| Introduction |
Western culture is immersed in verbal rhetoric. Everything is focussed on language as a way of knowing the world. Language is seen as the panacea for those who are searching for a deeper understanding of epistemology. Within this tradition, there is the study of semiotics with its forced declaration of the significance of oppositions as sign markers or its triadic sign function based on a rigid attempt of Kantian empiricism. Even those whofavor a more post modern approach to philosophy appeal to languagae as a major way of knowing the world (cf. Hans-Georg Gadamer, Sein und Zeit).
There are other ways of knowing the world and they are not structured in the same way as language systems. Visual systems, for example, are not linear. They arrange objects within a visual cognitive space and this space differs culturally. Some of these differences are discussed in this investigation of visual forms as epistemic forms.
Another way in which one knows the world is through music.The proposed systems of semiotics used by language advocates cannot begin to account for the complexity and the systemic interrelatedness found in music theory. Other forms of music are not discussed in this website. However, each of these forms of knowing stand for different epistemic forms of tonality and harmony.
There are other kinds of ways of knowing the world. This is the focus of research on the embodied mind. In this model, one begins with physiological models of vision, hearing, etc. and attempts to look at the biological transducers involved in taking information from the real world and incorporating it into the human biological system.
Finally, there is the philosophy of structural communication. This model re-works the old sign systems of Ferdinand de Saussure and Charles Saunders Peirce into a new model in which the relationship of epistemology to phenomenology is openly discussed and articulated. In this model, one is reminded that culture in the mind has its manifestations in culture in the material world. A significant part of this model is the reality-loop in which meanings are externalized into forms and already established forms are inerpreted into a system of meaning forming a reality loop. Meaning takes place within these loops. |
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The spiral of the chambered nautilus is a logarithmic spirals. This form can be found in the human body and nature, for example the inner ear and the star cluster nebula. What is interesting about these spirals is that they are related to the mathematics of the Fibornacci numbers. For example, the Fibonacci numbers 1,1,2,3,5,8,13,21,.. can be used to create a nautilus spiral. Take a square of size 1, the next square is 2 (1+1), the size of the next square is 3 (2+1), etc. If one continues to add the squares, what emerges is a spiral. The sides of two suares of width 1 creates the sides of a new square with a width 2 and the third square has sides 2 + 1 creating a width of 3. When the sides widths 2+ 3 creates a square of with 5, and so on.
These are epistemic forms. They are visual representations of knowledge. They provide information on the structures underlying them.
Sometimes, the study of these knowledge forms appear under the domain of sacred geometry. What is important about them is the fact that these platonic forms continue to reappear in nature. There is something about that that needs to be revealed. Why do the same forms continue to reappear? |
As noted earlier, the focus of this site has to do with meaningful forms or epistemic forms. This quest ranges from the
study of Archimedean and Platonic forms up to and including various
kinds of analogical reasoning found in verbal metaphors, visual
metaphors, and tonal metaphors. The journey begins with the most
recent of these investigations, metaphor. They are knowledge structures that are formed analogically. They are created by taking a source form and analogically developing a newer form, a target form. It is argued that coded forms are not neutral. They are value-laden. Hence, they are epistemic forms. |
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There are hidden forces and qualities in nature. The indigenous tribes of the Pacific Northwest were attuned to these and represented them in their animal totems. Totems are Jungian archetypes that capture the spirit of nature. It is part of the collective unconscious of mankind.
Human beings are part of nature and they need to be in contact with nature. Symbolically, this connection is captured in the imagery of the totem pole. Its symbols are primordial. They are encoded in the language of the natural world. They constitute visual metaphors. |
The cognitive space of the visual metaphors of the indigenous tribes and nations of the Pacific Northwest use many of the elements of visual languages. The first element that one notices is the circle. The visual forms is embed in a circular form. Western art tends to embed its icons in squares and the art of Asia tend to embed its forms in a elongated box that can be rolled up into a scroll. Colors have special significance and the use of symmetry also reflects cultural values. The Haida are well known for their beautiful artwork. These art forms were not limited to totem poles. They can also be found on clothing, family crests, wall carvings, etc.
All Haida are born either "Ravens" or "Eagles". The mother's affiliation determins this moiety. Within the moiety are lineages. The main crests are utilized for display, personal identity and ceremonial purposes. The details in a design includes: head, ears, eyes, nose, mouth, teeth, tongues, hands, claws, feet or fins, depending upon what the Art object is. Within the body parts there are faces that are used to fill the spaces and constitute an integral prt of the overall design.
Birds such as the "Raven" have a straight long beak which can bes easily distinguished from the "Eagle." The latter have short hooked beaks.
The "Bear" has round nostrils with an impressive display of pointed canines and usually is in a upright sitting position.
The "Beaver" has two large front teeth and may have a stick in its mouth or claws and the tail is rounded with cross hatching detail.
The "Wolf" is closely related to the Bear in appearance but the difference would be the body size and slender ears. The most distinguishing feature would be the curled tail with details at the tip.
Killer Whales have a dorsal fin; a blowhole often located at the top of the animal and a dominant tail. This symbol is used more often than other symbols and is recognized by most people.
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The aforementioned Haid art form is value laden. It is an important epistemic form in the visual culture of that tribal nation. The following links below deal with other kinds of visual metaphors.
| The Grammar of Visual Forms |
The cognitive space of language is not similar to the cognitive space of vision. What is similar is the fact that components within each domain are oganized into coherent systems of forms. Each has the basic elements. Each has their shapes (morphology). Each has their organization (syntax) and each has their meanings (semantics). Hence, a common theme in the philosophy of structural communication has to do with elements and how they are organized. From this point on, the semiotic domains of the visual and the verbal depart. Visual elements are very different from verbal ones. So what are the elements of visual communication? Some of them are provided below: |
The dot
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Dots can be used to organize shapes. When three dots are placed on a surface, they are organized by the mind into the form of a triangle (isoceles, equilateral and scalene). Dots form one of the basic elements of visual communication. |
The line
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When dots are placed in a row and they are not distinguishable from each other, they form a line. Lines can also be used to generate shapes. |
Shapes
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The three basic shapes are the triangle, the square, and the circle. The triangle is made up of three lines; the square is made up of four lines; and the circle is made up of one continuous line (the perimeter) which is equidistant (radius) from the point at the center. |
Volume
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A shape can be shown as a two dimensional figure (length and width). If depth is added, the figure that emerges is in the third dimension (length, width, and depth). Such an object has volume. |
Scale
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This refers to the relationship in size between shapes and objects. Once a reference has been established, one can ascertain how large or small the objects in the visual space are. |
Spatiality
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The way in which space is organized and composed in pictorial design is known as spatiality. Some visual elements are organized, for example, in a balanced pattern (symmetrical balance). What one finds on the left can also be found on the right. When the elements of a visual space are not balanced, they have an asymmtrical balance. The elements are not grouped in the same way around a reference point.
 
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Visual metaphor is a form of analogical thinking using visual elements. There is a source that provides the basis for the creation of a new target, a new idea.
The study of visual forms is important because they deal with the organization of visual space. It is a different kind of space than those that deal with grammar. They constitute a different kind of structural system. This is the driving force behind this investigation. What is this system? How is it organized? |
| Source of Visual Metaphor |
Target of Metaphor, new visual form |
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| Rhetoric has to do with the organization of the status quo. Dialectics, on the other hand, is concerned with new forms and new ideas. Hence, it is not surprising to find that visual metaphors are used in the construction of new concepts. |
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Tonal Forms
Tonal forms may appear to be linear or horizontal as when a melody is played over time. However, tonal forms are also verical in that they represent an ensemble of forms (chords) that co-occurwitin a linear space and consequently are vertical extensions of linear space. For this reason, music in not considered, in this essay, to be involved in linear space. This is especially true when one looks at the geometry of the circle of fifth and the theory of tonality.This is why the semiootic model fails to capture tonal forms. Semiotics assumes a linear space as evidenced in language. Musical space is not linear. |
Western music provides another kind of system of epistemic forms. While tonality is the most common form of organizing Western Music, it is not universal. Neither is the seven note scale universal. As many musicologists have noted, many folk musics and the art music of many cultures focuses on a pentatonic, or five note scale (China, Hungary, Japan). Many are based on atonic systems (India). The focus of this project is on tonal music and how it opeates as a system of knowledge. The instrument used for explication of these concepts can be found on the piano keyboard.
The keyboard is organized into white and black keys. The latter are organized in groups of two or three. Each key has a letter value. These are organized around the seven letters of the alphabet. Once, they are completed, they repeat the cycle.
Tonality in music is similar in function to that of perspective in painting. A perspective is a singular point of view that is used to sense perception and codify it from the point of view of the observer of a painting. Hence, it is a system for organizing visual space. Similarly, tonality is a system for organizing elements of music. It provides a tonal perspective for the listener and for the musical artists. It allows them to be able to interpret how the tonal center is projected onto tonal space. It also provides them with nomenclature and the traditions associated with that music.
The practice of tonal music is based on establishing a "tonality." This means having a tonal center within a tonal space. Within this space there is harmony (concordance) and patterns of disharmony (dissonance that is based on creating tension within a musical space by destabilizing it, and then re-establishing that key). All other chords in this musical space will have an established key ((tonic) but they are also felt to have a certain distance from that key. In classical tonal practice, the sounding of the dominant chord followed by the tonic triad is the basis for establishing a tonality.
| Function |
Roman Numeral |
Commentary |
| tonic |
I |
A music scale usually refers to a progression of single notes upwards or downwards in steps. A scale begins with a root, called the tonic. In a C scale the tonic note is “C.” The scale progresses either up or downward until it reaches the same note in the next octave. A scale in eight notes is called a diatonic. A pentatonic scale is scale of five notes. Pentatonic scales are not often used in Western music. The major exception to this rule would be in American blues and some rock music. They are preferred in other cultures though, such as Asian. Pentatonic scales are also common in Celtic and African music. |
| Supertonic |
II |
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| Mediant |
III |
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| Subdominant |
IV |
The subdominant is the technical name for the fourth tonal degree of the diatonic scale. The tonic is the domiant of the subdominant because it is the same distance below the tonic as the dominant is above the tonic. In the C major scale, the subdomiant is the note F. and the subdominant chord uses F, A, C. It is represented by the Roman Numeral IV. |
| Dominant |
V |
the dominant is the fifth degree (pitch) of a musical scale. in the Cmajor scale. Tthe dominant is the note G; and the dominant chord the notes G, B, and D. In music theory, the dominant chord is symbolized by the Roman Numeral V. |
| Submediant |
VI |
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| Leading |
VI |
the leading-tone is a note or pitch which moves a note from dissonance to consonance. |
Tonality focuses on "triads" of three notes. When these are sounded together they form chords. When they are broken apart they constitute arpeggios. The essence of tonality is concerned with establishing a musical center and a stable triad that form a piece of music, and relating other triads as leading to it. Other chords imply a distance from a basic triad, which the music is supposed to establish by melody and harmony.
The triad for C Major consists of the root (I), the subdominant (IV) and the dominant (V). These three notes are in harmony around a tonal space. There are C major triads (C F G) and C minor triads (C Eb G).
Chord name |
Component intervals |
Example |
Chord symbol |
major triad |
major third |
perfect fifth |
C-E-G |
C, CM, Cma, Cmaj, CΔ |
minor triad |
minor third |
perfect fifth |
C-E♭-G |
Cm, Cmi, Cmin, C- |
Porofessional musicians will find this overview of music to be rather uninspiring. The intend of this tour of music theory is dreicted at those who are engaged in semiotics. They propose a system of oppositions that they claim can handle all sign systems. There are several problems with this claim. They assume the basic sign system is can account for all sign systems. This is not so. The previous discussion of visual space and the current discussion of tonal space demonstate that far more complex systems of epistemic forms underly these systems. Music has to do with a tonal center and the notes that form harmonic relationship around that tonal center. The only feasible opposition within this system is between the contrasts of consonance and dissonance. Hence, it is a limited part of the tonal system. Furthermore, there are geometric relationships and progressions between major and minor chords that constitute a related system of the circle of fourths and the circle of fifths.
The numbers on the inside of the circle show how many sharps or flats would be in the key signature for a major scale built on that note. Thus a major scale built on A will have three sharps in its key signature. Relative minors are shown in blue and you can find accidentals for each key in parenthesis.
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