Graphical Musical Notation Systems

            This page is a description of some of the musical notation methods on this site. It is an attempt to describe as
clearly as possible the methods I used to create them. It also describes the logic that underlies why these rules were
chosen. It is essentially based on scientific reasoning and inventive intuition as an attempt to unify time, space, color
and pitch in a reciprocal way that is congruent. It also briefly describes some of the benefit to using these methods
as they apply to the hearing and visually impaired as well as the understanding of music as a whole.


Tone color is not a new concept in music theory, but it is traditionally used to describe the dynamics of the over tones, in that a tone is more colored if there are more frequencies present in each note. This notation system uses a different terminology for tone color, one based on Newtonís analogy of light and sound waves. In this way each shape has a surface color that is indicative of its pitch, when seen spectrographically, the colors that are or arenít present in its emitted light are used to tell what the composition is, i.e. what musical key it is. In this way a number of symbols may be established, in a 12 tone 12 octave system 144 unique symbols can be created and easily recognized. This is done by determining the color of the ground and the shape that is on it. In this painting the black and white shapes represent drum patters because drum sounds have much more broad bandwidths such as with black and white colors. In this case the background determines what the drum sounds will be, each containing 12 sounds organized in a series from low to high frequency. This brings the total number of symbols to 168. However, a red shape on a red background will be hard to distinguish, so a strong outline would be necessary, if these notes are left out there will only be 156 possible notes, as each octave will be missing one note. This will create an interesting type of limitation whereby the higher the octave the lower the key; many other systems may be established along these lines. This system can be seen here. Each shape is both a note as well as a graph of time and pitch. In this way the overtones of the sound are created by the shape of the note that signifies this frequency range, so that the top of the shape is several wavelengths above the fundamental pitch which is aligned with the bottom of the shape. The sound is created with computer software that scans across the shape and produces a pitch variation that is determined by the flow and progression of the shape itself. To do this the shape is photographed, digitally isolated and rendered as a sound, then the sounds of each chord are mixed together after each shape has been analyzed. This is done with another program that allows one to place the sounds exactly in the position in time that the notation signifies.                      


The visualization of sound can also be a method for the hearing impaired to create music. It has been noted that Beethoven, upon becoming deaf still sat at the piano to create music and could very possibly been feeling the vibrations of the music to compose, he was also certainly using his hands and knowledge of the keyboard to help him in a spatial regard. In a similar way by depicting sound with materials that resonate with a natural frequency at a specific vibration/pitch, a type of symbolic feedback mechanism is created which is used as a type of objective visual metaphor for sound and symbolism. A close example of this can be seen in the system of musical instrument categorization used by the ancient Chinese, who place instruments into categories based on materials. This is different than the western technique of categorization which is based on how it is played, such as with wind, or string. I propose a new categorization system that is metaphysical, it is based on melt. It uses a hypothetical material that is deformed by the back ground temperature, thereby altering the octave of the symbol and also its shape. It may be used in two ways, the artistic understanding of color by which blue violet, the top of the color spectrum is considered cool, and red, the bottom is considered warm. Or the scientific understanding of temperature, which is a reversal of this, in this case as shown by Wienís displacement law, red is cooler than blue. Each may be used but the color spectrum must be kept ordered and sequential.


Other rules are necessary to create a musical notation system, the primary requisites such as duration and rests must be established with a readable and quantifiable method. The use of rotation to quantify rests is the method used for this image, each helical turn can be counted; the more turns, the longer the rest. One turn represents a 32nd note two turns a 16th and so on. As for duration each note is composed of discrete parts that utilize the same method, one shape represents the shortest duration possible, in this image a 32nd note and so on as the rotation system also implies. Each chord may be composed of many notes with various durations, and complex chord progressions can be made by using multiple time lines and rotations to create polyphonic complexities.


Although this system may allow deaf people to compose music in a new way, a sculptural system is required to allow blind and deaf people to compose. I have not finished this system but the basic sculptural music notation method is complete. I have constructed a type of clay sculpture that utilizes color to describe pitch and rotation to create a geometric series describing the relationships between the chromatic scale. In this system strings of clay are rotated a number of times depending on the color. The rotation creates a system of waves when the lengths of each string are constant. In this way, magenta is 2 rotations and red 3 rotations. The clay is spun around a black or white string which has no hue so that it may be distinguished from the note, and is necessary to give the rotation physical strength. These sculptures can be seen here.


When 2 or more notes are to be combined in this way the ends are connected and they are spun again into another helix so that the relationships between the numbers of rotations for each color can be seen. Another method of rotation can be used to create a flatter structure so that the rotations may be counted easily and so that multiple sculptures may be stacked. This system of rotation does not rely on a single axis of rotation as the first method described. Each sculpture has a magnet so that it may be used on a wall, and the polarities are aligned so that they may be stacked.


This system may be used just as the visual method, but to conserve the necessary sculptures, different methods can be used. I have been working on a type of map of time for many years and I have developed one that may be used with the sculptures. It is essentially a drawing with concentric squares; the first one in the center represents the beginning of time, each one outward from that represents a 2 fold increase in time, starting from a 64th note. The idea uses a geometrical relationship between the sizes of the squares, so that the shorter durations correspond with smaller fractions of space. The system repeats for each of the four corners, which represent quarter notes and the entire image represents a whole note. This can be seen here. Almost every possible fraction may be created by measuring the distances between each square and delineating 32nd note fractions back in time from each square to the one preceding it. This time map system may also be used as a two dimensional one, if the spaces for each note are filled with a color; this can be seen here. This geometrical system can be compared to the ancient Indian philosophical concept of yantra, which is an image representing a structure of limits, in this case, fractions and positions in time. The beginning of time is signified by a point in the center of the image, which is comparable to the idea of bindu which represents a beginning or separation from oneness to the progression of time into infinity. 


A visually impaired person may use this system if the squares were constructed with raised lines which can be felt. If the rotations were constructed in an extremely accurate way they could also be felt and counted, and if the scale of each sculpture/note were measured, octaves could be distinguished. Durations can be signified with a string that extends from the beginning of the note where the sculpture is placed to the end, where the note extends in time. Other methods may be used to measure duration; counting stones can be used to alter the duration of each sculpture which will represents a given fraction of time. The stones are organized as such; metamorphic rock multiplies the duration by 2, because of the folding action of this stone. Igneous rock divides time by two because of the dividing process of intrusive igneous deposits. And sedimentary rocks add time because of the addition process of conglomerate stones. Larger durations are made with multiple stones of the same kind, and they may also be magnetically stacked. In this way the geological processes of each stone create a mathematical property inherent in its formation and can be used as mathematical symbols to quantify duration when the stones are magnetically attached to the sculpture notes. These stones may also be constructed in such a way as to be distinguishable to a visually impaired person.


The sculpture system has the potential to create a musical game, which is something not very new to the world. But I am working on a different type of game not simply designed to play back a song. The goal of this game is to score points and it is potentially a multi player game. Each person takes turns placing sculpture notes on the time map and points are awarded for certain musical compositional devices. For example, a 7th chord would be awarded a certain point value and a third another, as the game progresses each chord value changes and becomes diminished. Because of the complexity of music, it will take some time to establish the rules of the game, but ultimately the goal is to create a system by which friendly competition between players creates the best possible musical outcome and is a collaborative song. The concept that musical compositional moves may be awarded points may seem impossible due to the mysterious property of music but there are enough fundamental concepts to create a game in this way and still allow room for individual expression. In that the same song wonít be created each time just to score the maximum points. It may be necessary to use dice to prevent this, but I am hoping to not use chance, but make the game much like chess in that it is a unique game each time it is played and is dependent on the mental activity of the players not the randomness of dice. The sense of randomness will have to come from the activities of the players who make competitive moves.


Other musical notation devices on this website contain other methods. The musical drawing system utilizes chromatic circle, which is a Cartesian method to distinguish key by a position on a dial much like a clock. In these drawings the beginning of time is simply the end of the time line and this point is the locus to which the positions of the preceding notes are compared to. For example if the first note is directly below the origin point then it is F sharp. Octave is determined by the number of voids in each shape; the more voids the lower the octave. This system has the potential to create a large number of symbols. The notes are connected by a time line and the numbers of rotations of this time line create rests. The quantity of forms at each point in the time line are counted and this determines the duration of this note. These last two systems are the same as that of the painting notation method described above, the drawing method can be seen here. This was the proceeding method that lead up to the system of using color. This is an almost complete description of all the notation methods shown on this website. There are also other drawing systems, one of which does not utilize a chromatic circle but it utilizes voids to distinguish key, seen here. I have altered the systems many times in order to create a system with more expressive potential. The first system for example, utilizes chromatic circles and a time line, but there are no indications of rest or of duration, each note is distinguished by an angle about a nucleus and the color of this form is indicative of octave. This is the rice paper painting and can be found here. Another system is based on a multidimensional structure of overlapping circles, each circle represents a quarter note, so that the structure as a whole represents a whole note. Each circle is divided into a number of spaces with fractions to distinguish the placement of notes in time. It can be seen here. The angels about the center distinguish key with a chromatic circle, and color is indicative of octave. Each circle is rotated to be distinguished and black and white colors help to make each circle/quarter note visible.  

It is well known that the origins of abstract painting in the west are firmly connected with notions of music. The properties of music which are not figurative in themselves, because orchestral musical instruments are not naturally grown or representative of clearly defined concepts; have given these visual artists an excuse to make pictures of images that are likewise not representative of physical things, but like instrumental music, represent abstract feelings or undefined subjects. However, I would like to point out that traditional music that uses musical instruments is indeed using representation, all the musical instruments in an orchestra exist, and even if new materials are used to accompany them, it is still a form of representation, no matter how abstract the composition. Even electronic music which is a step forward towards a freer form of instrumentation, is highly dependent on the machines used to produce them. Ultimately the freest form of instrumentation is one in which the composer utilizes an invented method of notation as well as an invented set of overtones for each instrument. This would separate it from any form of representation which may alter the interpretation of the music by the listener, which will recall certain aspects of reality from the memory. This will create a truly abstract music that will be a step beyond music of the past in that it divorces the attachment to traditional instruments and notation itself without simply ignoring harmonics or fractions of time. It is an incredibly time consuming process where each instrument is created each time it is used, be it as a two dimensional graph of energy.     

Please let me know if you are interested in more information. Also, if you are interested in creating a system for auditory and visually impaired people to use let me know. Thank you for your interest and I hope you find this research significant.

Jon Axelrod
            May 2009