What is Music? Simply “organized noise” … or more?

by Pieter Volger

In 1952 the premiere of the three-movement composition 4`33“ by the famous American experimental composer John Cage was performed by the American pianist John Tudor. The score instructs the musician not to play a single note during the entire piece and simply to sit in front of the piano in silence. This provocative performance was not well received by critics and audience alike, who had expected to hear the performance of a musical composition. But John Cage, the composer, who was influenced by Zen-Buddhism, claimed that he was making a philosophical statement about the nature of music and that his composition consists of all the sounds the listener hears during the performance.

As early as 1921, the Italian composer Edgar Varese said: “What is music but organized noises! “[1] This definition of ″music as organized sounds″ prepared the way for what was called later “Musique concrete” by the French composer, Pierre Schaffer, who was one of the first composers to use electronic recordings of environmental noises as source material for his compositions, a technique which today is used as sampling in electronic music.

The questions behind these musical statements are ancient: “What is music and what is its origin? Is there a definable threshold between music, noise and just sound?”

In ancient Greece the Pythagorean saw music as an expression of divine mathematical perfection. For them a Number was in and of itself, an expression of divine perfection, and in music it was seen as the primary aspect which expressed itself in the different intervals of the overtone-series, which some scholars think was discovered by Pythagoras.

Music was seen as a universal phenomenon but two hundred years later the Greek philosopher, Aristoxenos, who wrote one of the first “empirical” music-theories defined music as a synthesis of human perception and the work of the human mind. He wrote: “The nature of melody is best discovered by the perception of sense, and is retained by memory”; and that “there is no other way of arriving at the knowledge of music.” [2] Most modern scholars today perhaps would agree with Aristoxenos.

Musicologists and scientists of different disciplines have tried to develop a general definition of music, a phenomenon which is so universal but also so diverse. As no human culture with clear signs of the inability to make music has yet been found, the question is very valid: Is music a universal phenomenon and is man a “musical being”? Is there perhaps a “Biology of music” inherent within the human system and perhaps even in the planetary biology as seen in the complex ″songs” of birds, whales and dolphins.

The basic material of music is sound. Sound in music is happening between noise as a more or less random distribution of frequencies and tonal sounds with a defined pitch. The transition between noise and tone is fluid. The huge range of percussive instruments from all cultures express this field of tuned ″noises” in different nuances of this spectrum. The noise of cymbals or a snare-drum, for example, is closer to pure noise than the sound of a tabla. The name “wind instrument” indicates the significance of the “un-” or “less” pitched sounds of the ″wind of breath”.

When we look at the distribution of the sonic spectrum, we realize that this wide spectrum of musical sounds expresses the balance between chaos and order. The frequency spectrum of musical noises is closer to chaos where the spectrum of a flute or violin shows a much more ordered harmonic structure. This order is determined by the distribution of overtones which build together, with a more or less prominent presence of noise in-between the colorful timbres of musical instruments.

So, a single note is in itself already a more or less harmonic experience. The more it sounds towards noise the less there is the harmonic experience of a defined pitch.

Distribution of Harmonics of an idealized string

The visualization of a harmonic spectrum shows the distribution of the nodes of the different waves. The higher Harmonics add more nodes to the cycle of the basic wave. The wave-form built by a certain harmonic spectrum shows different degrees of complexity due to the distribution of wave nodes.

Frequency-spectrum of the vocal U sung by a baritone

Thus, in a single musical tone we find a ″composition″ of different degrees of complexity which is expressed as the always changing timbre of musical sounds.

Building up sound patterns is not just a distribution of isolated notes in a certain time frame. It is always a complex weaving of harmonic complexity into pattern which never can be reduced to single parameters like pitch or rhythm. Musical compositions from a simple tune to the most complex symphony are an interplay of sonic wave functions distributed over time.

As the lower harmonics are building the basic musical intervals of octaves, fifths, fourth, thirds…. the inner structure of musical sounds is transmitted in the musical patterns of melodies, chords and tonal clusters. With the implementation of the 12-tone-equal temperament (12-tet), the division of the octave into 12 equal semi-tones, the intricate connection between the harmonic series and musical pattern building became less obvious.

Although the idea of 12-tet goes back to Aristoxenus (4th century BCE) it was Vincenzo Galilei (the father of Galileo Galilei) who published one of the first compositions which used an approximation to 12-tet. As the frequency of a note in 12-tet is defined by the factor of , which is an irrational number, there can only be an approximation to a certain note. The equal distribution of semi-tones makes a particular root note much less dominant and allows musical transpositions in all directions on every semi-tone-step. This culminated in the development of twelve-tone music which let go of any restriction of chord progressions by the harmonic series. Despite this independence the timbre of the musical tones is still there as the connecting link to the overtone series. But the less the music is connected to the chord progressions built on the basic intervals of the harmonic series, the less the music mirrors the inner harmonic structure of the sounds itself.

The 12-tet gave the composer much more freedom in building patterns of chord progression and melodic-rhythmic expression.

The advent of computer-technology after the Second World War gave a new tool to the composer to handle this freedom with the help of mathematical abstraction. But despite all the possibilities of porting musical patterns into the domain of mathematics, the Harmony of musical expression still depends on the harmonic structure of sound. The possibility of creating every imaginable sonic expression with the computer can be an expansion of musical creativity. But it also entails the danger of arbitrariness which is so obvious in the mass-production of commercial music with its reduction of harmonic content to an experience of “easy listening” and on the other hand, obsession with “new unheard sounds” in the atonal compositions of the wide field of “new music”. In between lies a field of sonic creativity which is ever expanding into new possibilities of musical expression. This ambiguity of order and chaos we find in every aspect of music. But it goes far beyond music into the creative process itself. The “Tohu wa Bohu” out of which God “created” this universal reality is the formless substrate out of which form arises as something which expresses a reality from beyond the chaos of the primordial. The emptiness of which the Buddha teaches in the Heart-Sutra is the formless substrate of infinite potential which expresses itself in uncountable forms. The musical tone experience with a defined pitch arises from the substrate of unstructured noise which it carries in more or less pronunciation within itself as the sonic space between the harmonics. An artificial synthesis of a flute-sound can never express the dynamic interaction between noise and pitch of a natural flute in perfection.

Whether we focus on the regularity of rhythmic patterns or the tonal structure of melody or a static harmonic structure which we find so often in the field of “easy-listening commercial music” that reduces the expressiveness of music drastically, music needs the indeterminacy of noise/chaos in order to be expressive, interesting and moving. In every complex musical composition, we find the evolution of musical expressiveness: tension and release, order and chaos, dissonance and harmony a never-ending weaving of “soundscapes”.

This tension is expressed so beautifully in Cymatics where the building of patterns is shown in water or fine dust. The soundwave transmits its vibration to a metal plate or bowl which is covered by the substance and we can observe the ongoing transition of order into chaos and into order again when we raise or lower the pitch of the soundwave. Only when the wavelength of the soundwave is in a harmonic ratio with the diameter of the plate or bowl, does the medium through which the pattern is displayed, form a stable pattern.

The cymatic patterns show the potential of tuned sounds to imprint order in fluid or other plasticized media. This formatting power of sound is found everywhere in nature. From the probability distribution of the electrons in an atom to the very background radiation of the Universe we find harmonic pattern formations which can be connected with pitched tones.

As every regular pressure wave with a certain stability over time can be expressed as sound, although not always in the human audible frequency range, the question remains: Is there music beyond human experience?

When we look beyond sound as the medium of music transmission, we find a highly structured process of mathematical transformations. This order of music transcends the sonic experience and touches on every aspect of reality.

Music needs time to express its intrinsic order. All parameters of music are actually measures of time. Frequency as the basis of pitch is measured as “cycles-per-second”. Melody, rhythm, chord progressions, even the modulation of harmonics in the animated change of musical timbres are functions of time. “Music consists of order relationships in time,” writes the German composer and musicologist Karlheinz Stockhausen (1928-2007) in the beginning of his very influential article “How time passes by”.[3] This order is expressed in time through the medium of sound.

As scientists realize more and more that our physical universe can only be explained as an expression of a higher dimensional information field which is not built by the matter-energy construct of the building blocks of the universe, we enter a post-materialistic science which sees “in-formation” not mainly as abstractions of a self-sustained material reality but as the source and the processing of the universe in all its aspects. Matter, energy, and space are just the expressive mediums for “in-formation” and not the source itself. The Russian scientist Nikolai Kozyrev saw time as an energy expanding this information into cause-and-effect processes onto space. Music is all about order in time. Rhythm, the pitch progression in melodies and chords, the layering of harmonics which build the timbre are all functions of time. The composer implements relationships between the different time-frames which build patterns which are then sonified in space.

If we reduce the concept of music to sound itself the very idea of music becomes obsolete. It is the creative impulse which generates order. Between sound and music, we find the working mind of a composing intelligence. The mind of a composer or the Minds of Higher Intelligence whether we define these as God, gods or intelligence-fields of a Multi-dimensional Universe are imperative for the musical process. The musical composition becomes an expression of the ongoing creative work of consciousness as the foundation of every kind of reality.

For centuries musicologists, mathematicians and composers have researched possibilities of visualizing musical relations. The conventional keyboard of a piano or synthesizer follows the chromatic scale of 12-tet in its strict division into semi-tones without any connection to harmonic correlations.

The mathematician Leonard Euler describes in 1738 the concept of a musical grid structure he called Tonnetz (German for tone network). He used this to develop a mathematical model of consonance. The 19-century influential musicologist Hugo Riemann further developed the Tonnetz into a device for visualizing harmonic relationships in melodies, chord progressions and keys in western classical music. The harmonic connections of the pitches are shown in the distances between pitches in the lattice. The bigger the distance between pitches the smaller the consonance of the interval.

Every note is surrounded by six consonant notes:  fifth, fourth, major and minor thirds.

The Tonnetz shows harmonic relationships in different geometries which become markers for the degree of consonance and dissonance.

By Watchduck (a.k.a. Tilman Piesk) – Own work. CC0. https://commons.wikipedia.org/w/index.php¢urid=33932849

With the help of the Tonnetz, Hugo Riemann developed a music-theory based on Triads as the basic building block of chordal progression. Although it seems quite static it shows an astonishing possibility for exploring the spectrum of consonance and dissonance in tonal music. Two hundred years later musicologists like Richard Cohn, David Lewin et. al. expanded the concept of the Tonnetz as a tool for exploring musical symmetries. They proposed a model where the Triad is the basic building block of all chord progressions in tonal music. This ″Neo-Riemannian″ approach is used today by many composers to find new ways of tonal expressivity, especially in film music.

In the past few years several music theorists have used topological models to explore the complexity of musical relationships. Topology, a branch of mathematics analyzes the properties of geometric objects which are preserved under any kind of deformation. Topological models are very important for new concepts of higher dimensional cosmologies. The topological approach allows for the exploration of Musical Compositions in terms of basic transformations in higher dimensional spaces. In terms of Topology, music is both a discrete topology built by the discrete values of pitch and Rhythm and a continuous topology in terms of the parameters of sonic modulation of sound itself. It becomes obvious that Harmony as the foundation of tonal expressiveness is based on higher mathematical formations which lead toward higher dimensional organization of musical code.

The complexity of musical experience whether as composer, musician or listener is by far beyond psychological concepts of cultural conditioning.  Music searches always for new ways of expressing harmonic experience. It sonifies the creative process which builds order from chaos while undergoing certain transformations and permutations and other mathematical distributions. The natural Soundscape of Nature expresses many musical attributes like rhythm, pitch, timbre which we hear in the sound of nature. Is this music? The answer lies in the complex relations of the different musical parameters. In the myriads of possibilities, the harmonic series remains the most important framework of music ‒ from prehistoric flutes to electronic instruments. Mathematical approaches show that this framework connects all the different musical parameters in any composed music. It is also inextricably connected with the chaos of noise.

Music’s ubiquity is not only an expression of the idea that ″every sound is music″. It also mirrors the all-encompassing work of a creative Mind expressing its own reality into the space-time continuum of our observable reality.



[1] Varèse, Edgard, and Chou Wen-chung. 1966. “The Liberation of Sound”. Perspectives of New Music 5, no. 1 (Autumn–Winter): 11–19.

[2] Aristoxenus: Elementa rhythmica. The Fragment of Book II and the Additional Evidence for Aristoxenean Rhythmic Theory Oxford 1990 (griechischer Text und englische Übersetzung).

[3] Karlheinz Stockhausen  Published in Vol.3 in the English  edition of “Die Reihe” musical journal 1959 The original version dates from 1957.



Music and the Body

by Pieter Volger

With the advancements in fMRI techniques at the end of the 20th century there has been a huge increase of scientific research in the field of musical cognition. And while neuroscientists and psychologists of the 20th century saw music mainly as a highly specialized brain function distributed between the auditory cortex and areas for speech recognition and the emotional brain areas like Thalamus and Hypothalamus, modern brain research shows that music listening is one of the most complex activities in the human brain.

For Mark Jude Tramo, a musician, prolific songwriter, and neuroscientist at the Harvard Medical School music is in our genes. He and his colleagues are working with individual braincells to uncover the encoding mechanisms of music in the human brain.

“Many researchers like myself are trying to understand melody, harmony, rhythm, and the feelings they produce, at the level of individual brain cells. At this level, there may be a universal set of rules that governs how a limited number of sounds can be combined in an infinite number of ways.” [1]

But perhaps the most significant discovery is that there is no singular pattern of brain functions responsible for the perception of music. There are certain brain areas which are always involved in the listening process. They seem to be closely related to brain patterns responsible for the processing of spoken language. The patterns of brain activity while listening to music seem to be highly individualistic. In terms of brain-activity it seems to make a big difference whether a skilled musician listens, focusing on the music, or a normal person listens just to enjoy the music. It seems that the more educated a person is in music the more complex the patterns of brain-activation during music listening. And the activation patterns are much more widely distributed in the whole brain than expected

The neuroscientist Petr Janata from the Department of Psychology and Center for Mind and Brain at The University of California, Davis, in his extensive research has scanned the brains of people with different musical backgrounds listening to music. While he discovered many diversities in the distribution of brain-activity for music-listening, he could show that one of the activation-centers always activated is situated in the medial frontal-lobe [2]. This area is mentioned by The Keys of Enoch® as the seat of a crystalline network connected to the third eye or sixth chakra responsible for connecting with higher language structures and the higher mind as the seat of paraphysical mind-functions.

Another area of music research which directs us to universal aspects of music dates back to 1976 when Richard Voss and John Clarke published an article which suggested that in very different kinds of music one can find a common distribution pattern of musical parameters, like pitch or power (amplitude). They discovered that the spectral density of fluctuations in audio power of many musical selections and of English speech varies approximately as 1/f (f is the frequency) … The frequency fluctuation of music also has a 1/f spectral density at frequencies down to the inverse of the length of the piece of music.”[3]

The 1/f distribution which is called Pink Noise in the audible range is a subset of a group of logarithmic distribution patterns found in many natural patterns. These so-called Power Law distributions show different degrees of balance between pattern repetition and chaotic behavior. The balance between repetition of rhythm or melodic themes in music and unexpected movement, predictability and surprise, can be seen as the very basis of the joy of listening to music. This balance is seen as related to the preeminent function of the brain’s reward center (nucleus accumbens) in music listening.

The use of mathematics for analyzing, modelling and understanding music dates back to the Pythagoreans in ancient Greece. The ability to model complex numerical patterns with modern computers proved to be as valuable a tool for analyzing music as Topology [4].

1/f distribution is an often-observed distribution of the frequencies of many natural events like earth quakes, sun spots, and is also discovered in biological systems, having been discovered by scientists to be the prominent feature of genetic information in the DNA molecule. An interesting aspect in regard to musical cognition is the 1/f distribution of voltage fluctuations on myelinated nerve fibers, which suggests that human sensory perception is functional in encoding regularities in the physical world which emerge as self-similar patterns [5]

In 2011 the neuroscientist and musician, Daniel Levitin and his colleagues [6] showed that not only pitch and amplitude but also the distribution of rhythmic patterns follow this distribution pattern.

Prof. Sandra Trehub from the University of Toronto’s extensive research with babies has been seeking the biological roots of music. In one of her studies a baby was sitting with the mother in a soundproof room and from a speaker in one corner of the room a simple melody was played in a major scale. At random intervals a musical note not fitting the scale was played and each time the baby turned its head towards the speaker as the notes was played. One might assume that the baby had already learned to recognize the notes of a major scale ‒ it is very common in children’s songs. But in another setting the tune played followed an invented non-western scale, and, again, the moment a non-fitting note was played, the baby turned its head towards the speaker even though the musical scale was totally unfamiliar to him.

Prof Trehub has studied the musical cognition of thousands of newborns and babies and is convinced that babies have an inherent appreciation of music on a much higher level of complexity than was expected. [7]

In the light of these discoveries, the idea that music is “hardwired” into the human brain and coded into our genes is not as far-fetched as it might seem anymore. Varied research projects point to a universality of music which surpasses the concept of a linear evolution of music perception and action in human culture. This research indicates the universality of the phenomenon of music which surpasses human culture. Music as a universal phenomenon is much more than “organized sounds”. It is the exemplification of divine order in terms of audible sounds. This order goes far beyond simple commandments or any kind of static “creationism”. It shows that beyond all structures of the universe from the human brain unto the universe itself we can see the work of an order-emerging spirit which brings forth a process of self-similar pattern formation in order to create fractal domains of existence which all come from the same spirit.

The task of Spiritual Music lies in creating musical structures which generate in the listener the experience of this divine order on any level of human consciousness.


[1] Harvard University Gazette, William J. Cromie, Music on the brain: Researchers explore the biology of music

[2] Liese Greensfelder on February 23, 2009 in Science & Technology: Study Finds Brain Hub That Links Music, Memory and Emotion [6] Voss R.F. Clarke J. (1975) 1/f noise in music and speech. Nature, 258:317–318.

[3] The Topos of Music, Geometric Logic of Concepts, Theory, and Performance. Birkhäuser (2002) ISBN 3-7643-5731-2.

[4] Yu Y, Romero R, Lee TS (2005) Preference of sensory neural coding for 1/f signals. PHYSICAL REVIEW LETTERS 94:108103.Verveen AA, Derksen HE (1968) Fluctuation phenomena in nerve membrane. Proc IEEE 56:906–916.

[5] 2012: Daniel J Levitin; Parag Chordia; Vinod Menon Musical rhythm spectra from Bach to Joplin obey a 1/f power law. Proceedings of the National Academy of Sciences of the United States of America 2012;109(10):3716-20.

[6] Fink, Bob, 1997. “Neanderthal Flute: Oldest Musical Instrument’s 4 Notes Matches 4 of Do, Re, Mi Scale”. Retrieved 2006-01-22.

[7] 2001: J.Glauiusz, Greg Beining in Discover Magazine August 2001 issue “The Genetic Mystery of Music:                                                                                Does a mother’s lullaby give an infant a better chance for survival?” August 01, 2001

The Origin of Music

by Pieter Volger

Many anthropologists and musicologists see the origin of music in the context of Darwinist evolution-theory. Drumming and chanting in prehistoric culture are often seen as being the first musical expressions which later led to more tonal singing, simple folk-songs and, even later, more complex musical compositions. If one accepts this concept, it would mean that more complex musical structures like melodies evolved later with the evolution of human social and cultural organizations.

But there are discoveries which allow us to question the idea of this idea of evolution of music.

In 2008 archaeologists found a bone flute made from a vulture bone in the “Hohle Fels cave ” on the Swabian Alp in south Germany which today is recognized as one of the oldest musical instruments on our planet. The bone-flute, which has been dated to 30 000 to 40 000 B.C., has five holes.

Replicas of this ancient bone flute are able to play beautiful melodies in a pentatonic scale which show that even by this early stage of human history tonal music played a significant role in the lives of humanoid beings.

In 2012 bone flutes found on the Geißenklösterle-Site in South South-Germany were more precisely dated during examination using high-precision radio-carbon to 42 000 to 43 000 B.C.

In 1996 in a cave at Divje Babe, one of the oldest archaeological sites in Slovenia, archaeologists found samples of the femur of a cave bear which shows two regular spaced holes. The structure of the fractures of the artifact indicates the presence of two more holes. Although this finding is still deemed controversial by scientists, new research by the Slovenian scientist Matija Turk supports the artificial origin of the holes. Computer tomography shows that the holes are not the bite marks of carnivores.  As early as 1997 the Canadian musicologist, John Fink wrote in an essay that the Divje Babe flute shows spacings which suggest that the instrument could play a diatonic scale which includes a half-tone step. [1]

In 2015, musicologist Bob Fink could show on a model built with the exact spacings of the original that a skilled musician is able to play a diatonic scale in a range of two and a half octaves. While the musical harmony of a pentatonic scale can perhaps be interpreted as an expression of spontaneous musical sensations due to the musical order of our inner ear, a diatonic scale points toward a more sophisticated musical experience perhaps even to early musical conceptualization. The possibility of complex music instruments as early as 50-60 000 years BC is striking.

Courtesy of: National Museum of Slovenia.

Despite the elementary nature of the instrument, building a flute is not a simple business or even if by happenstance, trial and error. It needs quite some intellectual work. The ratio of the tube’s diameter to its length, the shape and angles of the blowhole, and even the size of the tone holes in relation to their placement are some of the aspects which must be taken into consideration and planned carefully.

The confirmed age of these two artifacts suggest early Neanderthal man had an intellectual capability which is still not accepted by most scientist. Also, the social structure which is needed for this kind of handicraft appears to have evolved much earlier than hitherto expected.

The discovery of these flutes certainly calls into question the Darwinist concept of primitive man only being capable of simple drumming and perhaps singing.

The question arises of whether music has been present through all phases of human evolution. Was music perhaps one of the basic building blocks in the development of social and intellectual capacities in early man?


[1] Fink, Bob, 1997. “Neanderthal Flute: Oldest Musical Instrument’s 4 Notes Matches 4 of Do, Re, Mi Scale”. Retrieved 2006-01-22.