M-Space Overview

The concept of M-Space emerged from a desire to clarify and formalize jazz improvisation strategies, a discipline in which I was immersed during my jazz guitar training at the Berklee College of Music. In the pedagogies of Berklee tutors Hal Crook and his contemporaries, transcription and ‘lick learning’ were eschewed in favour of more directed and fundamental improvisational exercises. In Hal Crook’s seminars and in his seminal instruction book ‘How to Improvise’ (Crook 1991), one might encounter exercises such as:

  1. Improvise with only chord tones.
  2. Improvise a short phrase. Rest. Improvise a long phrase. Rest. Repeat.
  3. Improvise a phrase that starts with the concluding material of the previous phrases. Rest. Repeat.
  4. Improvise a solo with a prescribed dynamic pattern.
  5. Improvise a phrase with a particular intervallic structure, adjusting accidentals to negotiate the harmony.
Figure 1 An illustration of possible futures of a seed phrase based on fix/vary strategies. (Mermikides in Mermikides & Feygelson 2017)

I found improvising within such limitations was a surprisingly challenging yet profoundly effective approach to the forging of new ideas and avenues of exploration. Often the ensuing improvisations were more successful than prior ‘free’ attempts, and the strictures of the exercise rarely inhibited the potential musicality, with results that were unlikely to emerge without this ‘constrained freedom’. Indeed, this enforced locking in and opening up of small sets of parameters is a central theme in the pedagogies of influential Berklee tutors Crook, Ed Tomassi, Jerry Bergonzi, Jon Damian and Mick Goodrick (see Tomassi 1995, Bergonzi 1992. Damian 2001 and Goodrick 1987). By adopting this fix/vary perspective, any musical object can be seen to possess endless transformational opportunities and material for improvisation, as illustrated by Figure 1, where potential continuations of one ‘seed phrase’ are illustrated in terms of the fixing and varying of the object’s inherent properties, and these transformations can create a linked by endlessly variable ‘chain of thought’ (Berliner 1994) as illustrated in Figure 2.

Figure 2: 64 possible ‘chains of thought’ based on a handful of transformations. (Mermikides in Mermikides & Feygelson 2017)

Despite the effectiveness and potential of this approach, I came to find that its practice tended to be limited to the rather narrow genre of standard jazz (with its allegiance to prescribed harmonic and metric cyclical templates). However, from a fix/vary perspective, all musical objects exist in a rich and interlocking complex space of musical opportunity, even with a limited set of parameters. In Coltrane’s solo on Acknowledgement (1965) in which a key area but no harmonic template exists, one seed phrase – with pitch class set [0, 3, 5] – is modified in terms of three key parameters: 1) transposition 2) metric placement and 3) ‘rhythmic separation’. These three parameters can be readily visualised in a cube, with the ensuing improvisation as an elegant flight through this multi-dimensional musical space (M-Space). This offers a richer and more insightful vision of the underlying mechanics than available through standard notation (Figure 3).

Figure 3. Coltrane’s cube: The phrases of Coltrane’s Acknowledgement plotted in the three-dimensional musical space of metric placement, rhythmic separation and chromatic transposition, with a few coordinates illustrated with standard notation. (Mermikides in Mermikides & Feygelson 2017)

‘Coltrane’s cube’ can even be modelled and explored digitally, where not only Coltrane’s solo but the complete set of coordinates may be revealed. In this way, the solo can be seen not as a ‘flat’ fixed transcription but just one of countless possible journeys through this space, despite its modest set of parameters (Figure 4), akin to Borges’ ‘Library of Babel’ (Borges 2000).

Figure 4. A computer -rendered M-Space model. Coltrane’s phrases may be dropped into the cube forming endless variations in even a tight field of M-Space. Mermikides/McNamee 2015

Although Coltrane’s cube is relatively simple and visualizable, countless subsets of M-Space parameters may be modelled, and improvisations may be seen as possessing particular structures within those spaces. The Coltrane example demonstrates a tight ‘nuclear’ exploration of space, but other improvisational strategies exist. The following illustration demonstrates five examples of M-Space structures sourced from the jazz improvisation repertoire (Figure 5).

Decoupled from their origins, structures such as these may be applied to any musical object within any subset of parameters, and although these concepts emerge from jazz improvisational practice, my work engages these and related concepts very broadly. M-Space and related structures are employed in a wide range of contexts, analytical, compositional, improvisational, technological and visual.

Vital to this project is the use of technology which affords access to Emmerson’s ‘acoustic dislocations’ of time, space and mechanical causality (Emmerson in Dean 2011). However technology is used to constrain, model, automate, visualise, and afford new parameters in the exploration of this field of possibilities. Automating compositional systems such as Schillinger’s ‘parametric decoupling’ and Pärt’s tintinnabuli allows real-time human/machine improvisation fully engaged with Emmerson’s second paradigm of human/machine interaction (Figure 6). Electronic resources also allow the instrumentalist to reach out to otherwise unattainable parameters, stretching and breaking the instrument’s identity. Technologies such as the String Splitter and Fretboard Remapper can augment, distort and fracture the inherited pitch surfaces of our instruments.

Figure 5. Five improvisational structures: 1) Nuclear: phrases, with only occasional small anomalies, fall within one close field 2) Field Series: close phrases are played a few times with variances before repeating the process at a different point in M-Space  3) Pivot: one particular narrow field is played often, acting as a springboard to various satellite fields 4) Merged: fields are merged by the use of a transitional phrase of otherwise distinct phrase fields and 5) Unbounded a series of phrases with little proximity of one phrase to any other. (Mermikides in Mermikides & Feygelson 2017)
Figure 6. Second paradigm of human/computer relationships (Emmerson in Dean 2011)

This multi-modal approach to M-Space has encourage a liminality where several boundaries and conventions of musical practice are transgressed and blurred. These boundaries include those of style and genre, perception (of pitch, rhythm and timbre), analysis and performance, pedagogy and practice, the electric and acoustic domains, improvisation and composition, generative and intuitive process, instrumental identity, notation and illustration, and human/machine interaction.  Outputs from these projects have been published by Oxford University Press, Cambridge University Press, Computer Arts Society, Aeon Magazine, Guitar Techniques, Guitar Player, Total Guitar, Guitar World, Guitar Player, Universal Music Group, Extreme Music and Viribus, and have involved collaborations with Ableton, Cycling ’74, composer/invention/synthesizer pioneer Peter Zinovieff, Laura van der Heijden (2012 BBC Young Musician of the Year), Clarence Smith (Star Wars, Royal Shakespeare Company), harpist Maria-Christina Harper (2010 International Harpist of the Year), violinist Anne-Marie Curran-Cundy, composer Brian O’Doherty, classical guitarist Bridget Mermikides, classical ukulelist Samantha Muir (D’Oz). The resulting music has been broadcast and licensed globally by Sony UK, Sony Japan and MTV.

The content of this portfolio is arranged in categories of Academic Publications, Compositions (subdivided into Tension Blue, Invisible Man, The Moon is Ours and December Hollow projects), Technologies and Musical Illustrations. These categorisations are presented for convenience, however they are not distinct, but intertwined and symbiotic practices, collectively representing an exploration of musical space in its countless forms.


Bergonzi, J. (1992) Inside Improvisation Series: Vol. 1 Melodic Structures. West Germany: Advance Music.

Berliner, P. F. (1994) Thinking in Jazz. Chicago: University of Chicago Press.

Borges, J. L. (2000) The Library of Babel. New Hamphire: David R. Godine.

Coltrane, J. (1965) A Love Supreme. Album. USA: Impulse!.

Crook, H. (1991) How To Improvise: An Approach to Practicing Improvisation. Rottenburg: Advance Music.

Damian, J. (2001) The Guitarist’s Guide to Composing and Improvising. Boston: Berklee Press.

Dean R.T (ed.) (2011) The Oxford handbook of computer music. Oxford University Press

Goodrick, M. (1987) The Advancing Guitarist: Applying Guitar Concepts & Techniques. Hal Leonard.

Schillinger, J. (1978) The Schillinger System of Musical Composition. New York: Da Capo Press.

Tomassi, E. (1995) Improvisation Workshop. Berklee College of Music. 3 June 1995.

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