Category Archives: Composing How and Why

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:



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14 – Harmony and Chords

La Serenissima for violin and strings (after Vivaldi) – how its chords and harmonic sequences are made : generating a stream of pitches from a white-noise fractal : how to devise 4-part chords : how to create chord sequences : the idea of the function substitute-map : chaining score-scripts together : the problem of fashioning the solo part in the slow second movement : developing a trajectory generator to link intervals between chords : the third movement – a different approach to handling chords and sequences : marrying rhythmic articulation and harmonic rhythm.

In the previous section melody is seen as an ordered collection of pitches that can come together to form the material for accompaniment, and this is often a sequence of harmonic objects, some vertically aligned in chords, some arpeggiated, or as a melodic counterpoint. In this section harmony and chords are more closely linked, melody appearing as a result of composing harmony and chordal progression.

The piece chosen to illustrate how this might come about in a CAC system began life from a long-held fascination with an idea first expressed by the composer Antonio Vivaldi. His collection of 12 string concertos (includes The Four Seasons) owned the title Il cimento dell’armonia e dell’inventione (The Contest Between Harmony and Invention). These celebrated pieces for violin, strings and basso continuo have rightly enjoyed wide-spread popularity because of their clear-cut harmonies expressed in a rhythmic continuum uncomplicated or defused by counterpoint. Such music reveals an agreeable sonic structure  that transfers well into 20 and 21C styles and situations. There are many examples in the contemporary literature that adopt the play of harmonic invention found in the music of the Italian masters of the Baroque. In the opening of Michael Tippett’s 2nd Symphony the composer acknowledges ‘the pounding low Cs’ providing a Vivaldian spirit to the highly syncopated violin melody’. For a composition closer still in spirit and scoring Violin Concerto No.1 by Poul Ruders is a striking ‘take’ on the Vivaldi model including brief echoes of The Four Seasons.

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13 – Melody into Accompaniment

How a complete piece for melody and harmony instrument comes about – from first ideas to finished score : Selah for violin and piano : before the first note – constraints and conditions : creating melodic phrases by vector mapping to pitch : working with a tonality – the double harmonic : using the attributes parameter in Opusmodus to include ornamentation : generating chords from melodic phrases : the rough-prototype : Selah for cello and piano : similarities and differences.

In Part 1 the focus was on how the different parameters of note-length, pitch, dynamics, and structure came together in code-specific programming to compose music. Although there were many examples taken from compositions created entirely through CAC the whole narrative of a piece’s composition was not yet up for discussion. It was felt that the making of musical phrases, sentences and paragraphs had to come before the story of a composition might be told.

In Part 2 the emphasis in many of the sections will be how a complete piece comes about: following first ideas to final score. The example scores are not wildly experimental, indeed they play safe, if only for the reason that they were mostly commissions and had to be playable! It is this factor, connecting with the real-world of music composition and performance, that computer-assisted composition presents its greatest challenge, and where pragmatism and common-sense may need to be applied simply to get the project completed on time! Unless composing time is not governed by completion and rehearsal dates, only part of a composition project may be feasible for a composer in the early stages of working with a CAC system.

No matter what the style, genre or system a composition owns, there are certain universals that belong to the composing act. No matter where you are musically Melody and Accompaniment is likely to figure somewhere in most composing situations at some time. Often this is a necessity driven by the nature of the scoring chosen (or required). In creating a piece for violin and piano there is an assumption that these instruments take particular roles of melody and accompaniment. But there are also many variants of this form. It doesn’t have to be melody instrument with an accompanying harmony instrument in a subservient role. Mozart wrote piano sonatas with optional violin obligati, which is turning the idea on its head. The word dialogue can be a powerful clue as to how a composition having melody and accompaniment is often be composed. In Roberto Gerhard’s remarkable Gemini there’s a fine example of how violin and piano come together as though they were a single instrument, eschewing the idea of melody and accompaniment altogether. Whatever direction taken at the outset, it’s probable that melody will share some aspects of its material with accompaniment, and the most usual of these shared parameters is pitch,  in the form of a scale or pitch-row. Continue reading

12 – Structural Forms

LISP primitives in structuring : division – rotation – inversion – appending phrases together : using the function repeat to intensify structure : repeat devices in Statements for piano : palindrome and interpolation as structural mechanisms : Studies in Movement for violoncello – customising the gen-palindrome function : introducing pitch-interpolation : Continuum and Blues after Ligeti : pattern-matching from Symbolic Composer to create rhythmic structures : a pitch interpolation example from Opusmodus.

In the section ‘Being non-linear’ we saw how composers of the 20th century began to change the way music was structured, away from traditional forms towards a rich juxtaposition of episodic and motivic material, leading eventually into collage, open-form and non-linear structuring. Achieving this kind of organisation of material comes into its own in computer-assisted composition.

Before taking this kind of free-form structuring further into areas like live-coding, a programming practice centered upon the use of improvised interactive programming, we’ll examine some of the basic tenets of structuring musical statements in code.

It happens that most CAC systems, whether based on visual-programming or script-based coding, have tended towards using the LISP language. IRCAM’s OpenMusic and PWGL, Tonality Systems Symbolic Composer and the CAC system adopted for this e-book, Opusmodus, are all based on Common Lisp.  For the composer new to CAC systems LISP is a very practical and highly efficient language for working with the parameters of music.  Even in visual programming environments it’s useful to know just a few of the LISP primitives as many of these primitives are directly concerned with structuring or preparing material to be structured. Continue reading

11 – More on Rhythm

Metre – Rhythm – Note-length -  Duration – Tempo – Pulse – Expressive Markings : Five examples of how different composers work with the active parameters of time : Setting up an improvisation program to test rhythmic possibilities – in the solo violin part from La Serenissima : using the length of the content of pitch lists to produce rhythmic phrases -  in the first movement of String Trio (2012)  : taking the words of a poem to derive pitch and metre in Blaze for percussion ensemble : selecting sections : mapping pitches to untuned percussion.

Metre is the structure, rhythm inhabits metre, note-length makes up rhythm. A bar contains groupings of note-lengths we call rhythm. All around these descriptors duration lives and breathes. Then, there’s that character called tempo and his wayward friend pulse. Tempo aims to be steady and firm, pulse does what it can to obey the wishes of tempo, but those expressive markings? They tend to tamper with tempo and pulse: rallentando, ritardando, stringendo, allargando. You see the extent of the problem, perhaps?

This is further complicated still by the remnants of the tradition which for centuries linked time-signatures and metres to note-length and tempo. Of course most composers today are meticulous in their marking of all these elements, but this was not always so.

Look through Purcell’s harpsichord pieces of 1696  and we get a summary of tempo indications linked to time-signatures: 4/4 is slow. 2/2 is a little faster, 3/2 is very slow (except for a hornpipe), and so on.

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10 – Continuing with Pitch

Magnus Lindberg and Twine; creating a Study after Twine : working with intervals and pitch class sets : creating primary structural chords : making a rhythmic vocabulary after Lindberg : writing a program as an improvising machine : defining a ‘case’ : a serial Invention after Bach – working with interval sets : Lindberg’s Cantigas.

One of the most committed exponents of Computer-Aided Composition has to be the Finnish composer Magnus Lindberg (b.1958). Since the late 1980s he’s been working with a harmonic system based on progressions of primary structural chords.  Lindberg has adopted pitch intervals recognised in CAC systems as integers, and which can be brought into a computation to generate pitch-class sets. These sets were designated and ordered into a unique notation system by Alan Forte who extrapolated them from the Mathematical Set Theory of composer Milton Babbitt. The intention here was to provide a method for the analysis of both serial and non-serial atonal music. This means that Forte’s system can equally describe the music of Ives and Stravinsky as the music of Schoenberg and Webern.

Linderg’s pre-composition workings out have been studied by the American composer Ed Martin who has had the opportunity to interview Lindberg at some length about his composing strategies. Martin has produced an impressive paper on titled Harmonic Progression in Magnus Lindberg’s Twine.Published in the American journal Music Theory Online this gives a keen insight into Lindberg’s way of composing, even though it does not dwell specifically on the aspect of computer-aided composition. As much of Lindberg’s output has centered on music for large orchestra, to be able to get in close to a work for solo piano reveals much that might go unnoticed in the complexity of an orchestral composition.

“Primary structural chords” from Ed Martin’s analysis of Lindberg’s Twine

Sometimes it’s a valuable exercise for a composer working with a CAC system to make a short study exploring another composer’s approach and technique.  Having long admired Lindberg as a kindred spirit in composing with computer-aided systems, I was keen to see how Ed Martin’s revelations might be turned into a piano work of my own making. It also provided an opportunity to demonstrate how intervallic composition of pitch might be handled in a CAC environment.

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9 – Further Afield

Dynamics as parametric material: MIDI velocity and custom dynamics : A composition for sextet structured by a dynamic scheme: mapping parameters with substitution : generating clusters and cluster melodies : gen-cluster a function with arguments: scoring : orchestration by using an ambitus function : de-mixing and generating pauses.

One of the challenging aspects of composing to describe is that of the structuring of material, and here, parametric material. The section ‘Being Non-Linear’ explored the potential of collage, of improvising with small fragments of material, using programming to ‘play’ and experiment with structure  In looking ‘Further Afield’  structuring takes on another aspect, and an even more speculative and unusual one.

Dynamics are collectively a significant parameter within the parametric world of music. It isn’t one that has figured as a structural device in music of the past, except as a by-product of the use of echo effects common in music composed for large spaces such as the basilica of St Mark’s Venice. In this extraordinary building there developed a tradition of composition that utilised the positioning of singers and instrumentalists in different locations throughout the building. Andrea and Giovanni Gabrieli and Claudio Monteverdi structured their music for this large building to create echo and antiphonal effects. Their legacy remains today in the use of sound projection and the positioning of performers to emphasise and clarify musical statements. Continue reading

8 – Coming Together

Bringing together rhythm and pitch : simple mapping – pitch to note-length : ‘making’ OMN pitch and note-length into a single data stream : using binary processing to create rhythms : swallowing pitch : Three Canonic Duos after Telemann : disassembling a melodic phrase into discrete parameters of pitch and rhythm.

Songwriting is one of the few musical instances when rhythm and pitch often come together simultaneously in the imagination.  Usually there ’s a lyric with metre and rhyme that prompts this coming together. An art song can be a different matter. The poem may have a more complex rhythm and the metre won’t necessarily fall into a simple, steady pattern. This means a rhythmic sketch usually gets written first, though not before establishing a general sense of the right tempo. Then, as the rhythm falls into place some sense of the ‘right’ or appropriate pitches begins to appear, at the very least a rise and fall. Possible underlying harmonies reveal themselves, and the rhythm of their movement can also affect how rhythm and pitch join hands.

When composing instrumental music, the relationship with song and the singer is never far away. Music has to breathe, and wind and brass instruments have to take breath. Even in the figurated and continuous stream of repeated note-lengths we so often find in the music of Bach or the minimalist composers a sense of  ‘breath’ is suggested – by harmonic change. And without the press and constraint of words, variations and ornamentation may add pitch and rhythmic complexity to create intensity and drama.

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7 – Being Harmonious

Pitch collections making tonalities and chords : Morton Feldman and Howard Skempton : the chord object : devising harmonic objects : generating chords – exploring the complex arguments of the gen-chord function : how to build a function : creating unique tonalities to produce arpeggiated chords in TheWhite Light of Wonder – a piano work after Schumann’s Kinderszenen.

Rhythm is a linear phenomenon, whereas pitch can be arranged horizontally or vertically. When two pitches sound together a chord results. Since the early 20C composers have gradually come to think of the simultaneity of pitches as texture as much as harmony. Harmony itself has ‘moved on’ from the constraints of voice-leading and the traditional well-tempered key systems of Bach and Rameau.

CAC systems have become a natural test-bed for experiments in harmony, and for some composers this programming medium is where their chordal world takes shape.

Let’s explore a number of techniques that view chords as self-contained or discrete pitch-based objects. To do this it’s useful  to make a preliminary move from the traditional key system with its signatures, chord scales and voice-leading into areas of harmony which, whilst tonal, may extend the palette of harmonic effect. Many of these harmonic forms and devices retain a lively role in jazz, film and TV music, as well as music for games and electronic media. Most CAC systems will include the means to code harmony using jazz chord symbols, handle inversions, and provide libraries where exotic and world music scales can be accessed. It’s also quite common to find composers using Messiaen’s scales and modes or the resources of the Elliott Carter Harmony Book in commercial contexts, particularly film. And these materials are increasingly becoming part of CAC libraries.

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6 – Starting with Pitch

Pitch as a parameter : pitch – forms and functions : pitch collections – traditional, contemporary, experimental ; making scales, making tonalities : the Hopalong algorithm : scale-raga examples : fragmentation functions : ornamentation of repeated pitches : introducing OpusModus Notation (OMN) : using integers to generate pitches and chords : a chorale .

The parameter of pitch doesn’t have to mean melody, an immediate blending of pitch with rhythm. Pitch as a discrete parameter can exist on its own, and as such can be a starting point for tonality and harmony, the horizontal scale of pitch elements, and the vertical arrangement of pitch so as to create chords, and as an adjunct, arpeggios.

Composition practice since the late 19C began to explore the idea of pitch collections that could not necessarily be described as traditional scales or even modes. There was an appreciation that the idea of tonality had expanded to describe more than just a major or minor scale with a key signature, but a collection of related pitches that might belong within a scale in a key. And this was but a small step to establishing that the chromatic scale could be a base tonality.

As a result of this, the idea of a pitch set or pitch row developed. It brought with it a still developing theory of pitch organisation which, whilst not wholly part of new music today, remains as a vital way of organising, classifying and analysing pitch.

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