Our current monochromatic musical system is based on a static quantization of the continuous pitch spectrum into 12 equal subdivisions; a recurring, closed, octave circle schema. This may be visualized as vertically stacked closed octave pitch circles, each containing 12 equally spaced chromatic pitches. Each ascending circle starts again, one octave above (double the frequency) the circle and pitch beneath it. The octave is the fixed intervallic relationship upon which all chromatically based systems are based (octave equivalence).

Presently, pitch is conceptualized as a noun; a fixed and static ‘thing’, detached from any unique and dynamic harmonic context. Intervals are also defined in this way with fixed linear multi-pitch (polyphonic) relationships applied to nonlinear hearing perception.
(see pitch relativity)

12 tone equal temperament (12ET) was an efficient compromise, created in the 17th century, to allow a continuing evolution in the musical language from pentatonic (5 pitch system) to modal (7 pitch system) to chromatic (12 pitch system).

The basis of 12ET is that, by definition, the octave is the only interval purely in tune. The rest of the intervals are equally spaced pitches between the octave. Generally speaking, the minor intervals are flat, the major intervals are sharp and the ‘perfect’ intervals (P4/P5) are very slightly sharp/flat respectively.

However, if you listen to a low octave ‘C’ and a high octave ‘C’ on a keyboard instrument you may perceive that the high ‘C’ is flat.

Implication: the definition of an octave is based on the assumption of a fixed linear relationship (oct = 2xfrequency or 1/2f) whereas actual pitch perception ‘appears’ to be a nonlinear process. The octave equivalence upon which the chromatic system is based is a theoretical assumption (and essential principle) which mismatches with our sense of hearing pitch. With high pitch-resolution polychromatic musical scales, the notes, intervals and complex harmonies can be optimized to, and develop our hearing processes.

Consider… thinking of pitch as a verb, a contextually dynamic ‘process’ (relatively, flexibly defined), not as a noun or fixed ‘thing’ (absolutely, statically defined).

Historical Context

The modal systems, Pythagorean (based on pure 5ths) and Just intonation (simple ratio intervals, based on the harmonic series) were good basic premises from which to create early, low pitch-resolution (7 notes per octave) musical languages.

12ET was a compromise to allow for effective modulation into any chromatic key. This tempering of intervals created a mismatch between the tempered pitches and their (untempered) embedded harmonics. Our ears have become used to the impure intervals and the subtle mismatch of harmonics.

Historically, unequal tuning temperaments were less versatile yet more colorful, with each key having a unique and distinct characteristic sound color. Better modal intervallic and harmonic intonation was the rule, as well as a separation of the enharmonic tones (i.e. C# ≠ Db) as distinct, contextually defined pitches. The disadvantage of this system was that it only allowed modulation to closely related keys. More distant modulations sounded increasingly dissonant and out of tune.

Our current system of chromatic equal temperament homogenized all 12 keys removing the former system’s individual key uniqueness as well as collapsing enharmonic pitches to a single fixed pitch with 2 names (i.e. C# = Db). With the condensation and collapse of the prior pitch temperament systems, semitone pitches were fixed at an equal distance of 100 cents. This new quantitative uniformity of each key facilitated efficient chromatic modulation in all 12 keys.

Closer analysis of the 12ET octave reveals that the middle of the octave is the tritone (F# in the key of C). Even with the current consolidation of the enharmonic tones, two ‘pure’ values are delineated for the tritone interval : 590.22 or 609.78 cents. It appears that this is one point where the pitch spiral was conceptually collapsed into a recurring octave circle, with the major and minor tritone (augmented 4th and diminished 5th) fixed at 600 cents.


… a continuous, sonically colorful, open spiral ascending and descending infinitely; consisting of perceptually seamless, subcomponent pitch hues and limitless multidimensional harmonic combinations. This continuous spiral would be funnel shaped to represent the widening pitch space intervals at increasing frequencies (higher octaves). Thus, also visually depicting intervallic pitch relativity.

Further, an intuitive awareness that this multidimensional
spiral image is a representation of only a single fundamental pitch:
primary harmonics, extended harmonics (subharmonics as well as the embedded secondary harmonics contained within each harmonic), and implications of harmony (interaction of multiple simultaneous pitches/harmonics; perceptual gestalt anomalies) have yet to be considered.

… the development of an expansive auditory perceptual awareness and aural intelligence, reciprocally leading toward a continuing evolution of musical systems which more fully utilize the physical hearing apparatus in its optimal ability to perceive pitch differentials of as little as 5-10 cents (evolving high-resolution pitch, timbral, harmonic musical languages).

New musical possibilities

In 1983, the introduction of the MIDI (musical instrument digital interface) system, a communication and synchronization protocol for the exchange of musical information between electronic instruments, provided a foundation for future technological innovations that have enabled the creation of programmable microtonal instruments.

As with any new technology, these musical instrument and software developments facilitate the deeper exploration and understanding of pitch, harmony, and ultimately ‘music’. This technology opens new potentialities of exploration and creation -toward richer sonic realms ‘envisioned’ and limited only by the creative imagination.

Instead of adapting our ears to a simple, low-resolution, linear (mono)chromatic music systems, we can now adapt high-resolution, nonlinear polychromatic music systems to our ears. The creative possibilities and implications are immense within this new paradigm.

Conventional written musical languages (monochromatic) appear to be modeled after black and white, written discursive language, i.e. the alphabetical symbol ‘A’ and the pitch symbol ‘A’ represent absolutely defined, static building blocks; musical and linguistic phrases become defined/codified, conventional, cliche, unquestioned assumptions and abstractions; ideas and innovation becomes
confined within the limitations of the expressive-resolution of the linguistic system.

More expansive musical systems could be based an integrated perceptual language, utilizing visual color discrimination synesthetically tied to aural pitch ‘color’ discrimination – and possibly tactile/bone conduction and perception of sound).

A polychromatic paradigm utilized in the creation of new, increased pitch-resolution music systems would be primarily a perceptually based, integrated multi-sense language. Hopefully, these new languages would catalyze an evolution in musical consciousness toward further refinements in auditory awareness, discrimination and hearing, in perceptual contrasts instead of absolute pitch relationships and mathematically based abstractions (used in justifying and neglecting linguistic options, and as a ‘most rational’ basis of aesthetic judgement). In turn, increasing perceptual awareness and development would further expand the musical languages in a dynamic, bidirectional process.

An unending journey continues, into the mysteries of musical sound and perception …