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.

Before looking at how a collection of note-lengths (as rhythm) and pitches  come together, it’s necessary to point out the different approaches of mapping one to the other. Let’s use a pitch collection from a composition we’ve already met, but with a difference;  a change made to the amplitude of the sine wave:

8-18-2The simplest way to map these pitches to a single note-length value is by spanning: pitch to note-length. The function span calculates how many pitches are in the collection and then creates that number of individual note-lengths. Then the two are put together in a special function make-omn.

In Opusmodus, the particular CAC environment providing the examples for this ebook, there is a music language embedded in the system. This is called OpusModusNotation (OMN). This will be discussed in a separate section: the idea of having a dedicated music language able to present length and pitch in a single linear construct (a single line of text and symbols). For now, just notice that how an  ‘(s)  – a 1/16th has been added to the pitch output.


We can make rhythms by processing rather than mapping, and in certain situations this can be most effective. Notice in the example above that when using a sine-wave to generate pitches there are quite a few repeated notes. If we were to erase the repeated notes we’d immediately produce a distinct rhythm. A function gen-binary-change turns the pitch collection into a binary collection showing exactly where repeated pitches appear. And then the function binary-map maps the binary collection with a ‘(s) or 1/16th note-length value: you can see immediately that the binary zeros have become rest-lengths! Then, we use make-omn to bring pitch together with rhythm.

8-48-5There are two particular ways the pitch can be mapped to the binary rhythm. The example above shows the pitch collection hasn’t lost its repeated notes! But we’ve got rest-lengths. Let’s look at the other approach. Notice the added :keyword swallow. This is the clue!

8-68-7Yes, the repeated pitches have been swallowed by the binary zeros. You can imagine this approach makes for a valuable orchestration tool, whereas the mapping technique keeps all the pitches of the collection intact.

Let’s see this technique in action within a formal composition – a canon for two violins. This composition, the first of my Three Canonic Duos, is a contemporary take on one of the jewels of the Baroque, Telemann’s Canonic Sonatas for two melody instruments. It’s composed using the generative possibilities of a modulated sine-wave. Because it’s a canon for two voices there need only be one melodic strand, the second is the same as the first only starting to play a bar later. The program begins with a graphical plot of the modulated sine wave.

8-88-9Apart from the score definition that follows ,the code below is the entire program:


All functions used in this composition have already appeared in the text  so if you need to remind yourself about how they work just try a search. The function length-divide was integral to the rhythmic ‘play’ between ripieno string parts in La Serenissima. The function pitch-ornament was seen in the section ‘Starting with Pitch’ as an efficient way of producing a legato texture.

8-11Here are the opening measures of Canonic Duo No.1. This image is taken from the performance score. It’s available to see in notation and as Opusmodus score-scripts on the composer’s web archive. The other two canons employ a similar approach using sine-wave generation, but with quite different results. The Canonic Duo No.3 employs chordal textures (i.e. Double-stopping). This is achieved by setting up dyads based on a variety of intervals. Here’s the opening of the program:

8-128-13In order to produce pitch series the row collection is filtered:

8-14The chord series is filtered in a similar way:8-15

These fragments are then mapped onto the modulated sine-waves:

8-168-17The six different sections (r1 to r6) are then assembled together as the extract above shows.

Remember you can download from my score archive the score of Three Canonic Duos , and in versions for two violins, 2 violas or 2 violoncellos, along with the Opusmodus score-scripts.

As mentioned previously some CAC systems have their own integrated music language. This can be very useful if notation rendering is clear and ‘instant’. In the Opusmodus system there is an effective script language called OMN. The next example shows how a short statement of thematic material incorporating rhythm and pitch at the point of composition can be disassembled: to produce discrete parametric data for reuse in the composition. The score-script is from my own Two Movements for saxophone quartet. Here’s the code expression followed by the rendering of that code into staff notation:

8-188-19The code for this thematic material includes dynamics and expressive markings (or in OMN attributes) such as staccato and ties.

The important point to remember with this example is that the alto-sax expression was composed straight into code, just as a composer might write a complete statement in staff notation. The only major difference is that instead of drawing bar lines to divide the music metrically the code is organised into lists separated by open and closed parentheses. Furthermore, the CAC system adds up the note-lengths in each list and automatically outputs the appropriate time-signature.

In order to create a sax quartet from the alto-sax theme it’s necessary to disassemble the OMN lists:

8-20To go further with this disassembling another function becomes invaluable – find-unique:


The function mapcar is one of the few functions we’ve come across that is known as a primitive of the Opusmodus system’s core language,  LISP. This function mapcar, as its name suggests, ‘maps’ a function (in this instance find-unique) across a collection of lists (let’s call them sub-lists to collect only unique pitches – in others words any repetition is deleted. Finally, here are the opening bars of the full-score appropriately transposed.

8-228-23Movement 1 from Two Movements for Sax Quartet

The composition above was constructed from the outset from the coming together of pitch with rhythm and is presented in the score-definition for each saxophone as a single list. In Opusmodus this doesn’t have to be, and the score definition can be arranged to keep the parameters length and pitch apart. In a duo titled Duo Batterie for piano and vibraphone this is necessary to enable diminution and augmentation of material to be effected.

8-248-25To look at this score in detail it is available as part of a compilation of studies for sextet titled A Selection of Sextets [pdf] that includes the sextet Velocity in the next section, ‘Further Afield’.

Links, Resources and Further Reading
Nigel Morgan: Opusmodus Scores
Nigel Morgan: Three Canonic Duos, for two violins, two violas or two cellos
Opusmodus: Website

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