Further thoughts on the GoMAC.

SUMMARY
 

Geometry of Music And Color, II-III.  Part II of the three-part Geometry of Music And Art (GoMAC) series. 
A visual walk-through and summary of key concepts relating the ISL-derived Brooks (Base) Square, BBS, matrix 
with a geometrically derived division of the monochord resulting in the chromatic and diatonic major scale. 
Original soundtrack (A/B).
 

Part III focuses on a visual journey of how the color spectrum...and specifically the complementary colors 
of each hue...are based on the ISL. This visual walk-through and summary of key concepts relating the ISL-derived 
Brooks (Base) Square, BBS, matrix with a geometrically derived division of both the musical monochord...resulting 
in the chromatic and diatonic major scale...and the color spectrum, in which color complements inside and outside 
of the 400-750 nm visible spectrum dictate the colors that we perceive. Based on "The Geometry of Music, Art and 
Structure...linking science, art and esthetics" white paper, "Geometry of Music And Color, I" new media net.art 
project, and the  BBS matrix. Original soundtrack (C/D).
 

DESCRIPTION 
 

How the natural, geometric divisions of the musical monochord and the color spectrum are inherently derived 
from the same universal law that informs how light, sound, electromagnetism, gravity...indeed, "The 
Architecture of SpaceTime" itself...behaves. That law is the Inverse Square Law (ISL) and 
it has a specific relationship to all the quantitative, whole integer numbers as shown in the Brooks 
(Base) Square matrix (BBS).


Part II of the three-part Geometry of Music And Art (GoMAC) series focuses on a visual journey of how 
the musical spectrum...and specifically the chromatic and diatonic scales...is based on the ISL.
 

A visual walk-through and summary of key concepts relating the ISL-derived Brooks (Base) Square, BBS, matrix 
with a geometrically derived division of both the musical monochord...resulting in the chromatic and diatonic 
major scale...and the color spectrum (as seen in GoMAC part III).  Modulations around the Circle of Fifths and 
the Golden Rectangle are...key.


Original soundtracks (A and B).

Part III focuses on a visual journey of how the color spectrum...and specifically the 
complementary colors of each hue...is based on the ISL.
 

A visual walk-through and summary of key concepts relating the ISL-derived Brooks (Base) Square, BBS, matrix 
with a geometrically derived division of both the musical monochord...resulting in the chromatic and diatonic major 
scale (part II)...and the color spectrum, in which color complements inside and outside of the 400-750 nm visible 
spectrum dictate the colors that we perceive. 


Based on "The Geometry of Music, Art and Structure...linking science, art and esthetics" white paper, 
"Geometry of Music And Color, I" new media net.art project, and the  BBS matrix.


 
Original soundtracks (C and D).

STATEMENT

Our ears hear sounds as frequencies. Our eyes see colors as wavelengths. The shorter the wavelength, the higher 
the frequency, and vice versa.

The physics of sound divides up the frequencies within a monochord (string/wire/length of tube/etc.) into a 
fundamental tone (the whole string length), and, a series of harmonics (partial lengths), that may be organized 
into a series of pleasant and mathematically coherent arrays called musical scales. The octave in the Western 
chromatic and diatonic scales, with 12 and 7 pitch tone intervals, respectively, being the most predominant example. 
The "eighth" note of the octave is simply the repeat of the first note of the scale, only at twice the frequency. 
These octaves of sound range from near zero to infinity and our ears can comfortably hear 8-10 octaves. Every octave 
represents a doubling of the frequency of its predecessor octave. Thus the mathematical coherentness of how a monochord 
is divided is required to ensure the harmonics of each subsequent octave. 

Exactly the same physics occurs with light and color with the exception that our eyes have evolved to only 
perceive a single octave out of that vast array of octaves found in the electromagnetic spectrum. The focus is 
completely on the subtle micro-divisions (colors) of just a single octave of light ranging from 400-750 nm 
wavelengths (Purple-Blue Violet-to-Red-Infrared).

Treating both the frequencies of music and the wavelengths of color in geometric terms...that is, taking the 
fundamental wave properties of each and giving them a geometrical representation in the form of proportions, or 
ratios, in both numerical (x/y) and graphical (O) symbols...allows us to readily see the underlying mathematics 
that informs them both.
 

And what is that common, universal mathematical theme that is informing not only the musical and color spectrums, 
but all sound, light, electromagnetism, mass, energy, gravity, and more, distributions? It is the Inverse Square 
Law (ISL) and the numbers that describe it in the Brooks (Base) Square matrix (BBS). It's not all that surprising, 
in that the ISL-derived BBS matrix is proposed to provide "The Architecture Of SpaceTime" itself. That's right. 
The energy which describes each quanta of space-time is informed by the ISL...ensuring the communication between 
and the harmonies of the entire cosmos. No wonder the perception of sound and light that our little ears and tiny
eyes have come to be based on is the same ISL-BBS matrix dynamics. It's from these fundamental proportions that 
all our organic, life-giving proportions of the golden mean, rectangle, and spiral...as embodied in the dynamics 
of the pentagon...have evolved.