Tonnetz

Since Euler, and especially since Hugo Riemann, the tonnetz has been thought of as being generated by a combination of major thirds and perfect fifths. Reading an excellent paper by Yale's Richard Cohn, I have suddenly realized how this traditional approach could be generalized using the Matrix/ThumMusic paradigm.

It is much more general to think of the tonnetz as being generated by octaves and (tempered) perfect fifths, just like everything else in the Matrix/ThumMusic paradigm.

Here's a portion of the Matrix's two-dimensional note-space expressed in the ThumMusic System's isomorphic note-layout:



Each note is of the form [alpha, beta] where alpha is the number of octaves (each of width P8) and beta is the number of perfect fifths (each of width P5) which, when added together, give the width of the indicated interval. For example:

• the origin note[0, 0] is zero octaves and zero perfect fifths away from itself, (0 * P8) + (0 * P5);
• note[1, 0] is one octave higher in pitch than the origin, (1 * P8) + (0 * P5);
• note[0, 1] is one P5 higher than in pitch the origin, (0 * P8) + (1 * P5);
• note[-2, 4] is two octaves lower, but four P5's higher, than the origin, (-2 * P8) + (4 * P5).

Assuming that the P8 is 1200 cents wide and the P5 is 700 cents wide, the notes of the note-matrix would have these widths:
Now, let's build a portion of the tonnetz on the note-matrix, following Cohn's paper:


The minor triad Q is surrounded by three major triads P, L, and R.

• P: Parallel;
• L: Leading-Tone Exchange;
• R: Relative.

The above construction of the Q, P, L, & R triads from octaves and tempered perfect fifths is much more general than the traditional construction, because these intervals are the generators of the syntonic temperament, so the tonnetz's properties are invariant across the syntonic tuning continuum, no matter what the specific width of the P5 (within the range 686-720). This continuum includes an infinite number of individual tunings, not just the small number of N-edo tunings (in which N mod 3 = 0) over which Cohn's paper generalizes the tonnetz' traditional construction.

Cohn's paper makes much of the toroidal topology of such equally-tempered tunings (as do many neo-Riemann theoreticians). This emphasis overlooks the syntonic temperament's general topology, which is cylindrical. The tonnetz' octave axis forms a closed loop around the cylinder; its axis of major thirds runs parallel to the cylinder's inifintely-long axis; and its axes of minor thirds and perfect fifths form spirals around the cylinder's inifintely-long axis. Many common chord progressions, such as the IV-vi-ii-V-I, require only the syntonic temperament's cylindrical topology (without which the ii below the vi would differ from the ii above the V by a syntonic comma).

At those points along the tuning continuum that correspond to an equal division of the octave, such as 12-edo, 17-edo, 19-edo, 31-edo, etc., the cylinder snaps into a torus. Each n-edo's toroidal tonnetz has (a) all of the properties of the cylindrical tonnetz, (b) all of the properties shared by all toroidal tonnetzs, and (b) the properties specific to that unique n-edo's tonnetz. These points of equal temperament are like beads on a string -- but what's really interesting is not the beads, but the string.

From Thumtronics' perspective, the potential of the neo-Riemannian PLR operations to provide an invariant basis for music theory across the whole syntonic tuning continuum is very exciting (I think). Or, to express the same thought from the neo-Riemannian perspective, the Matrix/ThumMusic paradigm may give neo-Riemannian theory the opportunity to expand its scope to embrace the entire syntonic tuning continuum, and perhaps also the tuning continua (and tonnetz') of other rank-2 temperaments (e.g., magic, hanson, schismatic, etc.). These other temperaments temper out different commas, so their tonnetz' will be different from the syntonic tonnetz, but the same general principles ought to apply (at some level of abstraction, anyway).

Cohn's paper (like Riemann himself) makes a number of statements regarding the relationship between the tonnetz and "acoustics" that are only true if one assumes that "acoustics" means "the Harmonic Series." Yet the Matrix/ThumMusic paradigm generalizes "acoustics" -- by dynamically aligning a timbre's partials with a tuning's notes, as specified by a temperament's defining intervals -- such that the relationship between the tonnetz and "acoustics" is 1:1. The Matrix/ThumMusic tonnetz is a direct embodiment of generalized musical reality.

I think I'd read something about the PLR approach to chord relationships, chord progressions, and the like before reading Cohn's paper, but it hadn't clicked. Now, it has definately clicked. I suspect that the PLR approach to chord relationships will prove to be a very powerful tool in the Matrix/ThumMusic System.

Cool bananas! :-)

[Update, Thur Sep 25th: A couple of prominent neo-Riemannians have (very) informally agreed (a) that the proposed application of neo-Riemannain theory to the syntonic tuning continuum appears to be both novel and interesting, and (b) that they would read the relevant Matrix/ThumMusic papers and get back to me.]

Amdahl's Law

Amdahl's Law describes the efficiency gains that come from paralellizing part of a sequential process. I suspect that it will be useful in estimating the increase in efficiency that can be gained in music education from the use of the ThumMusic System, but I'm not mathematically astute enough to figure out exactly how.

The ThumMusic System has the potential to speed up many aspects of music education -- i.e., to increase their efficiency -- but not all aspects. What is the balance? It is possible to optimize the wrong thing, increasing its efficiency enormously without significantly improving the efficiency of the whole process. I don't think that this is the case with the ThumMusic System, because it improves the efficiency of everything from theory to practice by reducing the symbol, concept, and gesture sets, exposing the relationships among the set-members geometrically, and exposing the consistency of those relationships to more senses (touch and sight in addition to hearing). But...how do I measure this? Perhaps Amdahl's Law can help.

Increasing the Efficiency of Music Education

I've recently posted to the Web a draft paper that describes the ThumMusic System and its potential to increase the labor efficiency of music education.

The paper will remain there until it is submitted for publication to an appropriate journal, at which point I may have to take it down. In the meantime, comments are welcome.

Music Education & Dead Cows

For thousands of years, cattle had died of an unknown cause that sometimes affected cattle herders, too. In the late 1870's, French farmers recruited Louis Pasteur to help them understand and prevent this cause. Why Pasteur? Because he had previously identified the cause of spoilage in wine, beer, and milk, thereby increasing the efficiancy of those industries, and had identified the cause of death of silkworms, increasing the efficiency of the silk industry.

As a result of what he learned in these previous cases, Pasteur was formulating his "germ theory" of disease. He wasn't sure that he could help the French cattle ranchers, but then he looked at the dung of the dead cows, he found it to be swarming with germs -- bacillus anthracis, identified just four years earlier as the cause of anthrax -- that were not present in the dung of healthy cattle. Following Edward Jenner's work on vaccination, he developed (and patented) a vaccine, and thereby saved future cows and cowherds from dying.

What is the moral of this story?

If you are looking for opportunities for innovation, look for dead cows.

For me, the "dead cows" were the high percentage of students who failed at music education. Everyone knew that music education was hard, but they ascribed the high failure rate to lack of talent, diligence, properly-trained teachers, or any number of other likely suspects. And of course all of these are indeed contributing factors -- but then, some of the suspected "causes" of anthrax infection, such as overcrowding, did indeed contribute to the contagion of anthrax, even though they were not its root cause.

When my wife Patti explained to me why she was quitting her piano lessons, she said it was because "music notation is stupid. Sometime C is on a space; sometimes it's on a line -- and it's on different places in treble clef than in bass clef! It's like reading German with your left eye and French with your right. What moron invented this stuff?"

In that observation was the germ of the idea that became the ThumMusic System, with which I hope to increase the efficiency of the music education industry.

ThumMusic & National Standards for Music Education

As stated in the first line of MENC’s summary of its National Standards for Music Education, “There are many routes to competence in the arts.” The ThumMusic System is a new route.

How does the ThumMusic System help students, teachers, and schools meet the National Standards?

1. Singing, alone and with others, a varied repertoire of music: Many vocal music education methods, including those of Zoltán Kodály and Émile Jaques-Dalcroze, make use of tonic solfa (“moveable Do”), which focuses on intervals rather than pitches as the essential focus of music education. The ThumMusic System provides a convenient musical staff for tonic solfa, making it ideal for use with these systems, and providing a convenient stepping-stone towards the traditional pitch-based staff. Furthermore, the ThumMusic Keyboard can be played in Just Intonation in any key, making it ideal for use in accompanying singers. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.
2. Performing on instruments, alone and with others, a varied repertoire of music: The ThumMusic Keyboard is polyphonic, so enables the playing of a wider repertoire of music than that available to monophonic instruments. The ThumMusic Keyboard’s logical arrangement of notes reduces to a minimum the number of individual gestures that a student must learn, and reinforces the structure, meaning, and consistency of those gestures through the senses of sight and touch in addition to hearing, in a manner not done by instruments without isomorphic control interfaces. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.
3. Improvising melodies, variations, and accompaniments: The ThumMusic Keyboard places the notes of the diatonic scale of a given key in a dense vertical column of note-controlling buttons, and the notes of the pentatonic scale in a proper subset thereof. Within this vertical column, as elsewhere on the ThumMusic Keyboard, the “shape” of each musical interface is always consistent, facilitating improvisation. The geometrical relationship between the ThumMusic keyboard and the tonnetz, being concrete and tangible, makes movement through modes, chord progressions, and key modulations easier to visualize and grasp (literally) on the ThumMusic keyboard than on non-isomorphic control interfaces. These benefits reduce the amount of time and effort necessary to master the concepts and skills of improvisation. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.
4. Composing and arranging music within specified guidelines: The ThumMusic keyboard makes the relationships among intervals, chords, keys, and modes visual and tactile in addition to aural. ThumMusic notation (ThumLine) abstracts staff notation to the level of intervals, so that every octave and key is notated in the same manner, facilitating composition and arrangement. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.
5. Reading and notating music: By abstracting staff notation to the level of intervals, ThumMusic notation (ThumLine) notates every octave and key in the same manner, making music notation easier to teach, learn, read, and write. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.
6. Listening to, analyzing, and describing music: The ThumMusic System makes ear training something that happens naturally in the regular use of the system, so that it need not be taught in a separate course. The ThumMusic Keyboard is a tangible, concrete manifestation of the tonnnetz (harmonic lattice) used in neo-Riemann analysis, making its concepts something that students can see and feel as they play. In ThumMusic notation (ThumLine), the use of tonic solfa, along with indication of the current scale and current tonic (mode), notates the song at the same level of abstraction at which structural analysis occurs. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.
7. Evaluating music and music performances: If students can learn to understand music’s basic concepts and skills more rapidly, then they can devote much of the time gained to learning the expressive, emotional, and analytical aspects of music, such as those required to meet this standard. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.
8. Understanding relationships between music, the other arts, and disciplines outside the arts: The ThumMusic System does not directly contribute to understanding the relationships between music and other arts. However, is makes tangible and concrete the relationship between music and mathematics, and, by extension, between music and physics. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.
9. Understanding music in relation to history and culture: One aspect of the history of music that is not often taught is the history of tuning, because tuning theory is considered to be arcane and complex. The ThumMusic keyboard exposes the geometry of music in a tuning-invariant manner, so that the tunings of many other times – and other cultures – all have the “same shape” (and hence the same fingering) on the ThumMusic keyboard. No nion-isomorphic instrument has this capability. This makes the ThumMusic System uniquely well-suited to studying the music of many different eras and cultures. Using the ThumMusic System could help students, teachers, and schools meet this standard in less time and at lower cost.

Using the ThumMusic System could help students, teachers, and schools meet all of these National Standards in less time and at lower cost.

Music Education’s ROI

People are smart. By and large, they do what is in their economic best interest, choosing to invest their limited time & money in those activities which deliver the highest Return on Investment (ROI).

Over the last quarter of a century, the cost of acquiring the benefits of many activities has fallen dramatically, largely due to the falling cost, and increasing power, of computing. The cost of finding and acquiring music, videos, and information has fallen to nearly zero. Video games are cheaper (after inflation) and more engaging than ever before, and have become more social. TV has zillions of channels. Chatting with friends – always a popular pastime – is cheaper, easier, and more convenient than ever, even if those friends are far away.

These competing activities almost certainly have lower ultimate benefits than music education, but they deliver those lower benefits with a much lower investment, therefore delivering a higher ROI. For example, imagine an activity that delvers only 10% of the benefits of music education, but does so at just 1% of the cost. Its ROI is ten times the ROI of music education. If a student were to invest her limited time & money in ten such activities, she would gain benefits equal to those of music education, at just 10% of the cost.

Because of music education’s declining relative ROI, people are making the rational decision to invest their (and their children’s) time in activities other than music education. They aren’t doing this because they are stupid, ignorant Philistines; rather, they are doing it because they are smart.

Many music education advocates have responded to this challenge by providing evidence that music education delivers many non-musical benefits, too. By increasing the perceived returns from music education, this activity increases music education’s perceived ROI.

However, this approach does not address the elephant in the kitchen, which is music education’s cost. That’s the biggie. If the cost of music education – in time & money – could be dramatically reduced without also reducing its benefits, then no “advocacy” of music education would be required. Consumers and schools would choose to invest their scarce time and money in music education, because doing so would give them an ROI that was highly competitive with alternative activities.

That’s where the ThumMusic System comes in. By enabling students to understand and play music in a shorter time, on less-expensive instruments, it can reduce the cost of music education dramatically, thereby increasing its ROI.

Learning Styles

According to Wikipedia, “a learning style is the method of learning particular to an individual that is presumed to allow that individual to learn best. It has been proposed that teachers should assess the learning styles of their students and adapt their classroom methods to best fit each student's learning style.”

However, that only works if everyone in the class has the same style. Better, perhaps, to find a teaching method that addresses the special needs of all learning styles simultaneously.

The basic learning styles are said to be sense-based:
Auditory learning occurs through hearing;
Kinesthetic learning occurs through touching and doing;
Visual learning occurs through seeing, demonstrations and body language.

The ThumMusic System is unique in that it presents musical information to all three of these senses in a simple, consistent, logical manner, with each sense reinforcing awareness of the consistency of the information presented to the others.

For example, the shape of any given interval – say, the perfect fifth – is the same everywhere on the ThumMusic Keyboard. Auditory learners can hear this interval’s consistency; kinesthetic learners can touch it; visual learners can see it. Each sense reinforces the other, emphasizing the consistency and importance of intervals to the structure of music.

No person learns exclusively through one learning style. Visual learners may learn more efficiently by sight, but they learn by touch and hearing, too, although not perhaps as efficiently.

Because the ThumMusic System presents musical information to all three of these senses simultaneously, in a simple and consistent manner, it increases the learning efficiency of

1. Individuals, whose primary learning style’s needs are met – and their secondary styles, too; and
2. Classes, by meeting the needs of all the different styles equally and simultaneously.

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!

ThumMusic & IT’s MIS Bridge

Later today, I have my first meeting with a team of students from UT/Austin’s McCombs School of Business’ MIS Bridge. They will be working to define the technical infrastructure of the ThumMusic System’s online courseware. My objective for this first meeting is to scope out what they can reasonably be expected to do within the time they have available, given their existing knowledge and skills.

The general idea is for them to identify and specify the reusable software objects that must be developed in order for Web-based ThumMusic courseware to be developed and deployed using open source methods, such that the resulting courseware is highly interactive.

For example, the courseware should be able to use the computer keyboard as a musical keyboard; display any arbitrary piece of MusicXML in ThumLine staff notation, preferably in an interactive manner (for example, illuminating notes as when they should be played and/or when they are played); show animations of chord progressions, key modulations, etc. on the tonnetz in a manner similar to Mathieu’s excellent use of the tonnetz in his book Harmonic Experience, but interactively, and again driven by any arbitrary MusicXML file; and so on. The goal is not to have the students implement these software objects, necessarily, but rather for them to identify and specify them all so that they can be implemented by others. If the students can also implement some or all of the software objects, then all the better, if only to help them hone their specification skills.

I have suggested that the project be based on Moodle – a free, open source course management system (CMS) that appears to have attained critical mass. Using a free CMS will facilitate having the lessons themselves be free, and also facilitate having others contribute lessons for free.

Free, free, free. I love free. It’s my favorite price – and yours too, I bet. The freer the ThumMusic System is, the more rapidly and widely awareness of its benefits will spread, and ultimately the more Thummers I’ll sell. Thus does the Invisible Hand of economics direct our private actions to the public good.

Shift Happens

Paradigm shifts – the transition from one idea or technology to a new one – are not rare. They happen all the time. Here are some examples from my personal experience.

1. Slide Rules to Pocket Calculators
In 1974, I was in the last freshman mathematics class at my high school to be taught how to use a slide rule. This brilliant device had been the standard tool for mathematical computation for 350 years (since its invention in 1630 or thereabouts). However, by 1974 – just two years after the introduction of the first pocket calculator with slide-rule-like mathematical functions (the HP-35) – pocket calculators could perform more functions, with higher accuracy, less training, and fewer errors (such as mis-placing the decimal point). While the cost of a pocket calculator was still about the same as a good slide rule in 1974, the price of calculators had already fallen by half in two years, and was clearly going to continue falling. Pocket calculators made calculating simpler, cheaper, and more powerful. Shift happened.

2. Punched Cards to Video Terminals
In 1978, I was in the last freshman computer programming class at my university to be taught how to create and use punched cards. The punched card was the de facto standard of the computing industry for almost a century (since 1889) and the basis of IBM’s computing empire. However, by 1978 – just two years after the introduction video display terminals such as DEC’s VT52 and IBM's 3270 – video terminals were clearly out-competing punched cards. Video terminals made computing simpler, cheaper, and more powerful. Shift happened.

3. Geosynclines to Plate Tectonics
Also in 1978, I was in the last freshman geology class at my university to be taught about geosynclines as the fundamental paradigm of geology. By then, plate tectonics had become widely accepted as being a superior theory, but the school’s Intro to Geology textbook wasn’t updated to reflect this change until the following year. Plate tectonics provided a simpler model, in which fewer rules explained a larger number of phenomena more accurately, reducing the frequency of failed geological predictions (such as dry holes). Plate tectonics made geology simpler, cheaper, and more powerful. Shift happened.

4. Command Line & Text Mode to Graphical User Interfaces
When I started taking classes for a Computer Science degree in 1983, the dominant input paradigm was the command line, and the standard output paradigm was text mode. By the time I got my CS degree in 1988, the command line and text mode were being superseded by graphical user interfaces (such as the Mac & Windows user interfaces), which made computing more accessible to non-professionals, reduced training costs, and enabled powerful new applications like desktop publishing, digital photo editing, and Mathematica. Graphical user interfaces made computing simpler, cheaper, and more powerful. Shift happened.

Discussion
When a new paradigm delivers a desired outcome through means that are simpler, cheaper, and more powerful, then shift happens, even if the previous paradigm has been in place for centuries.

Conclusion
Once the Thummer and ThumMusic System are commercially available, they will make learning to play and understand music simpler, cheaper, and more powerful, establishing an important new paradigm for music-making.

Why? Because…Shift Happens.

ThumMusic System

I've placed a PowerPoint presentation on the website describing the ThumMusic System. It's a large file (25MB) because it includes an audio track of me narrating each slide. A version without narration is much smaller, and can be found here; its "note pages" contain the same info as my vocal narration. If you print out the notes pages and read from them as you click through the slies, you'll get the same information, albeit less conveniently.

The ThumMusic System is so visually-oriented that it is much more easily understood by viewing a presentation than by reading a text description (although a text description can be found as HTML here and as PDF here).

If you don't have PowerPoint installed, you can watch the presentation using a PowerPoint Viewer, available for Windows & Mac.

How?

How will Thumtronics make its innovations successful?

In the long run, Thumtronics’ innovations in the display and control of musical information – the ThumMusic System – are likely to have the biggest impact on the world, by making it possible for essentially everyone to understand, play, and create music. However, the ThumMusic System is going to be a tough sell, because its benefits are hard to communicate in a 30-second “elevator pitch.”

On the other hand, the benefits of the Thummer are obvious from a 30-second demo video (such as this one, and this one). Musicians playing the Thummer in a band, in live performances, or in YouTube videos will be “advertising” the Thummer for us, making the Thummer extremely viral, which is likely to lead to very rapid exponential growth sales growth.

How rapid? ThumClub members tell us that, if the Thummer lives up to their expectations, they expect to be able to convince an average of five other people to buy one. If they can do that in six months, with those five each “selling” five more, and so on, then Thummer sales will simply explode. Even if each Thummer buyer convinced only 1.4 additional people to buy Thummers, then from first year sales of just 1,500 units, Thummer revenues would exceed $10 million within three years and $100 million within six years (all else being equal). It’s the self-advertising, viral nature of the Thummer that makes it such a compelling commercial opportunity.

The success of the Thummer can pull the ThumMusic System along in its wake, just as the increasing popularity of the guitar made guitar tab popular. Once the ThumMusic System gains a foothold in the market, its growth rate can exceed that of the Thummer, because the ThumMusic System is also applicable to the standard computer keyboard and to the human voice.

At that point, the commercial opportunity of the ThumMusic System should be considerable – online lessons, sheet music downloads, certification exams, etc..

But first we have to make the Thummer successful.

We’ll do this by raising the capital needed to finish the design, engineering, and testing of the Thummer; selling the Thummer directly to consumers over the Internet from Thumtronics’ website; encouraging the independent development of associated websites (like Amazon Associates) through revenue-sharing; leveraging the free PR that we’ve already been offered by FOCUS, I Want That!, and other relevant media; and accelerating the viral marketing process through a variety of means, such as “discount for a friend” coupons, online video contests, and aggressive promotion of those musicians and bands who best show off the Thummer’s unique abilities. The incredible new possibilites presented by Dynamic Tuning – which only works on a Thummer – will tend to accelerate this process, once creative artists show the world how powerful Dynamic Tuning can be.

That’s the plan, anyway – loose and flexible, allowing us to respond to the market as we go along.

When?

I started working on Thumtronics’ innovations in September of 2003. Since then, as my long-suffering family can attest, I have been obsessed by the challenge of developing and commercializing Thumtronics’ innovations.

Shipping an affordable, expressive Thummer is Thumtronics’ one and only mission at present. Only after it reaches a high enough level of sales to make Thumtronics profitable can we consider devoting additional resources to commercializing Thumtronics’ other innovations, such as the ThumMusic System, Dynamic Tuning, or Dynamically Tempered Timbres.

Currently, Thumtronics is raising capital to fund the final design & engineering work needed to get the Thummer to market. It is expected that the Thummer will reach the market within approximately nine months of this capital becoming available.

At the moment, I’m collecting quotes from credible folks in Austin and beyond about the market potential of the Thummer. Although everyone knows that disruptive innovations can make huge profits, investors usually approach a given potentially-disruptive innovation with great skepticism. Because disruptive innovations redefine the market, exploit new channels, and attract new customers, it’s very hard to prove that the disruptive product will actually sell – until it starts selling. The quotes that I’m gathering are intended to reduce this perceived market risk, by establishing that experts in the relevant fields believe that the Thummer will sell.

I expect to start approaching potential investors in a couple of weeks. It’s hard to predict how long the capital-raising process will take. One smart guy with money, and I’m done – but more likely, I’ll need to find a half-dozen, and they’ll all debate the valuation & term sheet, so it’ll take months.

So don’t expect to see any Thummer for sale until mid-2008, at the earliest.