Toward a Cognitive-Based Theory of Music
This is a work-In-progress, with meanderings and musings, perhaps of no consequence whatsoever. I believe that each creative individual must re-invent the wheel, at the very least in order to discover for him or herself the essence of “wheel”. One might discover that the object of investigation is not a wheel at all. If one is very fortunate, maybe a new shape is revealed, or maybe a wheel with a very strange bump!
The role of the artist is to resist and reverse the tendency of human cognition to taste quickly and then render and re-categorize everything except food, sex and TV into a status of redundant, irrelevant, invisible.
This does not mean that food, sex and TV cannot be done artfully!
Art and Science are opposite sides of the same coin.
We (humans) like to watch each other. And we like to tell things to each other. We have an enormous need to explain things, as we we understand them, to each other. These are perhaps our greatest fascinations.
I tend to detest the consumer culture that keeps people glued to their televisions, where they sit hypnotized in a fabricated dream world that subsumes their consciousness, and fills them with a mass-market reality.
But this is what we like, or we would not do it so willingly.
We relinquish our individual perspective because
1) we are lazy;
2) we are children, at some level herded by our controllers (priests, politicians, entrepreneaurs, etc.) into the notion that we should not think too much for ourselves; and
3) because we quite simply like above all else the products and procedures of our fellow humans.
We are all mostly engaged in a huge human feedback loop, simultaneously feeding and reacting to each other on many levels, like a giant ant hill (the earth!).
There are a few folks who also like to look at and study other aspects of nature. These are artists, scientists, naturalists.
© 2005-2020 Joseph Martin Waters
All Rights Reserved
Contents may be used and replicated with prior permission of author.
Composition as Experiments in Cognition
• Music as Pattern Recognition
• Fractal Patterns
• Fractals in Afro-European Popular music
• Types of Randomness
• What is Pulse (Beat)
• Rate Of Transportation (Survival Frequency)
• Time Scales in Music vs. General Time Scales
• Syncopation: What is syncopation?
• A Few Thoughts on Dissonance
• Re-uniting Art and Science
• Ritual and Audience
• (my bias!) I am a composer, not theorist or musicologist.
• Topic: This document explores questions that I must ponder and seek to answer to continue my work.
• Bio: SDSU Professor of Music Composition/ Electro-Acoustic Music.
Orientation: I think of myself as a member of the 1st generation of classical composers who grew up playing in rock bands.
I am a Populist Composer — I need to be an active contributor to the aesthetic life of the general community, NOT isolated in an ivory tower or small ghetto of post-modernist experts.
My Work Concerns Five Areas of Creative Research:
1. Composition as Experiments in Cognition. Examining of fundamental questions regarding cognition as basis for process, structure & materials.
2. Relationship of Classical to popular/folk music
a. Historical: Folk music in Mozart (Austrian, Italian considered exotic)
b. Folk music today: much more complex: confluence many cultures, but especially Europe and Sub-Saharan Africa.
c. This poses new challenges, tensions, questions
3. Fundamental perceptual shift away from Euro-centric basis:
a. group composition as a creative dynamic
b. improvisation as key factor
c. African influence — folk music from another continent
• Dominant role of drums
• Dominant role of dance rhythms
4. Examining of natural processes outside of music as sources for process, structure & materials.
5. The Role of the Composer: Cultivation of a multi-layered style, which has the ability to connect with an intelligent, curious audience that may be mostly familiar with vernacular styles, (without “dumbing down” the music)
• Examining of fundamental questions regarding cognition as basis for process, structure & materials.
• Some ideas will be familiar to you, but I need to re-examine them in order to get a fresh start — please be patient! Apologies in advance.
• Why this approach? To address the need for a method of assessing and comparing music of widely different styles, genres, cultures, socio-economic groups etc. — to find a common ground among them.
• Why is this important?
1) In order to move forward as a composer one must have a way of assessing the many possible trajectories that are offered in a complex, multi-cultural global village.
• How do they relate?
• Are they essentially similar or different?
— Are there connections that are obscured by cultural dams and filters — that upon examination reveal fascinating and unexplored pathways for exploration?
• Goal of composer: For me, the goal of the composer/artist is to
1) absorb, assimilate, distill contemporary culture and
2) create works of art that probe beneath the surface, call into question established norms,
point out inconsistencies, draw connections between seemingly dissimilar cultural elements,
3) suggest a way forward, or at least create a reflection that deepens our sense of who we are.
2) To remove cultural bias in evaluating and comparing music
• Finding differences: Many in the professional community are focused on finding the differences among all the musics of the world.
• My mission is to find the similarities — to find a method for making meaningful comparisons between seemingly vastly dissimilar genres/styles etc.
• Finding the commonalities does NOT mean:
1) that dissimilar styles can be comprehended by naïve listeners, and
2) does not seek to conceal or deny the cultural underpinnings of a music, or
3) defend the cultural imperialism of one group over another at a particular period of history, or
4) to dismiss the specific, context-based meaning that a musical work might accrue for a specific person, of a specific age, in a specific culture, at a specific date etc. (e.g. A tune that has transcendent, life-altering significance to a 3-year-old may not carry the same weight to a 50-year-old.)
• Psychological Value Of A Work: (The psychological value that a work accrues is a rich, vast area involving many factors:
1) age of individual,
2) general culture i.e. Europe vs. Middle East vs. Asia or Christian vs. Muslim vs. Buddhist,
3) general psychological climate i.e. wartime/natural disasters vs. relative peace/prosperity,
4) socio-economic level,
5) education level, etc. etc. )
• Finding commonalities DOES mean:
1) seeks to explore something more fundamental about cognition and human/animal communication strategies, and
2) seeks to offer a solid footing for moving forward with new composition (without blindly following a strategy of denial of the previous tool sets).
• RE: Previous tool sets: The forward evolution of classical music in the past 85 years based on the systematic and conscious avoidance of the core parameters of previous 900 years (melody, harmony, rhythm) It is a murky way forward, based not on insight but on denial. (Breughel, 1550 The Blind Leading the Blind). For many today the only valid compositional method is exploration of noise/texture. For me is unsatisfactory.
• Based on cognition: It stands to reason that if music of whatever culture and genre is successful in gaining and holding the attention of other humans, it is probably drawing on important, underlying principles that govern cognition.
• If this is not so, then humans in different parts of the world may have fundamentally different cognitive strategies and possibly mechanisms. This is unlikely, though interesting to ponder.
• All music is experimentation in cognition. All music asks questions, tests perceptual mechanisms.
a. some questions are very simple: e.g. Is this something that has not been done before?
i. This is a simple question, but profoundly difficult to answer.
ii. Requires a conscious and unconscious assessment of all music that one has ever heard, or that anyone has heard before.
1. And then one must take a step beyond, a next perceptual step, and create a new summation of everything that has come before: a new reflection and comment
• All music, to some extent, is cut off from its past. It still reflects this, willy-nilly, through its connections with everything.
Thus Eminem is connected to Mozart, though due to cultural prejudices this may not seem tenable:
— Eminem and Mozart are NOT from different planets; they are NOT of different species. It stands to reason that if music of whatever culture and genre is successful in gaining and holding the attention of other humans, it is probably drawing on important, underlying principles that govern cognition.
— The predominant use of 4/4 time, and 4 bar phrases, is directly out of European music of the classic period (and European folk music)
— The other main stem of rap music is sub-Saharan Africa
An interesting example of cultural connectivity: Surf music and Arabic music (Dick Dale was raised in the Near east. He first learned to play there, on local instruments (Saz, Tar etc.) The characteristic virtuosic guitar tremolo associated with surf music was imported to California by Dale when he moved there (as well as the lowered 6th and 2nd scale degrees of the surf classic “Misserlou”)
• Theoretical Base: cognition as basis for process, structure & materials
• NEED: a Music Theory based on cognition
— Traditional music theory is more a record of historical practice. (common practice harmony, set theory, Schenkerian Analysis, etc.)
— Cognitive-based theory should be capable of comparing all styles, periods, nationalities, cultures, etc.
— Comparisons should be based on general cognitive/communicative parameters:
• information correlation
• information density per unit of time
• rate of change
With a cognitive approach one can consider the existing body of music (across all cultures) in its proper context: as naturally occurring phenomena – to be studied as rich pointers to and examples of what fascinates the human pattern recognition faculty.
We need to get away from moving forward based on refutation of the past as primary guiding principle (no melody, no notes, no pulse) – this is like swimming in murky water. Instead look at the products of culture (music) as natural phenomena, to be studied like weather, plate tectonics, bird migration, general relativity etc.
Branches of study:
— Existing music, especially naïve music, as natural examples of human cognitive function regarding pattern generation and attention fixation.
— Examination of the evolved human methods for organizing non–musical, time – based aspects of existence.
i. Pattern organization & utilization (i.e. the means of time measurement and management) has evolved to provide essential, practical means to navigate individual life, and collective society. It is hence a valuable source for study of stylized pattern organization in music.
ii.Examination of nascent pattern recognition mechanisms that we use to understand and navigate daily life.
Is this possible? Is a General Theory of Musical Cognition possible?
a. What are the differences between musical cognition and other types of cognition? Are there fundamental differences?
b. This questions is central to understanding cognition in general
c. If it is, can thinking in general can be codified?
d. Why would this NOT be possible?
i. Are there too many variables in cognitive, organizational strategies across cultures?
ii. Are there too many variables in cognitive, organizational strategies across life processes (eating, war, procreation, language)?
iii. Are there too many variables in cognitive, organizational strategies across species?
The Processes of Cognition:
1. Perception (input)
i. Scanning: while awake we continuously scan our environs for information relevant to survival
i. What types of objects/events do we/can we remember?
ii. There is around us at most times an incomprehensible amount of information in multiple sensibilities.
—We have filters that block out information that is uninteresting or irrelevant to survival (psychological limits and biases based on previous processing of data that is automatically/unconsciously judged as redundant.).
—We have physiological limits to the types of events that we can perceive and the acuity of our ability to perceive them.
• Similar events that occur too close together in time appear simultaneous. The threshold is ca. 20 milliseconds. However, a steady stream of events happening at intervals of 20 milliseconds blur together to produce the appearance of a steady tone of 50 Hz (50 per second). This rate exceeds our ability to track & label/organize the individual events. The maximum rate at which we can successfully notice, label and integrate new events is much slower, probably on the order of approximately 5 per second, (or 300 per minute).
3. Reflection (Processing/Integration/Correlation)
• Labeling/Organizing data: We compare similar objects/events in immediate space/time and assign them a significance within our
• We Compare w/similar objects/events in memory
Listening to music involves steps 1 – 3.
• Composition as experiments in cognition:
1. Each work poses an experiment in consciousness, whether intentional or not.
• The basic question: Will this work?
• What can we remember?
— How do we remember
— Should music be “about” remembering
— If so, what are the mechanics of memory?
How to proceed?: Musical form, style and content should be based on the contemplation of large, basic questions:
• • • WHAT IS MUSIC? • • •
At the most basic level, Music has to do with the deepest aspects of survival and consciousness, and at the core of this is our nascent, overpowering fascination and continuous involvement with Pattern Recognition, in every sensibility, through every facet of our mental activity.
—Why is a given piece of music boring? (Two reasons)
—Patterns too easy to elucidate: We process the patterning, see no new information, and move on to process more patterns
—Patterns too difficult to elucidate: We attempt but cannot process the patterns, even though we may feel that they are there (dodecaphonic, serial, and intergral serial music). This is frustrating, and eventually we give up (or we impose our own patterns cf. Darkside of the Moon as soundtrack to Wizard of OZ)
What is a pattern?
—repetition of a random event
Patterns represent order:
In understanding temporal events we unconsciously employ a basic perceptual logic to recognize patterns:
1. In any mode of perception, we continuously make same/difference judgments.
2. If something occurs once it has meaning only in the context of being unlike anything surrounding it. It is a random event.
3. If something occurs twice we note the potential establishment of a pattern
—This begs a question: Will it happen again?
4. When something occurs three times a pattern is confirmed.
—This has great symbolic significance: Our prediction is correct, so the world functions in a predictable way, so it (and symbolically life in general) makes sense
5. When something occurs four times a we are bored.
—We have already digested the pattern and it has no new information to reveal.
6. Question/Answer (in music) is a type of same/different judgment (related enough to merit a comparison): a cognitive pair.
7. Static visual data is easier to organize because it sticks around, and may be continuously re-considered, consequently only one re-occurrence is necessary to establish a pattern.
—We have much greater acuity with regard to perception of visual information, compared with aural. Example: Stand at the seashore and observe the crashing of the breakers. At every moment there are tens of thousands of discreetly identifiable points in the waves — millions of variations on light reflecting off of water, with many generalities but still uniquely observable and identifiable. Now close your easy and listen: How many discreet points can you identify? Perhaps 10 or 20.
—Hypothesis I: This probably has something to do with the nature of mechanical pressure waves moving through a medium as compared with electro-acoustic waves/particles
—Hypothesis II: This has to do with the acuity of our hearing apparatus vs. our seeing apparatus
The term “Fractal” was coined by French Mathematician Benoit Mandelbrot in 1976 to describe a unique type of curve and object, in which the physical measurement becomes infinite, though the curve or object is restricted within finite boundaries. He sought this in order to expand the concepts of Euclidean geometry, to yield better models for describing certain naturally occuring shapes, such as trees, river systems, mountain ranges, etc. Fractal curves and objects exhibit certain properties, among which the most important is Self-Similarity
— Refers to the construction of physical as well as time-based structures (flows of correlated events). Structures that exhibit self-similarity are constructed of multiple levels of similar (or identical) structures, that are nested within one another. Music is intrinsically self-similar, and when the correlation function of the pitch sequence, or even the fluctuation of electrical energy (in a music recording) is analyzed a self-similar structure is revealed.
— How does this manifest in music? Is it esoteric or recognizable?
— In fact it is eminently obvious, so obvious as to be invisible!
— This music, even the most basic pop anthem, employs at least 6 fractal levels.
The fractal structure of Afro-European Popular music organizes around the PULSE, at 6 self-similar levels of magnitude. (This describes most music in every culture. So-called “classical” European music has an additional level. )
At the most basic level is THE BEAT, that level of the pulse that we tap our foot to, clap along with and dance to. The tempo of THE BEAT is measured in beats per minute and is intrinsically tied to the range of tempos that we employ in our walking and running. It can range from approximately 40 beats per minute to 200 beats per minute
Tempos slower than 40 BPM (beats per minute) are boring to us, and impossible for us to track and synchronize with. To think about these we must fill them with small, equal units of faster beats. Tempos faster than 200 BPM are too quick for us, and we lose our ability to identify and keep track of the individual points. To think about these we group them into sets of small, equal units, nested within slower beats. This multiple group-within-grouping of beats has been talked about in a semi-understood way within normal music terminology for several hundred years, but without the overriding organizational structure of fractals, which reveals new ramifications for understanding and further development.
— What comprises the six fractal levels of Afro-European Popular music:
— Level # 1: sub-divisions of the beat. Depending on tempo of the basic pulse, there will be one or possibly two faster levels, in which the sub-beats are proceeding most commonly at 2, 3, 4 or 6 times the main tempo. At slower base tempos, there will often be 2 nested beat sub-divisions, either at 2 and 4 times the tempo, or 3 and 6 times the tempo. Certain genres mix sub-divisions of 2 and 3.
— Level # 2: THE BEAT, as described above. This is the level of pulse that we focus on, and that pulls us through time. It is tied to our most basic psysiological mechanisms having to do with fight, flight and food capture.
All animals that use limb-powered means of propulsion have similar pulse tracking skills. However the functional range of THE BEAT varies according to the survival needs of a given species. For example, in general birds function at a much higher beat rate than humans. Notice how most species seem to move their heads with quick, jerky movements. They need to function at a faster pulse rate in order to catch their food while flying. Humans probably look like they are moving in slow motion to birds, much as Galpagos Tortoises seem to be moving in slow motion to humans.
—Level # 3: MEASURE (BAR): The next lower hierarchical level involves (usually) continuous series of sets of the pulse (usually in groups of 2, 3 or 4, rarely 5).
—Level # 4: PHRASE: Measures are grouped into slower macro-pulses consisting of (most commonly, certainly in popular idioms) 4 measures, at 1/16 the tempo of THE BEAT. This is often referred to as the musical equivalent of the sentence in speech.
—Level # 5: PHRASE-GROUP (aka Verse/Chorus/Bridge): Phrases are organized into still larger self-similar structures, with extremely slow tempos of approximately 1/64 the speed of THE BEAT, usually in groups of 2, 3 or 4 PHRASES.
So if the metronome marking of the the beat is 64 bpm, the tempo of the PHRASE-GROUP is only 1 beat per minute!!! Try clapping consistently at that speed. The beats are spread out so far for our cognitive apparatus that we cannot remember when the previous one occurred. But maybe Galapogos Tortoises, or trees can.
In order for us to process this level of time grouping it must be hierarchically invested with nested self-similar interior structures. Understanding the ramifications of this basic idea is paramount to navigating creative journeys outside the solar system of available musical genres and styles and landing on ones feet in understandable, coherent alien worlds, instead of crashing blindly, as so many well-intended works of the past half century do.
—Level # 6: SONG Approximately four PHRASE-GROUPS comprise the largest pulse in popular music, which is the song. Songs are usually grouped together with other songs to make a collection.
— white noise: No correlation: The probability that any event can occur at any time, in any sequence, with no correlation to any other event.
— Brownian motion: statistical correlation to the immediate past (random walk on the piano: start at middle C, flip a coin, heads moves up a step, tails moves down a step. This gives a 50% prediction of the next note, a 25% prediction of the second note, a 12.5% prediction of the 3rd note etc.)
Although over a short period of time the “melody” will seem to make sense (demonstrate correlated patterning), rather quickly it becomes boring, as the correlation only applies locally (it has only 1 fractal level: the immediate future)
— Fractal 1/f noise: Technically a type of Brownian motion, but with correlation among data at different time scales, nested hierarchically within each other. This is the type of randomness that describes music. In order to fascinate the human pattern recognition apparatus, a series of events must demonstrate this type of multi-level correlation. When this occurs, we are drawn into a pursuit of unraveling of the multilayered connections.
— We organize and process all information, not just music, according to multilayered, self-similar, hierarchical ordering systems. — We not only seek these patterns in nature, but furthermore are hard-wired to organize both our time-based and spatial-based perceptions with fractal-like structures. Fractal ordering is intrinsic to human (and all animal) consciousness.
Everyone has had the experience of:
— Apprehension of a new pattern set (song)
— gradually growing to “like” it more and more, and to want to listen repeatedly to it,
— after repeated listening, eventually becoming less interested,
— ultimately reaching a point of complete disinterest and disdain for the tune (Turn off the radio whenever it comes on.)
This is because the song has become a personal cliché: One has unconsciously made a systematic evaluation and comparison of its internal patterns, has thoroughly familiarized oneself with the entire puzzle, to the point at which there is nothing left to discover, and consequently one moves on, seeking new puzzles.
We are hard-wired to move on to other patterns once we have successfully solved the puzzle.
a. Pulse is graph paper in time: a predictable set of points in the future, upon which information units can be “hung” and compared, thus creating the possibilities of groups of information points, which can themselves be inspected and compared.
— Since pulse gives us a method of predicting the future, by calibrating the passage of time, it is inherently very seductive. Because it gives us the feeling that we know what will happen, or at least have some good chance of predicting it, this provides great consolation, and a feeling of “oneness” with one’s context.
b. Method by which our consciousness measures the passing of time.
— We are hard-wired with the ability to predict when the next pulse will occur.
(If we are presented with a periodic series of pulses, within the frequency range of ca. 40 – 300 pulses per minute, we can easily predict when the next pulse will occur. ) This is wrapped up in our ability to walk/run. Efficient walking requires that we are able to produce a steady stream of footsteps. (Imagine trying to walk aperiodically: lame animals walk with great clumsiness. ) Survival requires the ability to walk efficiently. Hence our ability to produce a steady pulse is biological. Along with this comes the ability, as an added bonus, to track externally generated pulses, and with great accuracy to predict the occurrence of the next pulse in a series. This gets connected with our continuous, environmental-scanning apparatuses and is the basis for our endless fascination with music based on pulse (at least with periodic pulse sequences that lie within the frequency of our ability to track/label/integrate the individual event.).
— Frequencies that are too fast:
— Frequencies that are too slow:
— We enjoy tracking pulses and participating in the cognitive game of predicting the next pulse.
SYNCOPATION: (See below for a more detailed discussion of syncopation.)
Music that plays with our inveterate pulse tracking mechanism (keeps us guessing about where the next pulse will be) is intriguing to us. This is the basis of syncopation.
—To understand patterns we must label and compare discrete points,
—Continuity of perception:
—Is our perception continuous?
We receive continuous sensory input but how do we organize it?
• Must we organize it?
— Basic survival requires that we continuously organize, analyze and make decisions based on sensory input ;
— We are hard-wired to organize our perceptions.
— So-called god-consciousness requires that we merge with the present.
— In this state there is no pattern organization, only communing with the moment,
— In this state of mind individuality ceases.
— individuality requires a separation from the moment.
— paradoxically the shaman employs complex, pattern-based music as a means for seeking a state of cessation of individuality
• If we want to understand what we are perceiving we must look for patterns.
—This requires same/difference judgments.
—This requires the location and identification/labeling of discrete points.
—Like computers we have a sample rate
Continuous perception is not actually possible at all.
Instead our sense of continuity is a mirage.
This mirage is a composite image of space/time made by vector organization/consolidation of discrete perceptual points.
Our sample rate is variable with boundaries at fast and slow ends.
—We quasi-periodically sample and label points in time.
—Some series of correlated events happen too quickly for us to perceive and label (blurring of individual pictures into motion in movies and video)
—The frequency of 20 events/second represents a perceptual threshold.
—Below this we perceive individual events
—Some series of correlated events take place too slowly for us to perceive them as related or contiguous. (we cannot “see” flowers grow (revealed by time lapse photography – the opposite process of motion pictures)
—Order is created by organizing these discrete points into patterns.
Fractal Pulse: Perception of patterns within a periodic tempo grid.
•Nested hierarchical, self-similar patterns
•in music, tempo grid is self-similar, and fractal.
The Continuity of Perception; Human Sampling Rate; The Rate of Transportation (Survival Frequency)
The rate of periodic heart/limb movement necessary to successfully escape from predators and/or capture prey. This is not the same as the velocity of bodily movement across or above the surface of the planet (or through oceans/lakes). It concerns the frequency of periodic limb movement necessary for transportation. E.g. the speed of running could be stated as beats per minute (or pairs of beats per minute — a higher fractal level) — this does not translate directly to MPH (miles per hour) because MPH will vary depending on length leg and skill of stride. The frequency of a hummingbirds’ wings does not translate directly to speed of flight.
With regard to our minds’ vulnerability to synchronization/hypnosis by externally generated pulses — This is related directly to the frequency of limb/gyration, not the velocity of movement. Heart rate and limb movement ARE directly correlated and are approximately within in the same frequency range (Is this true for hummingbirds?)
•Traveling fast is thrilling, and so are fast tempos, but only to an extent: beyond a certain threshold we cannot remain comfortably in sync with the pulse, and need to bounce to a higher fractal level. What is this threshold? The fastest tempos in our music are around 300 BPM. This is due partly to the limits of human mechanical performance (How fast can we clap or run our fingers up the piano keyboard?). Electronically generated pulses can push the limit, but what is the cognitive limit of our sampling rate — at what tempo do we become disinterested in the pulse, at what tempo does the pulse lose its ability to hypnotize/synchronize our perceptual apparatus?)
• Pattern recognition in non-pulse-based music requires the same strategies that we must employ to decipher nature — It consequently takes more work/energy to comprehend.
• Pulse-based music establishes a sample rate and presents a smorgasbord of patterns to unravel and consider:
• The steady pulse provides a sample rate for us.
— This synchronizes our data-labeling apparatus, taking over our internal sample/labeling mechanism and making it periodic
— This happens within the range of our ability to track it.
— This is irresistible — we are hypnotized willy-nilly by pulse.
— The range of tempos that can effectively take over our labeling mechanism is limited by our survival needs, i.e. the average rate of data assimilation/correlation necessary for human survival.
— This is directly related to our need to capture prey or escape from predators,
i.e. the RATE Of TRANSPORTATION (Frequency of Survial)
— Therefore the range of tempos that can effectively hypnotize us and synchronize our data input is correlated to the range of speed of walking/running (and is also directly tied to the range of rates of the human heart).
— Small birds have a higher average data sampling rate than humans — their RATE Of TRANSPORTATION (the rate of periodic heart/limb movement necessary to successfully escape from predators and/or capture prey) — This is not the same as the velocity of movement across or above the surface of the planet (or through oceans/lakes) has to do with wings pushing air fast enough to fly. They also have a correspondingly much higher heart rate than humans.
• This simplifies our perceptual task — we do not have to spend energy deciding on where the next sample point is.
— This in turn allows us to delve into pattern organization within the establishment of the sample matrix.
— This is attractive, powerful, hypnotic and to large extent irresistible.
— The clock is an abstract grid for measuring time, which is tied to natural cycles. Our methods of time-keeping allow us to refine natural cycles into smaller, more precise units, and also expand them into larger structures.
— We naturally employ fractal organizational strategies for keeping track of time in all capacities: We use a multi — level fractal time scale to organize and keep track of our endeavors:
vi. Month (Moon)
— How many units are there at each level? Why?
i. Second = 60
ii. Minute = 60
iii. Hour = 24 distinct units, with clear social uses and meanings.
iv. Day = 7 distinct units, with names, and clear social uses and meanings.
1. Days are also grouped into months (w/28, 29, 30, 31 units) Ð but not individual names in this context.
2. Days are grouped into years (365 or 366 in leap years)
v. Week = 4/month (approximate) and 52/year (approximate)
vi. Month (based on the cycle of the moon) = 12 distinct units, with names, and clear social uses and meanings, and seasonal references/subdivisions.
vii. Year = 10/decade; 100/century; 100/millennia
viii. Decade = 10/century
ix. Century = 10/ millennia
x. Millennia = no grouping usually employed (except in science: evolutionary studies; geologic time studies)
xi. Periods of Human cultural development (Paleolithic, Mesolithic, Neolithic, Iron age, Bronze Age etc.)
xii. Periods of Human genetic evolution: Homo Sapien, Homo Erectus etc.
xiii. Periods of evolution of life
xiv. Geologic Time Scales
xv. Evolution of the solar system/galaxy/universe
Time Scales in Music vs. General Time Scales:
Of these 15 levels, 3 are rooted in natural cycles that we can notice and remember (day, month (cycles of the moon) and year). These have the greatest practical meaning for us: they govern or influence in some way most of the decisions that we make. The greatest (in scope of time) scales concern matters of our psychological centering within the overall framework of our understanding of existence, but we do not use them (except in a general, background sense) in the ongoing series of decisions by which we navigate our way through time.
The other, lower numbered levels are abstractions and are used to help us further delineate the 3 main cycles: Days are grouped hierarchically in three ways simultaneously: 7 days/week; 30 days/month; 365 days/year. Understanding this primal grouping of the darkness/lightness cycle within these nested circles gives a feeling of solidity. Our understanding has evolved to the level that we need in order to structure our activities on a social level. We can use these nested guideposts to help us easily plan and keep appointments at close and distant time intervals. Our practical knowledge and ability to place ourselves with these systems has its limits: We generally know what day of the week it is, and what day of the month it is (though this is easier to lose track of – it is a bigger number and hence a larger scale), but most of us do not know what day of the year it is, except in a very general sense (We know the season, we can say we are halfway through the year, but we would have to stop and do a string of calculations to determine how many days had elapsed since new yearÕs day.) And there are very few occasions that require us to know this with any precision. But it is important for us to have a sense of the total number of days – this gives a general time frame for measuring our accomplishments and goals.
Days: Days are analogous to beats in music. They are constant, predictable, steady pulses that we depend upon to structure our middle ground activities. We group them into larger structures for long–range planning (weeks, months, years) and sub-divide them for scheduling our immediate activities (hours, minutes, seconds). But the day is the middle – ground pulse, the beat, and everything that we do is attached to it, either within it or in groupings of days. The day is the indispensable backbone pulse upon which we hang our lives.
If it is analogous to the pulse (the beat) in music, what are the parallel functions, and what are the differences? Like the day, the pulse in music serves a middle-ground function. It comprises a backbone upon which we hang larger groupings (measures, phrases), as well as immediate, minute scintillation, surface ripples and ornaments that themselves are too ephemeral to remember, apart from the larger information structures to which they contribute.
The tempo of the pulse is very important and both fairly consistent and narrowly limited in practice in indigenous music throughout the world. As noted earlier in this paper, it is biologically tied to the range of rates, the tempo, that we must step, footwise, in order to survive. This tempo , from approximately 30 – 230 beats per minute, is consistent with the rates of footsteps ranging from slow walking to sprinting. Our consciousness, cognitive apprehension and organization and distillation of events are directly tied to this range of tempi.
At slower tempi we cannot predict the next occurrence with accuracy. At faster tempi we cannot count fast enough, and cannot keep track of the sequence of events by assigning and labeling them as discrete points on the time continuum, so tend to assign them as sub-beats, hence establishing a slower tempo at some lower ratio (1/2, 1/3 or 1/4) speed.
Why do we need a middle ground? And why is the middle ground for music de-limited by the rates of stepping, in contrast with the general middle-ground pulse for life (the day pulse)? Why is the day-pulse not usually employed to organize musical events? Is it possible that it could be employed to create a powerful musical backbone — as a backbone for hanging musical events — a macro-music that concerns large time scales?
It would not be consistent with time frames allocated for music in any traditional sense (though Balinese Gamelan concerts can go on for months — but in this case the day is not the middle ground pulse, but the largest structural shell.
Day-music would apply the concepts of beat creation, with accents, phrasing, syncopation, sub–beats and measures, to appropriate life events. In this context the week is analogous to the measure, and the month to a phrase. A season is a phrase–group and the year is a period.
Syncopation is the delaying or pre–empting of an expected timing point on the tempo grid.
(This could be the shifting of the tempo grid components themselves.) This implies that there is a defined, delineated grid of equally spaced points at several fractal levels. The grid points at greater (in duration) fractal levels comprise accent points.
Syncopation is exciting. Why? It is not an intellectual phenomenon. The delayed or pre-empted points are themselves repeated. It is this continuous comparing and keeping track of the expected, predicted point with the actual, perceived event that keeps our pattern recognition accountant busy. (We must continuously compare the predicted with the actual event and note that one is a substitute for the other, rather than a different point, or a point in another fractal level.) This adds another operation to our cognitive housekeeping operation, by continuously re-setting, re-triggering the pattern recognition algorithm (the sensing/tracking of the steady pulse-grid). In turn, this keeps our unconscious attention (or pre-attention) focused on the changing accents and keeps them from becoming redundant as quickly as they would otherwise.
This may imply that music that employs steady pulse almost requires syncopation to remain transfixing.
(How is syncopation achieved in Euro-centric music as opposed to African?)
Syncopation in Hip-Hop
It could also be that pre-empting the accent point has the effect of speeding up perceived time, and delaying the accent point has the effect of slowing down perceived time. In some types of music both occur within the same pattern (hip-hop etc.)
Two types of syncopation:
• pre-empting (anticipation) of the predicted accent point
• delaying of the predicted accent point
Some types of music cannot be syncopated. We do not associate syncopation with Euro-centric classical genres that fall within the schools of dodecophony and integral serialism (including noise and texture-based electro-acoustic music). These loose-pulse genres have deliberately forsaken the use of tempo grids that make syncopation possible. Can there be loose syncopation? Could this be effective at sparking a pattern recognition reaction?
Assuming that music involves the process of remembering, to be effective music in general must spark (elicit) a pattern recognition reaction. This is our hard-wired response to patterns in any mode of perception, and is pivotal and intrinsic with our means for making connections, understanding anything and everything.
Precise Time (pulse) versus Loose Time (pulse):
• Precise pulse: falls within the human speed of transportation, between 40–400 bpm. In that range we can accurately predict when the next pulse will fall.
• Loose Pulse: slower than ~ 40 bpm, we cannot predict exactly the next pulse, but use these tempos to:
i. Give proportions, i.e. a sense of scale in music – delineate sections, can be used in texture-based music.
i. Schedule life activities:
1. meals, baths, work, sleep
iv. Current abstract music (Euro-centric) eschews Precise Pulse, favors Loose Pulse (even though it may be precisely scored). Can Loose Pulse synchronize the human pattern recognition faculty?
We do not experience the world as continuous, but rather as (many) discrete points that we label and categorize according to complex schemes, some inherited, some learned. The architecture of some (maybe all) of these categorization structures is fractal: nested, self-similar hierarchically-nested levels (like most music).
We perceive a note, with pitch (frequencies with ratios of 1/1, 2/1, 4/2 i.e. octaves), timbre and duration, as a discrete point, for purposes of pattern building and pattern recognition. The element of pitch is extracted and placed hierarchically within a culturally specified grid, e.g. a major scale. We are hard-wired to extract pitch as a mnemonic (in and of itself an amazing ability!).
Hearing 2 or more pitches simultaneously poses a cognitive challenge: How do we label them for purposes of comparison (pattern recognition) within a hierarchically ordered, culturally specified grid (scale)?
Labeling a chord discreetly (as a collection of discreet pitches) is an extremely complex cognitive challenge, especially since in most cases each pitch is itself a collection of fundamental, plus harmonic and enharmonic partials. Since we naturally (biologically) understand the correlation among simple frequency ratios (2/1, 3/2, 4/3, 5/4, 6/5 and multiples) within a single note, we apply that same seeking-for-order to any set of frequencies, and attempt to understand the whole collection: notes and attendant overtones, as a correlated entity — a singularity, i.e. a major chord or its aberrations.
In order for this to successfully occur the ratios among the elements need to be pretty simple. (Jazz chords and other added note sonorities “play” with this, obfuscating the simple order of an underlying major chord (the “chord of nature”) with pitches that introduce complex ratios and skew our natural cognitive goal of easy hierarchical placement. (Jazz appreciation is a highly culturally specific endeavor.)
When we cannot successfully identify the frequency ratio(s) between 2 or more simultaneous notes, there are several possible outcomes:
1) we are frustrated and experience tension, i.e. dissonance;
2) we give up and quit listening;
3) the notes lose frequency as an identifying mnemonic, and hence become noise i.e. sounds that are identified by envelope, timbre and duration, but not primarily by frequency.
When, within a given work of music, we quit trying to hear complex frequency ratios as pitch-correlated mnemonics, they seize to annoy us, and are no longer dissonant (Xenakis’ clouds of pitches) but they can of course still be musically useful (clouds of notes are like non-pitched percussion). Playing around with all that within a composition is where a lot of the fun is!!
what is melody?
Melody evolved as a means for adding mnemonic information (pitch) to discrete rhythmic pulse-points.
o This makes the discrete rhythmic pulse-points easier to identify and
Consequently these pulse-points can be organized into patterns of greater complexity that are more vivid and easier to remember than unpitched rhythmic points.
o patterns of greater complexity become possible because rhythmic
hierarchies become delineated with
o Use of pitches does not guarantee ease of memory:
i. There are limits regarding:
a. The number of pitch classes employed within a set. Most cultures settle on 5 – 7 pitches as workable total. More than that becomes confusing, unless entailed by specific cues (i.e. the various types of chromaticism in European-based diatonic music: borrowed chords, secondary dominants, changing keys etc.)
b. The octave displacement of adjacent pitch classes: Octave equivalency does have limits: Placement of adjacent scale steps in different octaves weakens the hierarchical categorization.
c. Cultural familiarity: Pitch sets that fall outside of those employed generally within a given geographical-social structure will not be assimilated. (The quasi quarter-tone scales of Middle-Eastern music are indecipherable to folks whose musical culture draws on the legacy of Europe.)
ii. Evolution of diatonic scale
iii. The Magic Number 7 Plus Or Minus Two
1. number of total pitches
2. frequency ratios of pitch set
3. what is harmony?
a. Amplification of melody via the harmonic series associated
with a collection of pitch classes
Art and science are inextricably intertwined. Both arose in the religious and magical rituals of our ancestors.
The purposes of art and science are, respectively, to explore intuitively the connection of the individual to existence, and to objectively explain that connection.
In its best usage, art connects subjective individual experience, which is characterized by parallel associative qualia, with the objective logic of science. Art breathes life and warmth into science, gives it context, makes it substantive and connects it to consciousness.
Science without art is meaningless. Art is the essence of “meaning”, but without science harbors the danger of veering into superficiality or regressing into religion.
This does not mean that art works should be science experiments, per se. That would make for pretty bad art, since the pathways of inquiry are, beyond a certain fork, fundamentally different. Rather, the enterprise of art offers a powerful forum into ritual and celebration and also can properly be regarded as experimentation into consciousness. Every art work, from the most innocent pop tune to sohphisticated visual abstraction, contains implicit questions and contributes to the evolving dialogue of who and how we ARE.
Art and science are partners, and together offer a means of connection and vivification to the individual.
The combined purpose of art and science, and the challenge to artists and scientists, is nothing less than to give us enlightened, forward looking reasons to exist.
In view of the above, I would like to propose a new field that investigates the reunion of art and science into an overarching dome of inquiry and celebration. This opens up fascinating and powerful pathways for moving us forward as better stewards of this planet.
In recognition and deference to its evolutionary significance and the powerful role that traditional religious practice still exercises, (and at the risk of making scientists cringe, artists shudder, and preachers scream in protest), I suggest the working title Enlightened Religion.
I believe that it is a universal focus of music to continuously re-fresh the human need for catharsis and celebration. This is not the sole function of music, but it is the core. Catharsis and celebration involve ritual, which often involves music. Effective ritual demands a continuous engagement with the spiraling evolution of culture. Thus ritual (and its music) is entailed by its cultural milieu. Ritual-music is an inevitable manifestation of cultural forces. The challenge of composers and musicians, if they wish to be relevant social components, is to become transparent, immersive manifestations of these cultural forces.
How do we make an effective ritual in a post-religious culture? Ritual involves a merging of the self into something that is larger. Contemporary non-religious manifestations are social gatherings where communication is not one-to-one, but shared by many simultaneously, such as sporting events. Secular choirs (common in Europe) achieve this. So do “raves”, where participants are immersed in loud, hierarchically-nested pulse-driven music, and engage with this in non-specific bodily dance, often with the aid of drug-induced states of rapture (not by sitting as in a European classical music situation, or dancing one-on-one as in ballroom dancing and other mating rituals).
Does ritual take place in a traditional European classical music concert? Here the audience sits in quiet, mutual shared reverie, experiencing a synchronization of sensory input. An implicit goal (in addition to hearing the music in a “live” situation, is communion. (How important is the “communion” aspect of the concert? Consider this: if money was not an issue, would most folks prefer to have an orchestra perform for them in the privacy of their own private hall? How about a pianist in the privacy of their living room?) This is a quasi-religious ritual, having its origins in the religious worship of the Catholic church.
Is it implicit that the size of the audience be the same or larger than the size of the performing ensemble?
What do both types of ritual share in common?
• Symbiotic interconnection with the performers.
• Sensory input synchronization with fellow audience members (thus creating a shared sensual experience and social context.)
What are the social uses of music?
• ritual (leaving the self, merging with something beyond the self)
1) Ritual dance
3) drum circles
4) choirs, religious & social
• work (engage the mind to make tedious, repetitive activities palatable: work songs)
• mating rituals
• enhance and entail personal reflection
• sleep and elicit sub-verbal associations
• wall paper
1) muzak – designed to manipulate
2) music designed to “fill in” public spaces, or cover ambient noise
• entertainment (what is that?): diversion from one’s personal angst
• enhancement of stories (movie scores/ plays/video games)
• mood enhancement: elicit and alter emotional response
Who is my audience? Who am I composing for? After years of being imbued (told) that this is a vulgar, sacrilegious question, this question has become a central focus of my recent work.
In fact I now consider it the most critical question in any endeavor that involves communication.
Further considerations: The concert.
• The concert as a container for time:
i. To what extent is culture a container?
1. Local norms prescribe and limit the possibilities.
a. These can be stretched if one understands the rules and limits.
ii. There is a prescribed beginning and end.
iii. Is there an implicit ÒshapeÓ to this container for time?
1. Is there possibility for a Òsteady stateÓ Ð a continuous dynamic?
a. I.e. begins at full-tilt, and continues at full-tilt until an abrupt end. Ð Can this kind of model work?
b. Trance music: layered, repeated patterns
i. Sub-Saharan Africa
ii. Bali & Java (Gamelan)
iii. DJ and electronica
2. Is the concert experience implicitly developmental i.e. does the music grow and change by self-referencing and extension? Does development imply predictability?
•The concert as ritual:
iv. Ritual: a communal sharing of heightened, focused a Purpose of ritual: to create an intense, communal (shared) experience, in which there is heightened communication & a sense of euphoria, owing to the experience of heightened connectedness: a temporary escape from the individualÕs loneliness.
v. Habitual Ritual: (religious rituals) Does it need to be habitual? If it is, the participants know the rules, so it is easier to achieve the desired effect.
vi. Ritual i.e. concert experience of music: Collects people within a defined setting, creating an environment in which the music cannot be ignored. This in turn simplifies communication, by forcing a common information processing, pattern unraveling among all present. The inundation in an immersive musical environment specifies and controls exactly what everyone will be focusing on at a specific moment in time. Thus people can all agree on context and within that context share an experience of the moment among many individuals simultaneously. In this way a mass consciousness is created, and individualsÕ separation from others is temporarily suspended.
viii. The places where concerts occur:
ix. the concert as defining and limiting attention
1. element for a work of music:
a. To what extent does the idea of concert as a time-delineated structure, shape and limit the possibilities of a work of music?
b. Concert structure:
— enclosed acoustic resonator (important so that sound can be easily heard)
— public gathering
— identifiable destination
• Relationship of Classical to popular/folk music:
Connection of Classical Music to Folk Music:
1. When they are not connected and exerting continuous influence on each other, both suffer:
a. Classical music becomes too esoteric
b. Folk music becomes too superficial
2. Traditional Euro-centric models of classical/folk interaction
a. Mozart/Beethoven etc. drew from a set of contiguous, closely linked cultures, with shared history, religion, values etc.
i. Italian folk tunes would be considered exotic to Austrians
ii. No knowledge of remote cultures with different evolutionary stems
1. for example Arabic music, Sub-Saharan African, Asian, Indonesian, Indian, North American
3. What comprises contemporary folk music?
a. In USA and Europe, mostly a dual lineage of African & European concepts and values:
i. Afro-European Genres: rock, blues, jazz, hip-hop, reggae, disco, salsa, tango, samba etc.
ii. European base values:
1. Roman Catholic-based notions of the sacred:
a. Suppression of rhythm/pulse-based music
i. Rhythm = dance = sex = sin
2. goal oriented, linear development
a. expressed through Functional Harmony
i. resolution of the tri-tone (V7 ÑI) as the engine that powers European music from 1600
3. iii. African base values:
1. Africa-based notions of the sacred:
a. Pulse-based drumming as basis for seeking the divine
ii. Shaman ÒridesÓ the drum to discorporate
1. visits spririt world, world tree
2. brings back wisdom and advice from ancestors
2. Static, non-developmental trance-inducing
3. iv. African, European music brought together through slave trade:
1. Europe is politically dominant culture
a. European music considered superior by whites
2. African music/culture repressed
a. African music percolates up through culture, eventually takes dominant role
3. A potent folk music evolves that is a result of the confluence of European & African music
a. African elements:
iii. Drums dominate
iv. Complex rhythmic textures
1. hierarchical polyrhythms
b. European elements:
i. Cadence-driven, goal-oriented development
ii. melodic counterpoint
iii. complex harmonic schemes
1. resolution of the dominant
2. hierarchical tonal regions
b. Increasing influence of the East & Near-East
4. Contemporary Afro-European models of classical/folk interaction
i. Today, small, mostly white, middle-class audiences
ii. Complex harmony
iii. Complex rhythmic component
1. pulse is repressed
2. contemporary jazz not primarily for dancing