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. ;-)

Temperament, by Stuart Isacoff

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Dynamic Tonality References

An online version of the Winter 2007 CMJ article introducing tuning invariance can be found on the CMJ’s website, here (the CMJ’s “one free article per issue:”)
http://www.mitpressjournals.org/doi/pdf/10.1162/comj.2007.31.4.15

A second article, comparing & contrasting various tuning invariant keyboard note-layouts using various metrics, was accepted by the Journal of Mathematics and Music (for publication in Spring 2008). The version submitted for peer review, which does not include changes made to reflect the excellent feedback provided by its reviewers, can be found here:
http://www.thummer.com/ThumTone/Tuning_Invariant_Layouts_Last_Draft.pdf

Both of these papers refine, and expand on, ideas first documented in this omnibus paper:
http://www.thummer.com/ThumTone/X_System.pdf

The name “X_System” was just a placeholder until we could think of something better. The new name is “Dynamic Tonality,” which embraces Dynamic Tuning, Dynamic Timbres, and Dynamic [Whatever].

The musical potential of Dynamic Tonality is summarized here:
http://www.thummer.com/blog/2007/12/going-somewhere.html

A (crude, buggy) Max/MSP-based synth demonstrating Dynamic Tonality, using the computer keyboard as its musical input device, can be found here:
http://www.thummer.com/blog/2007/06/dynamic-tuning-mark-i.html