Dynamic Tonality Demo Video

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. ;-)

An Exceptionally Simple Theory of Music

I’ve watched with interest the reaction to the publication of Garret Lisi’s paper, An Exceptionally Simple Theory of Everything. He is being revered and reviled simultaneously.

When something happens that people think might be important, but they don’t really understand it, they tend to look around for an expert. If the experts disagree, then those who don’t understand the details are left with an ink-blot test, from which they divine meaning by faith alone. On the one hand, the decision to revere or revile tends to be based largely on internal factors – one’s faith in “progress,” for example. On the other hand, trivial and extraneous details of the ink-blot can become disproportionately influential – such as one’s feelings about surfing.

My collaborators and I are pursuing a similarly-simple Grand Unified Music Theory (which underlies the ThumMusic System). I suppose that we can expect it to receive a similarly split reaction…assuming anyone even notices. We have the advantage that our work’s foundations have been accepted for publication in peer-reviewed scientific journals (Computer Music Journal, Winter 2007, and Journal of Mathematics and Music, Spring 2008), which Lisi’s paper was not.

Oh, well. There’s no such thing as bad publicity, right?

sus4

Here’s an interesting effect in Dynamic Tuning.

Using the Max/MSP implementation of Dynamic Tuning found here, first

• Slide the slider on the lower left of the screen rightward to “fully tempered”
• Set the tuning slider to 696.6 cents (1/4-comma meantone or 31-tet)
• Play a major triad on your QWERTY keyboard (e.g., the buttons labeled H-K-U)
• While the triad is sounding, slide the tuning slider up to its maximum (720 cents, 5-tet)
• Hold the slider there a moment, and then slide it back to where it started (696.6 cents)

What did you hear?

What I hear is:

• A nice, pure-sounding major triad, then
• A sus4, then
• A major triad again.

How’d that happen?

Well, when you push the slider up from 696.6 cents to 720 cents, you’re widening the tempered perfect fifth accordingly. The pitch of the major third (and the placement of the fifth harmonic of the tempered timbre) is higher than that of the root by four tempered perfect fifths minus two octaves. That means that the major third is widening from

• ((4 * 696.6) - (2 * 1200) = (2786.4 - 2400) =) 386.4 cents, which is a nearly-just major third, to
• ((4 * 720.0) - (2 * 1200) = (2880.0 - 2400) =) 480.0 cents, which is 18 cents flat from a just perfect fourth.

Just by wiggling the tuning slider, you can go from a very restful major triad to a tense sus4 – with the sharpened P5 adding to the tension – and back again.

Cool! :-)

It Works!!!!

Two new things on Thumtronics’ website:
1. Online Thummer: an online implementation of the Thummer’s note-layout, driven by your computer’s keyboard (Windows only).
2. Dynamic Tuning, Mark I: A Max/MSP implementation of Dynamic Tuning & Timbres (DT&T), also driven by your computer keyboard.

[Added 23rd June: The latest version of the main Max/MSF file, which is undergoing rapid evolution, can be found here. Use it instead of the .MSF file that's in the above .zip file.]

A simple test of Dynamic Tuning is as follows:
- Set the width of the tempered perfect fifth to 700 cents (12-tet).
- Press the M & W keys at the same time. These two notes are the major third and diminished fourth of QWERTY’s B key, respectively (the actual pitches don’t matter). In 12-tet, they are the same pitch.
- While the notes are sounding, slide the tuning slider up to 702 cents.

In 12-tet, the pitches sounded by pressing the QWERTY keyboard’s M & W are the same – but in any other tuning, they aren’t. When the tuning is at 701.7 cents (call it 702), the two notes are discernibly different. In the schismatic temperament, you’d play “major” triads with the diminished fourth instead of the major third, because with a harmonic timbre, at that tuning the diminished fourth’s fundamental lines up perfectly with the root’s fifth partial (ignoring an octave or two), maximizing consonance.

But this app’s timbres aren’t harmonic. The timbre’s third partial lines up exactly with the tempered perfect fifth, whatever width you set the perfect fifth to be (a couple of octaves aside) – thereby eliminating the Pythagorean comma from both the tuning and the timbre. Likewise, the fifth partial has been adjusted to align with the major third all across the tuning continuum – so the syntonic comma has been eliminated, too, from both tuning and timbre.

What’s going on here? The background is discussed here, which is a draft of an article recently accepted for publication by MIT’s Computer Music Journal, and here.

Another interesting test is to play the chord progression from Pachelbel's Canon while changing the tuning dynamically (rather like Herman Miller’s Warped Canon, but dynamic, and timbre-adjusted). I found that it’s easiest to work out the note-pattern on the Online Thummer, then, having understood/memorized it, play it on the Dynamic Tuning test-app.

The additive synthesis algorithm used in this bare-bones synth is just a toy. We expect, in future, to be able to adjust the partials of any synth's output in real time, so that electronic musicians will have complete freedom of timbre within Dynamic Tuning.

This is all pretty bare-bones, of course, but it shows that Dynamic Tuning actually WORKS.

Whee! :-)

Dynamic Tuning, Mark I

Bill Sethares has recently implemented a demonstration of Dynamic Tuning & Timbres, running on top of Max/MSP. You can try it for yourself!

To run it, you need to already have the Max/MSP Runtime installed.

Then, right-click and "Save as..." this WickiSynth.zip file, unzipping them with WinZip.

Run Max/MSP, and open the wickisyn~.MXF file. There's a volume button to the lower-left; click it to activate your sound. Your QWERTY keyboard is now a QWERTY Thummer, with the Wicki note-layout. On the right-hand side, you'll see a slider controlling the width of the tempered perfect fifth. With your mouse, click and drag it up to increase the P5's width; drag it down to decrease the P5's width.

While playing (say) a major triad, drag the slider up and down. The pitches of the triad's notes will be adjusted automatically. So will the pitches of the partials that make up the tones sounded at those pitches.

The QWERTY keyboard is not an expressive instrument, nor are the timbres produced by with WickiSynth impressive. We don't expect that anyone is going to use this implementation in public (although, if you do, please post a video to YouTube and let me know!)

But...when you mess with this stuff, you are changing tuning and timbre dynamically, baby, using the Thummer's tuning-invariant note-pattern. That has never been done before.

Research Projects

I am occasionally asked if Thumtronics can propose research projects associated with its innovations. Please find a list below. I regret that I do not have the time to supervise such projects. If you undertake any research project related to Thumtronics' innovations, I would be happy to learn know how it turns out! :-)

Ease of Learning: Test the efficiency with which human subjects learn musical concepts using the piano and traditional notation vs. the ThumMusic PLUS System, and relate the human subjects’ differences in learning outcomes to differences in the systems’ respective Kolmogorov complexity.

Ergonomic Risk: What criteria are relevant to the ergonomic risk posed by playing musical instruments, what metrics are appropriate to these criteria, and how can all musical instruments’ ergonomic risk be normalized to a single common metric, such that the ergonomic risk of a given novel instrument can be benchmarked against the ergonomic risk posed by various traditional instruments?

Expressive Potential: What culture-independent criteria are relevant to the expressive potential of musical instruments, what metrics are appropriate to these criteria, and how can all musical instruments’ expressive potential be normalized to a single common metric, such that the expressive potential of a given novel instrument can be benchmarked against the expressive potential of traditional instruments?

ThumLine: Implement a ThumLine plug-in for Finale! or Sibelius. Add ThumLine support to Calliope, Lime, LilyPad, or any other open-source music notation editor.

ThumMusic Pedagogy: How should ThumMusic-based music pedagogy be different from traditional music pedagogy, to leverage the strengths of the ThumMusic System? What concepts should be introduced sooner, later, or differently, relative to the traditional system?

ThumMusic-based Music Education Materials: What materials should be developed to make the ThumMusic System’s pedagogical approach simple to deploy, use, and assess? How can modern digital media be leveraged to increase the cost efficiency of ThumMusic-based music education – that is, to maximize the positive learning outcomes while minimizing the cost of deployment, use, and assessment? How can these materials best support traditional approaches to music education?

Pressure-Sensitive Keyboard: Design a pressure-sensitive 57-button Thummer keyboard that uses a button-pressure sensing technology similar to that used by the Sony PlayStation 3 SixAxis game controller.

Motion Sensing: Design a motion-sensing module that uses a motion-sensing technology similar to that used by the Sony PlayStation 3 SixAxis game controller.

QWERTY Thummer: Implement the ThumMusic note-pattern on a standard alphanumeric (QWERTY) computer keyboard such that it emits standard MIDI and/or OSC, thereby allowing electronic musicians to use their laptop keyboards to control musical data using the ThumMusic note-pattern.

Web Thummer: Implement a Web-based applet that implements the ThumMusic note-pattern on a standard alphanumeric (QWERTY) computer keyboard such that the Web page responds to keyboard button-presses by (a) sounding the pressed note, and (b) indicating, on an interactive web page, the buttons/notes currently being pressed/sounded.

ThumTone Synth: Implement an electronic music synthesizer that implements some or all features of the X_System, e.g., (a) Dynamic Tuning, (b) tuning-aligned timbres, and (c) primeness, richness, dissonance, etc..

Dynamic Tuning: Compose music that creates and releases tension using the unique musical effects of Dynamic Tuning (tuning bends, tuning modulations, temperament modulations, new chord progressions, etc.). Induce or deduce the rules governing the effective use of these effects

Commas: Commas are ratios of small whole numbers that arise from the structure of the Harmonic Series to plague traditional music theory. Examples include the Pythagorean comma, the syntonic comma, and the schisma. Tunings such as 12-tone equal temperament "temper out" commas...but they're still in the timbre of harmonic sounds. Tempering the partials to match the tuning could eliminate the commas from the timbre, too. This suggests that pesky commas can be truly eliminated from the music theory of the X_System. Prove that this is or is not so, and if so, demonstrate the musical consequences of the result.

Ethnomusicology: Examine the tunings, timbres, and musical structures associated with the indigenous gamelan, renat, and balafon, to see if they can or cannot be explained by the X_System's pseudo-harmonic approach in a manner identical to the approach's treatment of the Western 12-tet. What do these results say about the X_System's generality?

Music Perception: For the human ear/brain/mind to accept a continuum of pseudo-harmonic tunings and timbres as being tonal, it would need to categorize pitch relationships in a tuning invariant manner. There is a hint of evidence that this is exactly what happens. Perform experiments to explore the perception of tonal structures when using a wide range of pseudo-harmonic tunings, timbres, and temperaments. What does these results say about the tuning invariance of pitch perception?

Musical Paradoxes and Illusions: Explore, using pseudo-harmonic timbres/tunings, a variety of musical paradoxes that are known to exist in harmonic/just music, such as the Missing Fundamental, Combination Tones, Shepard Tones, and Diana Deutsch's paradoxes and illusions. In what ways (if at all) does the perception of these paradoxes and illusions differ (a) among different pseudo-harmonic timbres/tunings, and (b) between harmonic/just timbres and pseudo-harmonic timbres/tunings?

How?

How will Thumtronics make its innovations successful?

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

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

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

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

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

But first we have to make the Thummer successful.

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

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

When?

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

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

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

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

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

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

What?

Thumtronics’ musical innovations, taken together, abstract to a higher level both (a) the structure of musical sounds, and (b) the higher-level forms of music arising from that structure. This higher level of abstraction is both simpler and more powerful that that used in the Western musical tradition.

Thumtronics’ first breakthrough is the combination of a concertina-like keyboard with tiny thumb-operated joysticks (like on a video game controller) and motion sensors (like on Nintendo’s Wii game controller), thereby delivering the most expressive polyphonic musical instrument ever: the Thummer. This expressive power is needed to control the many new expressive opportunities enabled by Thumtronics’ other breakthroughs.

Thumtronics’ second breakthrough is the combination of the Wicki note-layout, a chromatic staff, a tonnetz, tonic solfa, and the computer keyboard, thereby producing an easily-deployable system for the display and control of musical information – the ThumMusic PLUS System – which makes music easier to teach, learn, and play.

Thumtronics’ third breakthrough is its recognition that generalized note-layouts (such as the Wicki) have the same fingering not just in every key, but also in every tuning of a given temperament. That enables Dynamic Tuning, in which the performer can change the Thummer’s tuning in a smooth continuum while retaining the same fingering. Dynamic Tuning enables tuning bends, temperament modulations, and new chord progressions, all within the time-honored framework of tonality.

Thumtronics’ fourth breakthrough is Dynamically Tempered Timbres (X_Spectra & X_Timbres), in which the partials of a given timbre are adjusted, in real time, to align with the notes of the current (dynamic) tuning, to which they are related. This can deliver perfect consonance all across a given temperament’s tuning continuum, with additional real-time effects such as dynamic dissonance, primeness, conicality, and richness. These novel musical effects can make dynamic tunings sound pleasing and familiar, while giving composers an entirely new means of creating “tension and release.”

In Thumtronics’ approach, what matters are the relationships among intervals – that is, temperaments – but not pitches. A musical composition can be specified completely, yet leave the choice of key (i.e., tonic pitch) to the needs of the performing group (to reflect its current tessitura). Computer scientists will recognize this as an example of dynamic binding.

Taken together, Thumtronics' innovations hoist the description and control of musical information to a higher level of abstraction which is both simpler and more powerful than the traditional view.

These innovations also generalize music theory beyond the Harmonic Series, to embrace a wider set of timbre-structures. This widening consequently broadens music theory beyond Just Intonation to a wider set of tunings which are related to those timbres (or vice versa -- same thing).