The Harmonic Color-Tone Wheel

Color-Tone
When color symmetry is mapped onto the scale symmetry of a 7-tone diatonic scale, a perceptual correspondence can be established between vision and audition. Read More...

Piano Keyboard and the Gregorian Calendar

PianoKeyboard
I received this graphic from Bob Schlenker depicting the twelve months of the Gregorian calendar as a twelve-tone scale in an octave. Read More...

The Musical Structure of Life

Life
There is a simple equation describing how life grows and evolves. Read More...

Diatonic Standing Wave Model

DiatonicWave
According to harmonic interference theory, the 7-tone diatonic scale of common practice music can be represented as a frequency doubling (first harmonic) of a 12-tone octave standing wave. Read More...

Color Spectrum to Log Octave Mapping

Spectrum
The range of human vision is 370THz at the red end of the spectrum to 740Thz at the blue end. Read More...

Standing Wave Symmetry in Music

Stars
The major scale on a piano keyboard is only symmetric around one note, such as D in the key of C major. Read More...

The Dream Theatre

DreamTheatre
Here is a page out of my graphic novelette The Grand Scientific Musical Theatre. Read More...

Harmonic Organization of the Periodic Elements

Periodic
Harmonic science extends to the atomic level too. Read More...

Fish Archetype for the Cycle of 5ths

Fish
Through the study of harmonic science we can find connections between music and biology. For instance, music tradition suggests that the Cycle of Fifths is a natural harmonic chord progression. In fact, most music is based in some way on portions of this progression. Read More...

Mutually Orthogonal Isometric Hexagons

Isometric
The geometric figure on the cover of INTERFERENCE was part of a graphic art series entitled Cubing the Human Archetype. Read More...

The Geometry of Music

Geomusic
The geometric balance of chords around the harmonic center is the source of musical ethos. It represents the symmetry of a standing wave and its opposing flows of energy. Read More...

Music Visualization

Visualization
When the Standing Wave Model is projected out in time, chords and melodies take the form of tumbling geometric shapes. Read More...

Dual Ring Harmonic Models

DualRing
These are some of the harmonic ring models described in the fourth section of INTERFERENCE. Read More...

Harmonic Symbolism in Art & Music

Unfold
A harmonic archetype and incantation for the opening of Sortrilege (Sorcery for Three) by contemporary composer Robert Xavier Rodriquez. Read More...

The Octave Standing Wave Keyboard Model.

OctaveWave
The Octave Standing Wave Keyboard Model.
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Music and Reflective Interference Model

Reflective
Harmonic Interference Theory proposes a music theory based on human perception of resonance in both sound and light rather than Church tradition. Read More...

Tone-Color Dual Ring Model

DualColorRing
Color geometry - genesis of the Dual Ring Model (both diatonic and chromatic) in Harmonic Interference Theory. Read More...

Tone-Color Correspondence to a Double Octave

Double
This Tone-Color Correspondence to the Double Octave is based on the three color cones of the human retina. When the dark blue or indigo cone distribution is folded over the point of symmetry between the red and green cone distribution, it forms the four points of a 12-step color wheel. Read More...

Blackman Spectral Analysis of Two Tones

Blackman
This is a Blackman spectral analysis of two tones diverging over an octave, revealing the natural distribution of harmonics that are involved in the human perception of music harmony. Read More...

Key of C Major from the Fourier Series on D

Cmajor
Corresponded this morning with author Jill Mattson, resulting in the following email exchange about the golden ratio (phi) and its relationship to the perception of music harmony. Read More...

Babylonian Music Tablets

Archaeo
The field of archaeomusicology is the study of music in ancient cultures. Recent discoveries in this field have found that the mythology of ancient Mesopotamia is readable as tonal allegory when its numerology is decoded as tuning theory. Read More...

Bar Tritone in Rome

Bar
This little restaurant in Rome is where I had my surprise birthday dinner a few years ago. Appropriate, no?
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The Keyboard Models

KeyboardModel
This is something like what I visualize when I improvise jazz piano, only with additional layers and wave sets that unfold rapidly in time. I imagine sticking my hands into an oscillating web of harmonic waves floating over the keyboard and guiding the waves to shape different geometries. Read More...

Phi-Recursive Heterodyning

PhiRecursive
This is an illustration of "phi-recursive heterodyning" demonstrating how harmonics emerge from the golden ratio by following the Fibonacci series backward. Read More...

Golden Ratio in Pythagorean Tetrachords

Tetrachords
Dual golden ratios in the tritone function of a diatonic scale (relative to C major / A minor).
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The Twin PIllars of Hercules

After finishing my last article Eleven that described my experience (and apparent widespread phenomenon) of 'seeing elevens', I watched this excellent video about this same subject. Avia Venefica's comments about the symbolic meaning of the double ones of eleven and its duality are right on target, which prompted me to further connect this phenomena with the physics and mythology of harmonic resonance.

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Cymatic Symphony Video

Here is an excellent video of visual music... Read More...

Musica Universalis Model

In the book, a recursive Hilbert Space is proposed as a common geometric model for both the solar system and the human body. There was not enough space to present both together, so this post provides a high resolution diagram that clearly and simply demonstrates their shared harmonic properties. Read More...

The Solfeggio Scale

I have been getting a lot of email concerning the Solfeggio scale. It seems there have been several popular books about its healing effect on the body. Some have even purchased tuning forks tuned to its specific frequencies, which are higher than today's system. This post discusses the good news and the bad news about this scale. Read More...

Relationship between geometry and wave interference

This is a summary of my philosophy regarding geometry as a function of wave interference. Read More...

Aquamarine damping field

This post discusses the relationship between the golden ratio and the color aquamarine. Read More...

Interference pattern of the Helix Nebula ("Eye of God")

A picture taken by the Hubble telescope in 2003 has been making the rounds on the Internet because it resembles an eye. It appears that the formation of this Nebula follows the same laws of physics found the physics of harmonics as expressed in tonal diatonic music. Read More...

First Visualizer UI Design

One of the practical applications of Harmonic Interference Theory is use in computer-assisted music analysis and composition. To that end, I have begun a series of designs that I will begin to prototype in Flash and post in a new section here on the site. If you have question or comments about this, please send me an email. Read More...

Jazz examples of the Tritone Substitute

I have received some requests to explain what a "tritone substitute" is and how it is used in Jazz harmony. Here are four examples of how a tritone sub might be used in a common dominant-tonic cadence. Read More...