soldier’s Tale appeared in the first twenty years of the 20th century, it wasn’t until the 1950s that the mixed chamber ensemble came to prominence in the hands of the post-war modernist composers, Boulez with Le Marteau sans Maitre, the Birtwistle and Maxwell-Davies scores for their own ensemble the Pierrot Players, and later the rich and complex inventions of Elliott Carter, Milton Babbitt and Charles Wourinen.  It is probably these models that have had the most effect on composing large-scale works experimentally with script and visual programming, and with particularly with the inclusion of tape and/or computer-generated sounds. Jonathan Harvey’s Bahktiand Tristan Murail’s  Desintegrations provide good examples of such pieces. It is this music that points the way as possible models to composers who adopt programming environments to develop their work with computer assistance.

The sextet of flute, clarinet, violin, violoncello, piano and percussion has become a much favoured ensemble in the last twenty years. Much of the pioneer repertoire has been put in place by the Chicago-based Eighth Blackbird who have enjoyed collaborations with George Perle, Steve Reich and Steve Mackay.

This ensemble became a model for my own work in creating experimental pieces attached to the development of the CAC system Opusmodus. Known as Starting Points these pieces are six intense miniatures that focus on discrete parametric elements as ‘starting points’. In the section Further Afield there has already been an example taken from this collection, Starting Point : Velocity.

As the two score images shown earlier from the opening of Brahms’ Second Symphony suggest, one issue that is problematic in composing for orchestra or large ensemble is the scripting of pauses, particularly where the mix of instrumental colour and activity plays an important part of the narrative or argument of composition. A lively distribution of change in instrumental timbre and of sound and silence can hold the attention in a way similar to that in film or video where the rapid change of shot or focus can be a powerful attribute for holding attention and creating expectation. Of course there are works where such kaleidoscopic change is redundant, as it the music of Steve Reich, whose Double Sextet  and 2 X 5 enjoy a relentless tutti throughout. But it is management of the pause or rest that is one of the key challenges of the Starting Point : Pitch.

A prevailing feature of the Starting Points collection is the use of a motif from the Slonimsky Thesaurus, the first pattern in fact. This is a truly ambiguous go-any-place kind of pattern. An extension of this pattern into a scale has already  featured in the section Starting with Pitch, There, we mapped the pattern onto a stream of vectors generated from white-noise.

In this ensemble piece the generative mechanism  is simply this:


Contained in these five expressions is the pitch and rhythm material of the composition. There are two ways we could present the first two:







The advantage and potential of the second realisation is that the twelve generations can be seen a distinct metrical units. It’s just this kind of partitioning that can be highlighted with an orchestration scheme. But before that happens a further pitch and rhythm articulation might be beneficial:





The score here shows that a transposition scheme has been implemented and a rhythmic articulation created. The idea of using a binary conversion to identify repeated pitches has been shown in the section Starting with Rhythm.

Now to create the scoring or orchestration for six instruments. The first step will be to construct the score-template. There’s an example of such a template but for four instruments in the section Every Composer is Different. With a template  in place it becomes possible to score and audition material as it’s created. Scoring ‘after composition’ is certainly possible, let’s say from a completed piano score, but this can depend on the very nature of the material. A score with independent contrapuntal elements benefits from scripting in individual parts as in Nigel Morgan’s Contrapuntal Forms, where as homophonic material may be easier to originate from within the confines of a piano score, as in the same composer’s Origami Letters.

With a score-template in place and a thread of material as presented so far in this section, auditioning the ensemble is possible. But we have to make appropriate transpositions of the thread to enable the ensemble’s instruments to play within their ranges. This can be achieved without disturbing or duplicating the original material. Such transpositions can be placed within the score definition itself. Here’s an example:


If we were working in a MIDI sequencer-style environment we could now copy and paste the thread material to every part of the sextet, make the transpositions and simple orchestrate by erasure. Let’s make clear the difference between erasure and deletion in such situations. Erasure takes out pitches and their note-lengths leaving equivalent rests. Deletion takes out  pitches and their note-lengths AND their equivalent rests. Erasure keeps the music’s structure intact. Deletion changes the temporal structure. This is easily done of the virtual stave, but much harder to do within a program script.

We’ve already seen how rhythmic articulation can be created by applying a binary conversion – to identify repeated pitch, but we want to go further than this and take out (erase) whole bars from a part without disturbing its synchronicity with the thread on its return. Here’s the first three bars of the rhythmic articulation:

15-8Suppose we say: “Let’s make the first and second bars rest bars.” If we converted all the note-lengths in these bars to length-rests bars 1 and 2 would be silenced BUT bar 3 would sound out. We could invent a function length-to-rest that would do just that: changing a positive value into a negative value. So far so good – but the difficulty arises in doing this on a larger scale AND being able to visually scan the whole score. We could regard whole bars as binary sequences and thus produce a graphical representation of what plays and what is silent. In the example below integers represent the presence of the six instruments in each bar:

15-9This is OK, but it is still not acceptable as a visual scan. The musical mind, used to the physical layout of a traditionally notated score, doesn’t reorientate itself very easily. We really need the output to be able to be shown in a horizontal right to left form rather than  vertical top to bottom graphic representation, like this:

15-10The lower of the two graphic illustrations is based on the practice of Milton Babbitt who used a similar notation as a graphic reference in his early Composition for Four Instruments. Such references are common-place in the analysis of music, particularly in compositions using serial techniques, but they can be of great practical use during composition, as those who work with IRCAM’s Open Music will testify. In later examples the text will return not only to the issue of visual scanning, but to what the author has previously termed, in the section Starting with Rhythm,  ‘beat/space’ notation’.

There are two solutions to scoring by erasure currently implemented in the Opusmodus application. One is making bars silent by turning lengths into rest lengths. The other is generating a pause by replacing a list with a note-length equal to the length of the bar.

15-11Here are the concluding bars of Starting Points: Pitch:


In the second of the Starting Points it’s Rhythm that begins the flow of composition. The rhythmic material created here makes use of a function ql devised to enable efficient input of code. The first expression uses the OMS notation for note-length – s = 1/16, e = 1/8. There are five rhythmic motifs arranged in a list, followed by a list of integers. If we put both together as arguments within the function substitute-map, here’s the outcome:



The next step is to introduce pitch and then add chords into the keyboard part. Notice the use of substitute-map, this time with pitch:



15-16The rhythmic organisation and pitch collection of this score suggests a number of possibilities. One is bringing chords into the right hand of the piano part; the other is changing ascent into descent in the scalic passages:



The next Sextet under the spotlight is Starting Points : Intervals. It’s already been established that one of the attractions of script-based composing is conversion: from one parameter or data type to another. Intervallic composition is a very current preoccupation of many composers. Despite Alexander Goehr’s warning that ‘intervals are mean little things’ they still have the power to be music fingerprints. Witness the example discussed in the section Continuing with Pitch of Magnus Lindberg’s Cantigas.

The Intervals Starting Point begins with an expression that demonstrates how an interval series can be created from generating random numbers. Remember you can download the full-score here:

15-19 Let’s take it apart and see how it works:


Now to convert the interval sequence to pitch. Notice how the ambitus-interval function spreads and contains the interval lists:




When studying the full-score note that this interval-based collection has been adjusted to the range of the vibraphone, the instrument that plays this material as a kind of canto throughout the piece:


The two expressions above create the note-lengths and rhythmic groupings for the pitch material. The ql function featured in the Starting Point : Rhythm and provides a shorthand for generating groups of note-lengths. Here’s the result – and also the complete vibraphone part:



The orchestration of this piece is based on looping variants of the vibraphone part. To see how this works look at the piano part:

15-25The function get-span adds up the note-lengths in a list and produces, in effect, the time-signatures for each bar. The function length-span takes a note-length value and spans it to the value of bar-length. As the sixteenth (s in OMN) is set throughout the piece the pitches in the piano part will loop.


The last Starting Point to be discussed here is Starting Points : Chords. This is a miniature miniature! The material comes from the generation of six chords, again from collections of random numbers:


By using the function sort-asc the six lists of pitches are ready for being made into chords:



Looking at the voicings on these chords it would good idea to split them up into diads. This uses the function gen-chord set across a 4-octave compass (48):




In the other parts the function ambitus-pitch-remove is used to provide more clarity and produce a hocketing texture. In the vibraphone part, illustrated in the code expressions below, every pitch outside the ‘(f4 c6) is removed.



The set of six Starting Points for sextet is part of A Selection of Sextets published by Tonality Systems Press. In addition to the Starting Points sextets there are further computer-assisted compositions in duo, trio and quartet formats scored variously for the instruments of the sextet. 



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