Dolores Catherino


    Visible light is made up of a spectrum of colors, invisible except on rare occasions (rainbow, prism, etc.). Generally, these component colors (red, orange, yellow, green, blue, indigo, violet) are always present yet individually invisible. By analogy, imagine sound as consisting of component multidimensional aural-spectral colors, most of which are inaudible due to the perceptual limitations inherent in our low pitch-resolution, 12 note per octave ‘pitch color’ palette. 

    The pitch continuum is made up of unbounded fundamental pitches (tones), each containing an infinite series of harmonics (overtones). Presently, most of these embedded harmonics are inaudible due to perceptual (awareness) and physical limitations.


    A fundamental example of the pitch continuum:

    Development of refined fundamental

micropitch perception leads to further

refinement of extended harmonic

perception, and vice versa. This website

is an effort to expand perceptual

consciousness within the musical context.


    In addition to the physical and cognitive limits to perception,

limits of imagination/intuition are no less relevant. Creative imagination and intuition can expand the boundaries of learned cognitive/perceptual pattern recognition, meaning, expectations

and projections.

    Creative imagination and intuition are elements that can be considered to fit integrally within gestalt theory. The perceptual whole is greater than the sum of it’s sensible parts. - The creative (expressive) whole is greater that the sum of learned language, techniques and practice.


    An example of ‘in-between’ pitches beyond the auditory resolution and notation of our chromatic musical language:

Listen especially for the harmonics and

the powerful pitch space between the

minor and major 3rd.

Notice that there is no rising pitch

Doppler effect of the horn as the

train approaches, only increasing

frequency intensity (volume) and

brighter sound (more prominent

higher harmonics).

Also note the very significant (transient) Doppler effect of the horn

as the train passes (lowering of pitch/harmonics).

Notice that after passing, the end of the train horn sound rises to

the original pitch.

The subsequent horn sound has new prominent harmonics and an overall prominence of the lower harmonics (darker sound). The fundamental horn pitches are now the same after as before.

Interesting implications may result from the 2 observed phenomena:

1.    Dynamic harmonic spectral shifting with movement. [timbre]

  1. 2.   A perceptible collapse of the doppler wave function as the       

       passing train horn ceases sounding.


ex.  Primary and secondary harmonics on a low E string.

Try to appreciate the interlaced primary (overtones of the fundamental pitch) and secondary harmonics (overtones of a harmonic, spectral interactions) embedded within the low E fundamental pitch. 

ex. Gestalt (interactive) harmonics

Try to appreciate the harmonics created by the interaction of

two musical parts (input signals) which are present in neither

part alone.


   The potential impact of microtonality is in the development of an increasingly refined level of auditory pitch resolution and perception. This would, in turn, allow a progressively expansive perception of complex harmonic interrelationships embedded within the gestalt. An evolution in auditory intelligence.

    Philosophically, such an application of microtonality would constitute a movement away from a traditionally dominant quantitative perspective of music, toward a perceptual integration

of the pitch continuum as an unfragmented and dynamic whole.

    This holistic perspective is in complementary contradistinction to an application of microtonality as a process toward further ‘atomistic’ subdivision/quantization of the pitch continuum. This quantitative approach being initiated as part of a conceptual pursuit toward an audibly optimized, static ‘micropitch particle’ and its subsequent application as a ‘fundamental building block’ of music.


    We live in a visually dominant culture resulting in a relative lack of auditory descriptive words and concepts. We will gain initial clarity through the use of visual  analogy; with the use of language related to the visual domain in application to auditory phenomena and experience.

     As a metalanguage, in analogy to metaphysics, music lies in an intuitive as well as cognitive realm beyond concrete, absolute or definitive linear expression. As well, there is an overriding aspect which lies beyond mere technical execution. In the attempt to express creative, intuitive and metaphysical ideas in conventional language, analogy and metaphor can provide an indirect essence of the subject.

     Understood through intuition and creative gestalt integrations, metaphor and analogy are important tools of language, transiently engaged in an exploration/description of creative ideas which lie beyond the limitations of discursive language.

    To see’ through the eyes of an artist entails the perceptual development of increased color and spatial discrimination:

visual perceptual elements                                 analogous aural perceptual elements

Hue (discrete colors r,o,y,g,b,i,v,m)  -   Quantized pitch differentiation

Chroma  (intracolor variation)           -   Continuous pitch variation

Luminosity (bright/dark gradation)  -   Timbre  dynamic harmonic        

Texture  (surface quality)                                  spectral dimensions

Saturation  (color intensity)               -   Volume sound intensity     

Spatial visual dimensions                   -   Spatial aural dimensions

Temporal dimensions                                     -    Temporal dimensions

(dynamic process → static representation)         (dynamic process → dynamic,

                                                                                     transient representation)


    Pitch can be re-conceptualized as shades of aural color. The

traditional written musical language can easily expand from a black and white, two dimensional system, to a multidimensional color based notation system, enabling an intuitive visual designation of additional ‘shades’ of pitch color. This development would easily convey ‘increased resolution’ spectral aural pitch-color divisions along the pitch continuum.

    Such a microtonal notation development would constitute a 21st century evolution from monochromatic music systems (combinations and contrasts of black and white), to polychromatic music systems (encompassing higher resolution ‘aural color’ gradations of pitch), with exponentially expanded color combinations and contrasts.

    Timbre or ‘tone color’ can be abstractly referential to an artistic medium (oil, watercolor, pastel, clay, bronze...) with textural qualities described as brilliant, harsh, soft, warm,  etc. Beyond noticing which instrument is producing a given pitch, timbre can be conceptualized and developed into an unending complexity of gestalt perceptions (i.e. interactive harmonics).

   Optimally, the visual artist is able to creatively imagine and express through subtle hues of color, texture and dimension, an integrated perceptual resonance that can expand and deepen collective conscious awareness.

   The visionary musician can likewise refine auditory perception

and expressively bring into collective aural awareness an evolution

of sound spectra, encompassing emotional pitch/harmonic color and tonal/sound color (timbre) combinations beyond anything yet known or experienced. 

Contemporary Western Music Theorya different perspective:

    Our current 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 = 2f 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.


    Pitch as a verb, a contextually dynamic process, not a noun or fixed thing.


In the key of ‘C’: notice that the ‘A’ as a major 6th of ‘C’ is narrower (more flat) than the ‘A’ as a 5th of ‘D’.


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 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 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.


Pure intervals vs 12ET. Note the very sharp major 3rd as well as the harmonic blurriness and agitated resolution created by this compromise.


   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 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).


    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 ...



the greatest problems in life can never be solved. They must be outgrown, by attaining a new level of consciousness.

              - CG Jung