Lesson 005.0

Here's my first draft of Lesson 5 in JiMS iGetIt! Music System (source code here):


Same crummy state-controlling button-bar at the bottom, for now. I really must fix that.

This lesson is 640x480, rather than the much smaller dimensions of the previous lessons. The larger size doesn't fit this blog very well, but it makes the lesson's text easier to read -- especially the note-button labels.

In this lesson, we build the "Fundamental Scales" -- that is, music's "well-formed scales." I'm not using the "well-formed scale" phrase yet, because to do so, I also need to introduce Myhill's property, and we're still a few lessons away from that.

In Lesson 6, I expect to introduce the notion of tuning, to show how the world's different musical cultures are related, and to establish the argument that to learn music using JiMS is to use a very general approach -- not limited to traditional Western music, for example. I had hoped to put that into Lesson 5, but it was just too much information. It needed its own lesson.

As of this lesson, my courseware has not just drifted, but positively galloped away from mainstream approaches to music education. Yet one can see that the concepts it introduces are quite simple, when shown using JiMS isomorphic keyboard and on-screen animations.

This lesson is late because I spent a week doing the final packing, cleaning, etc. to get our Austin house on the market. That's done; the coast is clear. More lessons!  (More cowbell!)

Lesson 2

Here's my first cut at Lesson 2 in JiMS iGetIt! Music System (source code here):


No radical departures from mainstream theory or pedagogy, so far. I'm not super-happy with the state-based architecture that I'm using, and there are some bugs (unimplemented events, actually) in the Flex 4 beta that I had to work around, but...so far, so good.

Kodály, Wicki, and iSlate

The Kodály music education Methodstarts young students with pentatonic songs, then slowly introduces them to the "extra" diatonic intervals, and then eventually to the "extra" chromatic intervals.

Now, imagine that the youngest students were presented with a "pentatonic keyboard" in the Wicki/JIMS note-layout, like the one shown in the (non-interactive) image at right.

For the pentatonic songs used initially by the Kodály Method, this pentatonic-only keyboard would be ideal. It would contain only the notes (intervals) that the students were currently learning. (Other keyboard controls, not shown, would be used to indicate the tonic and define its pitch.) Also, it would give students a visual, tangible metaphor for tonal space, hence (potentially) accelerating their development of audiation skills.

Then, when they were introduced to the "extra" intervals of the diatonic scale, they could get a new diatonic keyboard.


As you can see, it's the same as the pentatonic keyboard, with the addition of Fa and Ti along the left and right edges, respectively. In effect, the diatonic keyboard's extra notes expand the "tonal space" to which the student is exposed.

Again, by containing only the notes in the scale currently being studied, such a keyboard has the potential to sharpen student's focus.

Later, as the student progressed to learning about chords, they could be presented with a two-handed diatonic keyboard, suitable for self-accompaniment. (The note-layouts are mirrored for cognitive convenience, and angled for ergonomic convenience.)

...which would, in turn, be superseded by a two-handed chromatic keyboard:

...and eventually, a two-handed enharmonic keyboard, featuring all 19 intervals of the enharmonic scale:

The latter keyboard looks rather overwhelming, and it probably would be, if it were the first keyboard a student encountered. However, after starting with the simple pentatonic keyboard and working progressively up through the diatonic an chromatic keyboards, the enharmonic keyboard wouldn't seem like such a big deal. It just adds a few extra notes at the outer edges of the keyboard, leaving its pentatonic/diatonic/chromatic core unchanged.

The main advantage of this approach is that the student always uses a keyboard that has precisely enough note-controlling buttons to achieve the required pedagogical goals, thus encouraging proper focus and minimizing distraction/confusion. Of all of the isomorphic note-layouts, the Wicki note-layout is best for this purpose. Each successively-wider Wicki keyboard enables the student to see farther into tonal space, literally expanding their tonal horizons.

The main disadvantage is that the student must trade-up keyboards rather frequently.

Perhaps this disadvantage could be ameliorated by using a virtual multi-touch keyboard, such as the much-rumored Apple iSlate (see article here):

Such a multi-touch sensitive display would perhaps lack the tactile feedback needed in a true performance instrument...but that's not the point. The Kodály Method stresses the use of one's voice as one's performance instrument. Hence, in a Kodály context, the Wicki note-layout keyboard would be used not for performance (absent the Thummer [sigh]), but rather for pedagogy -- i.e., in helping students apply additional senses (sight, touch) to the development of proper audiation skills.

Using a virtual keyboard would enable new intervals to be introduced not just one scale at a time, but one note at a time -- first just So and Mi, then also Do, then Re, then La, etc. -- following the standard sequence of the Kodály Method.

Apple's iSlate is likely to be to expensive for K-12 music instruction. Give it 10 years, however -- maybe less -- and iSlate clones will be cheaper than traditional band instruments.

La-based minor revisited

I have gotten a lot of feedback on my earlier post, Why La-based Minor?

 

In brief,

• my understanding of Do-based minor was wrong.
• I am now considering a different scheme, which seems to me to combine the best of both La-based and Do-based minor.

My new thinking, which is still somewhat half-baked, goes like this.

Do-based minor emphasizes the parallel minor, while La-based minor emphasizes the relative minor. Why emphasize one over the other?  Why not clearly distinguish between the two?

Case 1: Starting in Major
Let’s assume that you’re going to notate/play a piece starts in major (diatonic Do-mode), so you transpose the pitches under the keyboard to move the desired tonic pitch to Do. Let’s say that you’re playing in C Major, so Do is C, La is A, Mi is E, and Me is Eb.

When the piece begins, in Do-mode, all is well. The tonic is on Do (C), and that mode’s third degree is Mi (E), which is where we pegged the keyboard, so those notes have those pitches.

1a) If the piece wanders from Do-mode into its parallel minor (C minor), all is well. The tonic stays on Do (C), and Do-mode’s third degree is Me (Eb), but no new transposition of the keyboard/notation is necessary, because those notes already have those pitches.

1b) If the piece wanders from Do-mode into its relative minor (A minor), all is well. The tonic moves from Do (C) to La (A), and La-mode’s third degree is Do (C), but no new transposition of the keyboard/notation is necessary, because those notes already have those pitches.

The next question is, “where do the scale dots and tonic indicator go?”

We're starting in diatonic Do-major, so the scale dots are on the usual diatonic notes, Do, Re, Mi, Fa, So, La, and Ti, with the tonic indicator on Do.

1a) Moving from Do-major to Do-minor, the scale dots change to Do, Re, Me, Fa, So, Le, and Te, with the tonic indicator staying on Do.

1b) Moving from Do-major to La-minor, the scale dots stay the same (i.e., on Do, Re, Mi, Fa, So, La, and Ti), but the tonic indicator moves to La.

The interplay of the scale dots and the tonic indicator show, in JIMS staff notation, what is happening.

• If the scale dots change, but the tonic indicator stays on the same note, then the music has moved to a parallel mode.
• If the scale dots stay the same, but the tonic indicator moves to a different note, then the music has moved to a relative mode.

This is not a factoid to be memorized, per se, but rather something which can be observed from the note-patterns on JIMS keyboard as one plays.

This system usefully distinguishes Do-major's relative minor (La-minor) from its parallel minor (Do-minor). The two would be notated using different notes on JIMS staff, and played using different buttons on JIMS keyboard.

When used strictly by “La-based minor” singers, the notation and keyboard could be transposed such that both the parallel and relative minors always used La as their tonic. However, that would NOT be the general case. the main difference between my previous proposal and this one.

Case 2: Starting in Minor
Now, let’s assume that you’re going to notate/play a piece which starts, and remains primarily, in A minor, so we map A to La.

2a) If the piece wanders from minor into its relative major (C Major), all is well. The tonic moves from La (A) to Do (C), and Do-mode’s third degree is Mi (E), but no new transposition of the keyboard is necessary, because those notes already have those pitches.

2b) If the piece wanders from minor into its parallel major (A Major), all is well. The tonic stays on La (A), and La-mode’s third degree is Do (C)…wait a minute. That’s not right. We’re talking La-MAJOR now, not La-MINOR.

Case 2b above is (I suspect) at the heart of the conflict between the La-based minorists and the Do-based minorists. Who would ever expect to find a major scale with La as its tonic?

If Case 2b's minor-to-parallel-major-and-back movement dominated a given piece, then it would make sense to start the piece in Do-minor. Then, when the mode changed from the primary minor key to its parallel major, the major mode’s tonic would be Do, as one would normally expect. Using D-minor in this way would emphasize that the core relationship in this piece was parallel, not relative.

Let's look at the scale dots and tonic indicator in Case 2.

2a) Starting in La-minor, the scale dots are on the usual diatonic Do, Re, Mi, Fa, So, La, and Ti, with the tonic indicator on La. Moving to the relative major, the scale dots remain the same, but the tonic indicator moves to Do.

2b) Starting in Do-minor, the scale dots are on Do, Re, Me, Fa, So, Le, and Te, with the tonic indicator on Do. Moving to the parallel minor, the scale dots change to Do, Re, Me, Fa, So, La, and Ti, with the tonic remaining on Do.

If the music moves farther than one relative or parallel step away from the tonic, in either direction, then it has modulated (hasn't it?). One could either keep shifting the stack of scale dots to reflect the changing set notes in the current diatonic scale (much like introducing more sharps and flats into a key signature, with all of the disadvantages thereof), or simply transpose JIMS staff and keyboard (using a transposition indicator and user-interface gesture, respectively).

Limitations
If a piece's tonal center is ambiguous, then no tonally-focused notation (like JIMS) is going to offer significant advantages over less-tonally-focused notations (like traditional notation).

However, most music played and listened to by the majority of the people in the First World is strongly tonal (and even strongly modal, if one considers the major scale to be the Ionian mode), which plays to JIMS' strengths, so I don't think that this limitation counts for much.

Advantages
The above-described approach seems to me to combine the best of both Do-based minor and La-based minor, by distinguishing unambiguously between the relative and parallel relationships. The person notating a song would need to do a significant amount of work to analyze what’s happening in a given piece, in order to notate it correctly -- but that's a GOOD thing, because once this analysis is done by the notator, it is very easily accessible by the student and/or performer.

 

Having a clear distinction, in JIMS notation, between parallel and relative intervals helps distinguish between notes that have the same name but are a comma or two apart (in Just Intonation), thereby helping singers it the right notes. Nonetheless, for purely vocal music in the La-based minor tradition, one could transpose JIMS notation (and perhaps an accompanying JIMS keyboard) to keep the scale dots constant, i.e., to use a La-based minor whether that minor was relative or parallel. But this would not be *required* under the above-proposed revisions to the JIMS system.

 

I think that this refinement is a considerable improvement to JIMS. It exposes a meaningful difference—the difference between relative and parallel keys—in a clear and unambiguous manner. This is in line with JIMS' neo-Riemannian roots.

 

Perhaps this refinement is sufficient to make JIMS useful to those who teach music using a Do-based minor system. I hope so. In my wildest dream, I imagine that JIMS, with this refinement, might be sufficient to heal the centuries-long rift between the La-minorists and the Do-minorists.

Comments and corrections welcome!  :-)

Once upon a time...

Below is a copy of another post recently made to a discussion on Daniel Levitin's Facebook page.  It's a re-statement of the content in this older post, but I like the clarity of this new restatement.

In brief, my argument is that (a) there's a difference between "musical talent" and "the ability to handle arbitrarily high UI loads," and that (b) reducing the UI load in a given domain in can increase the success-rates that novices enjoy in that domain.

----------------------------------

Darin wrote:

> If someone has innate talent, then as that person
> practices and progresses, he or she will recognize
> the progress, will be recognized by others for the
> progress, and as a result, will develop real passion
> for the pursuit. If somone does not have innate
> talent, such person will practice, not make much
> progress, will see the lack of progress, and be told
> about it by others, and the passion will not take
> hold, but will wither, and the person will move on
> to some other endeavor.

>
> People with real talent are few.

I respectfully disagree. "Talent" has absolutely nothing to do with it. Please let me explain by example.

1. Once upon a time, the Cherokee were illiterate. The English alphabet was a poor fit with the Cherokee language, so efforts to spread literacy among the Cherokee failed. Then one Cherokee invented a writing system that fit Cherokee perfectly, enabling literacy to sweep the Cherokee almost overnight. Did the Cherokee suddenly gain a "talent" for literacy?

(http://en.wikipedia.org/wiki/Cherokee_syllabary)

2. Once upon a time, the Koreans were illiterate. The Chinese ideographic script was a poor fit with the Korean language, so the efforts to spread literacy among the Koreans failed. Then the Koreans invented Hangul, which fit Korean perfectly; now, "a bright child can become literate in a day, and a dull child in ten." Did the Koreans suddenly gain a "talent" for literacy?

(http://en.wikipedia.org/wiki/Hangul)

3. Once upon a time, physicists couldn't puzzle out the interactions of quantum mechanics, nor could students learn about them efficiently. Then, Feynman invented "Feynman diagrams," and students could understand such interactions in less than a semester. Did physics students suddenly develop a "talent" for quantum mechanics?

(http://en.wikipedia.org/wiki/Feynman_diagram)

4. Once upon a time, European mathematicians could not conceive of "x to the power of y," because Roman numerals could not notate the concept, and the Roman abacus could not calculate it. Then Fibonacci explained how to use Arabic (actually Hindu) numerals and algorithms, and the scope of European mathematical thought widened dramatically. Did Europeans suddenly develop a "talent" for mathematics?

(http://en.wikipedia.org/wiki/Liber_Abaci)

5. Once upon a time, the "value" of a church singer dependend as much on "how many songs he had memorized" as on how well he could sing them, because all songs had to be memorized by rote. Then Guido d'Arezzo invented staff notation and solfeggio, enabling novices to become valuable church singers much more rapidly. Did such novices suddenly gain a "talent" for singing?

(http://en.wikipedia.org/wiki/Guido_of_Arezzo)

6. Once upon a time, all mathematical calculations had to be executed longhand, making them expensive and error-prone. Then logarithms were invented, and many calculations could be accelerated by looking them up in tables of pre-calculated logarithms. Did this suddenly increase people's "talent" for calculation? Did the invention of the slide rule? Of the pocket calculator?
(http://en.wikipedia.org/wiki/Logarithms#History) (http://en.wikipedia.org/wiki/Calculator#Pocket_calculators)

7. Once upon a time, learning and practicing chemistry was extraordinarily difficult, with the properties of each element having to be learning individually, and its guiding principles (e.g., phlogiston) being fundamentally incorrect. Hence, few gained mastery over chemistry. Then Lavoisier discovered the combustion principle, Mendeleev invented the Periodic Table of the Elements, and Bohr deduced the planetary model of the atom, all of which reduced the investment of time necessary to master chemistry, thereby dramatically increasing the percentage of the human population that could afford to master chemistry. Did students suddenly gain a "talent" for chemistry?
(http://en.wikipedia.org/wiki/History_of_the_periodic_table)
(http://en.wikipedia.org/wiki/Phlogiston#History)
(http://en.wikipedia.org/wiki/Bohr_model)

YESTERDAY, learning and practicing music-making was extraordinarily difficult, with the patterns of each key, clef, scale, mode, tuning, instrument, timbre, etc., having to be learning individually, and its guiding principles (e.g., 12-tone equal temperament) being fundamentally incorrect. Hence, few gained mastery over music-making. Then [insert here a list of scientific discoveries and technological inventions that, arguably, have not yet been made], all of which reduced the investment of time necessary to master music-making, thereby dramatically increasing the percentage of the human population that could afford to master music-making. Did students suddenly gain a "talent" for music-making?

Of course not.

In all of the above examples, the problem was a lack of technology, not of "talent." The traditional technology of music-making—staff notation, instruments, and theory—is the problem. As with all of the above examples, fixing the technology will fix the problem.

Until we fix the technology of music-making, it hardly seems fair to blame the victims—music students—for their "lack of talent." (Why beholdest thou the mote that is in thy brother's eye, but perceivest not the beam that is in thine own eye?
(http://www.godrules.net/para/luk/parallelluk6-41.htm)

To argue otherwise is to argue that either

1. all of the above examples are wrong, or that
2. "music is different."

I would welcome the opportunity to dismember either argument. ;-)

Respectfully,

Jim Plamondon
Unaffiliated Musical Heretic

Notational Load

I define notational load as the cognitive load imposed on a learner by the notation in which a concept is expressed, rather than by the concept itself.

As examples of notational load, consider:

• Roman numerals vs. Arabic numerals: Arithmetic operations such as long division are much easier to teach, learn, and apply using Arabic numerals than Roman numerals. Indeed, the Romans’ numeric notation is often given as the main reason why the Romans contributed almost nothing to mathematics per se, whereas the Arabs made great advances in mathematics.
• Chinese writing vs. Korean writing: The use of Chinese ideograms for Korean writing restricted literacy to Korean elites until the invention of the Korean-specific Hangul writing system, which made it possible for “a bright Korean-speaking student to become literate in one day, and a slow student in ten.” Smilarly, the Cherokee-specific writing system produced a similar jump in literacy rates within the Cherokee-speaking population of the early 1800's.
• The musical staff vs. neumes: Guido d’Arrezo’s invention of sight-singing, including the musical staff and solmization, is credited with reducing the training time of Church singers from ten years to “one, or at most two” – thus reducing the cost of music education by between 80% and 90% without sacrificing quality.

The development of other notational systems, such as calculus, the Periodic Table, and Feynman diagrams, have similarly contributed to significant increases in the efficiency of education.

Perhaps of even greater importance, the development of new notations has often led to new discoveries that were literally “inconceivable” using the previous notations, because notations invariably constrain, in addition to reflecting, patterns of thought. Examples include the Arabs’ use of their numerals in developing algebra and algorithms (the names of which reflect their Arabic roots), Mendeleev’s prediction of new elements based on “holes” in his Periodic Table, and Feynman’s use of his own diagrams in making major contributions to quantum mechanics.

Cognitive load theory recognizes three kinds of cognitive loads (from an educational perspective): intrinsic load (inherent to the subject being studied), extraneous load (irrelevant to the subject being studied), and germane load (which is extraneous to the current lesson in isolation, but which reduces of the overall load of the lesson-sequence as a whole).

Notational load seems to me to be an entirely extraneous load. In opposition to this position, one could argue that the mastery of a given domain’s traditional notation is required for communication with other professionals within that domain, and that this “communication conformity requirement” makes mastery of a domain’s traditional notation intrinsic. For example, without the ability to read traditional music notation, musicians cannot read the works of other composers.

Or…can they? Using modern music notation software programs, musicians can convert any given piece of written music to alternative, non-traditional notations such as guitar tab. Many of these programs support a “plug-in” architecture that enables the developers of alternative notations to retroactively upgrade the software to support new notations The potential availability of such notation-translation software, in any given domain, and the ease of distributing it over the Internet, significantly reduces the communication conformity requirement, supporting the claim that notational load is extraneous.

Changes in notation are not easy to effect in any domain, especially among tightly inter-connected professionals. However, a dramatic increase in learning efficiency may make it possible for non-professionals to rapidly gain knowledge previously restricted to a domain’s professionals. For example, more people in the USA now read Guitar Hero’s scrolling tablature than read traditional music notation, and are, as a result, learning more about music than they otherwise would.

Federal Funding of Arts Education Research: Round 3

Here's the follow-up email I sent earlier today to the US Department of Education, in response to their response of June 9th to my policy inquiry of May 19th.

Basically, I just ask the same questions over again, after pointing out how their initial response was, er, unresponsive. I also suggest that perhaps the new head of the DoEd's Institute for Education Science (IES) – whose appointment had not yet been confirmed, nor term begun, when I sent my first inquiry – would be the best person to answer the questions, since the research funding programs are administered by the IES.

I await the IES' response.

------------------------------

From: Jim Plamondon [mailto:jim@igetitmusic.com]
Sent: Saturday, June 13, 2009 3:17 PM
To: 'Harvey, Edith'; 'Easton, John'
Cc: 'Geddes, Claire'; 'Jonathan Levy'; 'Ruth Clark'; 'Tom Rudolph'; 'Wendy Free'; 'Michael McCaul'; 'Kay Bailey Hutchison'; 'John Cornyn'
Subject: RE: US Department of Education response to your inquiry

Dear Ms. Harvey,

I appreciate your response of 9th June (below) to my email of 19th May to Secretary Duncan, in which I inquired as to whether the Department of Education would continue the Bush-era policy of excluding arts education research from receiving funding from the DoEd’s research grant programs.

I would have appreciated your response even more if it had answered the questions that I had asked. ;-)

In your response, you stated that “The Institute of Education Sciences oversees the research initiatives you inquire about. Their website can be found at the following address: http://ies.ed.gov.”

I appreciate your bringing this information to my attention, although my initial email (appended below)
(a) mentioned the Institute of Education Sciences (IES) and its relevant research funding programs by name;
(a) included links to IES website’s relevant web pages; and
(b) was copied to the IES staff member (Dr. Jonathan Levy) who administers those research grant programs.

[Jim: yes, I really did number these items a, a, & b – rather than a, b, & c – which I noticed only after I had sent the email.]

In your response, you stated that “The Department of Education funds several arts education grant programs.”

The only such arts-related program mentioned on DoEd’s website as receiving DoEd grant funding is its Arts in Education outreach program, of which, according to this web page, you are the overseer. Thank you for helping this outreach program, which is described on that web page as seeking to “encourage the involvement of, and foster greater awareness of the need for, arts programs for persons with disabilities.” While this is indeed a worthy program, which I heartily support, it is an outreach program, and my initial inquiry was focused specifically on *research* funding, not outreach funding. If the DoEd funds any arts education *research* programs, I would welcome hearing about them.

With arts education poised to bear the brunt of crisis-driven state and local school budget cuts, research into new means of significantly increasing the educational efficiency of arts instruction – thus giving it more bang for the buck – could not be more timely. This is particularly true, given that the percentage of the US economy that is driven by arts-based creative industries is high and rising. Unfortunately, the IES’ website states clearly that research funding is available only for research into “reading, writing, mathematics, or science” – a list which clearly excludes research into arts education per se.

For your convenience, I will re-state the questions I asked in my initial email:
1. Is it the official policy of the IES, under the Obama Administration, to continue to exclude arts education research from funding under the IES’ Education Technology research initiative?
2. Is it the official policy of the IES, under the Obama Administration, to continue to exclude arts education research from funding under the IES’ Cognition and Student Learning research initiative?
3. If the answer to either or both of the above questions is “yes,” then what change in circumstances would need to be effected in order to make those answers “yes" [Jim: should have been "no" – another typo/error] and what chain of events would be required to bring about that ultimate change in circumstances?

Perhaps these questions could be best answered by the IES’ new Director, Dr. John Q. Easton (whose appointment was confirmed, and whose term began, after I sent my initial enquiry on May 19th). I have taken the liberty of copying Dr. Easton’s presumed email address, John.Easton@ed.gov, on the “to-line” of this message. If this is not his actual email address, I would appreciate your forwarding it to him accordingly.

Respectfully Yours,

Jim Plamondon
Austin, Texas

It's over

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!  :-)

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.

Transposing Tradition

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?

The Epiphany of Helen Keller

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

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

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

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

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

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

What is “order”?

Kurzweil defines and discusses order as follows:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Metrics of Revolution

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

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

Here's the official blurb for the panel session:

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

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

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

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

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

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

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

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

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

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

Hangul for Music

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

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

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

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

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

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

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

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

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

Interesting,yes? ;-)

Baumol's Curse

William Baumol, a noted cultural economist, described the "cost disease" of the service industries -- specifically including education and musical performance -- in 1966. He noted that although the cost of services fell over time, it fell at a much lower rate than the cost of manufactured goods. He attributed the difference to the rates of increase in labor productivity. Technological advancements steadily reduced the labor cost of manufactured goods (through automation), but the amount of labor required to teach a student to play the violin or to perform a violin concerto remained the same year after year, steadily increasing the relative cost of music education and live performance. This relentless increase in the service industries' relative labor costs has become known as "Baumol's Curse." (Baumol wrote a related article, "Children of Performing Arts, The Economic Dilemma," in 1996, of which excerpts can be found here.)

Note that the fundamental cause of the differential is labor productivity. Therefore, if you want to reduce the relative cost of music education, you need to reduce the number of hours necessary to attain a given level of competence -- including both the hours invested by the teacher (per student) and the hours invested by the student.

The ThumMusic System has the potential to increase the productivity of labor in music education, thereby lifting Baumol's Curse -- or at least, ameliorating its effects for a while.

Increasing labor productivity is the source of rising living standards, because part of the profits from an increase in labor efficiency can be captured by the laborer through increased wages. If music educators want to make more money, they need to find ways to increase their productivity -- through means such as the ThumMusic System.

Furthermore, those who are among the first to adopt a productivity-enhancing technology can gain a short-term competitive advantage vs. their more laggardly peers, although this advantage will tend to fade once use of the new technology spreads.

The bottom line: Thumtronics' productivity-enhancing innovations should raise living standards for their early adopters in the short term, and for everyone over the long term.

We're making the world a better place...one note at a time. ;-)

Faster = Cheaper = Easier

I think I've been explaining the benefits of the ThumMusic System to music educators in the wrong terms.

• When I emphasize cost reduction, some educators freak out, associating lower cost with lower quality.
• When I emphasize ease of learning, some educators freak out, associating easier with dumbing down.

Instead, I think I need to emphasize "increasing the rate of learning." Music educators don't seem to have a reflexively negative association with the concept of "increasing the rate of learning." By avoiding their negatively-charged reflexive responses, I give music educators the opportunity to form a reflective response.

Cost, ease, and speed are all just different facets of the same gem. If a given level of musical understanding and skill takes a long time to acquire, then it's hard and expensive (in hours invested). If the same level can be gained in less time – that is, more rapidly – then it is easier and less expensive. Increasing speed increases ease and lowers cost.

It's my understanding from research papers that I read on the Web a couple of years ago (I'll look for them again later) that the #1 reason why students quit their music lessons is because they don't feel that they are making sufficient progress to justify the hours invested. Rapid progress is exciting; slow progress is boring. By speeding up the rate at which students acquire a given level of musical knowledge and skill, music education becomes inherently more exciting, so its drop-out rate should decline, and a higher percentage of students should be successful.

This is exactly what I've been saying all along, but I've been saying it in economic terms or ease-of-use terms. These terms resonate very well with investors and technology folks, but have not proven to resonate well with music educators. I'll try casting the ideas in "rate of learning" terms, and see if that works any better.

This is just a choice-of-language issue. I should speak not to music educators in the language of economics any more than I should address a Chinese audience in Japanese. Bad associations, either way.

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.

Growing the Market

The goal of Thumtronics’ musical innovations is to grow the market for music-making products by reducing the amount of time necessary to achieve a self-sustaining level of musical knowledge and skill.

According to NAMM's tri-annual Gallup surveys, nearly everyone in the First World attempts to play a musical instrument, often more than once (as a child, then as an empty-nester, and again as a retiree). Despite this near-universal attempt to learn to make music, US census data shows that only 4-10% of the US population plays a musical instrument regularly (depending on how you define “regularly”). Yamaha’s 2005 annual report cites the optimistic 10% end of this range. If nearly everyone's already trying to make music, but only 4-10% are successful, then lots of aspiring music-makers are failing.

Why?

The #1 reason why students quit their music lessons is because they "get bored" – that is, they feel that, at their current rate of progress, it will take too long to attain a satisfactory level of knowledge and skill to make the investment of time worthwhile. This prevents these students from reaching a self-sustaining level of musical competence.

The 4-10% of people who do reach such a self-sustaining level of musical competence continue buying the musical instrument industry’s products – sheet music, accessories, upgraded instruments, music-related software, etc. Most of these products have higher margins than beginner's instruments do, so increasing the percentage of music-makers in the population should increase the industry's margins in addition to increasing its revenues.

Therefore, the key to growing the annual global sales & margins of the music products industry is to reduce the amount of time necessary to achieve a self-sustaining level of musical knowledge and skill.

To achieve this growth, three goals must be accomplished:
1. A new solution to the problems of music education must be found.
2. Beginners must have free and easy access to the new solution.
3. Beginners must become aware of, and choose, the new solution.

Goal #1: Find a New Solution
Goal #1 has been completed. The new solution is the ThumMusic System, which (a) abstracts the display of musical information to the level of music theory (intervals, rather than pitches), and (b) anchors this abstraction in the concrete geometry of a specific “isomorphic” note-pattern, in which a given interval has the “same shape” wherever it appears. This makes the fundamental concepts of music easier to visualize and grasp (literally), and has the potential to dramatically increase the rate at which students learn to understand and make music, according to many experts. The ThumMusic System acelerates learning not by "dumbing down" music, but by exposing the fundamental simplicity of music's structure in a geometrically consistent manner.

If you’re looking for an analogy, the ThumMusic System’s keyboard is to music what the Periodic Table of the Elements is to chemistry. The Periodic Table is a two-dimensional drawing that presents the complex structure of the atom in a simple and revealing manner; the ThumMusic keyboard is a two-dimensional drawing that presents the complex structure of musical sound in a simple and revealing manner. Just as the invention of the Periodic Table led to the discovery of new elements, predicted by “holes” in the Table, so has the Thummer’s keyboard led to the discovery of new musical properties, such as tuning invariance and Dynamic Tonality (which arguably solves the problem of temperament, which has been plaguing music for 25 centuries). The discovery of these properties is strong evidence of the validity of Thumtronics’ approach.

Goal #2: Free and Easy Access
To accomplish Goal #2, the ThumMusic System must be made freely available and easily accessible. This is accomplished by providing free (for beginners, at least), open-source, ThumMusic-based online music education courseware which uses the standard computer keyboard as a ThumMusic Keyboard. Thumtronics is working with the University of Texas at Austin to develop this courseware, and would welcome the participation of other universities, companies, philanthropies, and individuals.

But, can any new music notation succeed? Literally hundreds have been proposed over the centuries, and all have failed…except for guitar tab. Why did tab succeed? In part because it made a common interface (the guitar fret-board) easier to learn. The ThumMusic System will make music easier to learn, too, using the most common interface of all – the computer keyboard. The music products industry’s widespread support for the new universal music notation file format, Music XML, makes the success of ThumMusic notation much easier. So does the widespread use of music notation software, such as Finale! and Sibelius, since these programs can be retro-actively upgraded to support ThumMusic notation through the installation of a simple ThumMusic software plug-in, distributed free over the Internet. Using such a plug-in, all of the world’s music can be instantly available in ThumMusic notation, without making any deals with music software or publishing companies.

So, Goal #2 above – giving beginners easy, free access to the ThumMusic System – can be easily accomplished.

Goal #3: Awareness and Choice
To accomplish Goal #3, novices must hear about the new solution and be persuaded to learn music using it. NAMM’s Gallup surveys show that 70% of beginners choose their own instruments (usually based on wanting to imitate cool artists, apparently). So to get students to choose to play the Thummer, we need to get creative artists to use them first.

It’s well-known that creative artists choose to use those tools & instruments which allow them to do make new music in interesting ways. So we need a ThumMusic-compatible instrument that gives creative artists the opportunity to make music that is truly new, but which can succeed in the commercial mainstream, thereby inspiring non-musicians to learn to play music using that same instrument. That instrument is the Thummer, a new USB-MIDI music controller which can control the sound of any MIDI-compatible electronic synthesizer, and which uses the two-dimensional note-pattern of the ThumMusic System.

The Thummer provides simultaneous control over more independent variables (degrees of freedom) than any other musical interface, whether acoustic, electric, or electronic. The Thummer is the only polyphonic instrument with the expressive power to exploit music synthesis techniques such as waveguide synthesis, so its players will be able to reproduce the sounds of acoustic instruments with uncanny realism while playing accompaniment, too. Furthermore, the Thummer makes new musical effects – such as Dynamic Tonality, which is simply impossible with any other musical instrument – trivially easy to control. You just wiggle a joystick, and cool new musical effects happen, with no theoretical understanding required (although the music theory underlying these effects is deep and revolutionary). It is expected that truly creative artists will flock to the Thummer because its expressive power and Dynamic Tuning allows them to make music that is truly new, while still fitting comfortably within the mainstream.

This conclusion is supported by industry experts. "As a VP at BMG’s Windham Hill label," wrote Grace Newman, "I decided which bands to sponsor, promote, and endorse, from unknown bands to Grammy-winning artists. I looked for musicians that had something new, something different, that would stand out in the market... and so did every other label. The first musicians to master the Thummer will rivet the attention of the entire music industry. If you're looking for a way to break out of the pack, this is it."

The music of these creative artists – and the coolness of controlling sound through motion – is expected to inspire musical beginners to want to play the Thummer, too. These beginners will be able to start learning to play the Thummer online, for free, using the ThumMusic System and their computer keyboards, to which so many of today’s youth’s are glued anyway. Their progress should be rapid due to the ThumMusic System’s ease-of-learning. When they exhaust the expressive potential of the computer keyboard (which won’t take long), they can step up to a Thummer, the expressive potential of which is unlimited.

Here’s one small example of how the Thummer was designed to appeal to non-musical consumers in order to help grow the market. The Thummer uses control devices that non-musical consumers are already familiar with, such as a keyboard that is intentionally similar to the ubiquitous computer keyboard and the thumb-operated joysticks and electronic motions sensors that are now common in video game controllers. Millions of non-musical consumers have spent endless hours developing fine motors skills with these control devices. Using a Thummer, they can apply these existing skills to expressive music-making. Leveraging consumers’ existing motor skills presents them with a much lower barrier to entry than would requiring them to learn entirely new motor skills such as (say) manipulating a bow, developing an embouchure, picking a guitar, etc. Their success will tend to keep them in the MI market, stepping up to more advanced instruments, buying more sheet music, buying more accessories, taking more in-person lessons, etc. – potentially growing the MI market to double or triple its current size.

A “Pocket Thummer” could put four octaves of fully-integrated polyphonic musical power in your pocket for less than the price of a good harmonica. It could become “every beginner’s first instrument, and every musician’s second™.”

The Opportunity
Between the computer keyboard, the Thummer, and the ThumMusic System, a higher percentage of beginners could succeed at reading music fluently, composing music knowledgeably, and performing music expressively.

The Thummer has been designed to be enough better, in enough ways that consumers care about, to diffuse rapidly in the mainstream consumer market. The conservatism of traditional retail distribution can be overcome through direct sales over the Internet (see The Long Tail), which can aggregate thin global demand into very respectable volumes, allowing prices to fall and awareness to rise to levels necessary to support traditional retail distribution. Because the Thummer is so tiny, has so few moving parts, and is all-electronic, it is remarkably cheap to manufacture, store, ship, and stock – the ideal instrument for Web-based sales directly from manufacturer to consumer.

Because Thumtronics’ innovations’ many patent applications are sailing through the international patent process, it has the potential to erect high barriers to competition, ensuring that it and it alone captures the value of this future growth. This could make that company the industry’s revenue and profit leader within a decade. Market leaders are regularly toppled in this manner, as a result of paradigm shifts to solutions that are simpler, cheaper, and more powerful – solutions like Thumtronics’.

Growth, growth, growth. Thumtronics’ innovations are all about growing the market.

Conclusion
Shift happens. Industries and ideas that had seemed stable for centuries can shift with surprising speed, once a new approach comes along that is simple, cheap, and powerful. This can happen to the music products industry, too – and all indications are that Thumtronics has the innovations necessary to drive such a shift.