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.

Now, turn to the opening section of Refrains and Choruses by Harrison Birtwistle. There’s four tempo marks, the pulse is in 1/8ths, ranging from 50 to 80, there are several accelerandos  and rallentandos, and 13 changes of metre in the 20 bars before letter A.

In Louis Andriessen’s Workers Union there’s a one tempo mark of quarter = 96 throughout, and 8 bars (all repeated ad lib) of 3 different metres before the first rehearsal letter.

Meanwhile, in  Eclat  by Pierre Boulez there’s seemingly no metre at all, no tempo markings, the bar lines are only there to contain groups of pitches of similar note-lengths (some 1/16ths, some 1/32nds, even some 1/64ths), anything sustained is a breve, and there’s expressive indications over almost every sonic moment: liberamente, excessivement rapide, tres lenge, tres longtemps and so on.

And finally here’s a score created with a CAC system using fractal mathematics. It’s a movement titled SINK  from the solo piano work Seven Imperatives by the Norwegian composer Rolf Wallin. As with Birtwistle’s Refrains, Wallin’s piano work includes ornaments, acciaccaturas particularly. These ‘crushed’ notes further intensify note-lengths and rhythms, reduce durations of preceding or following notes, but rarely disturb the pulse or metre.

11-1This snapshot of what is contained as active parameters within the time element of music makes for an almost bewildering degree of options and possibilities.

In this further section on rhythm three examples of rhythmic composition are looked at. The first example reviews the opening of the solo violin part of  La Serenissima, my string concerto after Vivaldi’s L’Estro Harmonico. We’ve already seen in ‘Starting with Rhythm’ how the ripieno part for strings begins life as sequences of pulsed note-lengths, and with division and binary filtering becomes an effective texture for the ensemble.

In the solo part the plan was to create within the program code a partially- improvised music where the composer could trial possibilities before deciding on ultimate statements.

The idea of the code that produced  this solo part works like this. It begins with the basic rhythmic outline for the ripieno accompaniment. This is established in the variable e-rhy where the e-pulse is divided randomly – twelve divisions from 1/8th into 1/16ths. The significant workings of the function substitute-map are explored in the section ‘Further Afield‘.

11-211-3Rhythmic material for the violin solo part is set up with the def-case format discussed in Study After Twine in ‘Continuing with Pitch’.

11-4This ‘definition’  means ‘if the program comes across an 1/8th note-length it will replace it, either with (1/16 1/16) note-length  or ( -1/8 ) rest-length. Otherwise, if  it meets any other length, the program will output (1/32 1/32).

11-5See the notation for this expression in the example below:

11-6The pitch material for the solo comes from this expression:

11-7The white-noise algorithm generates the sum total of e-pulse and then converts the vectors to pitches with the compass g2 to g5.

11-8Again, the function substitute-map is used in the same way as for rhythm. Finally, the range of the pitch output is constrained through the ambitus function to fit the compass of the solo violin.

11-9Now we can put violin pitches together with violin note-lengths using the make-omn function. This outputs the single OMN list bringing pitch and note-length together.

11-10The output above is just the first three bars of the OMN list, which yields:

11-11Extract from bar 13 -25  of the first movement of the violin solo of La Serenissima.

This approach to creating rhythmic variants is flexible and effective. So too can be setting up a list of possible note-length rhythms activated by the length of pitch lists.

Another example of this approach to making rhythm is in the 1st movement of my String Trio (2012). This score includes many passages of ornaments that are randomly generated as pitch groups of different sizes. Then, using the def-case technique, the pitches are matched speculatively to rhythms of note and rest lengths.

11-12What happens here is that if ornamentation has been previously added randomly to bars throughout the String Trio, there will be groups of pitches 1, 2, 3 or 4 in length. With the function length the content of each list can be counted and their values  presented to the def-case definition rhy-orn (see above). This triggers a rnd-pick function that selects one of the lists of note-lengths. If we look at the length output for the violin from bar 17 -23 it reads  (3 1 1 4 3 ), and this is the choice made in the violin part:

11-1311-14From bar 17 in the first movement of the String Trio (2014).

The LISP primitive length joins flatten, append, list and mapcar as a small but necessary collection of  functions that provide the glue of making expressions. All of these occur in the code presented in this text so far.

For the third example we’ll look at my  composition for percussion titled Blaze. This five-movement piece is for up to eight percussionists playing a mixture of tuned and untuned instruments with or without MIDI triggered live electronics.

The structure of Blaze is that of a poem Deep Sea Diver by Robert Francis. The words of the poem actually create the metre. Here’s the first section of the poem, which will create both pitch and metrical material for the first movement of Blaze. For clarity, it may help to listen to the reference recording provided on the web rather than live performance with live electronics on YouTube. The MP3 and the full-score can be downloaded here.

11-15Most CAC systems will make it possible to map the symbols of the alphabet into pitch. Like this:

11-16 In Blaze it was decided to sort the pitch material in an ascending form:

11-17The next step was to reverse just some of these ascending pitch phrases. To achieve this we have to have a :keyword within every function that enables that function to act selectively through a :section list of integers. Or, we could create a  function select-section that uses a visual template. Both have advantages and disadvantages.

11-18In this example we’ll chose the function select-section to enable visual scanning to select sections rather than have to count section integers in a long list.

11-19The next step is to associate the length of each word with a metre. Each letter is to be ‘played’  according to a length value applied to it. Here’s the first verse of the poem as a list of lengths followed by the metre calculation. Notice how the LISP primitives mapcar and length create the list of lengths.

11-20As the program continues we have to contend with further mapping: from pitch to the special requirements of untuned percussion instruments – although Blaze requires tuned as well. When writing for percussion, and using the standard GM MIDI pitches for drums, it’s often more convenient to map percussion sounds (single pitches) to alphabetic symbols. An untuned instrument setup (or kit) for drums looks like this:

11-21Then, we can ‘play’ the drums easily as lists of symbols. Remember the maximum number of letters in the first section of the poem is eight so here might be a set of percussion patterns.

11-22The score-file of Blaze goes through many and further transformations, but what is shown here should be enough to demonstrate the potential of such non-musical data – words and their alphabetic symbols.


In further sections they’ll be an opportunity to view other scores that use the written word and alphabetic symbols to construct computer-aided compositions, notably Origami Letters for tenor voice and string quartet and Quintet for piano and winds.

Links, References and Further Reading
Opusmodus: Website
Symbolic Composer: Website

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