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The Color/Shape/Sound,
Ratio & Symmetry Calculator is a final design project/thesis
for Interactive Media, and Architectonics: Ratio and Symmetry. The
final implementation of this piece will be realized in Director/ Shockwave,
and be web-accessable. The only equipment needed will be a computer
keyboard and a mouse.
questions/comments: gdunne@quilime.com |
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Color/Shape/Sound
Ratio & Symmetry Calculator
©2002 gdunne |
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Introduction
The Color/Shape/Sound calculator will generate a three-dimensional
shape as a result from musical input from the user. The calculator
will also attribute color to certain notes, creating a harmonious
relationship between Shape, Color and Sound.
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The Circle of Fifths
The Circle of Fifths is an easy way to learn the key of a given musical
composition. The Circle of Fifths tells you how many sharps or flats
are in a given key. C has no sharps or flats. The diagram is called
the Circle of Fifths because as you go clockwise you go up a fifth.
For example, the fifth note of the C major scale is G. The fifth note
of the G major scale is D, and so on.
Notice that every other note is succeeded by the one before. C, skip
G, D, skip D, A, etc. Also notice how there are twelve notes corresponding
to twelve numbers on a clock. C is in he 12 noon position. G is in
the 1 o'clock position (likewise has one sharp; F in the 11 o'clock
position.) D is in the two o'clock position (likewise has sharps;
F and C). A is in the 3 o'clock position (likewise has 3 sharps; F,
C, G). E is in the four o'clock position and has 4 sharps (F, C, G,
D). B is in the 5 o'clock position and has 5 sharps (F,C,G,D,A). F#
is in the 6 o'clock position and has 6 sharps (F,C,G,D,A,E; everything
is sharp except B; notice also how this corresponds with the key of
F in which it has one flat, Bb).
If you follow the gray lines of the inner star, you can visually see
how a single octave of sound is represented in this circular fashion.
As we move counterclockwise around the wheel, we begin to see a pattern
of the amount of sharps contained in each major key. There are no
sharps in the key of C. There is one sharp in the key of G, and two
in the key of D, etc.
C |
0# |
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G |
1# |
F# |
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D |
2# |
F# |
C# |
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A |
3# |
F# |
C# |
G# |
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E |
4# |
F# |
C# |
G# |
D# |
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B |
5# |
F# |
C# |
G# |
D# |
A# |
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F# |
6# |
F# |
C# |
G# |
D# |
A# |
E# |
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C# |
7# |
F# |
C# |
G# |
D# |
A# |
E# |
B# |
To count the number of flats, we move backwards along the wheel. There
are no flats in the key of C, one in the key of F, two in the key
of Bb, etc.
C |
0b |
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F |
1b |
Bb |
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Bb |
2b |
Bb |
Eb |
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Eb |
3b |
Bb |
Eb |
Ab |
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Ab |
4b |
Bb |
Eb |
Ab |
Db |
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Db |
5b |
Bb |
Eb |
Ab |
Db |
Gb |
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Gb |
6b |
Bb |
Eb |
Ab |
Db |
Gb |
Cb |
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Cb |
7b |
Bb |
Eb |
Ab |
Db |
Gb |
Cb |
Fb |
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The Circle of Notes
The Circle of Notes is my own invention, which allows the positioning
of one octave to be placed around a circle in an immediate fashion.
The only relationship between the notes is the actual distance in
which they are spaced from each other on the keyboard. C is spaced
away from C# the same distance as A is spaced from Bb, etc. Hence,
the Circle of Notes is simply a representation of a single octave
wrapped to 360 degrees.
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The Color Wheel In Relation to Music
The Color Wheel describes the relationships between colors. It is
laid out so that any two primary (red, yellow, blue) are separated
by the secondary colors (orange, violet, and green).
When we composite the Color Wheel behind the Circle of Notes, we can
create a working relationship between the two. As we move along the
wheel clockwise, we can relate specific notes to specific colors,
eventually looping through an octave will also loop through the entire
spectrum of color.
According to this model, C relates to Yellow. E relates to Red, and
Ab relates to Blue, (the primary colors). If we look at these notes
on a keyboard, we can see that they are spaced two tones (steps) apart,
or four semi-tones (half steps) apart. An octave consists of twelve
semi-tones total, so four semitones is an exact third of an octave.
Exactly the same relationship that the primary colors have to the
color wheel -- they are spaced apart in perfect thirds. By this model,
C, E and Ab are the 'primary notes' of the octave.
If we rearrange the notes on the Circle of Notes so that the wheel
becomes the Circle of Fifths, and let the corresponding colors follow
the move, the result is a very dissonant color wheel:
According to our model, a very interesting relationship is illustrated,
simply because of the dissonance between certain notes. Complimentary
colors stay in the same, but their arrangement in a circular fashion
is distorted to follow the Circle of Fifths model.
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Secondaries In Relation to the Circle of Notes
The notes in between the 'primary notes' then represent the secondary
and tertiary colors represented in the color wheel.
While the keyboard is beginning to look more like Fisher-Price, we
begin to notice a definite pattern and relationship. As we move up
and down the octaves of the keyboard, the color wheel loops 360 degrees,
managing to assign a specific color to each note in the octave.
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Notes, and Their Relationship to Ratio & Symmetry
Pythagoras observed that when the blacksmith struck his anvil, different
notes were produced according to the weight of the hammer. Number
(in this case "amount of weight") seemed to govern musical
tone. Further, he observed that if you take two strings in the same
degree of tension, and then divide one of them exactly in half, when
they are plucked the pitch of the shorter string is exactly one octave
higher than the longer:
Again, number (in this case "amount of space") seemed to
govern musical tone. Or does musical tone govern number? He also discovered
that if the length of the two strings are in relation to each other
2:3, the difference in pitch is called a fifth:
...and if the length of the strings are in relation to each other
3:4, then the difference is called a fourth.
Thus the musical notation of the Greeks, which we have inherited can
be expressed mathematically as 1:2:3:4
All this above can be summarized in the following, with some other
additional ratios and their names:
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Whole Note |
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1:1 |
Diapason |
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Octave |
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2:1 |
Diapason Diapente |
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1.5 Octaves |
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3:1 |
Disdiapason |
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2 Octaves |
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4:1 |
Diepente |
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The 5th |
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3:2 |
Biatessera |
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The 4th |
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4:3 |
Tonus |
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Whole Tone |
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9:8 |
These ratios can of course be represented visually:
Whole Note (1:1) : |
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Diapason (2:1) : |
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Diapason Diapente (3:1) : |
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Disdiapason (4:1) : |
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Diepente (3:2) : |
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Biatessera (4:3) : |
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(5:4) : |
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(4:9) : |
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Tonus (9:8) : |
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Notes, and Their Relationship to Ratio & Symmetry,
Combined with the Relationship of Color.
To develop an interface that would allow interaction between shape,
color and tone involves an initial choice. Which aspect would the
user interact with? Would they chose colors and have the program draw
a shape, and play the relating sound? Would the user draw a shape,
and have the program chose the appropriate color in the relationship,
and play the corresponding notes? The third possibility would be to
have the user play a piece of music, and have it relate directly to
shape and color. I have decided that this will be the initial implementation
of the first version of this application.
Essentially, the user will play a sequence of notes, the program will
calculate the ratios between these notes and draw a shape, as well
as attribute each note to a corresponding color on the color wheel.
In the future, it's possible that additional versions of the program
will allow the user to interact with all three, and see how the different
factors of shape, color, and sound relate to each other no matter
which aspect is modified. |
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