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.

Hard Work

While the percentage of music educators that are enthusiastic about the ThumMusic System is high, those who are unconvinced sometimes seem to be opposed to anything that might make music education easier. They want music education to be hard. This view is captured in the Children's Music Workshop's Twelve Benefits of Music Education, in which Benefit #7 is described as follows: "Through music study, students learn the value of sustained effort to achieve excellence and the concrete rewards of hard work."

However, this benefit can be obtained from lots of alternative activities, including team sports, weight-lifting, macramé, and even video-game playing, just to name a few examples. Therefore, emphasizing this common benefit is a distraction from, and devalues, music education’s unique benefits.

Here’s another way to frame the issue. Let’s say that this minority of hard-work-loving music educators had to choose between making music education 10% easier or 10% harder, with all else being equal, and the status quo not being an option. Because these educators consider “an appreciation for the benefits of hard work” to be an important outcome of music education, then of course they would prefer the “10% harder” option. Surely one can’t increase a student’s appreciation for “the benefits of hard work” by making something easier!

Yet this is clearly self-defeating (which is probably why it is a minority viewpoint). Taken to its logical extreme, this viewpoint would make music education so hard that no one would be able to succeed. That's clearly not a desireable outcome, because then no one would attain the unique benefits of music education (whatever those might be).

On the other hand, let's consider the other logical extreme. Imagine that music educators could wave a magic wand and instantly change a non-musician's brain, muscles, cardiovascular system, etc. to precisely match the changes would have resulted from years of musical study and practice through traditional methods of music education (but without the Repetitive Stress Injuries). Let’s further imagine that waving this magic wand was guaranteed to deliver the unique benefits of music education with no unpleasant or unexpected side-effects. Talent and inspiration would not be guaranteed, but then, they never are.

If the unique benefits of music-making are good for individuals and for society, then waving this hypothetical magic wand would be, too, wouldn’t it?

To argue otherwise would be, in effect, to advocate educational flagellation in the belief that the self-mortification of unnecessarily hard work will deliver spiritual benefits.

According to the Twelve Benefits of Music Education, Benefit #3 is that "Students of the arts learn to think creatively and to solve problems by imagining various solutions, rejecting outdated rules and assumptions. Questions about the arts do not have only one right answer" [emphasis added].

A high percentage of music educators have acquired this benefit, and are eager to deliver the unique benefits of music education to as many students as possible, by any means necessary -- magic wands, the ThumMusic System, or whatever. The flagellants, on the other hand, would apparently rather see students fail with traditional methods than succeed with a new one, lest -- God forbid! -- they attain the unique benefits of music education without as much hard work.

Thank goodness that music education's flagellants are in the minority!