A Hidden Order: Revealing the Bonds Between Music and Geometric Art – Part One
The following chapter describes a method of translating music into geometric art and vice versa. This translation is achieved through an exploration of the mutual foundations – in mathematics and its role in harmony – of both music and geometric art. More specifically, the process involves the implementation of principles derived from traditional Islamic geometric art and contemporary mathematics, including fractal geometry and aperiodic tilings.
The method was discovered by Mara in 2011 and was subsequently developed during his collaboration with composer Lee Westwood on the project A Hidden Order. Examples from this project are used to illustrate parts of this chapter.
Also discussed are the implications of establishing such a connection between music and geometric art. These include the possibility of unique creative processes that combine practices from both visual arts and musical composition, as well as facilitating the application of developments, practices, and creative processes from one discipline to the other.
KeywordsMusic Geometry Visualization Sonification Islamic Art Fractal Aperiodic Tilings Harmony
- Bibby N (2003) Tuning and temperament: closing the spiral. In: John F, Flodd R, Wilson R (eds) Music and mathematics from pythagoras to fractals, 1st edn. Oxford University Press, New York, pp 13–14Google Scholar
- Boulez P (1971) Notes of an apprenticeship. Faber & Faber, LondonGoogle Scholar
- Caivano JL (1994) Color and sound: physical and psychophysical relations. Color Res Appl 19(2):126–133Google Scholar
- Griscom W (2015) Visualizing sound: cross-modal mapping between music and color. PhD, University of California, Berkeley, P1Google Scholar
- Grünbaum B, Shephard GC (1986) Tilings and patterns. In: Klee V (ed) . W.H. Freeman and company, New York, pp 540–570Google Scholar
- Howat R (1983) Debussy in proportion. Cambridge University Press, CambridgeGoogle Scholar
- Jacobson R, Ray SF, Attridge GG, Axford NR (2000) The manual of photography, digital and photographic imaging, 9th edn. Focal Press, OxfordGoogle Scholar
- Kandinsky W (1914) Concerning the spiritual in art. Dover Publications, New York, p 25. (1977)Google Scholar
- Krumhansl C (1989) Why is musical timbre so hard to understand? In: Olsson O, Nielzén S (eds) Structure and perception of electroacoustic sound and music, 1. Excerpta Medica, Amsterdam, pp 43–53Google Scholar
- Lendvai E (2000) Bela bartok: an analysis of his music. Kahn & Averill, LondonGoogle Scholar
- Livio M (2002) The golden ratio: the story of phi, the extraordinary number of nature, art and beauty. Review, London, p 193Google Scholar
- Messiaen O (2002) Traite De Rythme, De Couleur, Et D’Ornithologie, tome VII. Alphonse Leduc, Paris, pp 95–191Google Scholar
- Padovan R (1999) Proportion. Routledge, New York, pp 221–227, 2008Google Scholar
- Steinitz R (2013) György ligeti: music of the imagination. Faber & Faber, London, pp 267–269Google Scholar
- Taylor C (2003) The science of musical sound. In: John F, Flodd R, Wilson R (eds) Music and mathematics from pythagoras to fractals, 1st edn. Oxford University Press, New York, p 51Google Scholar
- Tymoczko D (2011) A geometry of music: harmony and counterpoint in the extended common practice. Oxford University Press, New YorkGoogle Scholar
- Wittkower R (1953) Brunelleschi and “proportion and perspective”. J Warburg Courtauld Inst XVI. Idea and Image, Thames & Hudson, London, p 131, 1978Google Scholar