20 – Instrumentarium Novum

The new instrumentarium : the Baroque idea of music as speech : the ‘affections’ of music : the contemporary jazz orchestra : the ‘open’ score : towards a model for coding orchestral music : Piece d’Orgue – the adoption of i-functions and the score-sheet : the problem of visualisation in code-based scores : rough prototyping and optimum ensemble size : Six Concertos for self-directed orchestra : phrase partitioning with find-change and find-anacrusis : Concerto 1 – three stage example of prototyping : two forms of short-score : Migrations for orchestra : expanding i-functions : using integers  in Objects of Curiosity for string orchestra ; novel tonalities in To the Dark Unseen for string dectet.

The title of this chapter is taken from a term found in a groundbreaking book of the 1990s Baroque Music Today: Music as Speech by the conductor Nikolaus Harnoncourt. The Instrumentarium is occasionally found in musicology to describe the collection of instruments used in music making at a particular point in time, so a ‘new instrumentarium’ is taken to mean either what is current today or what might be proposed for the future.

The composition of music in the 21st century challenges traditional ensembles and their attendant musical forms. New instruments and ways of extending existing instruments enrich our instrumentarium as they have through musical history. Amongst the established instruments of Classical Music composers find innovative techniques and the means towards the production of beguiling sounds. Look no further than the host of markings now considered the norm in scores for strings, mostly concerned with timbre and sound production.  But, for the most part, there is a significant cultural investment in the maintenance of traditional instrumental ensembles and in the formal instruction and education surrounding musical techniques and ‘period’ performance practice.

In the Baroque period all music was new music so it was unnecessary to school players or maintain instruments for the performance of past music. Consider that by the time of Bach’s demise many of the instruments of his instrumentarium had became outdated – the recorder, the lute, the harpsichord, the viola da gamba.

In the mid-18th century the relationship between what a composer provided and what was required of a performer began to change. The composer’s needs became more exacting and well defined. The notation of scores lost much of its former speculative nature and gained written out dynamics and ornamentation, expressive names and articulation. Previously, so much in a written composition was left to the skill, imagination and intuition of the performer. There was an expectation that musical systems composers used were well understood by performers, and to the extent that improvisation was an established norm. Not so today, when it is quite common that a performer may have little or no idea how a piece of music is made, but can and does play and realise exacting instructions bound into notation. In Harnoncourt’s book it explains how it was a musician’s understanding of the rhetoric of musical affect enabled musical structure (in composition and performance) to communicate the emotions meaningfully. This study countered the mechanical exactitude of much performance practice of early and period music and led the way to a more theatrical and looser to and fro of musical statements.

Harnoncourt’s vision of Baroque music and its relationship to speech (and rhetoric) which encouraged the author / composer  to reconsider the nature of contemporary aspects of ensemble performance (and performance practice) as it relates to composition forms and techniques. Harnoncourt himself suggests that there is much within a musician’s engagement with music during the Renaissance and Baroque periods that may continue to be of value for us now – in the production and performance of new music. And one of the most resonant of his observations was that music in earlier times was more of a speculative art than we might imagine.

Within this speculative spirit of music making comes the practice of composing a score that has the potential to exist effectively in many different forms and arrangements. Right up to the introduction of sound recording orchestral scores were ‘reduced’ for keyboard performance or arranged for smaller ensembles. Think of Lizst’s arrangements of Beethoven’s Symphonies,  Brahm’s own versions for piano duet of his symphonic opus, even Webern’s quartet version of Schoenberg’s Chamber Symphony. Such was possible because the emphasis on pitch and rhythm had yet to be overwhelmed by the fascination with  timbre and texture. In a keyboard version the musical argument, the musical ’text’, can be experienced under the musician’s hands, which in the case of Stravinsky,  Debussy and Ravel was how the music first came about – at the piano. But that aside, in early orchestral compositions there was rarely any pre-conceived idea of an exact instrumentation to be used.

Along with a host of other earlier practices surrounding composing and performing Harnoncourt’s vision held many attractions. Although he doesn’t mention the medium, that of the contemporary jazz orchestra operates in many aspects like a large Baroque ensemble or pre-classical orchestra. Whilst there is usually a fixed scoring, it is flexible, and the players are flexible in responding to on-the-fly spontaneous instructions, often making personal decisions to effect instant changes, often dependant on the location and circumstances of a performance or recording. In examining such considerations computer-aided composition  can be a lively partner in devising more ‘open’ scoring (including scores in Open-Form) for ensemble, and indeed orchestral playing.

The author / composer has written extensively on the rationale and the early development and progress towards composing instrumental scores that align with Harnoncourt’s vision. These writings and attendant scores are collected and available within the composer’s web archive under the title Instrumentarium Novum, and point to some of the preliminary works already discussed in the last chapter.

Having set the scene and the context, this chapter will now focus on the first composition to employ the code model later adopted for the composer’s Six Concertos for self-directed orchestra.

This model brings together many of the innovations and techniques already described in the previous chapter, but contains a further development: the use of i-functions and the adoption of a score-sheet upon which these functions are placed.

The composition in which these two devices first appeared was Piece d’Orgue, a three movement work for 3-manual organ based on a reinvention of the Piece d’Orgue by J.S.Bach BWV 572. This is a remarkable three movement composition in the French style having an elaborate five-part Fantasia at its centre, and it is this central movement that will form the focus of what follows.

The code innovations set out in this movement significantly improve the workflow of the composition. The workflow concept is predicated on the the idea of rough prototyping, and it has shown itself  for this composer / author to be effective in chamber and solo works as well as orchestral compositions. Rough Prototyping has been described as’ an efficient and economical way of conveying intent.’ In a music composition it should allow the concept of a piece to be seen and heard as a sounding score. Although many composers use verbal descriptions of their ‘intent’, words are open to misrepresentation, whereas a sounding notated score is rarely so. With computer code very small adjustments can make for quite dramatic changes, and they can usually be rendered instantaneously. A prototype of the first movement of the composer’s Concerto 1 takes under 3 seconds to compile and display in notation.

But, such prototyping of an idea for an orchestral score is best achieved with the least possible collection of data streams outlining instrumental parts. A fully notated orchestral score may have thirty or more parts, albeit some being close copies as instrumental ‘doublings’.

In the path towards an effective prototype format the three manuals of an organ provided an excellent starting point. The modern organ does after all contain its own instrumentarium of stops and mixtures, the very potential for richly orchestrating its music. But such orchestration was not a consideration in the original Piece d’Orgue because Bach himself rarely indicated a necessary or required registration of stops in any of his organ compositions.

The means of choosing an instrumental part or layer has already been explained with previous images and code of the timesheet visualisation. Here it is for the central movement of Piece d’Orgue.

20-1Timesheet of the second movement, (Fantasia)  showing activity in manuals (I & II)
and pedal (III).

What is viewed here above is a bar by bar play of activity and stasis, where the music plays and where it is silent. The next objective was to streamline the process of composition so that its linear nature might be scanned by the eye and ear in code just as in a notated score. Most composers will acknowledge that visual scanning of a composition as it develops is an essential prerequisite of the continuation process; it has more cognitive impact than listening to an audio stream.  It’s easy to achieve on paper by simply laying out pages of music already completed – which is why composers often have large drawing boards or tables on which to place their manuscripts . A good example can be seen in the short film made by Tom Mustill on composer Harrison Birtwistle titled Notes from the Bottom of the Garden. Some computer software for music notation is able to simulate this ‘spreading out of pages’, but only in a severe reduction of page size, as here in the Nightingale score display.


Such visual scanning when applied to a score-script is rarely as effective. You can’t easily glance at pages of code and get an immediate sense of the activity and the general linear aspect of the composition. In fact, some composers score-scripts are all but impenetrable to such scanning.

It was partly this issue that led towards the concept of i-functions and the score-sheet.

As can be seen in examples of code shown in previous chapters the function can include many arguments with slots for values and flags, for example gen-chord in Opusmodus discussed in the chapter Being Harmonious. It’s this kind of complexity that can stand in the way of the visualisation of process. What if a function definition could contain a single argument and be titled possibly by an abbreviation or alias ? And could such an abbreviation be placed on a lattice that allowed the composer to see at a glance what processes were being applied to each bar of each instrumental part?

Instead of :

20-3perhaps this?

20-4The first attempt to apply such ideas can be found in Piece d’Orgue whose timesheet and orchestration of the organ’s keyboard manuals has been shown earlier. But before any discussion of the making of a series of functions, let’s start with from the stream of pitch data converted from 512 samples of vectors produced by generating white noise: 

20-5Such a group of expressions can be found at the beginning of each movement of all Six Concertos for self-directed orchestra. The expressions labeled source and sym show the vector output and its conversion to symbols a to m, symbolic notation for 12 semitones when the tonality is ‘chromatic’. To search for repeated symbols , and thus produce a partitioning or phrase boundaries the functions find-change and find-anacrusis are applied to  sym. The resulting output produces a sequence of phrases containing pauses to enable the music to breath, to resemble phrases of speech as discussed earlier. These functions do not occur in the Opusmodus application but there is a workaround using a binary conversion.


Here are the Symbolic Composer functions applied to Opusmodus architecture and able to produce a basic OMN list. The composer has to supply a length value:

20-7The final expression shown in the example from Piece d’Orgue employs functions c-list-rotate and create-lists:

20-8The value of these functions will become clear when a portion of the output of the expression c-sym is shown as below.


The function symbol-divide ‘maps’ the length of each partitioned phrase (contained within the variable c-sym) as the dividing factor, and outputs a list of each phrase as a newly named variable:


Now we have the data stream as 50 possible ‘bars’ (phrases) of pitches (though this is in a symbolic state). Each ‘bar’ is shown with a rest-length (=) at the start or end of each ‘bar’, giving the music that all-important breath or punctuation. The phrases can also be rotated (with c-list-rotate) so that the rest-length does not always appear at the beginning of each phrases. Because each bar has been made into a variable we can apply a random ordering that will result in a measure of repetition, for this composer a necessary factor in a stream of pitch material. The final r-sym variable evaluates the n-list ‘bars’ to produce an output which is eventually mapped to the tonality of f chromatic. The opening six ‘bars’ only will be shown here matching up with the score illustration:


Now  to see this output as part of the score of Piece d’Orgue:


This is the moment for i-function list to appear. In Piece d’Orgue the list is limited to just fifteen processors activate by a two-symbol abbreviation. By the completion of the Six Concertos this list had trebled:

20-14These two expressions above show how the abbreviation (the i-function su) is arrived at and in the code below processed from the score sheet:

20-15Just as in the movement Game of Pairs from Quatuor des Timbres, discussed in the previous chapterthe entire material in each part is the original stream of pitches. The combination of the timesheet placement and i-function processing then creates variant  material. Examine the II manual part, bars 2-4, and notice that the bars are processed via the score-sheet  as create-chords , symbol-upward, symbol-upward

20-16Notice also that more than one i-function can exist in a single  ‘bar’ on the score-sheet as in the opening bar of the III manual part, symbol -downward and symbol-skip.


The addition of the i-function and score-sheet now completes the technical attributes that provide a basis for coding a rough prototype of an orchestral or large ensemble composition. Taking the step from Piece d’Orgue to the Six Concertos was complemented by a realisation that to retain the principle of rough prototyping a piece of an orchestral nature (lasting 15 to twenty minutes) certain conditions were beneficial to the outcome. The most prominent is to decide what can be the minimum number of parts that will produce an efficient and effective prototype. Although with the adoption and use of the computer score-writer and sequencer composers are becoming used to writing (almost) immediately into full-score, the short score is a kind of proto rough prototype that has been a format favoured by many, particularly by those composers who work directly from the piano.

The author / composer has adopted two formats of short-score: a seven layer ensemble and 2-piano layout. The seven layer format looks like this:


This format makes possible scoring for High and Low Woodwind, Brass, High and Low Strings, Percussion and Keyboard (continuo). Notice the symbolic notation at the top and scoring (at this stage)pitches  entirely in unisons and octaves.

The next example shows the effect of processing (via the score-sheet) with a selection of i-functions:

20-1920-20Already the i-functions used here depart from and extend those used in Piece d’Orgue. Creating the i-function collection was in itself a valuable exercise because the composer had to define what was necessary to meet personal style and technical needs, rather than simply use what might be available in the software library. What must be recognised is that any arguments, for example those that might be used in a transposition function, have to be fixed. This means in a function that will render transposition, upward and downward transpositions have to be separate functions, as usually they are wrapped into one function by virtue of having a transposition value argument that can be plus or minus an amount. The i-functions such as symbol-skip, symbol-cut, symbol-figurate have in-built random selection. What makes these i-functions work effectively is partly the restriction of the pitch stream compass to a chromatic octave.


In the score example above the same three bars have additions and edits created ‘by hand’ without any intervention of further programming.

To examine this process in more detail and with the scores and code it is recommended that the reader downloads this PDF titled Guide to Composing for Orchestra. There are also two further PDF publications available within the web archive pages for Six Concertos.


The PDF publication shown has a detailed resume of the script-based programming approach to the composition of these concertos. It is designed in a portrait format to be printed to hard copy as a guide for musicians and directors. The PDF booklet below is designed to be accessed at the computer (hence the landscape format). It contains a summary of the background scores and details the rationale for such compositions. It has a host of examples in score and a summary of each movement of the Concertos. These include MP3 playback alongside excerpts from the scores.


Finally, let’s look at an alternative way approaching format to composing for orchestra with script-based programming: working from a 2-piano version. This is not a reduction because when composed the idea for the orchestration was only loosely conceived. The 2-piano score was composed as just that!

The work is titled Migrations and served as a nine-minute orchestral study for a larger work Sounding the Deep for bass voice and orchestra.


What is unique about the composition of this piece is that it begins with the same formula as the Six Concertos but after the generation and partitioning of the pitch stream constructs tonalities from analysing the pitch content of the partitioned phrases. Essentially, the pitch patterns are turned into scales. The function that enables this process looks at a list or lists or symbolic patterns, filters out any repeated or rest symbols, and sorts the content in an upward scalic list, in other words a tonality:


As in the Six Concertos the orchestra includes an important part for the continuo group: electric keyboard, double bass, tuned and untuned percussion. As in the concertos this group underpins the unique tonalities thrown up by the phrase partitioning process. It is this very continuo that enables these orchestral pieces to be self-directed, or rather led by a team of players who come to the first orchestral rehearsal already knowing the work. The continuo part contains the proviso to drop out or elaborate at any moment in the score thought to be appropriate. The presence of the continuo also makes possible reduced versions of the scores, as in Axioms, the version of Concerto 1 for sax quartet (with optional continuo). Here below is the version for sax quartet alone.


And now with the addition of the continuo:


To date, it has proved difficult to reconstruct the code structure devised for this music in any other software environment but Symbolic Composer. It is hoped that by publishing at least an outline of this approach it may encourage other composer / developers to adopt aspects of the design in other systems.

There are a number of other compositions that are not part of the Instrumentarium Novum collection but use the I-function / score sheet approach. These include four works for strings. Of these Objects of Curiosity (SuperCity) has already been referred to at the conclusion of the chapter Duos, Trios, Quartets. This is the first part of a trilogy of works that take their starting point from the work of contemporary architects. The sub-title SuperCity comes from a book and exhibition by Will Alsop.

Written for Kronos in 2005 it was an intermission in the composition of the Six Concertos and later in 2007 extended for string orchestra with the addition of a double bass part, a part that was not the ‘usual’  octave doubling of the cello part. It is the subject of an formal academic paper and keynote lecture at the Peninsula Arts Contemporary Music Festival 2007. The paper, lecture (with slides) and score is available along with a code annotation of the original string quartet.

What is different about this score is the use of integers alongside symbols as a means of making the structure of this single-movement work. Here’s the opening code, which is very similar to that featured in Piece d’Orgue and the Concertos.


Conversion from symbols to integers supplies a powerful extra layer of data to the symbol-stream enabling a metrical structure to be fashioned. So from a very early stage it was possible to create a visualisation in notation rather than in the beat / space format.

In this composition the i-function list is significantly expanded to include dynamics and string techniques such as tremolando and pizzicato. The work also makes use of a play of musical ‘affections’, musical sections that are titled after descriptions by the architect: with spirit and edge, full of light and colour, nervous and excited, like a slow dance.


Further compositions using this approach include the 4th of Four Commentaries for cello and piano, ‘Phrases’ from Studies in Movement, and To the Dark Unseen for string dectet.

To the Dark Unseen is a double-violin concerto in miniature. It is part of a suite of pieces for student performers called Shoals. The ripieno parts are in two choirs (one tuned a tone lower than the other) and played entirely with open strings and harmonics with the solo parts created from the hopalong algorithm (featured in Starting with Pitch). Here the tonalities are created based on scales of open-strings and harmonics and the timesheet is set a resolution of 1 beat per second:


In revealing something of the way script-based programming serves the orchestral composer, perhaps the most revelatory aspect must be how orchestration may be woven into the very act of composition itself. Once the pitch stream is partitioned, and ‘filled’ the template of the time-sheet, the composer is able to compile (and print or display) a notated result. Thus, decisions about applying i-function processes can take place with visual / aural guidance from an orchestrated score (in 7 parts) albeit showing thematically a single melodic line an in unisons and octaves. This ‘solution’ lies partway between using orchestration decisions to decide the nature of the musical material (pitch, rhythm, harmony), and working from an orchestration-free piano-score once the material is composed.

The First Symphony of Peter Maxwell-Davies, it is said, owes much to the generation of pitch and rhythm by Magic Squares into a network of unorchestrated parts. This means that the orchestrated result was arrived at, or at best confirmed, after the pitch and rhythm composition was arrived at. Magic Squares are essentially arrays, but working with integers rather than pitches. Constructing patterns of orchestration by arranging instruments as array contents to give differently weighted outcomes makes for very particular levels of control. And so with the activity and / or silence of instruments chosen before i-function processing begins, the musical outcome can be more closely defined.

Links and Resources
J. S. Bach – Piece d’Orgue BWV572
Harrison Birtwistle – Notes from the Bottom of the Garden
Peter Maxwell Davies – Symphony No. 1, Op.71
Nigel Morgan – Instrumentarium Novum works, Six Concertos, Piece d’Orgue, Sounding the Deep, Migrations, Axioms, Objects of Curiosity (SuperCity), Objects of Curiosity and the Composing Continuum (lecture), Four Commentaries IV, Studies in Movement: Phrases, To the Dark Unseen
Arnold Schoenberg – Chamber Symphony No. 1, Op. 9 (arr. Anton Webern)

SCOM Guide to Composing for Orchestra (PDF)


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