Composing with Limitless Accelerations and Warped Time

Music that seems to limitlessly accelerate can be created using Risset Rhythms. This remarkable fractal effect (often compared to the Barberpole illusion) remains underexploited in musical composition. Building on examples from a range of genres including classical (Haas, 2022), electronic (Autechre, 1998) and Gamelan, this practice research PhD will investigate how attributes of rhythm (metre, phrase, form) and time can be adapted to Risset Rhythm textures.

It will demonstrate that the technical and expressive potential of this technique far exceeds the description in Risset (1986).

Because pulse is an emergent quality from a combination of musical parameters, while no one element can accelerate limitlessly, pulse can. This is achieved by 'refreshing' an accelerating texture, by discreetly removing faster durations and introducing slower durations.

Risset (1986) describes one refresh method, a loop in which the fastest durations fade out while the slowest fade in. Many compositions and the small body of technical literature (Madison, 2009; Stowell, 2011; Ghisi, 2021) are focused exclusively on this refresh method, but many others are possible. Though now widely known as Risset Rhythms (hereafter 'RRs'), the same essential technique has been discovered independently many times (see below).

This project will reframe RRs from being a mechanical auditory illusion to being a broad type of rhythmic texture with huge unrealised musical potential. Primary research questions:

RQ1: How can RRs be exploited in composition, and how do these interact with other elements (pitch, timbre, architecture) of music? RQ2: How can established theories of pulse, metre, phrase, and form be enriched and informed by RR contexts? RQ3: What do limitless accelerations reveal about how musical time can be warped?

Examples of RRs exist across many genres. Gamelan music has a concept called change in irama (a refresh method) which is used to create brief decelerating RRs (Sutton and Vetter, 2006.) Sibelius' Symphony No.5 (1919) and Symphony No.7 (1924) feature long accelerations where the fastest durations are gradually removed while a slower harmonic rhythm is introduced. Druphad features a related approach to long accelerations (Sanyal and Widdess, 2004.)

Carter composed the first examples of complex and extended RRs, in Variations For Orchestra (1955), String Quartet No.2 (1959), and Double Concerto (1961). Norgård does the same in Between (1985), Helle Nacht (1987), and later works, and wrote a technical article on accelerations (1985). However, the complexity of Carter and Norgårds' rhythmic styles means it is usually difficult to hear a clear pulse.

In contrast, Haas' weiter und weiter und weiter... (2022) has as its main material a 40-minute audible limitless acceleration. Textures relating to RRs are also present in Murail's Ethers (1978), Adams' Shaker Loops (1978), Andriessen's De Snelheid (1983).

The most notable popular electronic example is Autechre's Fold4, Wrap5 (1998), which led to interest among other IDM (intelligent dance music) producers such as Stretta (Calculus (2010)) and Sevish (Starfish (2021)). In general however, across genres there is only extremely sparse usage of RRs compared to other novel rhythmic techniques.

This is a practice research project, with a series of composition outputs supported by a commentary which will outline a theoretical framework for RR textures as part of the research narrative. I will build upon my theoretical framework and analyses in my portfolio of compositions (RQ1, RQ3).

There is a growing interest, especially online, in composing with RRs but only extremely narrow approaches are detailed in the literature. My cross-genre research will fill this gap, enabling the creation of original music using RRs. It will also provide a new basis for further research into 'musical time'.