ThumMusings

Open Source Thummer

2010-02-27T10:31:00.000-08:00

Want to make a Thummer? The design docs are available here.

Ideally, Georgia Tech, MIT's Media Lab, or some such will assume responsibility for leading the open-source design initiative, aimed at producing an annually-evolving, freely-licenseable reference design for Thummers.

By focusing on the cooperative design of a single new musical instrument, the academic "music technology" community could, collaboratively, advance the state of the art much farther and faster than it is currently.

IMHO.

Happy hacking! :-)

Thummer's Eaton Prototypes

2010-02-26T12:02:00.000-08:00

The red (Eaton) Thummer prototypes communicate with an application called ThummerSetup via USB. For the Eaton Thummers to communicate with a computer, one must first intstall on that computer:

The ThummerSetup application, and
The Thummer's USB drivers.

These have been compressed for downloading:

Also, read the setup instructions.

iGetIt! Music blog

2009-04-04T11:29:00.000-07:00

This blog will receive no new entries after this one.

I've started a new blog devoted to iGetIt! Music. See you there! :-)

It's over

2009-04-02T08:50:00.000-07:00

Thumtronics is dead. :-(

For years now, I've been trying to raise money to finish the Thummer's design and to manufacture its first production run. In that time, I received many promises, but no checks. Now, the global financial crisis has dried up all funding for early-stage companies. Thumtronics is now in bankruptcy. It's over.

To Thumtronics' investors, I offer my sincerest apologies. I did my best. I put everything I had into it -- every penny, every hour, every effort. I'm sorry. I hope that you will forgive me, and more importantly, that you won't hold my failure against the next guy who comes to you with a great idea.

I've tried diligently for years to license Thumtronics' patents to other companies, with no success. Most of Thumtronics' (pending) patents will fall into the public domain due to non-payment of fees.

Once Thumtronics' bankruptcy is final, I'll place the design documents for the Thummer prototypes on the web, as the basis of an open-source hardware project. Completing the Thummer's design would be a great team project for an electronics/mechanical engineering class. Once an open-source reference design was completed, anyone who wanted to make Thummers could do so.

For example, a firm like Hong Kong's Medeli to work with HK UST's students to finish the Thummer's design, then to collect partially pre-paid orders online until receiving enough orders to justify making the initial production run. If nothing else, this would be a great way to identify (and hire) the university's best students.

Hopefully, through an open-source approach, Thummers will someday become available. I hope so, because I want one! :-)

In the meantime, I've started a new company, iGetIt! Music. It has no website yet (although I've registered the domain). iGetIt! is just me and an Internet-connected computer in my bedroom -- a classic micro-ISV. iGetIt! is focused on developing online music education courseware using the computer keyboard (and possibly iPhone) as its input device. iGetIt! doesn't have the potential to rake in the big bucks that Thumtronics had, but if I'm lucky I ought to be able to make a living out of it. In these troubled economic times that's a whole lot better than nothing.

My biggest challenge now is getting back into the swing of computer programming. It's been 22 years since I got my Computer Science degree, and 17 years since I last programmed for a living. I was on the cutting edge of object-oriented programming back then, and mostly I'm finding that today's tools make it very easy to do things that required lots of hand-coding back then. I'll start a new blog shortly to document my progress and share what I've learned.

So...Thumtronics is dead. Long live iGetIt! Music! :-)

Tonnetz

2008-09-18T01:04:00.000-07:00

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.]

Matrix

2008-08-27T07:38:00.000-07:00

One of the coolest things about working on the Thummer has been using it to discover new things about music. Its isomorphic button-field (keyboard) is like an X-Ray lens that lets people see the deep structure of music.

Bill Sethares and Andy Milne did the heavy mathematical work to prove that what we were seeing was really there. Their proofs can be found here and here (with more papers in the pipeline). These papers, while appropriate for their purpose and venue, are mathematically impenetrable to people with tiny little heads like mine.

Therefore, I've recently posted a draft paper that presents our new musical paradigm, the Matrix, in language that is nearly math-free. You need to know what prime numbers are, and that any natural number can be factored into an unique combination of prime numbers, and that a two-dimensional array of numbers is a matrix (hence the name of the proposed paradigm), but that's about it.

Although I do not claim to be an expert in the history of science, I do know a thing or two about it, and the Matrix model of music theory has all of the hallmarks of a paradigm-shifter. For example, it solves old problems, explains previously-anomalous experimental results, makes predictions that are falsifiable, and has enabled the discovery of new properties (e.g., tuning invariance, which is the basis of Dynamic Tonality).

The Matrix paradigm accomplishes all this as a result of questioning a single key assumption of Western music theory: that musical sounds are those that follow the Harmonic Series. This assumption is embedded so deeply into Western music theory that most musicians and many theorists don't even realize that they are making it. It has been received wisdom since Pythagoras first plucked a string 2,500 years ago.

The Matrix paradigm, in brief, uses a temperament to temper both tuning and timbre in real time. It's the tempering of timbres that's new (building on Bill's previous work). This is, in effect, a generalization of the relationship between Just Intonation and the Harmonic Series that forms the core of Western music theory.

It is hard to imagine a more fundamental alteration of the theoretical basis of music than this. Hence, paradigm shift.

Amdahl's Law

2008-08-07T12:57:00.001-07:00

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

2008-08-07T12:53:00.000-07:00

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.

Transposing Tradition

2008-07-27T21:25:00.000-07:00

In a letter to the Austin Chronicle dated July 17, 2008 and titled The Question: How Good are the Musicians?, author Tom Bowman asks

Who wants to go down to Red River and get their ears assaulted by band after band of “musicians” who know about 10 chords, write insipid lyrics, and can’t even transpose their own songs from one key to another? If the level of talent were higher, the established clubs wouldn’t have to bring in so many touring acts.

How fascinating that Mr. Bowman equates the ability to “transpose songs from one key to another” with the bands’ “level of talent”! This is by no means an isolated example, however; the ability to transpose is often equated with musical skill and/or talent. A Google search for the keywords +transpose +sight +key +talent turns up almost 3,000 hits.

Yet the difficulty of transposition has no relevance whatsoever to musical knowledge, skill, or talent. It is merely an artifact of the pitch-focused design of traditional musical instruments and notation. At most, it is an artificial barrier placed in the path of aspiring musicians.

Using the ThumMusic System, transposition is a complete non-issue.

I am reminded of upper-class English schoolchildren, who were compelled to learn Latin as recently as the 1980’s. Why? Because Latin was the universal language of scholarly discourse…200 years previously. To be recognized as being One of Us, one had to speak the upper class' secret language, for purely exclusionary reasons. Anyone who could not afford to waste time and money learning an utterly useless secret language was excluded from the upper-class club.

I don’t think that Americas' taxpayers can afford to waste their time and money attempting – with a low success rate – to teach its children the secret language of music’s upper classes. By using the ThumMusic System, students can concentrate on learning about music.

Which is the point, really, isn’t it?

Keiretsubator

2008-07-21T10:05:00.000-07:00

An interesting new business model is emerging here in Austin: the keiretsubator, a combination of an incubator and a keiretsu.

Keiretsu is the Japanese word for a set of companies with interlocking business relationships and shareholdings, usually headed by a bank which finances the group’s companies. Examples include Mitsubishi, Mitsui (Toyota), and Fuyo (Canon, Hitachi, Nissan, Yamaha).

An incubator is an organization – usually not-for-profit – which provides start-up companies with shared infrastructure, basic business services and equipment, technology support services, and assistance in obtaining outside financing from angel groups and VCs. Examples include the Austin Technology Incubator, Georgia’s Advanced Technology Development Center, and Washington State’s William M. Factory Small Business Incubator.

In the keiretsubator model, investors invest directly in the keiretsubator, which then invests in a small number of firms which share the same technology & industry focus (e.g., electronic music technology). In addition to the usual incubator services, the keiretsubator hires senior start-up veterans to fill the senior management roles – CFO, CTO, COO, VP Marketing, etc. – of its member companies on a shared basis. For example, one top-flight Chief Financial Officer will be hired by the keiretsubator, whose services are then shared by the member firms, none of whom attract or afford such a top-flight CFO on their own.

It's a pretty good deal from the CxOs' perspective, because they get to work on a number of interesting projects while being compensated with cash and equity in the keiretsubator – and thus indirectly with equity in the keiretsubator's member companies.

The keiretsubator model thus combines the hands-on management and financial services of a keiretsu with the early-stage focus of an incubator.

The keiretsubator model appears to be ideal for tiny start-up companies with great ideas, no money, and no management other than their founder. Such tiny firms can rarely attract the top-flight management needed to steer the company to success. By banding together, they can pool their opportunities.

Generally speaking, only one in six start-ups ever goes public, and only one in three is acquired by another firm, so incubation – in any model – needs to spread its risk among a number of different member firms to minimize its overall risk. On the other hand, venture capital firms that focus on early-stage companies have earned more than 20% per year over the last twenty years – so if well-managed, a keiretsubator could be a very good investment.

Will the keiretsubator model work? If it attracts great people, great ideas, and sufficient capital, then the odds are in its favor.

ClarisWorks, OLE vs. OpenDoc, and Microsoft

2008-07-18T12:34:00.000-07:00

An online history of ClarisWorks contains the following passage:

Before ClarisWorks 5.0 was finished, the rift between Claris and the remaining development team grew too wide. Scott Holdaway, Tom Hoke, Scott Lindsey, Bruce Hammond, and Carl Grice left Claris, and formed what would later become Gobe Software. These were the core engineers, the ones who had been on the project the longest. Several newer engineers remained. Three in particular were responsible for OpenDoc integration. At Apple WWDC '96, they demoed a version of ClarisWorks with OpenDoc support. Apple was particularly eager to demonstrate to developers that a flagship product was supporting the new component technology - ergo, everyone else should too. Not surprisingly (to me, anyway), the following week the three engineers were recruited by Microsoft. Result: no OpenDoc support in ClarisWorks 5.0. That maneuver is just one typical example of the way Microsoft stifles competition [emphasis added]. Ironically, in this case it hit a product conceived in defiance of the Microsoft way.

This is a complete mis-characterization of Microsoft’s role.

With Windows sales booming in 1992-1993, Claris’ customers – who had previously used only Apple’s Macintosh computers – had acquired Windows-based computers too. They needed versions of Claris’ applications that ran on both Mac and Windows. These customers made it clear that if they didn’t get cross-platform versions of Claris’ applications soon, they would have to switch to some other company’s products. This put Claris’ management under the gun to get Windows versions of Claris’ applications onto the market ASAP. Producing Windows software was major change for Claris, because it was a wholly-owned subsidiary of Apple Computer, which made the Macintosh, which competed against Microsoft’s Windows.

As Microsoft’s Technology Evangelist to Claris, I facilitated Claris’ exploration of Windows’ technologies. I worked mostly with Larry Slotnick, Claris’ VP of Product Development, and Don Bradford, Claris’ Senior Director of Integrated Product Development.

As I understand it, Don hired outside contractors to implement two different test versions of ClarisWorks, one using OpenDoc (backed by Apple, Novell, and IBM)and one using OLE (backed by Microsoft). Based on the results of this experiment, Don concluded that OpenDoc objects were too slow and heavy to meet ClarisWorks’ need for a fast, lightweight, cross-platform object model. Don and Larry decided that ClarisWorks 4.0 would use OLE instead of OpenDoc (as would FileMaker, BTW).

When informed of this technical decision, Apple’s management was furious, insisting that ClarisWorks WOULD support OpenDoc, emphasizing that “we OWN you, and you WILL do as you’re told,” with the clear implication that any Claris employee who persisted in championing OLE would be fired, irrespective of the prevailing technological realities.

In response to Apple’s threat, the entire ClarisWorks team had an all-day off-site meeting (at Vancouver’s Red Lion Inn at the Quay) to discuss its options. At the end of the meeting, Don called me at my office in Redmond, with his entire team participating by speakerphone.

As I recall, the conversation went something like this:

DON: James, I’ve got the whole ClarisWorks team together here, and we’ve been talking all day about Apple’s decision to ram OpenDoc down our throats.

TEAM: [boos, hisses, etc.]

DON: We’ve decided – and we’re all amazed at this decision…

TEAM: [laughter]

DON: …we’ve decided that we all want to join Microsoft as a team.

JAMES: [pause] Excuse me?

TEAM: [laughter]

DON: Microsoft is the only company that’s big enough to keep our whole team together so we want to join Microsoft, don’t we, guys?

TEAM: [cheers, laughter]

JAMES: Cool! I’ll see what I can do.

I called a senior staffer in Microsoft’s HR group (I don’t remember who) and suggested that she send a recruiter right away to hire the entire ClarisWorks team. She nearly had a coronary! She explained that because Microsoft had a competing product (Microsoft Works), hiring the ClarisWorks team would be seen as “predatory hiring” – a violation of anti-trust rules – despite the team’s “invitation to hire” (which I would have thought to be a water-tight defense). However, if INDIVIDUAL Claris employees wanted to explore career opportunities at Microsoft, then…fine. So Microsoft ended up cherry-picking the best people out of the ClarisWorks team.

Microsoft’s first hire was Don, who formed Microsoft’s new Macintosh Internet Team in Silicon Valley, into which he hired many other Claris folks. His team went on to produce Internet Explorer 2.1 for the Mac, which won every comparative review and was subsequently licensed by Apple as its default browser.

Within months, Apple realized that Don and Larry had been right – that is, that OLE really was the only viable technology for ClarisWorks 4.0 – and aligned its development efforts accordingly. After much delay, it released ClarisWorks 4.0 in late 1994 with extensive OLE support.

About the same time, Novell released PerfectOffice 3.0, also with extensive OLE support. The release of these OLE-supporting products from two of OpenDoc’s leading backers told the whole world that OpenDoc was dead, and it happened in late 1994. By the time Microsoft hired Claris’ last three OpenDoc-savvy engineers – in 1996, according to the above – OpenDoc was already deader than Babbage’s Difference Engine.

In summary, the ClarisWorks story is not, in any way, “an example of the way Microsoft stifles competition.” It is, instead, a story of Apple’s early-1990’s management being critically out of touch with technological reality. Claris’ technologists tried to speak truth to power, but those in power at Apple refused to listen until it was too late. All Microsoft did was provide a better technology option, and pick up the pieces when Apple shattered its own ClarisWorks team.

The Epiphany of Helen Keller

2008-07-18T09:57:00.000-07:00

Most people are at least somewhat familiar with the story of Helen Keller, whose illness at 19 months of age left her deaf, blind, and without any sense of language. The story of her breakthrough in re-discovering the concept of language five years later is a parable of ignorance, imitation, frustration, and epiphany.

Here’s the parable in Ms. Keller’s own words, from her autobiography of 1903 (to which I have added paragraph headings).

[Ignorance]
Have you ever been at sea in a dense fog, when it seemed as if a tangible white darkness shut you in, and the great ship, tense and anxious, groped her way toward the shore with plummet and sounding-line, and you waited with beating heart for something to happen? I was like that ship before my education began, only I was without compass or sounding-line, and had no way of knowing how near the harbour was. "Light! give me light!" was the wordless cry of my soul, and the light of love shone on me in that very hour.

[Imitation]
The morning after my teacher came she led me into her room and gave me a doll. When I had played with it a little while, Miss Sullivan slowly spelled into my hand the word "d-o-l-l." I was at once interested in this finger play and tried to imitate it. When I finally succeeded in making the letters correctly I was flushed with childish pleasure and pride. Running downstairs to my mother I held up my hand and made the letters for doll. I did not know that I was spelling a word or even that words existed; I was simply making my fingers go in monkey-like imitation. In the days that followed I learned to spell in this uncomprehending way a great many words, among them pin, hat, cup and a few verbs like sit, stand and walk. But my teacher had been with me several weeks before I understood that everything has a name.

[Frustration]
One day, while I was playing with my new doll, Miss Sullivan put my big rag doll into my lap also, spelled "d-o-l-l" and tried to make me understand that "d-o-l-l" applied to both. Earlier in the day we had had a tussle over the words "m-u-g" and "w-a-t-e-r." Miss Sullivan had tried to impress it upon me that "m-u-g" is mug and that "w-a-t-e-r" is water, but I persisted in confounding the two. In despair she had dropped the subject for the time, only to renew it at the first opportunity. I became impatient at her repeated attempts and, seizing the new doll, I dashed it upon the floor. I was keenly delighted when I felt the fragments of the broken doll at my feet. Neither sorrow nor regret followed my passionate outburst. I had not loved the doll. In the still, dark world in which I lived there was no strong sentiment or tenderness. I felt my teacher sweep the fragments to one side of the hearth, and I had a sense of satisfaction that the cause of my discomfort was removed. She brought me my hat, and I knew I was going out into the warm sunshine. This thought, if a wordless sensation may be called a thought, made me hop and skip with pleasure.

[Epiphany]
We walked down the path to the well-house, attracted by the fragrance of the honeysuckle with which it was covered. Some one was drawing water and my teacher placed my hand under the spout. As the cool stream gushed over one hand she spelled into the other the word water, first slowly, then rapidly. I stood still, my whole attention fixed upon the motions of her fingers. Suddenly I felt a misty consciousness as of something forgotten--a thrill of returning thought; and somehow the mystery of language was revealed to me. I knew then that "w-a-t-e-r" meant the wonderful cool something that was flowing over my hand. That living word awakened my soul, gave it light, hope, joy, set it free! There were barriers still, it is true, but barriers that could in time be swept away.

Helen Keller, The Story of My Life, 1903

Back when I was a high-school musician, I felt my musical ignorance in exactly the manner that Ms. Keller described. Eventually, I learned to imitate other musician’s improvisations – scat-singing a solo, or improvising a bass line, or whatever – but I had no idea how the notes all fit together, so I couldn’t create anything new or uniquely personal. It was very frustrating, as a scientifically-minded person (even then), to be told that music was "too mysterious and complex for a mere high-schooler to understand." At least, that was the excuse I was given when I sought to learn more, and the college-level music theory textbook in the high school's library did nothing to convince me otherwise.

More than 20 years later, when I had the time to dig into music again, I was able to peer though a magic X-ray lens -- the isomorphic keyboard -- to see the bones and sinews of music, stripped of the superfical complexities of traditional music theory. It was inexpressibly delightful to have my own series of epiphanies, which gave me the insights needed to contribute to the creation of the Thummer, the ThumMusic System, and Dynamic Tonality.

It is my greatest hope that the musically-curious will find the ThumMusic System to be an “epiphany guide,” leading them to their own string of music-making epiphanies, so that they won’t languish in ignorance, settle for imitation, or give up in frustration, as so many budding musicians do.

Compression, Concreteness, and Concurrency

2008-06-27T10:30:00.000-07:00

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

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.
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.
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

2008-06-25T13:33:00.000-07:00

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.

Fixed Performance: Contrast the prices at which different systems attain a given level of performance.
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:

Fixed Performance: The total cost of developing a given average level of musicianship in a given population of students.
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

2008-06-25T10:09:00.000-07:00

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

2008-06-24T20:44:00.000-07:00

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

2008-06-24T19:32:00.000-07:00

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? ;-)

Disrupting Music Notation & Controllers

2008-05-11T11:08:00.000-07:00

I often hear that "musicians won't switch" from their traditional instruments & notation to the Thummer and (optionally) ThumMusic System. Who cares? The success of Guitar Hero shows that a new instrument and notation can have phenomenal success without "converting" anyone.

Since the release of Guitar Hero in November of 2005, the number of instrumental music-makers in the USA has doubled.*

Doubled. In two years. Doubled.

Wikipedia describes Guitar Hero's controller, notation, and pedagogy as follows:

An extended guitar neck is shown vertically on the screen (the frets horizontal), and as the song progresses, colored markers indicating notes travel down the screen in time with the music; the note colors and positions match those of the five fret keys on the guitar controller. Once the note(s) reach the bottom, the player must play the indicated note(s) by holding down the correct fret button(s) and hitting the strumming bar in order to score points. Success or failure will cause the on-screen Rock Meter to change, showing how well the player is playing (denoted by red, yellow, and green sections). Should the Rock Meter drop below the red section, the song will automatically end, with the player booed off the stage by the audience. Successful note hits will add to the player's score, and by hitting a long series of consecutive successful note hits, the player can increase their score multiplier.

Guitar Hero (GH) doubled the music-making population by simplifying the tools of music education (instruments, notation, and pedagogy). It attained this simplification by applying the time-honored process of dumbing down.

GH's dumbed-down system enables players to climb the first steps of music's learning curve very rapidly. However, this same dumbing-down places a very low ceiling on what players can learn from GH. They can learn about rhythm, and about the separation of hand-functions on a guitar (one hand strumming, the other controlling the fret-board), but that's about it.

The problem with Guitar Hero is not that it's incompatible, but that its dumbed-down tools place such a low ceiling on the acquisition of musical skill and knowledge. Those GH customers who want to rise above this ceiling have to leave the GH product line.

But what if GH's tools did NOT impose this low ceiling? What if a serious student of music could use GH's (incompatible) controller, notation, and pedagogy to rise to unlimited heights of skill and knowledge, while still having as much fun as with the current version of GH?

If GH had no ceiling, then its 16 million American players would be marching right up its learning curve into serious musicianship right now, with tens of millions of additional music-makers joining that march every year. Soon, the number of music-makers who used GH-based tools would exceed those using traditional tools at every level of musical skill and knowledge. The percentage of musicians who used traditional instruments & notation would shrink every year, not because they were "converting" from traditional to GH-based tools, but simply because huge numbers of new musicians were using the GH-based tools. Sheer weight of numbers would define the GH-based tools as being the new de facto standards for music-making and music education.

All else being equal, simplicity trumps compatibility, and high ceilings trump low ceilings.

* The numbers: the US Census Bureau's 2008 Statistical Abstract cites the percentage of the US population that "plays a musical instrument" as a leisure activity at 5.3% (counting only those people who play at least as often as "once per month"). Given a US population of 300 million, that's 16.3 million people. In January of 2008, Activision announced that the Guitar Hero series (GH) had sold more than 14 million copies in North America. If one simply divides GH's total units sales (14 million) by the number of months GH had been on the market as of this press release (26 months), that's over half a million units per month, or two million more units since the press releases was issued, bring GH's unit total to 16 million. Now, the two sets of numbers aren't strictly comparable, in that the US Census Bureau's data is based solely on the US population of 300 million, whereas GH's sales numbers are for North America (and therefore include sales to Canada's population of 33 million and possibly to Mexico's population of 100 million). However, given the essentially flat sales of traditional instruments in North America and the exploding slaes of Guitar Hero, it's only a matter of months until the precise data catches up to the approximation used in this blog article.

Thummer as Purple Cow

2008-04-19T12:15:00.000-07:00

I recently had the founder of a music technology company tell me that he wanted to hire me to evangelize his company's music technology products, because I “must be an incredible evangelist to have gotten such amazing national press for the Thummer” (e.g., the Wall Street Journal story and a forthcoming story by CBS News Sunday Morning).

He missed the point completely. The Thummer is getting remarkable press because the Thummer is remarkable – literally “worthy of remark.” The Thummer is, in Seth Godin’s memorable phrase, a Purple Cow.

Here’s the essence of Godin’s Purple Cow Theory, drawn from the above-linked article:
When was the last time you noticed a cow? Saw a cow on the side of the road, pulled over and gawked… Not likely. Cows, after you've seen them for a while, are boring. They may be well-bred cows, Six Sigma cows, cows lit by a beautiful light, but they are still boring.

A purple cow, though: Now, that would really stand out. The essence of the Purple Cow — the reason it would shine among a crowd of perfectly competent, even undeniably excellent cows — is that it would be remarkable. Something remarkable is worth talking about, worth paying attention to.

Boring stuff quickly becomes invisible. The world is full of boring stuff — brown cows — which is why so few people pay attention. Remarkable marketing is the art of building things worth noticing right into your product or service. Not just slapping on the marketing function as a last-minute add-on, but also understanding from the outset that if your offering itself isn't remarkable, then it's invisible — no matter how much you spend on well-crafted advertising.
Overhauling the product with dramatic improvements in things that the right customers care about can have an enormous payoff.

If being a Purple Cow is such an effective way to break through the clutter, why doesn't everyone do it? Because people are so afraid. "Playing it safe" and "following the rules" seem like the best ways to avoid failure. Alas, that pattern is awfully dangerous. In a crowded marketplace, fitting in is failing; not standing out is the same as being invisible. The more intransigent your market, the more crowded the marketplace, the busier your customers, the more you need a Purple Cow. Today, the one sure way to fail is to be boring. Your one chance for success is to be remarkable.

The Thummer is not just remarkable, it’s remarkable in four different ways – (1) its unparalleled expressive power, (2) its unprecedented ease of learning, (3) its revolutionary Dynamic Tonality, and (4) its shockingly low price (compared to other button-field controllers like the Tenori-On and Monome, which don’t even come close to the Thummer on any of the first three points).

These are exactly the benefits needed to disrupt the music products industry.

As Bill Gates once famously said, “to create a new standard, it takes something that's not just a little bit different. It takes something that's really new and really captures peoples' imagination.”

It takes a Purple Cow – a purple cow like the Thummer.

Dynamic Tonality Demo Video

2008-04-15T14:45:00.000-07:00

You can find a video demonstration of Dynamic Tonality here:
http://www.youtube.com/watch?v=Nd4h8vmEsQM

The sound quality is terrible, because I had to record it from my laptop, the microphone jack on which is busted, and using demo-creation software which couldn't tap into the speakers directly -- so the sound you're hearing is coming out of its speakers and into the laptop's built-in mic, which is a recipe for feedback. Noisy fan, too. Please accept my apologies for this.

But, that being said, the demo still makes the point -- clearly, I hope -- that the Thummer keyboard’s note-layout makes microtonal music brain-dead simple, by exposing tonal intervals consistently in every tuning of the syntonic tuning continuum.

Next month, a paper is being published in the peer-reviewed Journal of Mathematics and Music which rigorously proves that the Thummer's Wicki/Hayden note-layout is optimal for controlling Dynamic Tonality. No other note-layout -- not the Janko, nor Fokker, nor Bosanquet, etc. -- packs so many octaves of tonally-relevant intervals into such a small area over such a wide tuning range.

It's easy to dismiss microtonality as an irrelevant fringe interest that has no appeal whatsoever to mass-market consumers. But this ignores both history and current practice, in which tuning matters.

Currently, Western musicians bend their notes constantly – intoning them towards Just Intonation, Pythagorean tuning, expressive exaggerations thereof, or blue notes. Monophonic instruments have dominated Western orchestras in part because they allowed such note-by-note intonation. Tuning matters. The Thummer allows musicians to intone notes polyphonically -- bending many notes at once towards their Pythagorean tuning, for example (with the sharps getting sharper and the flats flatter).

Also, there is a big wide world out there beyond the West, and many non-Western cultures use non-Western tunings. The Thummer's keyboard has the same fingering in 7-edo (related to Thai & Mandinka music) and 5-edo (related to Indonesian music) as it does in Western 12-edo. Even the Turkish 53-edo schismatic temperament fits the Thummer's note-layout, too (albeit with different note-choices than are used in the syntonic temperament, e.g. d4’s in place of M3’s). The Thummer supports all of these different cultures' tunings. To musicians from non-Western cultures, or to Western musicians who wish to learn about or to mix and match the music of non-Western cultures, tuning matters.

Historically, 12-edo is recent, only having been widely adopted between 1850 and 1900, give or take. Before that, Pythagorean tuning, 1/4-comma meantone, and various well temperaments dominated Western tuning for thousands of years. All of these pre-modern Western tunings have the same fingering on the Thummer's keyboard, too. You can see a piece of the soft-synth's controller for Just and irregular tunings in the above-mentioned Dynamic Tuning video, to the left of the tuning slider, towards the top of the screen (look for the phrase "Minor JI"). If you want to play music in its historically-accurate tuning (albeit perhaps on a modern instrument), then tuning matters.

In addition to past and current practice, one should also consider the future. The new musical effects enabled by Dynamic Tonality -- polyphonic tuning bends, new chord progressions (!), temperament modulations, and the like -- enable entirely new styles and forms of music. Consider the expansion of form enabled by the chromaticism of the Romantic period, or the staggering popularity of the non-equally-tempered blues scale over the last hundred years. Tuning matters.

These ideas may seem complicated, because Dynamic Tonality is brand new. However, as you can see/hear from the demo video, Dynamic Tonality is brain-dead simple to USE. You just change the tuning -- by wiggling one of the Thummer’s joysticks, perhaps -- and cool new musical effects happen. You don't have to understand prime numbers, ratios, logarithms, or any of the other arcana of tuning theory. You just wiggle a friggin' joystick. The Thummer knows music theory, so you don't have to.

Hostorically speaking, every change in tuning -- Pythagorean to 1/4-comma, 1/4-comma to well-tempered, well-tempered to 12-ET -- has expanded music's possibilities. Some of these initially seemed complicated and perhaps even diabolical, largely because these tunings moved notes away from their alignment with harmonic partials. But Dynamic Tonality generalizes the relationship between the Harmonic Series and Just Intonation by adjusting a timbre's partials (in real time) to align with the notes of the current tuning, then one gets pure consonance all across the syntonic temperament's tuning range -- as you can hear in the demo (through the noise of the lousy recording -- sorry). So again: you don't need to know music theory to use this stuff; the Thummer knows music theory, so you don't have to.

In short: one of the main reasons to prefer the Wicki/Hayden note-layout over all other isomorphic layouts is that it enables unique support for Dynamic Tonality.

The ThumMusic System was also designed with Dynamic Tonality in mind. It emphasizes those aspects of music -- intervals, and the relationships among intervals -- which are invariant in the music of the past, the present, and the future, across many different cultures, while deprecating those aspects of music – most notably tying each note to a fixed pitch -- which assume a single, static tuning, unique to one time, place, and culture.

Or that’s the idea, anyway. ;-)

Temperament, by Stuart Isacoff

2008-03-23T15:12:00.000-07:00

Last week I read, for the first time, Temperament: How Music Became a Battleground for the Great Minds of Western Civilization, originally published in 2001. It was written by Stuart Isacoff, a “pianist, composer and writer, the founding editor of the magazine Piano Today,” and Lecturer at Purchase College, which is part of the State University of New York system. I found it to be fascinating, penetrating, and a very enjoyable read.

I was also pleased to discover that, indirectly, it presents a very strong argument in favor of Thumtronics’ musical innovations.

Superficially, Temperament could be read as a paean to 12-edo (Equal Division of the Octave, called simply “equal temperament” in the book). For example, Isacoff writes that:

12-edo is “the final solution” (p. 6).
“if music depended on harmony for its expressiveness, then [12-edo] was crucial, because it offered any keyboard instrument a unique ability to facilitate harmonic movement” (p. 209).
“equal temperament [is] a system that casually discards the simplest, purest musical ratios…for the sake of pleasing the ears” (p. 175).
“no keyboard can execute all these different scales in meantone tuning without falling prey to the ‘wolves’” (p. 215).
12-edo’s adoption was “inevitable” (p. 224).
“the temperament wars, after centuries of struggle, had essentially reached an end…[12-edo] settled in as the philosophical ideal” (p. 227).

However, the book frequent mentions an often-proposed alternative solution: extended keyboards and tunings, i.e., those with more than 12 notes per octave.

“Instrument makers proposed the creation of keyboards with extra keys, so performers would have more than the usual number of choices for finding a note with the proper proportion. It was a cumbersome solution” (p. 18).
“As late as 1768, the Foundling Hospital in London [installed an organ] capable of playing more than 12 pitches in an octave. Nevertheless, these complicated musical inventions found little acceptance” (p. 19).
“one solution to [the problem of wolf intervals in meantone] was to offer extra keys, giving the performer a choice of playing either la-flat or sol-sharp…The idea would gain new adherents over time…but it was cumbersome, and ultimately unsatisfactory” (p. 104).
“Nicola Vicentino…constructed an entirely new instrument, the archicembalo, with six rows of keys, to allow different versions of each scale member to be played (commas and all)” (p. 127).
“Fabio Colonna’s sambuca, based on a division of the octave into thirty-one parts” (p. 131).
“Mersenne, for example, urged the adoption of an instrument with nineteen keys” (p. 181).
“Constantijn Huygens…used logarithms to calculate the division of the octave into thirty-one equal parts…Models of [his] keyboards, designed to fit over ordinary harpsichords, were, he reported, actually constructed in Paris” (p. 185).
“Newton’s method boiled down to the cumbersome method of offering performers a greater-than-usual choice of notes to play” (p. 196).

Isacoff consistently uses the same word to explain the failure of extended keyboards: cumbersome, defined by the Merriam Webster Online Dictionary as meaning “unwieldy because of heaviness and bulk." The Thummer is one-thirtieth the size and one tenth the weight of an electronic keyboard, and vastly smaller & lighter than an acoustic piano.

Clearly, Isacoff considers the “cumbersome-ness” of any given keyboard design to be a significant factor in its acceptance or rejection.

Perhaps the Thummer's relative non-cumbersome-ness can be seen as a significant advantage.

Another word that Isacoff uses to describe extended keyboards is complicated, defined as “difficult to analyze, understand, or explain.” An alternative definition of cumbersome provided by Wiktionary, also smacks of complexity: “not easily managed or handled; awkward.” Does Isacoff prefer the simple and easy to the complicated and difficult? Apparently, he does.

Isacoff quotes d’Alembert as praising Rameau for being “the first to have simplified the practice of [music] and made it easier,” implying that being simpler and easier – i.e., less complicated – are positive qualities (p. 223).
Isacoff praises the innovations of Guido d’Arezzo – solfege and the staff, specifically – saying “The impulse to explore greater musical horizons demanded advances in technology…Portraying music visually made its structure easier to grasp and to vary; it enabled choirboys to learn in a few days what had taken weeks, and gave singers and composers newfound freedom to experiment. Musicians could more easily pose the question, ‘what if…?’” (p. 50)

The latter quote above is particularly important, as it elucidates a subtle point that is often lost: that by making things simpler, you can also make them more powerful. To quote Wikipedia, "A solution may be considered elegant if it uses a non-obvious method to produce a solution which is highly effective and simple. An elegant solution may solve multiple problems at once, especially problems not thought to be inter-related."

The Thummer’s isomorphic keyboard is said to be much simpler and easier than the piano keyboard, especially when also using the ThumMusic System to display and control musical information. (One might think of its solfege-based ThumLine staff as reuniting Guido d’Arezzo’s sundered innovations.) The Thummer’s ability to facilitate the exploration of “greater musical horizons” is discussed below.

Perhaps the Thummer's being less complicated can be seen as a significant advantage.

Throughout Temperament, Isacoff praises those instruments and tunings which enhance expressiveness and versatility:

“Temperaments…unfettered the engine of musical progress” (p. 8)
“Each of Leonardo [da Vinci]’s musical inventions seemed to break new ground in extending an instrument’s expressive possibilities” (p. 89)
“The stretching of musical boundaries [in the late 1500’s] fueled a demand for more versatility from the keyboard instruments themselves” (p. 162)
“For many musicians, the invention of the piano was a wish come true. Composer and keyboardist Francois Couperin had pleaded in print for the creation of just such an instrument in 1711. He would be ‘forever grateful,’ wrote Couperin, to anyone who could render the monotonous harpsichord capable of expression” (p. 210)

Independent experts claim (here, and here) that the Thummer, with its thumb-operated joysticks and internal motion sensors, has more expressive potential than any other instrument. As to versatility, the Thummer’s keyboard can be used to play the music of many different cultures and eras (which require tunings other than 12-edo), all with the same fingering. As to “unfettering,” the Thummer encourages musical progress through such novel effects as Dynamic Tonality.

Perhaps the Thummer's being more expressive, more versatile, and more enabling of musical progress can be seen as a significant advantage.

Isacoff also hints at the intimate relationship between tuning and timbre that is fundamental to Dynamic Tonality:

“Unless the strings used to create the harmony are made of the same ‘material, length, thickness, and goodness,’ they simply won’t be in tune with each other…(the gut strings used in lutes, for example, will produce equal-tempered thirds that are more pleasant sounding than the ones produced on strings made of steel)” (p. 143).
“Indeed, [the piano’s] timbre, like the lute’s, made the modified intervals of equal-tempered tuning easy to take” (p. 214).

During the time covered by the book Temperament, the only possible approach to the problem of consonance (described in the book as concordance) was tempering one’s tuning; it was not possible to temper the timbres of acoustic instruments. However, as Isacoff says (p. 39), “In our sophisticated, scientific age of black holes and anti-matter, dealing with such entities is child’s play.” Using electronic music synthesis, both tuning and timbre can be tempered together, opening the entire dynamic sweep of the syntonic temperament’s tuning continuum to exploration without sacrificing consonance.

This approach to solving the problems raised in Temperament is – as far as my collaborators, myself, and our papers’ peer-reviewers know – entirely novel. This use of “tempered timbres” slices through the Gordian Knot of temperament at an entirely new angle. Its result is not just one arguably-optimal approximation of Just Intonation – 12-edo – but rather a broad, continuous sweep of tunings, each maximally-aligned with its related timbres’ partials. Indeed, our approach embraces not only the syntonic temperament, but every rank-2 temperament, including the schismatic, Magic, Hanson, Porcupine, etc.

This newfound flexibility of tuning and timbre – “Dynamic Tonality” – is simply impossible to replicate on the piano-style keyboard, because a two-dimensional note-layout is required to capture the structure of a two-dimensional (rank-2) temperament, and the piano's keyboard is one-dimensional.

Perhaps the Thummer and Dynamic Tonality will be seen as offereing a more flexible solution to the problem of temperament.

There’s one last thread running through Temperament that’s relevant to Thumtronics’ innovations: Isacoff’s frequent praise for those creative musicians, scientists, and theorists who went against established orthodoxy in proposing new ways of balancing the needs of beauty and utility. However, this praise is offered more in tone than in text, so I can’t provide specific quotes.

It is unclear whether Isacoff's praise is for rational & experiential iconoclasm in general, or only for that which supports an anti-Pythagorean & pro-12-edo agenda. Thumtronics' innovations are certainly anti-Pythagorean (in that they modify the Sacred Harmonic Series itself – gasp, horror, heresy!), but they are hardly pro-12-edo. Nonetheless, they are built atop a firm scientific foundation, with mathematical proofs published in peer-reviewed scientific journals and with a demonstration synth that can be experienced by anyone.

In conclusion: Stuart Isacoff’s excellent book, Temperament, praises those innovations in the history of musical tuning, instrument design, and notation that enhanced simplicity, versatility, freedom, expressiveness, and progress, while being less cumbersome. I submit that the Thummer delivers all of these same benefits, and would welcome Dr. Isacoff's comments on it.

Tempered Calendars

2008-03-12T21:07:00.000-07:00

A one-dimensional count of days, such as the Julian Day Number, has no inherent periodicity. Divide it up into 7-day weeks, however, and you get a calendar which is seven days wide and infinitely tall (usually clipped to display a single month’s days).

The periodicity of astronomical phenomena such as the rotation of the Earth around the Sun and the rotation of the Moon around the Earth are used as the basis of many calendar systems, such as the Buddhist, Chinese, Gregorian, Hebrew, Islamic, Korean, Mayan, or Persian. However, these astronomical phenomena can’t be captured perfectly in any calendar system because they are mutually indivisible. For example, it takes 365.2424 days (i.e., 365 days, 5 hours, 49 minutes and 12 seconds) for the Earth to orbit the Sun, and 29.530589 days (29 d 12 h 44 min 2.9 s) for the Moon to orbit the Earth – numbers which are not mutually divisible.

Each calendar system is a set of rules which defines the relationships among its various periodic intervals. Because the intervals are mutually indivisible, the rules of any given calendar system must favor one intervals over another. Therefore, these calendar systems can be viewed as temperaments. They compromise some intervals to capture the purity of others.

For example, the Islamic calendar compromises the purity of the solar interval in order to have an absolutely pure lunar interval, with months that precisely match the rising and setting of the Moon, but with years that drift relative to the Earth’s orbit around the Sun. On the other hand, the Gregorian calendar has a pure solar interval, but its months start and end with no relationship whatsoever to the rising and setting of the Moon. Other calendars temper their intervals differently, but they’re all temperaments, one way or another.

No such tempering would be necessary if the Earth orbited the Sun in exactly 336 days, and the Moon orbited the Earth in exactly 28 days. Then, every year would have 12 months of 4 weeks of 7 days. The new moon would rise on the first of each month; solstices and equinoxes would fall on the same dates (and days of the week) every year.

Unfortunately, we can’t temper the planets to conform to our calendrical needs. ;-)

Mapping Periodicity

2008-03-12T20:47:00.000-07:00

I’m collecting examples of regular two-dimensional mappings of linear, periodic data. If you know of any good examples, please let me know.

Here are the best examples I know about.

The earth is a three-dimensional object, but maps are two-dimensional. They have to discard an entire dimension in order to present the curved surface of the Earth in a conveniently-flat manner, and there are lots of projections than organize this discarding in a systematic manner.

But what if you want to go the other way ‘round? What if you have low-dimension data, and you want to display it at a higher dimensionality?

Chemistry provides a famous example. Each of its elements has an atomic number, corresponding to the number of protons in its nucleus. Atomic numbers form a one-dimensional continuum from 1 (Hydrogen) to at least 118 (Ununoctium). The continuum of atomic numbers has no inherent periodicity, but the physical properties of the atom impose a periodic structure on this otherwise-undifferentiated continuum of atomic numbers, as seen in the Periodic Table of the Elements.

Another example is the calendar. One can think of time as a one-dimensional count of days, such as the Julian Day Number, which has no inherent periodicity. Divide it up into 7-day weeks, however, and you get a calendar which is seven days wide and infinitely tall (usually clipped to display a single month’s days).

Music provides the third example (and the point of this article). The human ear has a hearing range that runs from about 20 Hz up to about 20,000 Hz. This one-dimensional range of frequencies has no inherent periodicity, but if two tones from a harmonic source are sounded together within that range, the coincidence of their harmonics makes some inter-frequency ratios sound more consonant than others, giving rise to the musical intervals recognized as octaves, perfect fifths, and so on. Using only the octave and tempered perfect fifth to generate all other tonal intervals, one can map linear frequency into a periodic set of intervallic relationships, as seen in isomorphic keyboards.

If linear data contains periodicity, then that periodicity can supply the information needed to provide an extra dimension.

This seems to me to be rather magical: An entire dimension of data conjured up out of thin air!

If you know of any other examples, please let me know! :-)

Thummer Plays the Blues

2008-03-10T04:00:00.000-07:00

What is the blues scale?.

In Africa and the Blues, Gerhard Kubik describes the blues scale as arising from two overlapping harmonic series, one starting a perfect fourth higher than the other. He shows this using a diagram showing only the 5th through 9th partials (harmonics) of each note's harmonic series, which I have modified as shown below (at right).

In the figure at right, the lower-pitched harmonic series is Do (outer ring, with harmonics as black-filled circles), the upper-pitched one is Fa (inner ring, harmonics as unfilled circles). Partials 5 through 9 are shown for each. There's very good alignment between Do's 8th partial and Fa's 6th partial (and of course the octaves thereof), and also between Do's 6th partial and Fa's 9th partial. These well-aligned pairs are a perfect fifth apart.

An alternative way to visualize two overlapping harmonic series is shown below.
In the figure at left, the harmonics of Do are in black while those of Fa, offset a perfect fourth higher, are in grey. At 700 cents above Do's fundamental, Do's 3rd, 6th, 12th, & 24th harmonics align with the 9th & 18th partials of Fa -- hence aligning the Do6 and Fa9 partials as in the circular figure above. Likewise, Do's 1st, 2nd, 4th, 8th, & 16th partials (far left, at 0 cents) align well with Fa's 3rd, 6th, 12, & 24th partials (far right, just past 1199 cents) -- hence aligning the Do8 and Fa6 partials as in the circular figure above.

At the top of the figure above and left, scale degrees are shown. The 3rd and 6th scale degrees are underlined, with each underline joining two stacks of harmonics. The third degree joins Do9 and Fa7 (and their octaves), while the sixth degree joins Do7 and Fa5 (and their octaves). According to Kubik (if I understand his section of his book correctly), these not-quite-aligned Do9/Fa7 and Do7/Fa5 pairs enable the tunings of these scale degrees to be flexible within a fairly wide range.

Another point raised by Kubik is that the 7-edo scale -- also known as the "equiheptatonic" scale, dividing the octave into 7 intervals of equal width -- is common in some parts of Africa. A "third" in 7-edo tuning is 343 cents wide, which is right in the middle of the range of the 3rd scale degree in the above-left figure, providing yet another source of instability in this range.

Does the Thummer suit the blues?

Played in today's standard Western 12-edo tuning (i.e., an “equal division of the octave” into 12 pieces), the Thummer should be at least as blues-capable as the piano or guitar. Its expressive controls (thumb-operated joysticks & electronic motion sensors) allow the user to play the blue notes "between" the notes of 12-edo as a guitarist can do by bending strings, and which a pianist simulates by "crushing" adjacent keys.

However, the Thummer's real potential as a blues instrument arises from the tuning invariance of its isomorphic keyboard, which gives it the same fingering in any tuning of the syntonic temperament, which includes both 12-edo and 31-edo (i.e., an “equal division of the octave” into 31 pieces, in which the tempered perfect fifth is 696.8 cents wide -- only 3.2 cents narrower than 12-edo's tempered perfect fifth).

The use of septimal (7-limit) ratios for the blue notes is explored by W.A. Mathieu in his excellent book Harmonic Experience (Chapters 17 & 33).

In 12-edo tuning, the augmented second (A2) has the same width as the minor third (m3) -- 300 cents -- so they are often treated as if they were "the same" interval.

However, in any other tuning, including 31-edo tuning, the A2 and m3 have different widths, each signifying a different just interval, as does the M3.

31-edo's A2, at 271.0 cents, is only four cents narrower than the just septimal minor third (7/6 = 266.9).
31-edo's m3, at 309.7 cents, is only 5.9 cents narrower than the just minor third (6/5 = 315.6).
31-edo's M3, at 387.1 cents, is less than one cent wider than the just major third (6/5 = 386.3 cents).

This harmonically-relevant distinction between the A2, m3, and M3 gives musicians a choice of three different notes to play across the range of blue 3rds. They can use the A2 to signifiy the 7/6 ratio, the m3 to signify the 6/5 ratio, or the M3 to signify the 5/4 ratio. All of these notes provide a better match with the harmonic series when using 31-edo than when using 12-edo.

Perhaps even more importantly, 31-edo distinguishes the augmented sixth (A6) from the minor seventh (m7).

31-edo's A6, at 967.7 cents, is only 1.1 cents narrower than the septimal minor seventh (7/4 = 968.8), making it well-suited for the harmonic seventh, also known as the "babershop seventh," chord.
31-edo's m7, at 1006.5 cents, falls almost exactly between just intonation's Pythagorean minor seventh (16/9 = 996.1) and diatonic minor seventh (9/5 = 1017.6), making it well-suited for use in a dominant seventh chord.

Hence, musicians can use the A6 to signifiy the 7/4 ratio, or the m7 to signify the 16/9 and/or the 9/5 ratio. Either way, musicians get a better match with the harmonic series when using 31-edo than when using 12-edo. (Well, actually, 12-edo's m7, at 1000 cents, is a better match with the Pythagorean m7, but it's a worse match with the diatonic m7 and is completely useless as a septimal m7.)

According to this reference, the tonic, subdominant, and dominant chords (I7, IV7, and V7) should be played as harmonic seventh chords (i.e., with an A6) except for the V7 at the turnaround, which should be played as a dominant seventh chord.

If I understand this correctly -- which I very well may not -- then in C, using the tuning described above, the I7, IV7, and V7 blues chords would be played in 31-edo as:

I7: C-E-G-A#
IV7: F-A-C-D#
V7: G-B-D-F (turnaround) or G-B-D-E# (otherwise)

31-edo supports free modulation as well as 12-et does, with a caveat or two. For example, you can't play Coltrane's Giant Steps in 31-edo, becuase Giant Steps' chord progression relies on the fact that 12-edo's way-too-wide 400-cent major third tempers out the diesis , so that a chord progression through three M3's will return to the same pitch class. 31-edo's major thirds are almost perfectly just at 387.1 cents, so progressing through three of them will bring you to a point that's 38.7 cents short of the starting pitch class. Oops! In 31-edo, Giant Steps is a giant stumble, because it relies utterly on the unique structure of 12-edo -- whereas most blues relies on a structure that mixes 7-limit intervals with 5-limit intervals, at which 31-edo excels.

So, how does the Thummer compare to other blues instruments?

On the piano keyboard, making a distinction between the A6 and m7, or the A2 and m3, is impossible. Both intervals share the same key. Pianists can fake it by crushing adjacent keys, but that's clearly a kludge, which does nothing to distinguish among the relevant harmonic ratios.

On the guitar, it's possible to play perfectly intoned notes -- through string bending -- but difficult. In this YouTube video lesson from Berklee, the instructor states (2:09 in) that "String bends are kinda tricky. They take a little getting used to...like YEARS, actually, to develop a good sound."

On the Thummer, you can learn to play perfectly-intoned blue notes in minutes. To paraphrase Bach, you just press the right button at the right time, and the instrument plays itself. In C, for example, if you want the A2, you play the D# button; if you want the m3, you play the Eb button; if you want the M3, you play the D button. You can use the portamento controller to slide smoothly from one precisely-tuned note to another, with no guesstimation involved. Or, you can play any of the notes above, and use pitch bending to slide 'em around at will.

31-edo is good for other musical styles, too. It is nearly identical to 1/4-comma meantone, which dominated the early centuries of Europe’s Common Practice Era, of which the use of augmented sixth chords was distinctive part.

31-edo may also be well-suited to klezmer and gypsy music, which use many augmented intervals.

If 31-edo is so cool, why hasn't it been more widely used? Apparently, because it was thought to require the use of an instrument with 31 keys per octave, for which there could be no mass-market in a 12-edo-dominated world.

This barrier may have been eliminated by the recent discovery of tuning invariance, combined with electronic transposition. Despite having only 19 buttons per octave, it appears to be true that all of the tonally-relevant 5-limit and 7-limit intervals of 31-edo fall on the Thummer's keyboard. (The above-mentioned neutral third does not, because it's an 11-limit interval.) Add to this the Thummer's expressive potential (controlled by its thumb-operated joysticks and internal motion sensors), and the Thummer could be a very credible blues instrument.

However, it's important to realize that 12-edo and 31-edo are just points along the syntonic temperament's tuning continuum, along which the Thummer can be retuned dynamically in real time. On the one hand, that means that a Thummer player can slide smoothly back and forth between 12-edo and 31-edo (or Pythagorean, or 7-edo, or whatever) in real time, choosing the tuning that best fits the current note or phrase. On the other hand, this real-time flexibility enables entirely new musical effects such as expressive polyphonic tuning bends, tuning progressions, and temperament modulations.

My collaborators and I have barely scratched the surface of the possibilities of tuning invariance -- our initial scientific paper was published just three months ago -- so we're not yet sure how big the creative opportunity really is.

Now, if y'all could please point out the errors I've undoubtedly made in this blog article, I'd appreciate it, and will update the article accordingly.

Thanks! :-)

Technology Evangelism

2008-03-04T12:45:00.000-08:00

The goal of technology evangelism is the establishment of a new technology as a de facto standard within a given market. In markets dominated by network effects, the status quo tends to be locked in, making it impervious to alternative technologies that offer only minor advantages. However, these same network effects tend to favor new technologies that offer disruptive advantages, such as being simple, cheap, powerful, and unique.

The technology evangelist’s job is the creation of a critical mass of support for a new technology. Once critical mass is reached, the new technology becomes self-evangelizing, and the technology evangelist’s efforts can be invested in some other new technology.

In evangelism, speed is critical. The new technology must reach critical mass before the status quo’s backers can blunt its momentum – because change is always resisted. Once critical mass is reached, a new status quo will emerge, centered on the evangelist’s new technology.

The technology’s evangelist must:

create materials that facilitate each potential adopter’s progress through the decision process,
bring these materials to the attention of those potential adopters who have the most leverage (see below),
organize a system of incentives to encourage early adopters to actively engage their leverage on behalf of the new technology, and
drive a public relations campaign to publicize the early adopters’ support of the new technology, thereby
maximizing the technology’s benefit from bandwagon effects and social proof.

Leverage is the ability to get other potential adopters to adopt whatever technology you adopt. The more people your technology adoption influences, and the more powerful your influence on each such person, the more leverage you have. Identification and exploitation of leverage is the key to efficient evangelism.

At each stage of the technology evangelism process, the technology evangelist's focus must always be on ensuring that the adopters of the new technology gain compelling benefits (a) directly, from adopting the new technology, and (b) indirectly, from getting others to adopt the new technology, too. "Ask not what your adopters can do for your technology; ask what your technology can do for your adopters." (Unless your technology is a whole lot better, don't even ask that.)