Three-dimensional aspects of an octave in music
Research proposal: Isidora Krsti?
Collaboration partner: Prof. Herbert Edelsbrunner - IST Austria
The work researches the spatial and visual qualities of the octave in music and how a logical, spatial (three-dimensional) visualization could be achieved. Furthermore, an accent would be put onto the interactive and reactive aspect of the structure.
The octave, comprised from eight tones from C to for instance C-1 (C, D, E, F, G, A, H, C-1) is first presented as a straight,
two-dimensional line. To schematically visualize the amplification and at the same time repetition of tones, each subsequent
octave is lined up in a straight, linear mode. The problem is that, in this scheme, there is no association between every
higher tone (for example the tone C and tone of for example C-1 of a higher octave and so on). It seems that in the linear
drawing, the tones just rise, without the notion of having basically the same tone repeated but for an octave higher.
This problem can be solved if the initial straight line is bent into a spatial form. The spatial form that will answer the problem concerning the association of the same tone would be exactly the shape of a spiral in space. The nature of the octave and half tones between the tones E-F and tones H-C seem to make the spiral bend in space, where the original one starts forming another spiral.
In the spiral form, the same tone but of a higher octave, is repeated just above it. The same rule applies for each and every tone in the octave (D with D-1, E with E-1 etc.).
Through the collaboration with prof. Herbert Edelsbrunner from the Institute of Science and Technology (IST) Austria, an attempt will be made to research the spatial and topological qualities of the shape of the spiral as an octave. This would mostly be done through the lens of mathematics and topology of Wrapped Tubes formulas, differential geometry and the Frenet-Serret frames.