Compression, Concreteness, and Concurrency

Here's a different way to describe the sources of the ThumMusic System's benefits.

1. Compression: By notating and controlling intervals (i.e., ratios between frequencies) instead of pitches (i.e., log representation of frequencies), musical information is compressed by a factor of approximately 12, as the music of all 12 keys shares a single representation.
2. Concreteness: Anchoring abstract tonal relationships in the concrete geometry of a specific isomorphic keyboard facilitates makes these concepts tangible, facilitating interactive learning and the formation of mental models.
3. Concurrency: Exposing the consistent patterns of music to the senses of sight and touch, at the same time that they are exposed to hearing, engages more of the student’s brain in the learning process.

I don't know enough about cognitive psychology to cite references as to the importance of these factors (your suggestions would be welcome!), but it seems intuitively obvious that they out to have a synergistic cognitive impact.

The Law of Accelerating Returns, Order, Efficiency, and Music Education

Ray Kurzweil’s Law of Accelerating Returns states that “as order exponentially increases, time exponentially speeds up (that is, the time interval between salient events grows shorter as time passes).”

What is “order”?

Kurzweil defines and discusses order as follows:

Order… is information that fits a purpose. The measure of order is the measure of how well the information fits the purpose. In the evolution of life-forms, the purpose is to survive. In an evolutionary algorithm (a computer program that simulates evolution to solve a problem) applied to, say, investing in the stock market, the purpose is to make money. Simply having more information does not necessarily result in a better fit. A superior solution for a purpose may very well involve less data.

I submit that there is only one possible metric for measuring the order of any commercial information system: price/performance, which I’ll call “efficiency.” This same metric can be posed in two ways.

1. Fixed Performance: Contrast the prices at which different systems attain a given level of performance.
2. Fixed Price: Contrast the levels of performance attained by different systems a given price.

A familiar example is the ever-increasing efficiency of the personal computer. Compared to this year’s computer, next year’s computer will have twice the power at the same price, or have the same power at half the price, or some balance thereof.

The efficiency of education hasn’t changed significantly for generations, due to its inability to benefit from the kind of technological innovations that have improved the efficiency of other industries (a situation studied by economist William Baumol and known as Baumol’s Curse).

Let’s assume for the sake of argument that the purpose of education is to facilitate a student’s internalization of as much of world’s accumulated skills & knowledge as possible. Then the “order” of different systems of education can be measured by comparing the efficiency – the price/performance – with which they deliver the most skill & knowledge to the most students at the lowest cost.

For music education, the two perspectives on efficiency can be expressed as:

1. Fixed Performance: The total cost of developing a given average level of musicianship in a given population of students.
2. Fixed Price: The average level of musicianship attained within a given population of students at a given total cost.

In education, time often dominates price. For example, in Writing Right's comparison of different writing systems, the time it takes to achieve functional literacy using a given writing system is the price of using that system.

It can be argued that arts education should focus not on the average outcome, but on the exceptional outcome. That argument can be accomodated simply by restricting the “given population of students” to those who are exceptional, and by raising the “given average level of musicianship” accordingly. Either way, the efficiency metric still applies.

I submit that the ThumMusic System has the potential to provide an exponential increase in the “order” of musical information, by reducing – through abstraction and isomorphism – the amount of data needed to describe any given musical structure (whether tonal, atonal, harmonic, or inharmonic).

The Law of Accelerating Returns suggests that such an increase in order should result in a shortening of time between salient events. What kind of salient events?

• In music education, those moments when the student suddenly “gets it,” solidifying past learning and broadening the foundation for future learning.
• In music theory, the emergence of new ideas that abstract, unify, and simplify.
• In music, the emergence, development, maturity, and senescence of new musical styles.

As Kurzweil wrote, “Sometimes, a deeper order – a better fit to a purpose – is achieved through simplification rather than further increases in complexity.”

A better fit to a purpose is exactly what the ThumMusic System offers, through its simple geometric exposure of the music’s deep structure.

The Metrics of Revolution

I'll be leading a panel discussion on the topic "The Metrics of Revolution" at the College Music Society's 2008 National Conference, in Atlanta. The panel is to be held from 8am-9am on Saturday, 27th September, in room Marriott L504-505.

The CMS is said to be quite conservative, so its conference committee is to be commended for being willing to accept a panel proposal from a potentially-revolutionary outsider.

Here's the official blurb for the panel session:

This conference’s Call for Papers described music education as being desperately willing to consider revolutionary ideas; it even dared to state that ideas which served us well in the past might now be holding us back. Let’s presume that in response to this call, a flurry of new approaches to music education will be proposed.

By what criteria and metrics will these new approaches be compared and contrasted with the status quo and with each other? For example, all else being equal, would it be a good thing to increase the rate at which students attained a given level of skill and knowledge (i.e., reduce the amount of time it took)? How about reducing the cost of music education? Increasing the success rate? Broadening and/or deepening the level of knowledge and/or skill attained?

It is unlikely that any – let alone all – of these metrics can be dramatically improved when using traditional instruments & notation. What core knowledge and skills of music-making exist independently of traditional instruments & notation? How can these core abilities be reflected in the criteria and metrics by which novel approaches to music education are measured? Or is it all just too hard, so that we’d all rather fail with traditional approaches than succeed with non-traditional ones?

The conference's version of my bio reads as follows:

Jim Plamondon – an outsider to music education, self-taught in music theory – is the co-author of papers in the peer-reviewed Computer Music Journal and the Journal of Mathematics and Music. Nearly all successful revolutionary ideas come from outsiders, and although insiders to tend to reflexively dismiss revolutionary ideas (the Semmelweis Reflex), it behooves them to consider such ideas objectively. Jim is interested in facilitating the identification of the criteria, metrics, and benchmarks by which alternative approaches to the status quo of music education – such as his proposed ThumMusic System – can be objectively compared and contrasted.

The session's confirmed panelists are:
Thomas Rudolph, President of TI:ME
Monty Cole, Mercer University
Maud Hickey, Northwestern University
Colby Leider, University of Miami
Gil Weinberg, Georgia Institute of Technology
Carlos Xavier Rodriguez, University of South Florida

I expect to hand out a ballot at the start of the session. Each attendee will have 100 votes, which they will distribute across a number of potential metrics to indicate the weight that they would like to see each mettic have in a combined metric for comparing and contrasting the effectiveness of alternative methods of music education.

• Percentage of Test-takers who pass The Test after studying The Method's Student Materials for a given number of hours
• Average number of hours of study invested in studying The Method's Student Materials by those who pass The Test
• Percentage of those who begin to study for The Test using The Method but drop out before passing it (per week)
• Average amount spent acquiring The Method's Student Materials by those who pass The Test
• Average amount spent acquiring instruction by those who pass The Test
• Sum of "Cost of Acquisition," "Cost of Instruction," and any other Method-specific costs (excluding the value of the student's time)
• Same as Cost of Competence, but for those who Drop Out before passing The Test
  Percentage of legally-disabled persons whose disabilities do not preclude passing The Test using The Method
• Percentage of performance gestures required by The Test that are ergonomically risky, weighted by frequency and degree of risk
• Percentage of target population that can afford the Method's Cost of Competence
• Of the music used in The Method's Student Materials, the percentage written by composers who were alive when The Materials were assembled
• Of the music used in The Method's Student Materials, the percentage that is based on compositions that have been in Billboard's Top 40
• Of the music used in The Method's Student Materials, the percentage recognized by first-lesson students (on average)
• Using Normalized metrics: [Pass Rate] / ( [Ergonomic Risk] * [Time to Competence] * [Cost of Competence] )
• Percentage of those who pass The Test using The Method who, without any additional study or practice, also pass equally-standardized Tests on other musical topics

Here are some definitions for terms used in the above proposed metrics:

• The Test: a standardized test of musical competence. There are many possible tests – GCE, AMEB, ABRSM – each with its own strengths and weaknesses. Selection of a particular Test, and debate over the value and consequences of teaching to such a Test, is outside the scope of this discussion. Primary, secondary, and tertiary music education are likely to target different tests. It is presumed for the sake of simplicity that The Test is pass/fail.
• The Method: any given potentially-revolutionary method of music education.
• The Student Materials: the tools a student must acquire in order to use The Method to gain the knowledge and skills necessary to pass The Test. Can include lesson books, DVDs, online materials, instruments, sheet music, metronomes, software, etc.
• The Traditional Method: By default is assumed to use of the piano keyboard and traditional staff notation, aimed at passing The Test.

Musical Intuition

We denote this primary wisdom as Intuition, whilst all later teachings are tuitions.
(Ralph Waldo Emerson)

Intuition is a funny thing. Mostly, intuition means that “something new corresponds with your expectations,” which means that it corresponds with your experience.

But what if your experience was misleading?

Consider, for example, a caveman observing the Sun. It is "intuitively obvious" to this caveman that the Sun is moving around a fixed Earth, because that’s what he experiences every day. Or consider the incidence of infectious diseases. In a unsanitary city of foul water, tainted food, and ubiquitous disease-vectors like mosquitoes, fleas, lice, and cockroaches – that is, in almost any city in the world, until very recently – it would have been “intuitively obvious” that illness, health, death, and survival were all essentially random, or in the hands of the Gods. The underlying patterns were hidden by the experience of randomness.

So it is with music. Most people’s experience with music-making misleads them into thinking that music is about pitch, because pitches are what’s notated, pitches are what are controlled by traditional instruments’ interfaces, and pitches are what musicians talk about among themselves. It seems intuitively obvious that music is about pitch.

However, this experience is misleading. Music is not about pitch. It’s about intervals – i.e., the gaps between pitches. At this level of abstraction, any given musical structure – an interval, a melody, a chord, a chord progression, or even an entire musical piece – is the same in any octave or key. This is not at all obvious to most instrumental musicians, for whom the ability to transpose “on sight” is rare and awe-inspiring. Those who’ve learned music by singing using tonic solfa are more likely to recognize this higher-level abstraction, because their key-independent experience prepares their intuition to recognize the “invariance” of musical structures across keys and octaves.

Likewise, the experience of most musicians is misled by their implicit assumption that musical timbres are, and must be, harmonic – i.e., follow the spectral pattern defined by the Harmonic Series. This assumption is so deeply ingrained in Western music theory – dating at least from Pythagoras, 2,500 years ago – that most music theorists assume it without even recognizing that an assumption has been made. When the music of some indigenous cultures – in Indonesia, Thailand, and Mandinka Africa – was discovered to be inharmonic, this physical basis for music theory was challenged. Many people just threw up their hands and said that musical structure had to be “just cultural; just experience” – i.e., intuition.

However, if you abstract music to the next higher level – i.e., to patterns of relationships among intervals, as defined by a comma sequence – then it becomes clear that the music of the above-listed cultures and that of the West all share the same deep structure, and that the sonic spectra (timbres) of the instruments used by each culture bears an invariant relationship to its characteristic tuning within that deep structure. Yet this “tuning invariance” – first described just last year (2007) – is so non-intuitive that it had been overlooked by generations of music theorists, arguably because their experience was so firmly grounded in the Harmonic Series that their intuition misled them.

It is remarkable that so many of the world’s musical cultures use combinations of tuning & timbre that share the same deep, invariant structure. Why this one structure, and not others?

It is entirely possible (but entirely speculative at present) that the human brain contains a hard-wired isomorphic note-layout which reflects this deep structure. Such a note-layout presents any given musical interval, chord, chord progression, etc., with invariant geometry in all tunings of such a deep structure. The findings of many recent studies in music cognition can be interpreted as supporting this hypothesis. Like everything else in Western music theory, those studies have tended to be pitch-based, and to assume the use of 12-tone “equal temperament” tuning, but Occam’s Razor suggests that this one entity – a hard-wired isomorphic note-layout of interval-detecting brain cells – can explain their findings very simply. No studies have yet been performed to determine whether such a hard-wired note-layout exists, in part because the discovery of tuning invariance is so recent, and was made by relative outsiders to the music cognition community (as is so often the case).

Which brings me back to the tonic of this piece: musical intuition. The only possible source of “intuition” that’s deeper than personal experience is the hard-wired physical reality of the human brain. If the brain did indeed contain a hard-wired isomorphic note-layout, then that note-layout would be the ultimate source of musical intuition – invariant across octaves, keys, tunings, and cultures.

For the experience of music-making to be deeply and truly intuitive, the tools of music-making – music notation, music control interfaces, music synthesizers, etc. – would need to reflect this hard-wired geometry of music. This hasn’t been technically feasible until recently, nor commercially feasible until even more recently, but it is entirely feasible today.

If music-making were to be made truly and deeply intuitive, in a culturally-invariant way, then the percentage of the world’s population that could afford to successfully gain a self-sustaining level of musical competence could increase dramatically. Furthermore, it would elevate music to being truly a single universal language, with lots of interesting regional dialects.

I submit that this would be a maifestly Good Thing.

Hangul for Music

South Korea could be a leading adopter of the ThumMusic System, for two reasons: South Korea’s relentless obsession with education and its experience with (and reverence for) hangul.

Hangul is a written phonemic script organized into syllabic blocks which represents the sounds of spoken Korean. It was developed as an alternative to the use of Chinese hanja characters, of which there were so many – nearly 50,000 altogether – that attaining functional literacy required a huge investment of time. Korea being a poor country then, the vast majority of Koreans could not afford this huge investment in hanja literacy, so Korea’s literacy rate was very low.

Hangul's ease-of-learning reduced the cost of attaining literacy by so much that a bright Korean-speaking student could learn to read and write in a single day, and by a not-so-bright student in a single week. It has been described as being "the world's best alphabet" and "the most scientific system of writing” (see Writing Right, by the Pulitzer Prize-winning science author Jared Diamond).

Hangul’s democratization of literacy was adamantly opposed by Korea’s intellectual elites, which correctly saw hangul as threatening their monopoly on the benefits of literacy. Hangul was recognized as Korea’s official written script after WWII, and since then, hangul has become nearly universal in Korea, with hanja rapidly disappearing.

Hangul’s impact on Korean culture has been profound. Using hangul, Korea rapidly attained the highest literacy rate in the world – an important factor in its emergence as a top-tier industrial nation. Korea is so proud of hangul that it celebrates Hangul Day every year. Korea’s new capital, Sejong City, was named after King Sejong the Great, whose ‘greatest’ accomplishment is considered to be the development of hangul.

Thus, Korean society is well-disposed towards the idea that the use of a non-traditional symbol system can dramatically improve learning outcomes, as the ThumMusic System is poised to do. Positioning the ThumMusic System in Korea as “hangul for music” could help lead to rapid success there.

The second reason why the ThumMusic System could take off in South Korea is its absolute obsession with education, delivered in large part through private cram schools, on which Korean parents spend US$15 billion per year – the world’s highest per capita investment in private education. As one leading cram school entrepreneur stated, “The most important thing for students is time, so the quality of educational services is critical – they have to learn as much as possible in a short space of time.” In the highly-competitive cram school market, the school which first adopted the ThumMusic System could gain a significant advantage.

Together, these two circumstances could lead South Korea could be a leading adopter of the Thummer and ThumMusic System.

It happens that Korean manufacturing giant Hyundai recently acquired Kurzweil Music Systems and appointed Ray Kurzweil to be its Chief Strategy Officer, to “build Kurzweil Music Systems into one of the largest music instruments brands in the world,” according to Kurzweil.

Interesting,yes? ;-)