From 3ed3155cba46324706171883f7e7cd17b1c3d843 Mon Sep 17 00:00:00 2001 From: Gabriel Dunne Date: Sun, 11 Dec 2022 09:08:13 -0800 Subject: [PATCH] Color calc fixes --- _posts/projects/2002-05-01-colorcalc.md | 40 +++++++++++-------------- 1 file changed, 18 insertions(+), 22 deletions(-) diff --git a/_posts/projects/2002-05-01-colorcalc.md b/_posts/projects/2002-05-01-colorcalc.md index 8efe0e3..92a285f 100644 --- a/_posts/projects/2002-05-01-colorcalc.md +++ b/_posts/projects/2002-05-01-colorcalc.md @@ -21,11 +21,11 @@ The Circle of Fifths is a way to learn the key of a given 12-note-scale musical 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. -
![]({{site.baseurl}}/m/colormuscalc/circleoffifths_star.gif)
+![]({{site.baseurl}}/m/colormuscalc/circleoffifths_star.gif) As we move clockwise 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 : G : F# D : F#, C# @@ -34,11 +34,10 @@ E : F#, C#, G#, D# B : F#, C#, G#, D#, A# F#: F#, C#, G#, D#, A#, E# C#: F#, C#, G#, D#, A#, E#, B# -
To count the number of flats, we move counterclockwise 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. Because it's neater, we write everything as flats. -
+ C : F : Bb Bb: Bb, Eb @@ -47,34 +46,33 @@ Ab: Bb, Eb, Ab, Db Db: Bb, Eb, Ab, Db, Gb Gb: Bb, Eb, Ab, Db, Gb, Cb Cb: Bb, Eb, Ab, Db, Gb, Cb, Fb -
## The Circle of Notes The Circle of Notes is something I came up with to describe arranging the notes chromatically around a circle. 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. -
![]({{site.baseurl}}/m/colormuscalc/circleofnotes.gif)
+![]({{site.baseurl}}/m/colormuscalc/circleofnotes.gif) ## The Color Wheel 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). -
![]({{site.baseurl}}/m/colormuscalc/colorwheel.gif)
+![]({{site.baseurl}}/m/colormuscalc/colorwheel.gif) ## The Color Wheel In Relation to the Circle of Notes 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. -
![]({{site.baseurl}}/m/colormuscalc/circleofnotes_color.gif)
+![]({{site.baseurl}}/m/colormuscalc/circleofnotes_color.gif) 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. -
![]({{site.baseurl}}/m/colormuscalc/keyboard_rgb.gif)
+![]({{site.baseurl}}/m/colormuscalc/keyboard_rgb.gif) 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: -
![]({{site.baseurl}}/m/colormuscalc/circleoffifths_color.gif)
+![]({{site.baseurl}}/m/colormuscalc/circleoffifths_color.gif) According to this 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. @@ -83,11 +81,11 @@ According to this model, a very interesting relationship is illustrated, simply The notes in between the 'primary notes' then represent the secondary and tertiary colors represented in the color wheel. -
![]({{site.baseurl}}/m/colormuscalc/keyboard_spectrum.gif)
+![]({{site.baseurl}}/m/colormuscalc/keyboard_spectrum.gif) 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.
-
![]({{site.baseurl}}/m/colormuscalc/keyboard_stacked.gif)
+![]({{site.baseurl}}/m/colormuscalc/keyboard_stacked.gif) ## Notes, and Their Relationship to Ratio & Symmetry @@ -99,25 +97,25 @@ 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: -
![]({{site.baseurl}}/m/colormuscalc/ratio_01.gif)
-
![]({{site.baseurl}}/m/colormuscalc/ratio_02.gif)
+![]({{site.baseurl}}/m/colormuscalc/ratio_01.gif) +![]({{site.baseurl}}/m/colormuscalc/ratio_02.gif) 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: -
![]({{site.baseurl}}/m/colormuscalc/ratio_01.gif)
-
![]({{site.baseurl}}/m/colormuscalc/ratio_03.gif)
+![]({{site.baseurl}}/m/colormuscalc/ratio_01.gif) +![]({{site.baseurl}}/m/colormuscalc/ratio_03.gif) ...and if the length of the strings are in relation to each other 3:4, then the difference is called a fourth. -
![]({{site.baseurl}}/m/colormuscalc/ratio_01.gif)
-
![]({{site.baseurl}}/m/colormuscalc/ratio_04.gif)
+![]({{site.baseurl}}/m/colormuscalc/ratio_01.gif) +![]({{site.baseurl}}/m/colormuscalc/ratio_04.gif) 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: -
+ @@ -169,11 +167,10 @@ All this above can be summarized in the following, with some other additional ra
 9:8
-
Represented visually: -
+ @@ -212,7 +209,6 @@ Represented visually:
Whole Note (1:1) :   
-
## Notes, and Their Relationship to Ratio & Symmetrym, Combined with the Relationship of Color. -- 2.34.1