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Below are some additional animated models to illustrate some of the concepts described in the book and slideshow. You will need Flash 7 or higher installed on your computer to play the animations.

The INTERFERENCE Function

This animation provides a step-by-step explanation of the core function proposed by Harmonic Interference Theory and how it can be used to organically describe human perception of music harmony. The book goes into much greater detail, citing neurophysiological studies and mathematical systems to support the concept.

The Harmonic Hierarchy

One of the key principles of Harmonic Interference Theory is the idea that coherent wave interference of any kind is recursive in space and time, nesting the same pattern inside itself synchronously in order to maintain coherence. The theory proposes a 5-level 12th-power hierarchy to explain the natural organization of harmonic sound and, thus, how we recognize it. The five recursive levels begin as twelve octaves that cover the entire auditory spectrum, then replicate itself at one-octave, one-twelfth octave (or semitone), a single tone and then one-twelfth tone. In this way, the harmonic waves composing the timbre of a tone align at Level 2 while also aligning with an octave at Level 4. The entire hierarchy can be expressed as f(n) = 2^((12^n)/12), n = {-2 .. 2} which means that equal temperament (with its 2^(1/12) semitones) are actually a natural property of the harmonic series. The following animation will take you on a tour of each of the five levels, showing how they fit as a Gaussian pattern within one another and how the golden ratio acts as a constant - a golden pillar, if you will - holding up the entire auditory structure.

The Synesthetic Color Model

The colors used in the various harmonic models defined in the book are based on the simple idea that the visible color spectrum represents an octave frequency range just like a musical octave. Just as a musical octave is a frequency doubling of x to 2x, such as A440 Hz to A880 Hz, the color octave is also a frequency doubling from 370 THz to 740 THz. As a result, the Newton 12-step color wheel may be assigned as isomorphic spectral proportions to each of the tones in a musical octave using the Harmonic Center (D in the key of C) as a polar axis. This is discussed a little more in the excerpt located here.

The Keyboard Standing Wave Model

The Keyboard Standing Wave model represents the inspiration that led to Harmonic Interference Theory, introduced in the excerpt located here. It shows the Tritone Function oscillating inside the common practice V-I chord cadence in the key of A from Dominant E7 to Tonic A major. This illustrates the symmetry around the Super Tonic, or what I refer to as the Harmonic Center, and how the tritone contracts across two opposing golden ratios in each half octave. This is significant because Landau damping theory identifies the vertical silver bars (in particular the darker thin bars intersecting the stars) as calm regions where energy jumps between waves. Harmonic Interference Theory proposes that it is the flow of energy across these two "Phi-damping locations" that accounts for perceived qualities in music, such as consonance, dissonance, tension and resolution. In short, this model is the heartbeat of harmonic perception.

The Diatonic Standing Wave Model

This model defines the 7-step diatonic scale to be a 2:1 coherent pathway of the Keyboard Standing Wave model, which amplifies the alternating odd-even wholetone harmonic components. This means that diatonic scales are recognized as a frequency doubling (or octave harmonic) of the fundamental. This higher frequency (or "higher order") pathway is then a new standing wave that alternates between two major scales exactly a tritone apart while following symmetrically opposing energy currents. This is discussed further in the excerpt located here. Illustrated as first the C major scale and then the F# major scale in alternation, this animation reveals a natural harmonic "breathing pattern" over an octave.

As I was creating this model, I suddenly realized that it matched the three circular regions of the human torso introduced in the excerpt here and in greater detail in the Idea Generator here. While Harmonic Interference Theory proposes the idea that diatonic scales (meaning "through the body") are perceived naturally as a coherent pathway through the harmonic series, the human body itself can also be seen to follow the same standing wave model. The following animation applies the Diatonic Standing Wave model to the human torso, suggesting an explanation for the Indian Hindu chakra system and likely organizing principle behind human physiology.

Of course, Western medical science doesn't recognize anything like this, but it may be how cells communicate to one another to maintain coherence and pump things through the body.