A Brief  Synopsis of Holistic Tonality by Peter McClard

1. All music is timbre. Corollary:  Music and timbre are interchangeable. Music is timbre applied to consciousness. Music and timbre do not exist outside of consciousness. Outside of consciousness, music is merely wave and particle motion through space-time. Music and timbre can exist in an entirely imaginary realm because it requires consciousness of some degree to have imagination.


All music theories seek to make sense of and codify the relationships created by variations in perceived pitches over time, usually in the form of timbre, notes, chords, rhythms and structures. Because computers and digital audio processors have given us supreme control over the fine details of sound, a modern music theory must include the panoply of new possibilities. The long tradition of theories going back to the Greeks whose disciplined use of modes was geared in creating a set of rules by which music could be made more logical, harmonious and, generally, more appropriate toward the goal of exalting God in the service of the Church, does not adequately equip modern composers and musicians for the future.

Early theory such as put forth by Boethius [1] or Tinctoris [2] , were concerned with resolving the imperfections of musical notes as the use of aliquot ratios such as 1:3, 2:3, 4:5, etc. caused octave inequivalence and dissonance which was thought to be unholy and undesired. Also, early theories were concerned with the formal notation of music so that it could be conveyed from place to place and generation to generation. Music scholars of those times proscribed the use of unison and parallel motion, which was very limiting yet still produced sublime results such as Gregorian Chant.

Later theories began to expand into the world of polyphony where chords became more advanced over time and eventually counterpoint and complex forms of musical structure evolved. Polyphony remained relatively simplistic through much of the Middle Ages and up into the early Renaissance leading to the  advanced musical theory of Rameau [3] which was a turning point on the cusp of equal temperament during the Baroque period which led to an explosion of complex music that endures as supreme examples in: Vivaldi, Scarlatti, Bach and others.

The Theory of Holistic Tonality builds upon other music theories, most notably that of Schenker [4] whose work on harmony and counterpoint is far more comprehensive. However, Schenker could not have anticipated computers, synthesizers and fractal mathematics so his theories could not be fully extended into the modern era.

In all traditional phases of music up until the mid 20th Century, musicians were generally limited to instruments which relied on the timbral qualities produced from naturally vibrating materials such as wood, skins, strings, or columns of air all of which were direct analogues of the most important instrument of all, the human eardrum. In other words, as the string vibrates, so does the eardrum. In the end, all instruments causes the air between the instrument and the listener to be set into motion, culminating in the physical vibration of the eardrum which in turn converts the vibration via a series of tiny bones and the cochlea into electro-chemical signals to the auditory portion of the brain which then creates the sensation or perception of music.

Even modern synthesizers eventually drive the surface of a speaker cone (an even closer analog to the eardrum) or other device, which must vibrate according to the laws of physics. It is no surprise then that theories would center around vibrational patterns that would be perceived as harmonious or “pleasing to the ear.” It wasn’t until Helmholz [5] analyzed these vibrations more closely that it was understood that timbre was the sum of a complex “vibrational chemistry” where some quantity of overtone mixed with others to create a unique tonal quality such as that of a violin, flute or piano. Holistic Tonality simply states that: All music is only Timbre.

2. Timbre operates independent of time scale.  Corollary:  Perception of timbre is governed by the sampling rate of the auditory system of the listener.

The nature of Time itself remains to this day a mystery. It is even feasible with modern quantum physics that all possible music throughout the Universe is in the process of playing or has already played within the confines of the Grand Big Bang. Holistic Tonality seeks to first remove the human element from musical perception and suspend the bias we have for our time scale linked to the days and spans of our lives. Naturally, since we perceive time to flow at a certain pace, we will be attracted to musical events that occur on our scale. It is now known that some animals can better hear not only higher or lower pitches than us, but can communicate complex social messages in timbre.  For example, a particular birdsong may appear to us as unified single sound but nonetheless contain rich details of pitch and harmonic changes and convey hidden messages to potential mates or adversaries. Rats have been discovered to laugh in a high frequency range that sounds to us like squeaks and crickets slowed down sounds like singing. One creature’s squeak is another’s laugh. Time scale is critical to the perception of music but not to the musicality itself, which is independent of time scale. Likewise, we can be assured that an entire long symphony for us, or our speech itself may sound as a squeak to a consciousness that operated at a larger time scale or as a ponderous slow motion drone to a short time scale consciousness. 

The band, Bear In Heaven, pre-released their album, I Love You, It’s Cool streamed over a period of several months slowed down 800,000 percent but at the same pitch (FFT) of the original which resulted in a long drone of ever-shifting timbral qualities which was as valid musically as the works played at 100% speed.

Going back to traditional music theory, it was the imperceptible “squeaks” of the higher frequencies that stealthily governed the need to have a Dominant or Subdominant since these were strong components of the overtones they were hearing and to this day dominate musical timbres. Many overtones are perceived on a subliminal basis, no doubt linking us to our evolutionary ancestors that operated on a faster “speed of consciousness.” Very few people are aware of the individual tones that make up a timbre and we tend to unify these tones into a single sound. Holistic Tonality states that timbre governs or suggests structure, and that since traditional timbres are structured in the classical Overtone Series, the larger structures that were suggested were similar to those found in the Human Music Catalog.

Holistic Tonality does not distinguish between sound and music. The musical experience is left to the observer.

It is not until one starts to deconstruct the temporal aspects of musical structure that one can see clearly that timbre is equivalent to structure, if only on a different time scale. By understanding the relationships between timbre and structure, the modern composer is able to create new masterpieces where there are no boundaries between timbre and structure. In other words, one can compose timbre that freely morphs into musical structure, mixes with it, becomes it, and vice versa, larger musical structures which wind themselves into timbre on another time scale. In a sense, this is no different than what composers have always done using orchestration, dynamics and musical constructs to flow through time musically and tell their story to the listener.

3. No two (biological) observers can experience the same music. Corollary:  Music is composed for a target audience that is expected to appreciate the composer’s musical intent.

There are biological limits to the conscious perception of short sounds that should be taken into consideration as one can study considerable research on the topic including The Neurophysiological Bases of Auditory Perception by Enrique Lopez-Poveda, Alan R. Palmer and Ray Meddis and the work of Al Bregman in auditory scene analysis. However, timbre strikes the mind on the subconscious level as well as the conscious and little research is available on the effects of otherwise imperceptible “tones” on the subconscious which itself is still largely misunderstood. It is obvious that our brains are not equipped with fine-tuned oscilloscopes that can discern each peak and valley of waves that hit our eardrums and are decoded as “the sound” of an instrument, yet we can easily hear the difference between a violin and a cello. The question here is only whether a music composer could use this or that effect at such and such a time to elicit a desired emotional response in the target listener. Due to the nature of qualia, or the impossibility of having another's exact experience and the fact that no two listeners can occupy the same space at the same time, it is safe to say musical experience is unique to the listener.

Classification of and Definitions of Timbre

I found it necessary to create a new nomenclature in order to convey the principles of Holistic Tonality. While I don’t expect these terms to be adopted for common use and also don’t claim that these are the best terms for such, they will hopefully provide a cohesive language with which to talk about Holistic Tonality.

I have formulated numerous experiments which have led me to classify a new class of musical structures I call: sonons, superintervals,  hyperintervals, superchords, hyperchords, etc. In these experiments, for simplicity, let us first use an idealized synthetic instrument that itself has very little color, essentially producing a pure sine wave. This instrument is also able to play a sequence of pitches at any speed but we must have a reference so that we can make valid comparisons. Let’s use 60 BPM as a reference tempo so that our quarter note is exactly one second. In the world of holistic tonality, traditional notation proves limited because within a one second span hundreds of “notes” can go by so our quarter note is really only a durational placeholder for timbre.  The work of Schillinger [6] could lead to a functional notation for this sort of music but he did not anticipate the extreme control over timbre that were later developed with digital synthesis to it would need to be modified to incorporate the deeper level of composition that is now possible..

For our first experiment we play a one octave C Major scale in the span of our quarter note producing a now classic video game sound. This sound is a timbre. To prove this, change it to play 2 and then 3 octaves in the same span producing a totally different sound yet with similar characteristics. Any musical scale can be used for this and each scale of course takes on the tonal characteristics of the scale: eg. chromatic, whole tone, gypsy, 19-tone, etc. Now, let us add another dimension of motion to the experiment by introducing a second “carrier scale.”  To do this we simply transpose our original C Major scale along a C Major scale, thus: C Maj, D Maj, E Maj, F Maj, G Maj, A Maj and B Maj, each time with the entire inner scale playing within our quarter note giving us 7 seconds of a C Major scale made of Major scales. This is a hyperscale. During these experiments it is important to swap in different scales and record the perception that occurs. For example, now play a C min scale made of Majors and a C Major made of minors and a Minor made of Minors, etc. and record the differences perceived. Because there are too many permutations to consider and it will be left to future generations to catalog the possibilities, we must construct computer-based HyperInstruments [7] that can freely examine these and make them useful to musicians and composers. These experiments can be sped up so that individual tones are not perceived by the human ear but their effects are—very much like overtones behave.

Now let’s simplify our experiment to examine the temporal chemistry when only 1 or 2 tones are used. Play a sequence of 32 C tones in our quarter note (technically 1/128th notes). This will produce a straight C tone. Now introduce at first 1 G tone in the sequence which will alter the timbre but it will remain a C tone. This is a superinterval (a superfifth). Introduce more G tones and in different patterns and it will take on qualities of a perfect 5th yet no two patterns will sound identical because they do not have timbral equivalence.

Introducing a parallel superinterval produces a hyperinterval.

Introducing 3 or more parallel superintervals produces a hyperchord.

Using tones that form a triadic or higher order chords (as opposed to two tone intervals) produces a superchord.

Multiple parallel superchords also produce hyperchords.

A single timbral unit (the smallest possible) is referred to as a sonon.

4. Sonons are not timbre, nor are they music. Corollary:  Sonons can have timbral qualities that are only recognized on other time scales, but not the time scale it is being used to compose on.

Sonons produce superintervals which produce hyperintervals which produce hyperchords .

All music is comprised of sonons which are the smallest musical units, or musical quanta. Sonons are the only musical units that are not timbre.

Any consecutive sonons comprise timbre.

A Composition is any music that is played, composed or otherwise created for the purpose of listening to it. Imaginary compositions only exist for the imaginer though they can be realized for other listeners, depending on the skill of the composer and the instruments available. A composition must utilize at least one instrument or sound. A null composition is silence as the example created by John Cage [8] .

Compositions can be broken into the following categories:

·      Structural makes use of traditional compositional techniques such as orchestration, arrangement, counterpoint, harmony and somewhat defined sections. Uses instruments to play notes and is somewhat timbre invariant. Examples: symphony, song, jazz standard, sonata, blues, etc.

·      Timbral focuses on instruments, sounds and textures with less defined structure and sections. Examples: ambient, electronic, trance, techno, noise.

·      Holistic seamlessly combines structural and timbral where musical structure is continued into the finer details of sound.

·      Hybrid, a combination of any of the above.

·      Null, a composition comprised entirely of rests or silence.

An instrument is any single named voice used in a composition. An unnamed instrument is a sound. Physical instruments are instruments that directly cause air to vibrate based on physical actions of a player. Virtual instruments are those that cause air to vibrate based on software outputs. Virtual instruments can be controlled via software User Interfaces of via HyperInstruments, physical interfaces for virtual instruments. All instruments create timbre.

Measures are absolute units of time intervals. Measures can vary in length in the course of a composition or can remain constant. Measures can be delineated in beats or seconds.

A Beat is an arbitrary division of a measure, most commonly 1/4th of a measure is referred to as a quarter note. But this simple classification falls flat when you divide measures into anything but multiples of two. For example we have no concept of an eleventh note. For this we use the tuplet notation, ie. 11-tuplet but when using computers we are only limited by clock speed and math. This bias toward time octaves is no doubt built in to our inner brain and for some reason we are good at halving and doubling or even tripling tempos but we are not as natural at odd divisions or multiples of time where we become less accurate without electronic assistance.

Time domain is any arbitrary contiguous segment of a composition. Absolute time domain is marked by the beginning of a given time domain, in seconds, relative to the Big Bang [9] and the duration of the time domain. Relative time domain is marked by the beginning of a time domain with respect to the beginning of a composition and duration. All compositions start at zero in the relative time domain. Pick-up notes can be represented starting at a negative time. Time zero is beat 0 of any composition but can be referred to as beat 1 in traditional notation.

Tempo can be measured as seconds per measure, measures per second, beats per minute (traditional), minutes per beat, beats per second or seconds per beat. Tempo can change arbitrarily in the course of a composition. As we dive down into the audio level of holistic composition, tempo exists on a different order where kilohertz is used, or thousands of cycles per second. For most people anything above 15 KHz is inaudible, though it may still be perceived by the subconscious.

The sum of all measures in a composition comprise the Length of the composition or the compositional time domain.

A musician is anybody who plays a musical instrument.


A virtuoso is a musician who demonstrates extraordinary skill either by innate abilities or from dedicating a large portion of his or her life to the mastery of an instrument or instruments. A society without virtuosos is musically inactive.


Musical notation is a means by which timbre and envelopes are conveyed from one musician to the next. Roughly speaking, notes are analogous to sonons and dynamics to envelopes. Traditional musical notation is entirely geared toward the human time-scale and is not adequate for composing holistically.


A composer is someone who imagines, plans, evolves or discovers musical ideas and then uses a means of recording, such as musical notation or digital recording to make their ideas available to others. Composers are often musicians and vice versa.


A composer’s or musician’s job, whether practical or artistic, is to create a sequence of sonons with a given envelope.

Envelope is the amplitude of timbre at a given time.  The analog to envelope is dynamics. Each instrument in a composition has its own envelope that can combine with other instrument envelopes to create the composition envelope.

All rhythmic and dynamic structures in music are envelopes for timbre. Silence is a null envelope and is in the context of a given music-space. For example, if musicians rest on a note and someone in the audience coughs during that rest, the rest only exists in the composition-space of the piece but not in the performance-space. The cough is included in the timbre of the performance. Also, during a rest there may be reverberation, ambient or ancillary musician-generated sound such as breathing that is also in the performance-space.


Rests are parts of timbre with no (or near-zero) amplitude for a given instrument. Rests are of arbitrary duration.

Timbre with no amplitude is silence or global rest. Rests do not necessarily create silence in timbre since they may only apply to certain instruments and not others.

Rhythm is the employment of rests and envelopes to create metric patterns and syncopation. Many aspects of rhythm are intangible, such as swing, groove and feel and the human ear is highly attuned to small variations in rhythm. The possible theoretical permutations for rhythm are infinite since any time domain can be mathematically be broken into an infinite number of subdivisions in combination with every possible envelope and accent pattern. However in practical terms the rhythmic possibilities and permutations for a given time domain would be finite but extremely large. Also, we humans tend to gravitate toward rhythmic patterns based on heartbeats and breathing, the most primal rhythms.

Musical Structure is the timbre and envelope of a composition relative to a system of measures.

Pitch is the proscribed fundamental frequency of timbre at a given time. The analog is note. Perceived pitch is subjective.

A Note is any timbre that can be perceived by a listener to have a distinct pitch. Notes have arbitrary duration left up to the composer or player.

Melody is any single-line composition for any instrument or sound that varies in pitch at least once. Melodies that have no significant variance in pitch are drones.

Harmony is any composition that involves simultaneous melodies or melodies combined with drones.

Modality is an arbitrary set of pitches within which melody or harmony operates in a given time domain. The analog for modality is musical scale such as chromatic or pentatonic.

Synchronization is the alignment of one timbre of one instrument or music with another in the time-domain using a grid system of beats and measures.

Dissonance and consonance are subjective qualities or effects of music. One listener’s consonance is another’s dissonance though we know that physics and mathematics plays a strong role in this perception.


Cacophony is the highest level of dissonance and results from superimposing unsynchronized timbres and sounds, the result of which is always timbre.


The tonal quality of music can be categorized as follows:

Tonal: music that makes more use of consonance within the chromatic 12-tone scale based on divisions of octaves by the 12th root of 2.

Atonal: music that makes more use of dissonance within the 12-tone scale.

Macrotonal: music that uses intervals greater than the twelfth root of 2

Microtonal: music that uses intervals smaller than the twelfth root of 2

Crosstonal: music that combines any of the above tonal qualities.


A scale is any ordered set of 3 or more discreet pitches and come in the following forms:

Octival: a finite set that exactly repeats in each octave (linear) with octaves of each note

Meta: a set that repeats over N octaves greater than 1 (linear)

Melodic: a set that changes per octave (nonlinear)

Natural: a set that retains octaves in the tonic only but where notes within the octaves are not octaves of each other

Unnatural: a set that has no octaves

Algorithmic: a scale which pitches are calculated in real-time

Hybrid: a set that combines any or all of the above


A scale can be tonal, atonal, microtonal or combinations thereof. A continuum is not considered a musical scale, though it may share attributes. Some scales are only useful in the field of audification and musification (see below).


The first element of a scale is said to have an integer index of E1 and the last is EN.


The minimum of a scale is the pitch value of the lowest element.


The maximum of a scale is the pitch value of the highest element.


The range of a scale, expressed as an integer, is the difference between its lowest pitch index and its highest pitch index (R = EN.- E1).


The octave range of a scale (RO) is the number of octaves that can contain the scale. This can be expressed as an integer or as a floating point decimal for precision.


The domain of a scale, expressed as 2 integers (equal temperament) or 2 floats where Middle C = 1.0, the first being the offset from Middle C of the scale’s bottom

element E1 and it’s top element EN. The standard 88-key piano keyboard has a domain of {-39,48}. If the domain of the scale is above middle C then both numbers would be positive. Domain maps roughly into the traditional concepts of: Bass, Tenor, Alto and Soprano.


The Size of a scale is the number of individual pitches it contains, S.  Theoretically, scales can extend to frequency zero and infinity. However, for practical reasons they are limited to the range of hearing of the listener.


The Octavity of a scale (O) is the average number of pitches per octave. This can be expressed as an integer or as a floating point decimal for precision. Meta scales can have an octavity < 1.0. For example a Meta 9th has 14 half-steps per pitch. A meta double octave has an octavity of 0.5. A meta octave has an octavity of 1.0. The chromatic scale has an octavity of 12.


Audification is the process by which pure data or information is converted into audio. With computers it is possible to audify any data from any format, most commonly the: CD, MP3, DVD but also including images, video, text and more. Any data can be audified. Audifation is governed by algorithms.


Musification is a similar process to audification but where data is converted into musical structures, mapped into scales and generally made more suitable for musical performance. Technically, musification and audification both produce timbre and are therefor the same, differing only algorithmically. I wrote a program called Pixound which maps RGB information from images into scales and it makes extensive use of all scale types: Octival, Meta, Melodic and Hybrid. Because RGB are fundamental color components of our eyes, Pixound has a claim to musical permanence for all future generations who wish to use color or light as a musical controller. Ideally, one would be able to seamlessly move between audification and musification, controlling musical output on several levels.


In the process of musification where data of higher ranges is mapped into scales of smaller ranges, scale expansion can be used. In this case, scales are padded by repeating adjacent pitches (usually isometrically) to make data mapping more convenient. Increasing the octave range of a scale is another method but can produce undesirable low or high notes.


Any non-parallel superintervals, superchords or hyperchords comprise supercounterpoint.


Supercounterpoint is a subclass of timbre.


Any supercounterpoint can be composed but only synthetic timbres can be composed. Natural timbres cannot be composed due to quantum physics and chaos. Theoretically, one could use a quantum computer to compose hypertimbres which would be analogs to natural timbres.


Mixing any two or more supercounterpoints comprises a hypercounterpoint.


The effect of timbre on a listener cannot be fully controlled due to qualia 12therefor music will always be subjective.


We can never experience the full performance of music since we have only two ears with limited frequency response.


Tonality is an arbitrary system of composition and modality within which a composer operates in a given time domain. Pitch sets can be discrete or non-discrete.

Key Signature denotes a relatively small set of pitches which are expected to occur in a given time domain. In general, it is only useful in notation and performance but is not particularly helpful in composing timbre.

5. Every timbre is a composition and compositions are independent of time scale. Corollary:  Time signatures are time-domain independent. The traditional idea of time signature is still valid insofar as a composer desires to create envelope patterns relative to measures but other more subtle patterns may exist at other levels of the composition completely unrelated to the structure or time signature.

Traditional compositional structures such as: Blues, Sonata, Symphony, Opera, etc. are arbitrary formats for human-scale experiences. In holistic tonality, these are still considered timbres.

Musical style template is any recognizable combination of structure, envelope and timbre.

All Rhythmic and Dynamic structures are envelopes for timbre. Silence and rests are only in the context of a given sonic unit. For example, if musicians rest on a note and someone in the audience coughs during that rest, the rest only exists in the composition-space of the piece but not in the performance-space. The cough is included in the timbre of the performance. Also, during a rest there may be reverberation, ambient or ancillary musician-generated sound such as breathing that is also in the performance-space.

We can never hear the full performance since we have only two ears with limited frequency response.

Timbre can be structured or unstructured, organic or synthetic, homogenous or heterogeneous.

Timbres can be composed of other timbres and, depending on the targeted time scale, can become recognizable compositions.

Every musical composition is a drawn out timbre on one time scale or another.

The fractal dimension of timbre is a useful form of classification.

The largest musical unit, which is also The Timbre, is referred to as the Cosmosone (all sounds in the Universe). There is only one Cosmosone per Universe (or black hole).

All music takes place within the timbre of the Cosmosone.

There are an arbitrary number of musical units including but not limited to:

·      Cosmosone: all sound in cosmos

·      Galactisone: all sound in galaxy

·      Stellasone: all sound in star system

·      Terrasone: all sound on Earth

·      Biosone: all sound in biosphere

·      Hydrosone: all sound in water

·      Urbasone: all sound in city

·      ________sone: all sound of that type

Music can never be completely extracted out of its Musical Context. Any time you hear music, it is before one thing and after another. Musical Context itself is timbre. When you listen to a concert or an album, it is heavily colored by which song or work goes first, second, etc. There are many factors that contribute to this such as tempo, key, instruments, lyrics, etc. Whether intentional or not, every musical context is holistically related to every other context. Thus does a concert become one unified performance of music with changing dynamics. In fact, the entire life works of a given composer (composesone) has its own timbre on one time scale or another. The fractal dimensions and other analytical parameters of his or her music characterizes a musical style which is more or less original and unique. A composer who is aware of the musical connection between everything they do is able to compose the greatest possible music, which is life itself.

Imaginary music is free of the limitations of vibrational physics but there is no current way to bypass the timbral limitations of the eardrum and inner ear for physical music.

Imaginary music can only be heard by the imaginer.

All music has a fractal dimension which can be calculated (usually between 1.65 and 1.68 [10] ).

It is conceivable through timbral composition to create different musical systems which suggest different musical structures or emphasis. For example one could construct a system whereby the Dominant was not based on a perfect 5th but on a Tritone. But since the human ear is tuned to the 5th, we cannot fully appreciate such musical systems. The 12-tone equal temperament system is adjusted to our eardrums, though only approximately—except for octaves.

Octaves represent tonal equivalence in different time scales. Octaves apply to all vibrational phenomena including electromagnetic and matter. Physical matter can also be considered timbre. For example, water is a 2:1 ratio of Hydrogen to Oxygen which have a 16:1 atomic mass ratio. This is likely why water tastes like an octave sounds, very satisfying but not particularly interesting.

6. Holistic Tonality is not based on equal temperament and applies equally to all microtonal constructs.

Larger creatures tend to respond to lower frequencies and smaller ones to higher frequencies, though there are many exceptions such as dolphins. By speeding up or slowing down other species’ communications we can better understand them and they will tend to have the same fractal dimension as ours.

Composing Music Holistically

While all music is already holistic by nature by virtue of Postulate 1, composers have not usually been aware of the fact. A true holistic composer is one that is not only an expert on the melodies, harmonies, rhythms and dynamics of composition but is also an expert in sound design with an imagination that flows freely between these levels. The closest we have to this are skilled electronic musicians with excellent musical training who are comfortable in a world of software, sequencers and synthesizers. These composers tend to be less versed in complex counterpoint and compositional arrangement and more interested playing with sounds so the larger musical structures tend to be repetitive (trance, rave and club oriented) or they forgo composition altogether. Traditional composers may have impressive orchestration skills but tend to rely on ready-made, traditional instruments and various expressions that those afford and tend to be purists eschewing electronica. Holistic composers would put all these skills together and the resulting compositions would have other worldly qualities where melody and harmony seamlessly melt into timbre and interesting audio transformations, freely flowing between the different levels of musical structure, consequently affecting the listener on more levels at once. In an extreme case, the composer would create a body of work in the course of a lifetime that would itself be considered a composition of highest order.

As of 2014, the tools are not quite in place to compose properly in a holistic manner, but the possibility is real if the right software and/or hardware were created. I predict by 2020 it will exist and several precursors to exists such as HyperScore from MIT and MAX.

Synthesizing Musical Structure

Heretofore, synthesizers have been considered tools for constructing new sounds in the traditional meaning of timbre. Using various frequency and amplitude modulation techniques combined with envelopes we use synthesizers to perform the role of traditional instruments, playing such and such a note at such and such a time.

Holistic Tonality frees us to use the same synthesizer controls to create musical structure. An example of this put into practice is the iPad App, Different Drummer. This software borrows various LFO and Oscillator controls to govern the behavior of notes, rests, ties, dynamics and spacial positioning, independent of the instrument sounds used. In this software, a fundamental frequency is expressed as Cycles per Measure (ƒ >= 1) or Measures per Cycle (0 < ƒ <1). Musical structure thet is created using trigonometric means is said to be Cyclophonic.

7. Any melody can be synthesized using sufficient oscillators. Corollary:  Harmony can only be synthesized using parallel systems of oscillators. This is a direct consequence of the Fourier Series where any continuous curve fitting an arbitrary set of points (ie. notes on a staff) can be fit according to the law: note = y = ƒ(x) = a1sinx + a2sin2x + a3sin3x + …  where x represent time relative to a system of measures.  Corollary 2: Any system of synthesis can be used for the purpose creating musical structure and melody can be thus synthesized at will.

Performing Holistic Compositions

It’s hard to imagine sight reading a complex score that included instructions for how sounds were to be modified on a timescale of milliseconds or less but it is possible with the use of assistive devices or by a cleverly devised notation that referred to presets that could be modified in real-time. The live playability of a composition need not be considered a crucial factor in its artistic merit any more than we might expect all artists to be speed artists and paint before our eyes to a catchy beat.

Because it is important that music not be restricted in any way, nothing dictates what instruments or sounds can be used or combined when composing or playing music. Therefore it should be considered perfectly natural to use traditional instruments, synthesizers of all types and any other sound in any measure, quantity, combination or arrangement since the result is always timbre.

8. Playability is governed by the physical skill of the musician and the nature of physical or virtual instruments available. Corollary:  Not all music is playable, though it may be constructable and recordable.


It can be confusing to talk about timbre in all its glory and levels and try to relate it to our everyday experience of music "down here on Earth." It's also problematic to use the word timbre to represent all music because it presents issues of self-reference and recursion or even tautology creating a "chicken without joints," not to mention that timbre has a well-established meaning already. However, please keep in mind that this does not change the meaning of timbre, only its scope and we should always strive to put music in the context of the entirety of existence and not limit it to our preferences or bias except in cases of specialization.


It should not be construed from Holistic Tonality theory that any music is more or less inferior to another or that any music is primitive or modern but only that humans will constantly search for the next form of musical expression using the tools of the realm and the era. Nor should it be construed that a single drummer or flute player or any other instrumentalist should be required to explore computerization or synthesis and in fact I would greatly encourage the sublime mixture of any and all forms of musical expression without limit whatsoever.


It would not be right to merely say we have reached the end of musical possibilities and everything we do from now on will just be a variation on what has gone before. One can only wonder what the music of the 22nd Century (let alone the 30th Century might sound like but perhaps the ideas presented here will give the next generation a clue on where to begin the next phase of musical evolution. It is entirely possible that music of the future will be directly conveyed to the mind, bypassing certain physical limitations or that some strange, post-singularity [11] cybernetic humans of the future will merely hear music on demand inside their quantum circuits




Peter McClard has founded numerous companies including Hologramophone Research, Gluon, CaptureWorks and Techné Media and has been writing music and music software for several decades including: HyperChord, Pixound, Cyclophone, Different Drummer and others. peter.mcclard@gmail.com


© Copyright 2014-2016 Peter McClard. All rights reserved.

[1] Boethius' De institutione musica, between the years of 1491 and 1492

[2] Diffinitorium musicae, Liber de arte contrapuncti  1475

[3] 1722 Treatise on Harmony

[4] Harmony (Harmonielehre, or "Theory of Harmony”) published in 1906

[5] In 1863 Helmholtz published Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (On the Sensations of Tone as a Physiological Basis for the Theory of Music)

[6] The Schillinger System of Musical Composition

[7] A term coined by Tod Machover at MIT to denote a sort of meta instrument that plays things beyond what the player “inputs” into the system or otherwise amplifies their ability.

[8] John Cage is a 20th Century composer who wrote 4’33”, the worlds first null composition.

[9]  Theoretical Beginning of the Universe currently unknown

[10] PP Choudhury - 2009

[11] Ray Kurzweil’s book the Singularity is Near speaks to the fact that technology is on a geometric path that will lead to artificial consciousness.