An objective of my interest in musical geometry is to create musical objects that are based on cross-modal perception or thought. Conceptualizing and experiencing music in terms of multi-sensory relationships has been one of the most stimulating exercises of cognition I have encountered to date. I hypothesize that by invoking other senses, the mind and brain gain exponential access to neural associations, and this results in an increase of computational power available to multi-sensory processes. It seems to me that there is no reason for music as a discipline to evolve incestuously without the concern for its relationship to external disciplines like geometry, mathematics, or astronomy (as defined in the quadrivium). In no way is this an exclusive list of subjects which stand to benefit the art of music, but these are particularly important in defining the structural components of music.
For improvisational purposes, geometric visualization has been an invaluable tool to conceptualize, memorize, and express musical values. At times, the relationships I use are intentionally assigned. In this case, a given melodic phrase may be a shape that is transposed through different keys which are visually defined as colour or height. Colours behind the melodic shape might define the harmonic backdrop on which the line is superimposed. At other points, the relationships of colour, shape, texture, and pattern co-emerge organically with sectors of the image relating to sections of music. When this happens it is extremely easy to navigate this music in memory compared to when the association are intentionally assigned, even though the memorability of intentionally assigned figures already marks an improvement from purely aural recall. This happens during moments of greater immersion into the music an is often associated for me with the ability to recognize pitches in absolute pitch-space in addition to relative pitch-space. These phantasms are clearly associated with kinesthetic emotional and physiological sensations distributed throughout the body and correspond with factors of pitch, timbre, intensity/volume, duration, etc.
Usually, the latter phenomena of involuntary association occurs while listening to music or playing in a relaxed state, and in my experience, it does not come on command but is instead ‘given’. One particular instance of the involentary order took place after a four hour session sitting in silence, as I emerged and began to imagine music. I recall walking into the washroom and beginning to think as music rather than in verbal language about music. Thoughts immediately identified with and as music, and it became evident that the sensory relationships were beyond those of normal. I first noticed that everything I was seeing WAS sound. It is not that I went out of my way to explicitly visualize or imagine something. Of greatest interest was the inversion of control of the senses. In order to hear something different, I had to see the image change. Without changing the image, I had no control over the contents of the sound as such. It was also evident that with this unique association I had much more control of the complexity of music that I was capable of hearing. To test this, I began to imagine a melodic line in the style of Bach. I immediately heard two contrapuntal lines and could easily expand this to four, six, and eight melodic figures. This confounded my mind somehow, given the previously incomprehensible level of independence that could be exercised with each line only be seeing the changes visually. Somehow, these visual changes immediately corresponded to the sound I was intending to hear, and yet, if I tried to hear them, I still had no ability to do so. To give an analogy, it was as though one had suddenly grown a vast number of limbs and had the controls for left and right switched with one another. This experience was so disorienting that I could only sustain it for about five minutes, after which point the overwhelm required that I rest and shelf the possibility for some years to come. This glimmer of potential has been a rich source of ideas for future forms of art. The prospect of an audio-visual instrument capable of realizing musical and 3D visual information simultaneously, perhaps even controlled through the medium of thought, is one that often occupies my mind. Such an instrument would depend on the ability to translate audiovisual signal generated by the brain into real-time digital information, and this will likely require further advancement in the field of neuroscience and technology for cognitive interface before it can be implemented on the consumer level.
The power of geometry in the mathematical sense also has extensive application in understanding the form of music. Music theorist Dymitri Tymoczko has published interesting book on this subject in ‘A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice’. Along similar lines of geometric analysis, jazz guitarist Miles Okazaki has undertaken to visualize all permutations of harmonic and scalar relationship occurring in one octave as points of equal division in a circle with each set of notes defining the resultant shapes in two dimension space. Properly speaking, to exhaust the permutations of shapes in the 12-tone system, this needs to be extended into three-dimensional space with points occurring along spiralled octaves. Perhaps in future iteration of 3D virtual music notation this will be possible. Regardless, geometric form can be used to model virtually any musical object. For example, in composing or analyzing the form of a piece of music, geometric modelling can be used to open a plethora of creative options: the form of a song can be as pentagonal as it can be divided into an aaba figure. The later of these options would be an instance of arithmetically derived forms whereas the former would be geometrically derived. The five sections of a song with pentagonal form may bear some relationship as determined by a careful analysis of the geometry of the pentagon or may contained 5 entirely different sections, depending on the interpretation. This is but one of a wide array of examples.
Without delving into greater depth, I want to say that this kind of visual thought is beneficial for anyone who has even the slightest inkling of interest in this kind of thought: interest indicates capacity. I expect that the majority of musicians have some familiarity with this set of experiences. Several I have spoken with over the years have shared this kind of visceral sensory response and I hope to encounter other musicians with which to further investigate this subject academically and creatively.