Junto Profile: xiiixxi

From York, England: growing up with Italian opera, working with Euclidean rhythms

This Junto Profile is part of a new series of short Q&As that provide some background on various individuals who participate regularly in the online Disquiet Junto music community.

What’s Your Name? My name is Dominic. I have published material out under my surname Peel, and my previous surname, Hayward-Peel, when I was married. I have been using the name xiiixxi (pronounced zik-see) for about a year, mainly because ThirteenTwentyOne was already taken. And I’m fascinated by Fibonacci ….. … .. .. .

Where Are You Located? I currently live in York, England, but have spent the majority of my life in and around London. I was actually born about 20 miles up the road from here in Ripon. I have lived in West, East, and North London over the years, but never over the River in the South — which has always been viewed as akin to Mordor where I was growing up. ;-)

What Is Your Musical Activity? I was raised in a household full of the sounds of Italian Grand Opera: Puccini, Verdi, Mozart, Wagner, etc., and I saw my first opera, Turandot, at the age of 6. I played the piano and flute and sang as a boy soprano in various semi-professional choirs. As I got older, and because we had moved to London — Shepherds Bush — I became desperate to be in a band, eventually leaving school before finishing my A-levels to do so. I played in various bands in and around North London before deciding to return to full-time education, and did a degree in Music at Goldsmiths, University of London. Following this, because of a growing love of musical analysis, I studied for a Master’s at King’s in London in Music Theory and Analysis, where I specialised in the music of the Second Viennese School: Schoenberg, Berg, and my particular favourite, Anton Webern. This is all highly relevant to me at this time because, like him (well, all of them) I am fascinated by music as strands, or rows, or sequences, melody defined by the space between pitches, the intervallic content rather than the pitches themselves, that are then subject to rigorous, ordered transformations and development to produce developing variation and, eventually, structure. My current projects are generated by exploring this tenet: a basic sequence — not tied to a timeline — which is then processed through Euclidean rhythmic development, and transformation through transposition, intervallic inversion, expansion and contraction, reversal and any others I can think of at the time, to inspire and facilitate the creation of a fixed musical statement.

What Is One Good Musical Habit? Always back-up or record your ideas for a rainy day.

Live from York, England: xiiixxi

What Are Your Online Locations? I listen to music on SoundCloud and Bandcamp, and occasionally by searching through YouTube. I read things wherever I can find them and have spent a disproportionate amount of time recently on the Juce forum due to my recent C++ addiction.

What Was a Particularly Meaningful Junto Project? My favourite piece of music is generally, and genuinely, the one I’m working on at the time but, the project Octave Leap (Disquiet Junto 0564) helped inspire me to produce what I feel is going to be a perennial second favourite, because I think, for all the apparent “dryness” of the exposition above concerning process and technique, this piece shows that it can work very successfully in creating organic, naturally developing, and well-structured tunes that capture, for me anyway, the feeling of a moment in time. It shows that the key to using process to inspire is to know when to break it and deviate, or tarry a while, just because it sounds good … .. .. .

Could you explain, for those who are not familiar with the concept, Euclidean rhythmic development? The Greek mathematician Euclid discovered the algorithm, or mathematical process, which now bears his name, in around 300 BC. It was designed to evaluate the greatest common divisor between two numbers but has since been used by many mathematical disciplines to now embed itself within a huge variety of modern theorems and equations. The maths itself is relatively simple — but I guess all the really clever bits of mathematics are less about the algebra and more to do with the concept itself and how far it can reach. If you are interested in the maths behind it then the Wikipedia article is a good starting place.

It took until the early 2000s for a computational scientist Godried Toussant (wikipedia.org) to draw a direct line between Euclid’s algorithm and its possible involvement in explaining the success of some of the world’s most identifiable musical rhythms. He proposed that Euclid’s equation could be seen as a way of organising temporal — rather than physical — space, and also pulled in the work of Eric Bjorklund, who was working on an extraordinary theory within the science of nuclear physics in which nuclear timing sources were being evaluated and graded with regards to their “uglyness” — which totally depended on how even the pattern of pulses were; the more even the distribution of pulses, the less ugly they were … .. . . brilliant! 🙂. Toussaint’s work is here: PDF.

A detail from Godfried Toussaint’s work

In it he treats the two numbers that Euclid worked on as two groups of different events. One is silent, the other (the smaller one) has some event on — let us say a drum hit. The magic of Euclid distributes these two groups as evenly as possible, which results in what we hear as a rhythm — drums hits over time separated by silences — the silent pulses still being “felt” as part of the total sequence length. Bjorklund uses a slightly different algebra to get the same result as Euclid but, in the equations of his that I’ve used, we only have to give the algorithm the total number of pulses (both those with a hit and those which are silent) and the total number of hits. This is the basis of most Euclidean rhythm generators around today: How many pulses in total is the sequence and how many hits are needed to be distributed. Toussaint’s paper shows these rhythms as both a series of 1s and 0s, and also as a series of Xs and dots [ 1 0 1 0 ] = [ x . x . ]. Interestingly (for me anyway, as a musical analyst), he also introduces the concept of interval-vector notation, which I first came across at uni when I studied Allen Fortes’ system for Set Theory analysis (wikipedia.org). The numbers inside the () describe the sub-groupings within the main rhythm allowing, in the future, the development of an analytical system to draw bigger collections of Euclidean rhythms into meta-groups through comparison of their constituent sub-rhythms — a definite yawn for a most I guess. 🙂

The upshot of all of this is a way of subdividing a stream of pulses (with hits) as evenly as possible, which has proved very popular in recent years, adding interesting and unusual percussive rhythms over a drum beat, not only by layering a Euclidean rhythm directly over a similar number of bars, or beats, but also in layering longer or shorter Euclidean rhythms over the top — maybe a six pulse rhythm over a 4/4 beat, or a 21 pulse rhythm over 4 bars of ¾. The experimentation is almost endless. Conventionally, both Toussaint’s and Bjorklund’s Euclidean rhythms always start with a hit but these days most devices allow you to “rotate” the rhythm — move the whole thing up or down a number of pulses to create syncopation — allowing a whole lot more experimentation. Ultimately it is the musician’s ears that will define whether these experiments result in something “good” (and not Bjorklund’s “ugly”); it is all in the ear of the listener to decide.

My own use of Euclidean rhythms moves this on a bit further. I have removed the “backbeat,” as it were, and rely on layering different lengths of rhythm over each other to produce “hybrid” rhythms — loosely influenced by the concepts behind Leon Theremin’s Rhythmicon of the 1930s (wikipedia.org). The hybrids can extend for extraordinary lengths of time if one wishes by combining prime number pulse lengths — for example 23, 29, and 31 pulses — which won’t coincide until over 20,000 pulses have elapsed. Crucially though, this does not mean that there won’t be more regular, smaller scale repetitions along the way — depending on the internal Euclidean rhythm that each sequence is assigned. To be honest, I think explaining exactly what (I think) I might be doing will probably take a bit too long for this interview, but I will definitely keep working on writing it all down, with references, so that the process and thinking behind it is clear. I have been working on this for about 8 months — mainly through the Disquiet Junto challenges. I purposefully make use of really simple sounds for this process, as I’m really interested in understanding how the melody and rhythm develop over time before complicating this further with timbre and instrumentation. The resulting music is overtly polymetric but does use some polyrhythms at times. The “Chromaticon” aspect of the music will definitely have to wait for another day.

Please feel free to contact me if you would like any further info about the process. Below is a link to my Soundcloud playlist of Euclidean Chromaticon pieces (the software I am developing to make using these ideas easier).

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