JimPlamondon

Excellent points! Please let me addeess them one at a time. "THE TRUE MICROTONALIST" One of the co-inventors of Dynamic Tonality is Bill Sethares, whose microtonal work appears to be broadly respected. I don't know whether his approach is that of "the true microtonalist" or not. If by "true microtonality" you mean the exploration of Just Intonation involving prime partials above 5, we're not doing that, exactly. Instead, we define all intervals -- between notes in a tuning and between partials in a timbre -- as combinations of a very short list of intervals (e.g., the octave, tempered perfect fifth, and syntonic comma, for the syntonic temperament). By adjusting the timbre to match the tuning in real time, we deliver the same KIND of consonance that Just Intonation delivers with harmonic timbres, but we can deliver it across a number of different temperaments' tuning continua. The best way to understand what we're doing is to run the demo synth, play a single note, and listen to how its timbre changes as you move the tuning slider. Then play two notes a perfect fifth apart, and move the slider similarly. In the syntonic temperament, the root's third partial is moved such that it always aligns precisely with (an octave of) the fundamental of the note that is a tempered perfect fifth higher than the root, even as the width of the tempered perfect fifth changes as driven by the tuning slider. Likewise, the root's fifth partial will always align precisely with (an octave of) the fundamental of the note that is a tempered major third higher than the root. Both the partials and the notes are shifted in real time to reflect the width of the interval controlled by the tuning slider (in the syntonic temperament, it's the tempered perfect fifth). The theoretical details are discussed in Invariant Fingerings Across a Tuning Continuum, Computer Music Journal, Winter 2007, Vol. 31, No. 4, Pages 15-32. So, what we're offering isn't traditional microtonality. Whether it's true microtonality is not for me to say. TONAL MUSIC Yes, Dynamic Tonality is heavily biased towards tonal music, just as you suggest. On the one hand this is limiting, but on the other hand it is liberating to be able to conveniently control simultaneous, systematic changes to tuning and timbre in real time (I hope that this phrasing works for SSC!) across the tuning continua of temperaments such as the syntonic. It's a trade-off. "WHERE ARE ALL THE NOTES OF 31-TET?" Having only 19 buttons per octave is an engineering trade-off. It's the largest number of notes per octave that one's fingers can span (ie., reach across without moving the wrist). The use of thumb-operated expressive controls and internal motions sensors requires this restriction. Only by limiting the keyboard to a maximum of 19 buttons per octave can we keep the player's hands fixed in position relative to the button-fields, thereby enabling enable the performer to manipulate thumb-operated joysticks and internal motion sensors while also playing notes with the fingers of both hands. However, this limitation may not be as limiting as it first appears. Above is an isomorphic button-field in which each button is labeled with a traditional pitch name. Below is the same button-field (of two octaves rather than three), in which the buttons are labelled with tonic solfa interval names instead of pitch names. Think of a guitar, and playing a song with a given set of gestures. Snap on a capo, and those same gestures will produce the same song, but in a different key. Move the capo, and those same gestures produce the same song in yet a different key. Generally speaking, the capo enables you to play a given song in any key with the same set of gestures, just by moving the capo. The tonic-solfa-labeled button-field works the same way. It presumes that a simple UI gesture can "move the capo" -- i.e., transpose the keyboard to a different key -- so that the same set of gestures are used to play a given song in any key of any tuning. This keyboard-transposing gesture can be performed as often as is necessary within a given piece, thereby keeping the current tonic near the center of the keyboard. It appears to be true -- althrough we have not yet analyzed enough music to be sure -- that no matter how finely one divides the octave, 19 intervals per octave are sufficient for tonal music in the syntonic temperament. For example, when writing tonal music in (say) 31-TET, no more than 19 of the possible 31 intervals are used in any given key. In 605-TET, no more than 19 of the possible 605 intervals are used in any given key. Each key of an N-TET tuning uses a different set of (at most) 19 intervals drawn from its N possible intervals. If a button-field is pitch-based, then all N notes must be represented by buttons. However, if the button-field is transposed electronically to keep the current tonic on the button-field's white buttons, then the button field only needs 19 buttons, at most. However, the above approach is NOT limited to diatonic music. Consider this. For purely pentatonic music, only five buttons per octave would ever be needed (Do Re Mi So La) -- the same five buttons for every key and tuning. For purely diatonic music, no more than seven buttons per octave would be needed (Do Re Mi Fa So La Ti) -- the same seven buttons for every key and tuning. For purely chromatic music, no more than 13 buttons per octave would be needed (Do Di Re Me Mi Fa Fi So Si Le La Te Ti, with Si and Le being enharmonic in 12-TET) -- the same 13 buttons for every key and tuning. With 19 buttons per octave, scales of much higher complexity than the diatonic can be supported, with the same fingering in every key and tuning. So...where are the "other notes" of 31-TET? They aren't there, but you don't really need 'em anyway, if you use an "electronic capo." "CHORDS LIKE C E G A# DON'T LOOK VERY CONVENIENT TO PLAY." Please note that you can play any perfect fourth or perfect fifth interval with a single fingertip, so C & G would be played with one's index finger, E with one's middle finger, and A# with one's ring finger or pinkie. The ability to play P4's and P5's with a single fingertip, or to play a stack of P5's by laying a single finger along a P5 row, simplifies the playing of many otherwise-complex chords (e.g., the extended diatonic tertian chords). ATTACHMENTS I was going to add some discussion of the complexity of playing a given chord being related to distance among its notes in tonal pitch-space -- hence the other attachments -- but this posting is too long already. ;-)

I appreciate your taking the time to respond to this. I have two concerns about this line of reasoning. First, it is focused solely on recordings; it makes no allowance for live performance as a "musical result." I do not see why live performance should be excluded from the definition of "musical result." The rise of file sharing has decreased the importance of recordings as a source of income for most musicians, while the importance of live performance, especially touring, is increasing. Second, even if it were true that the Dynamic Tonality could be simulated programmaticaly using CSound or whatever to painstakingly adjust the tuning of each note's fundamental and to re-arrange each note's partials to align with the notes of the current tuning, this programmatic approach would be impractical for use in live performance. The use of an isomorphic keyboard and Dynamic Tonality enable *real-time* adjustments to tuning and timbre. Arguably, any conceivable musical effect is programmable using CSound or an equivalent -- but this simulation may require a combinatorial explosion of parameters. The combination of an isomorphic keyboard and a Dynamic Tonality-enabled synth reduces the parameters to just one -- the width of the tempered perfect fifth -- and enables real-time control over both this variable and note-selection in a tuning-independent manner. This dramatic reduction in parameters makes it possible for musician, performing live, to control in real time what would otherwise require far too many fingers & brain cells. Would accept as valid the following claim? "The combination of Dynamic Tonality and an isomorphic keyboard enables, for the first time, real-time control of musical effects such as polyphonic tuning bends, tuning progressions, and temperament modulations, thereby making these effects available to live performers."

I apologize for being thick about this, but you're coming at this issue from a sufficiently different angle that I'm having trouble following your argument. let me paraphrase what I'm hearing back to you, to see if I'm understanding it. First, your focus is "the musiical result," by which I gather you mean a MP3, WAV, or some other electronic sound file. Second, you're suggesting that any such "musical result" that is generated using the means provided by Dynamic Tonality could also be produced by other means. For example, one could use a musical programming environment such as CSound to independently control (a) the pitch of each individual note and (b) the placement of each note's individual partials, such that the "musical result" of the CSound approach would be aurally indistinguishable from that produced by Dynamic Tonality. Third, you're asserting that if the "musical result" produced by Dynamic Tonality can be attained by other means, for example by using CSound as above, then it is inaccurate and inappropriate to claim that Dynamic Tonality enables any "new musical effects," because those effects were and are attainable by pre-existing means (albeit perhaps only with considerable difficulty). Is that an accurate paraphrasing of your argument? I apologize again for getting testy about this earlier. I appreciate your taking the time to walk me through your line of reasoning. Thanks! :-) --- Jim

In my post to which you're responding, there was some discussion of the dynamic alignment of a note's partials with the current tuning's pitches. Is this dynamic change in timbre irrelevant to your argument regarding the equivalence of pitch bends and tuning bends?

I apologize for making this remark. It was incorrect, unwarranted, and ungentlemanly. You derserve better. I am sorry. I won't do it again.

I'm clearly failing to explain this well, for which I hope you'll forgive me. Let's look at what's happening to just one note: the tonic. First, make sure that the demo synth's "tonality diamond" control is set to "Max Consonance." Then, play the tonic note and bend the tuning up by (say) 25 cents. If you were performing a pitch bend, that would bend the pitch of the tonic up by 25 cents, right? But since this is a TUNING bend, and we're playing the tonic note, it's pitch doesn't change at all. However, the gap between the note's 2nd and 3rd partials widens by 25 cents; the gap between its 4th and 5th partials increases by 100 cents; and so on for other partials (according to a formula that is beyond the scope of this posting). These changes to the note's timbre ensure that its partials align with the notes of the altered tuning. So, a tuning bend is not a pitch bend. A pitch bend changes the pitches of the fundamentals of all notes by a given interval, while leaving their timbres unchanged. A tuning bend systematically alters the pitches of the fundamentals of all notes by different intervals, and adjusts their timbres accordingly. We can say "it's just a old pitch bend" and "no, it's a new effect" to each other in this forum all day long, but a) if you try the demo synth, you'll hear the aural proof b) if you read the peer-reviewed scientific papers referenced at the end of the Wikipedia article on Dynamic Tonality, you'll find the mathematical proof. --- Jim

Excellent point! :-) The 7th partial doesn't fit the syntonic temperament very well, except in a narrow band of tunings around P5=696 cents (1/4-comma meantone & 31-TET). There, it aligns quite nicely with the augmented sixth (A# in C Major). This is perhaps why the augmented sixth was used extensively in the centuries-long period during which 1/4-comma meantone was the dominant keyboard tuning (German sixths and all that). The narrowness of the band of septimal tunings is due to the augmented sixth being eight notes away from the tonic along a line of perfect fifths. For every cent wider one makes the perfect fifth, the augmented sixth increases in width by 8 cents. It's really flyin'. Widen the P5 by just 12.5 cents, and you've changed the width of the augmented sixth by an entire semi-tone. Therefore, the valid range of septimal tunings is inevitably narrow. The same reasons make the syntonic temperament's unidecimally-valid tuning range even narrower. Does that answer your question satisfactorily? However, let me emphasize that the best way to explore this is experientially, by messing around with Dynamic Tonality on your computer keyboard, using the previously-indicated free synth. Just play with it, and a lot of these theoretical points will be illuminated in "aha!" moments.

[quote name=SSC;254691 Why is this in this forum at all? This sounds all more like advertising... Speaking of which' date=' doesn't wikipedia have guidelines against promoting original material/research/bla? Or, for that matter, using it to promote your personal crap? This sure sounds like it...[/quote] The foundations of Dynamic Tonality have been publised in peer-reviewed scientific journals (see the references at the end of Wikipedia's Dynamic Tonality article), so it is neither personal crap nor original research. My original posting included a reference to a web site at which a free synthesizer implementing Dynamic Tonality could be downloaded, for use with one's computer keyboard. If I were selling the synth, then my posting here would be advertising, but I'm not. I understand that the vast majority of people are ignorant about even their presumed areas of speciality, and resistant to change under the best of circumstances. However, don't artists bear a singular responsibility to question the status quo, to look deeper, and to find the common links among us all? If you can cast aside the blinkers of cynicism for even a moment, you may find what you're looking for in Dynamic Tonality.

A pitch bend changes the tuning of all affected notes by the same interval. A tuning bend does something entirely different: it changes the tuning of every note differently, depending on its distance from the tonic along a line of perfect fifths. Consider playing a C major triad with C as the tonic, in 12-tone equal temperament. Bending the tuning up by (say) 25 cents - leaves the pitch of C constant (because it's the tonic), - raises the pitch of G by 25 cents (because G is one perfect fifth higher than C along a line of perfect fifths), and - raises the pitch of E by 100 cents (because E is four perfect fifths higher than C along a line of perfect fifths). If one added an F to the chord above, it would be lowered by 25 cents, because it is one perfect fifth lower than the tonic along a line of perfect fifths. So, in a polyphonic (many note) tuning bend, every note is shifting in pitch by a different interval, determined by its dstance from the tonic along a line of perfect fifths. Furthermore, with Dynamic Tonality, the structure of the underlying timbre is being changed in real time to align its partials with the tuning's notes. In the above example, the timbre's third partial is raised by 25 cents to align with G, and the timbre's fifth partial is raised by 100 cents to align with E. This delivers consonance even as the tuning changes; without such shifting of partials. Fortunately, one doesn't have to understand the math to USE Dynamic Tonality, becuase the theory is encapsulated in the isomorphic keyboard's note-pattern. Just wiggle a joystick of shift a slider, and the tuning & timbre changes accordingly; your fingering patterns stay the same in every tuning.

Regarding CMaj vs DMaj -- good point. :-) The tuning moves smoothly between 19-tet (P5=695) and 5-tet (P5=720) along the syntonic tuning continuum (see attachment). The only tone that's stable when the tuning changes is the tonic; all other pitches change. So, for example, A4 is never equal to 440Hz (standard concert tuning) except as the tuning passes momentarily through 12-tet (P5=700) (unless it's the tonic). When the notes' pitches are changing like this, the traditional pitch-based note-names aren't terribly meaningful. I think the composer simply stopped thinking in terms of pitch names, but found the name "C to Shining C" to be catchy, and to imply pitch-movement.

If I understand the structure and purpose of this forum correctly, then its readers are "young composers of avant garde and electronic music," in whch the avant-garde seek to "push the boundaries of what is accepted as the norm or the status quo, primarily in the cultural realm." To push a boundary -- that is, to be avant-garde -- one must move out of one's comfort zone, stretch oneself, do something one has never done before, something one might even fail at. Truly great artists moved beyond the comfort zones of entire societies, doing things that NO ONE had ever done before -- thereby blazing a trail for the merely imitative to follow. In choosing a boundary to push, an artist must make a trade-off between opportunity and risk. How can one weight the opportunity/risk trade-off presented by Dynamic Tonality? The opportunity is vast. Dynamic Tonality provides the opportunity for entirely new structural effects in music, such as polyphonic tuning bends, tuning progressions, temperament modulations, and the like. The closest analogy I can think of is the discovery of the blues scale and 12-bar form in the previous century -- a novel structure that opened a vast new creative frontier. Yet the risk is low. Although Dynamic Tonality is entirely new, its effects merely extend the time-honored framework of tonality (as did the blues, arguably). One's compositions can explore and exploit the as-yet unkown emotional affect of Dynamic Tonality's new structural resources (thereby meeting academia's need for novelty) while still delivering tonal familiarity (thereby meeting commercial music's need for familiarity). You can have your cake and eat it, too. This combination of high opportunity and low risk is rare in art. Picasso, Pollock, Armstrong, Schoenberg, Coltrane, etc. took much larger risks to open asrtistic frontiers that were (arguably) smaller. (This assertion could start a huge flame war; let's please skip it by agreeing that "only time will tell.") They could have simply continued to do what everyone else did, with tiny variations; instead, they chose to challenge themselves, push boundaries, and open new frontiers. As young composers, you have the least to lose, and the most to gain, by exploring and exploiting the novel musical frontiers opened up by Dynamic Tonality. Every grant making board, music critic, review committee, tenure committee, and talent scout is looking for something NEW...but not too new. Something that's challenging, but not too challenging. Something that pushes one boundary, while respecting others. Something like Dynamic Tonality. I hope that you will choose to explore it for yourselves. Thanks! :-) Jim Plamondon Austin, Texas

Nah...for my writing to sound like TimeCube I'd have to decry all humans as "evil bastards." While that might be cathartic, I can't see how it would be constructive. ;-) More generally, to be a crank (as perhaps jujimufu is suggesting), I would have to "contradict rigorously proven mathematical theorems or to deny extremely well established physical theories, such as the special theory of relativity or a round earth." However, (a) I am not denying the well-established relationship between the Harmonic Series and Just Intonation; rather, I'm abstracting that relationship and generalizing it to apply to a wider range of tunings and timbres. This is the normal means by which science provides art with new tools. (b) Mathematical proofs of the foundations of Dynamic Tonality have been published in peer-reviewed scientific journals (see references here). Regarding Ferkungamabooboo's suggestion that "No one can accurately hear some of the shifts in freq: 380 cents to 386.3." The shift in the *width* (not frequency) of the M3 interval in "C to Shining C" is not from 380 cents to 386.3 cents as suggested by Ferkungamabooboo, but rather from 380 cents to 480 cents: a full semi-tone. Most people can distinguish intervals that are this far apart. I apologize to Ferkungamabooboo for the lack of clarity in that section of Wikipedia's description of Dynamic Tonality, and would welcome suggestions on how to clarify its wording to make such misunderstandings less common.

Gentlepersons, Please accept this invitation to explore the musical posibilities of Dynamic Tonality. First, listen carefully to C To Shining C by Bill Sethares. The novel effect you're hearing is Dynamic Tonality. Bill composed and created this piece using his computer keyboard and a Max/MSP-based synth, TransFormSynth, for which the installation instructions can be found at the bottom of this page. Note that the effects of Dynamic Tonality can only be controlled by an isomorphic keyboard, which provides the same fingering in every key and tuning across the syntonic tuning continuum. The piano-style keyboard can't do this. But don't worry! TransFormSynth (above) can turn your computer's keyboard into an isomorphic keyboard. Your computer is all you need. I suspect that the more "traditionally tonal" a piece is, the more its use of Dynamic Tonality will stand out. You can have the popular appeal of tonality, and advance the state of the art, too. What can YOU do with Dynamic Tonality? I hope that this posting piques your interest. I look forward to hearing your comments -- and your compositions! Thanks! :-) Jim Plamondon Austin, Texas