Dynamic Tonality

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."

Now we're talking about different issues.

First of all, concerts, recordings, etc are all considered musical end result. Unless you aren't aware you can "perform" electronic music just the same as you can any other type of music, this makes absolutely no difference in the argument.

Second, as for the claim, you'd have to reword it. First of all, I object to what you're calling "dynamic tonality" if you're going to use it as serious terminology. Terminology must be explained or it's worthless. The danger with what you're using to describe dynamic tonality is that you can reduce it to even simpler elements and render the term itself moot since it's easier to explain it without it. In other words, new terminology is only accepted if there are good reasons for it and here I don't see them.

The statement if it's to pass any real scrutiny should be something like:

"Using a special peripheral (the keyboard thing) together with a set of rules that manipulate pitch bend to conform to a mathematical model, it is possible to enable this manipulation to occur in real time (such as in a live performance.)"

It's the same thing you said, except without the dubious terminology or any claims of "newness." I took those out because

A: new terminology introduces problems (you need to explain why you're using it, rather than calling what things are by their traditional names)

B: "Newness" claims don't impress anyone, and for all we know someone may as well have done exactly what you're doing before but we aren't aware.

C: Someone may come off the idea that what you're doing HAS been done before plenty of times, which puts the "newness" argument in a hard spot as you have to start justifying it with historical research, facts, etc.

Something you have to understand is that nobody really cares for someone who starts branding things on their own, specially when they already have names or don't even need names at all.

All of this is taking into consideration you want to make an addition to the field of musicology and so on. If you are just taking all of this to be a private thing and don't care about everyone else, you can really do whatever you want but with the consequence that you're not going to be taken seriously.

Remember, all of this works a little like Occam's razor. The less new things you introduce that need justification/explaining/testing/etc the more solid your proposal is going to be. You can propose theories all you want, but you can never blind yourself to what is it that you are really proposing. In this case, I tried to boil down your claim to its most basic elements so that it is readily understood without the need to clarify any new terminology. If I can do this, it brings into question why use any new terminology at all if it can be done without?

I think it might help to go a bit further in explainig "polyphonic tuning bends' date=' tuning progressions, temperament modulations, and the like," so that we know why we might want them.

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Quite right. My initial posting was intended to give the minimum necessary interest to spark interest, starting with a demo song.

I would love to be able to post additional songs, each demonstrating a different aspect of Dynamic Tonality, but I don't have any such examples. Dynamic Tonality is brand spankin' new. "C To Shining C" is the only demo song we've got so far. That is why I posted my original link to this forum: to see if I could get additional demo songs from its members.

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.

Well, I understand that the septimal and undecimal intervals only really appear around the 31-ET area (and with surprising accuracy!) but what I really meant was the keyboard layout. Chords like C E G A# don't look very convenient to play. And it isn't very clear where all the notes are in the different tunings. I'm assuming the diagrams name notes the pythgorean way, so that we call everything by it's place on the circle of fifths. So where are all 31 notes of 31-ET? Do you sell extended keyboards with all the double sharps and flats? (The keyboard looks ideal for 19-ET though... or a 19 note subset of 31-ET which I've been exprimenting with lately.)

What really bothers me is that the system seems designed for tonal music. And by tonal I mean common practice harmony or popular music harmony. There's talk of temperaments and overtones and such, but I don't see much for the true microtonalist; however I would like to look at the system in closer detail before I judge.

Also, what you say about the augmented sixth's history is not really true. The augmented sixth only shows up as an "accident" here or there in the Renaissance and early Baroque. In the late Baroque they are more frequent (though not common); by then well-temperaments were the standard all around Europe except perhaps on older organs. The augmented sixth only became really common in the Romantic period, well after meantone was forgotten (though slightly before the rise of equal temperament).

squlech new looks on old ideas. squelch them

Chords like C E G A# don't look very convenient to play. And it isn't very clear where all the notes are in the different tunings. I'm assuming the diagrams name notes the pythgorean way, so that we call everything by it's place on the circle of fifths. So where are all 31 notes of 31-ET? Do you sell extended keyboards with all the double sharps and flats? (The keyboard looks ideal for 19-ET though... or a 19 note subset of 31-ET which I've been exprimenting with lately.)

What really bothers me is that the system seems designed for tonal music. And by tonal I mean common practice harmony or popular music harmony. There's talk of temperaments and overtones and such, but I don't see much for the true microtonalist; however I would like to look at the system in closer detail before I judge.

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. ;-)