The reason for writing a book of this sort was determined by the realization that the things in life which are bypassed as of little consequence, have, on the contrary an immense importance to our development as human beings.
This work is a reducing of complexities to a symbol. The symbol is being able to determine our responses to emotion, thought, and psychic awareness. How little we know of the irritations or pleasures which influence our mental states. If we should know such things as sequences, we could predict events. If we should know such things as accelerations and decelerations, we could better understand time. If we could find a way to utilize the energies within us, to direct and focus them, we could be productive individuals.
The ideas here presented could be used as a springboard for an entirely different approach to life. That they should be given a wider and broader audience is based on the realization of the response of many individuals so far to these ideas, and it has compelled me to make them available to others.
They seem to have a unifying effect on those exposed to them, as if the facets of each life have loose dangling strings, and it is possible to pull these together taut. So often our lives are compartmentalized, as is our society. Yet we all long to feel a whole. And if even one of us can make a whole of some of the parts, others are able to do likewise.
Therefore this work is proposing that universal harmonies exist, that we perhaps have long lost sight of.
These harmonies are most manifest in music and proportion in the arts. If we can take the principals behind these harmonies and analyze them, we not only discover guidelines for the arts, but for living harmoniously as well.
If we can define these harmonies without even using sounds, we can begin to understand some of the principals lying underneath the surface. Once these mysteries of harmonic analysis are uncovered, a whole process of growth, healing forces and aging processes are revealed. Each person following his initial overtone structure, could develop his full potentiality intuitively, intellectually, emotionally. One could expand consciousness through effort of understanding at all levels.
The arts have traditionally been considered an expanding of the mind to the consciousness of the human race. Now, at a crucial point in the development of the arts, where the forces of materialism and an intellectualization of a negative sort are threatening to choke off the life source of creativity, a positive approach, not competing with science but reinforcing this important branch of human endeavor is desperately needed.
The iconoclasts of our age have finally reached a point where everything has metamorphically been smashed, and it is up to all of us to begin putting the pieces back together again.
One thing I wish to emphasis is that Glimpses is not merely a collection of diagrams from different disciplines. A few are borrowed from other works, with credit given, but these have either the music grid framework I developed superimposed on them, or are diagrams juxtaposed to show similarities in shape, or concept alone. Most of the diagrams were devised on my own, sometimes picking up an idea from a verbal description, but for the most part the diagrams developed out of their own system.
There are certain aspects of this work I would like to explain. First, many of the sources were second, third or fourth hand. The reason for this was that having found a framework, so to speak, I was intent as an artist, to see if some discoveries from other fields would fit into this system. The intention was never scholarly, in the sense that I always felt that I was basically an artist, not a writer nor scholar. At the same time, I felt that I wanted to communicate not so much to the expert in the fields I chose, but in a broader sense to a wider public, artists, who tend not to know the semantics of musicology, and the general public.
Therefore, in using terms such as octave, musicologist might have said "diapason" or wholeness. In this case octave meant, seven, sixteen, or even 53 notes within a whole, depending on just what scale we were dealing with. The universal ladder of sounds would be a "diapason", as would the grid of either eight or sixteen points. For the tones I used Do, Re, Mi, Fa, Sol, La, Ti, in place of C, D, E, F, G, A, B, C, or even more precise tonic or fundamental, Unison (C), minor second (C# (Db)), major second (D), minor third (D# (Eb )), major third (E), fourth (F), augmented fourth (F#), fifth (G), minor sixth (G# (Ab)), major sixth (A), minor seventh (A# (Bb), major seventh (B) and octave (C).
The sharps and flats I used wherever they fell on the grid. Since, in most cases the grid only went up to 16 points I only considered the flatted notes, which are equivalent to sharped adjacent notes, i. e. , Mib, or D#, Lab, or G#, TIb, or A#. Also, different from musicologists, I have used distance to determine the note exclusively, whereas, I could have used the relationship of tone to tone determined by ear only, but that would have no bearing on the visual determination of pattern and distance, from the stand point of this work. Also I simplified considerably the whole idea of proportion based on fractions. Since single fraction can be visually determined by using the relationship of the denominator to the numerator i. e. 2/3 numerator/denominator, this was the basis for the work. The "partial", or the part left over from dividing a string, was only used in one case, Illustration P-13. I did not deal with any groups of notes as a harmonic cluster, but the notes would be seen more as a simple melodic line. I did not go into any theory dealing with harmony or counterpoint, nor did I feel the need for using music scores to illustrate certain points. However, I have often thought of the feasibility of stretching strings over a drawing, for example, tuned to the notes involved. Sixteen strings, for example tuned from C2, E2, G2, B2, D1, F1, A1 as the base notes and C, E, G, B, D, F, A, as the treble, where one could trace the outline of the forms, in a direction progressing from left to right and would directly join sound with vision. Also, since the notes I was dealing with could be approximated by the process of halving a string, successively, this also was a simplification to most systems.
I could have used technical terms for the rays of multiples fanning out from the grid, known as the Lambdoma", or identity rays for each note, named by the Neo-Platonism Iamblichus.
The hexagon or Mib could have been called a "senarius", or sixth on the scale, which is our Mib, where the major scale ends. Of vibrating waves I only used the "transverse" or up and down, rather than the longitudinal, back and fourth, whereas combining them would have yielded another dimension. I was puzzled over many aspects of seeming contradictions such as the inversions of the fractions I encountered while studying these facets. Helmholtz, for instance, claimed that the fractions with the denominator large were the ascending notes, whereas, Levarie and Levy claim the opposite.
Also the correspondences worked out by applying the reasoning of logic to the I. Ching do not correspond with the numbers given for the notes on page 89 of Danielou's "Traite Musicologie Comparee" where Do is five, Re is nine and four, MI# is eight and three, Fa is not included, as being a tritone, Sol is even and two, and La# is six and one, and Ti is not included.
Both Levarie and Levy, and also Ouspensky hinted at analogies of the octave to the periodic table of elements, but not in any structural way which I could determine.
I would have liked to go into the major-minor modes, and the Greek Modes to compare the scales developed under this system, with others, but as much has been written already on comparative studies of this kind it would have been repetitive and not one of depth, so the best I can do is to cite the sequences discovered under this system, So in essence, taking a very tiny part of music theory, was enough to weave many thoughts, around certain visual problems, and come up with an enormous amount of visual ideas, which could then be translated into words, and perhaps in the future be retranslated into music.
"There are three kinds of music, the music of the worlds, the music of humanity and the music of instrument. Of the music of the worlds, one is of the elements, another of planets, another of time. Of that which is of the elements, one is of number, another of weights, another of measure. Of that which is of the planets, one is of place, another of motion, another of nature. Of that which is of time, one is of the ways and the vicissitudes of light and darkness; another of the months and the waxing and waning of the moon; another of the years and the changing of spring, summer, autumn, and winter. Of the music of humanity, one is of the body, another of the soul, another in the connection that is between them. " Hugh of St. Victor (1097-1141) "Didascalicon de Studio Legendi"1
How, what, when, where, why? Questions that we ask about everything. When we focus on one fact, often discoveries are made which bear little relation to what we are absorbed in at the time. This was the case when compiling a lexicon of images, relating abstract concepts of music and art. Suddenly all sorts of ideas seemed to fit into place. A whole was being built up which dealt with phenomena far beyond music or art. Or, perhaps these phenomena always existed in the arts but were veiled to most of us. I call these discoveries GLIMPSES. Perhaps they are only subjective, but I believe they are universal fragments of truth.
I have decided to focus on the How and the What. How these forms were constructed, so that others may experiment with them, and What is the significance of these images of thought.
This book,Eyes + Ears = Ideas, is an expansion of the original Glimpses and was conceived in the nineteen seventies after having come across Pythagoras' ideas of coding musical notes with corresponding colors. I had been a visual artist since the nineteen fifties, and had been re-studying music for eight years at the New England Conservatory of Music, trying to find a link between art and music. I had come across a book on "Tone a Study of Musical Acoustics" in the early seventies which featured an ancient diagram as a two dimensional matrix which mathematically linked ratio to harmonic intervals in music. By combining the color coding of ratios of notes by Pythagoras and the Lambdoma matrix, I was able to translate from color to musical interval in a new art way for me. I am convinced that Pythagoras knew of the Lambdoma matrix as it was predominately used in ancient Greece.
After going back to each image, which were drawn on a treated canvas called "primac", I began to express in words what I had been thinking visually.
The comments are based on the same insights I had while making connections between the intervals, notes and ratios while drawing. This work of pleasure shows the beginning of a long journey toward the fuller understanding of what is called the Lambdoma.
Later in the seventies I wanted to create a music score for each drawing. For the section called "Start Stop and Think" a flutist played the painting/drawings at a solo exhibit at Max Protecht's Gallery in Washington, DC.
I then took a seminar at Robert Ceely's BEEP recording studio and wrote and recorded the scores from each drawing of the section called "The Other Side of Art" on a moog and mini-moog synthesizer.
If the viewer/reader maintains an open mind, there are some insights which might be a spring board to others to further explore this fascinating path.
Barbara Hero (December 1993)
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