How to use each key (in case anyone needs help!)

The actual interesting bit of that article is the calculations and so on, but the opinions on pleasantness are entirely subjective. Hell, I find "dissonances" entirely subjective and to someone like Schoenberg he dealt away with both words and settled for "sonance" since "dissonance" and "consonance" are within a hierarchy based on a tone organization system (major/minor tonality.)

I fail to see how that paper has anything to do with aesthetics and/or cognitive musicology besides the vague mention that they think consonants are pleasant and the whole bullshit with "tension" that nobody really defines seriously.

You are mixing up the term consonance with goodness. I'm not saying consonance is always good. What I am saying is that there exist the most "resolved" or "resting" intervals, and the width of these intervals is defined by the partials of the timbre of the sound one uses to create them.

Woah hold on there tiger. You first talk about objective pleasantness, but you don't see how that's a slippery slope by definition? You really should pay more attention to what you say. You say there's no formula to create "good music," but you already describe how to create it the sentence before that.

No. I described how one might or could do it, to prove my point about the lack of a formula for good music, not to tell people that those examples are the only way. Stop twisting my words to create arguments instead of addressing my real points relevant to our discussion.

I'll take that as a joke on your behalf, since if you're arguing something like this and you're not aware of such basic music knowledge, I'd feel very disappointed. Moving on.

Ok, there's tonaly, modality, and atonality. Dynamic tonality is equally relevant to modality as it is to tonality. So still, atonality is the only thing not applicable. And, like I said before, if it's your thing that's fine, just don't bother with these new tools. A lot of music, most of it actually, is tonal or modal.

... Not really. There's plenty of people writing microtonal works out there, and certainly you're not FORCED to do anything. You just have to work harder to get your stuff done, that's it. It's not any different now either with or without the instruments and the synthesizers.

Ok, when I said "forced", it was obviously a hyperbole, but we are very constricted by convention and the average musical environment.

And you make my point when you say that it's "just harder". Just harder? Harder is not "just." It should be "this music is unfortunately harder to produce" or "To the dismay of those interested, one is forced to work much harder to produce these types of music".

The reason it's harder is that there are fewer means through which one can produce it. Which is because it is just less popular. Why is it less popular? Because less people play it. Why do less people play it? Because it's harder to play. Why is it harder to play? Because all other inter phases, like a micro tuned piano keyboard, put the smallest increment of the equal temperament chosen right next to the next, so that every different micro tuning has a different fingering. Different tunings, like those of 19 or 31 tones per octave, each have a combination of those tones that create those tunings' respective major/minor scales/chords, but they all have different respective fingerings on a micro tuned keyboard because they are all different numbers of keys away. On a two dimensional axis of pitch determined by the parameters of tuning theory, the intervals that create major and minor scales are always in the same shape, even when they are different distances (in cents) away. (for anyone else reading this, see previous posts' links for explanation.) So this tool, that is the use of a two dimensional pitch axis, and the method of basing it off of intervals determined by a tuning, creates something that IS different than synthesizers or other current means by which we employ micro tonality, not even considering the manipulation of partials. That difference is that it becomes accessible to anyone with an interest because it is easier to play.

Some look at this as "cheating" because you no longer require an understanding of exactly how many tones per octave you are using, but really all it is doing is changing the mindset that is required for playing alternate tunings.

Plus, there are millions of ways to do it, both live and digitally. On top of that, just because you haven't really realized the options available to you, as Charlie pointed out, it doesn't mean they don't exist. Plenty of instruments are capable of playing different tunings/microtonal stuff, what's the problem?

You're blowing a non-problem out of proportion.

I think I addressed this above; I realize there are other means through which one can explore microtonality but the inter phases (instruments) with which we are supplied nowadays are not intuitive and are harder to play, or at least require you to relearn all of the basic patterns that are applicable to the new tuning. Which is why the idea behind isomorphic instrument layouts tuned using the same parameters as tuning theory IS unique and groundbraking. It makes playing alternate tunings easy and accessible.

Have you actually read my posts? I wonder. In any case, I'll reply since you aren't understanding my argument at all and you are instead simplifying it without the proper context. It's like this:

I don't care about the means you use to make your music using "dynamic tonality" in this case. If I didn't know better, it'd sound like very controlled pitch bending (electronic of course.) So, if I wanted to recreate it, I could just do it that same way and get a pretty reasonable approximation of what was done without having a clue it was "dynamic tonality" or any of that crap.

BLATANTLY WRONG. The means by which we go about creating dynamic tonality are EVERYTHING. Without these means (i thought this would be obvious) you, uh, can't have it. But you still don't seem to have a grasp of what dynamic tonality is. If you did, you would realize that NOTHING else is out that that can create these effects for performance, and therefor you could not just go off and make these same effects yourself all willy nilly.

The end result for the entire thing is simple:

What formulas or how you manipulate pitch bending is not the point here. The point is that it all can be reduced to much simpler terms, without using new terminology or inventing anything. What your system does is just set up a set of parameters by which pitch variation is controlled, but at the end it's just that. Pitch variations/bends/etc being controlled.

So here it looks like you have accepted that dynamic tonality is more than just pitch bending, but you do still appear to think that it can be reduced to "simpler terms". I guess it can, but not just generally as "Pitch variations/bends/ect" as you describe it. You described it as so because you still don't actually seem to know what dynamic tonality really is, or what these "variations" are. They are as I've said before, the changing in partials to fit the tuning and create the same consonance we experience in other tunings based on the harmonic series that use harmonic partials. Since these "simpler terms", in this combination, have never been used before, they are NEW, and so we have rightfully described them as a whole as dynamic tonality.

Again you fail to understand what is meant here. You can "perform" a recording, so to speak. So really, the fact you can manipulate stuff in real time is nice but it's irrelevant to the previous point.

That makes no sense. What is sounds like you are saying is that anything we have on a recording we must therefore be able to reproduce in a performance. But that is so obviously not so. In order to imitate dynamic tonality without the tools of an isomorphic keyboard built off of the intervals of tuning theory and an application like the transformsynth, one would be required to create the whole thing from scratch on a computer program that allowed the manipulation of partials, pitch, and rhythm placing every note in place and adjusting it accordingly. And once this would be done, you would then have a recording that you would be unable to perform, because you made it on a computer.

Unless you haven't noticed already, what I'm attacking is claiming "new!!!" sounds and introducing new terminology, when I'm not seeing the point for its adoption. Realistically, all this deal is is simply a new type of keyboard and a software that has controlled pitchbending according to a series of formulas and parameters. There's nothing wrong with any of it, I just fail to see what's so new about it or why bother with calling it anything else than what it really is.

AGAIN, DYNAMIC TONALITY IS NOT JUST PITCH BENDING! HOW MANY TIMES MUST I SAY IT!?!?!? It is the combination of pitch bending into alternate tunings along with the changing of the partials of the tones to fit the newly bent pitches and their tuning.

Above (and in previous post even) I already have proven that dynamic tonality IS new. NO OTHER APPLICATION IN EXISTENCE can change the mapping of notes and partials to fit a given tuning and still allow the same fingering, let alone in real time.

Apparently even the points you think you made are invalid.

Pythagoras, Christiaan Huygens, Francisco Salinas, Gioseffo Zarlino, Andreas Werckmeister, Francesco Antonio Vallotti, Adriaan Fokker, Harry Partch, etc. didn't have these things available to them (btw, if you have to look up any of these names or don't know what temperaments go along with them, you've got a lot of reading to do, my friend, before you can talk this big game you've been talkin'... I'm not implying that you don't, I'm just saying, if you're going to talk tuning, you need to know them). Nor did anyone up until a few years ago. Even with the invention of the synthesizer it was still quite cumbersome. All of these super-easy, do it for you, microtonal resources being readily available is a recent thing (not that I'm saying that that is a bad thing!). Actually, it is kind of a bad thing to an extend, because if you can just click "21-tone Pythagorean scale" on your keyboard, you don't actually learn how it works or how to actually create the tuning. But that's not the point.

When I started writing microtonally I hadn't "found" any of that stuff either. I just read articles, did the math, and did it sans help from "2-D instruments" and "transformsynths". I was not "forced" to stick with 12tET, and in fact, despite my use of Just intonation, Pythagorean tuning, 15tET or 7tET or 30tET, I still come back to 12tET on occasion. You speak about 12tET like its this evil thing. Its not (don't tell anyone I said that though, thats like blasphemy in the microtonal world :laugh:). People are more than aware that its not the only tuning out there. Just because they're comfortable using it, enjoy the way it sounds, and don't want to expand beyond it doesn't mean that you or me or SSC or some guy in Mexico or anyone is limited to it. In fact, traditional folk musics of just about any region use non-12tET tunings. Including these here United States of America. How about those barber shop quartets that were so popular... and sang in Just intonation?

Sorry I made it sound like there were no other alternatives to play in alternate tunings, this was not what I wanted to say. As I described in my response to SSC, theses methods are just so abstract and difficult that it is usually not worth it to attempt to get involved, even for someone who is particularly curious. With the use of isomorphic keyboards and dynamic tonality, it becomes easy and intuitive, and therefor worth exploration even by those that are barely interested at all.

The whole "it does it for you and therefore you don't gain an understanding" thing comes from a mindset where one is used to seeing pitches define tunings, whereas these new methods are based on intervals and combinations thereof. They really just require a new mindset that says "in these new tunings the same theoretical intervals such as an augmented fifth or minor third are different sizes but can be used similarly, and are created by the method of combining and subtracting fifths and octaves, and their sizes are determined by the tuning". Which is why they are the same shape on the button field of an isomorphic keyboard.

First of all, you said "stack of perfect fifths", so you're talking Pythagorean now? Wait a minute, remapping partials? That doesn't sound so "natural" or "perfect" to me. Weren't you the one complaining about the "imperfections" of 12tET? And the defectiveness of meantone, which you say "force compromises"? Isn't "remapping" partials a "forced compromise"?

Sorry, my bad again. Not always perfect fifths. I should have said "stacks of the size of the theoretical fifth defined by that tuning". That should make more sense in context.

About the remapping partials, we are absolutely not compromising anything. In fact it is a requirement if one wants to play in some alternate tunings. Cultures who's traditional music employs tunings other than ones close to the tunings ideal for harmonic partials do so because the traditional instruments of their culture, by chance, are odd enough shapes and designs that they emit non harmonic partials, which causes the consonant intervals of those instruments to be of different sizes than our just intervals, and the applicable scales to be of different number of tones per octave than ours.

So when we remap the partials, we are just imitating the series of partials required to make that tuning sound "in tune". For example, if you played in 5-TET with a cello like instrument (or any that emits harmonic partials) it would sound terrible, not because of the players skill, but because what sounds in tune on an instrument it defined by the sound it emits, its partials. The same goes for the odd shaped eastern instruments that are used to play in the alternate tuning of their traditional music. If they tuned these same instruments to play the fundamentals of our tunings based off of harmonic partials, it would sound equally terrible, because the partials of the instrument would not line up with the tuning.

Also, "changing" the partials kinda means you're not using actual partials anymore, huh? You can't change the harmonic series. Yeah, you can move the pitches on the computer, I guess, but then you've got an "altered" harmonic series. So technically they're not overtones anymore.

Unless my definitions are incorrect, overtones and partials aren't necessarily harmonic unless you refer to them as so. So technically one would not be using harmonic overtones anymore, one would be using the overtones that fit best the current tuning. They are still "actual" partials, just not harmonic.

Plus, why would you even want to? A clarinet wouldn't sound like a clarinet if it produced even numbered partials, now would it?

Check out the two sounds here. They show you how you can change the partials/overtones of an instrument without changing the character of the timbre much.

This is a gong, regular:

http://homepages.cae.wisc.edu/~sethares/Sounds/Gong.mp3

And this is the gong with all of its partials mapped to multiples of (I think) 64 Htz:

http://homepages.cae.wisc.edu/~sethares/Sounds/Gong65.mp3

Notice how although the second one is obviously different and has pitch, it is still recognizable as a gong.

And here is a "song" where a (nice coincidence) clarinet of electronically altered partials performs.

http://homepages.cae.wisc.edu/~sethares/Sounds/Legend.mp3

This is what it is like to remap the partials. The timbre will sound a little different and this new sound will fit the different tuning while still retaining its character.

And for the record, you technically can manipulate an acoustic instrument's harmonics via, lets say for example, pizzicato on a violin, which forces inharmonicity. But that's a whole other topic, and not really what you're talking about.

That's true, and any change to the character or timbre is manipulating partials as I understand it, but my point was that you can not map every partial specifically to fit any tuning like dynamic tonality allows, on any acoustic instrument.

Also, you need to get off of the electronic thing. You're confining yourself with electronics just as much as you claim 12tET does.

I don't know. With acoustic instruments you have benefits/constraints and with electronics you have benefits/constraints. I also play trumpet and appreciate very much how much I can do with it that I can not do with my electronics, who's degrees of freedom do not extend beyond velocity sensitivity, but you can't do the things with acoustics that you can with electronics. I very much so realize they both have their advantages, and don't intend to come off as one who thinks one is superior.

wall of boring text

Did you not see the stamp?

Ok, there's tonaly, modality, and atonality. Dynamic tonality is equally relevant to modality as it is to tonality. So still, atonality is the only thing not applicable. And, like I said before, if it's your thing that's fine, just don't bother with these new tools. A lot of music, most of it actually, is tonal or modal.

...

Check out the two sounds here. They show you how you can change the partials/overtones of an instrument without changing the character of the timbre much.

I'm going to stop now, someone with such gaping holes in their knowledge isn't worth my time to try to debate, if this is even called that at this point. Get an education, then come back and we'll talk.

Sorry I made it sound like there were no other alternatives to play in alternate tunings, this was not what I wanted to say. As I described in my response to SSC, theses methods are just so abstract and difficult that it is usually not worth it to attempt to get involved, even for someone who is particularly curious.

Its not that difficult. In fact, I've done it with ease without the aid of any tools (except for maybe a calculator... just speed things up).

With the use of isomorphic keyboards and dynamic tonality, it becomes easy and intuitive, and therefor worth exploration even by those that are barely interested at all.

So its not "worth exploration" without an isomorphic keyboard?

The whole "it does it for you and therefore you don't gain an understanding" thing comes from a mindset where one is used to seeing pitches define tunings, whereas these new methods are based on intervals and combinations thereof. They really just require a new mindset that says "in these new tunings the same theoretical intervals such as an augmented fifth or minor third are different sizes but can be used similarly, and are created by the method of combining and subtracting fifths and octaves, and their sizes are determined by the tuning". Which is why they are the same shape on the button field of an isomorphic keyboard.

So pitches don't define tunings? Since when?

And if you're using combinations of intervals, aren't you still using pitches to define tunings?

And to your statement about "theoretical intervals", that's the problem with many microtonal compositions and a lot of the thinking! Trying to force a hierarchy upon a tuning that it doesn't work in! A tuning will dictate its own hierarchies based on the intervals that can be found in it. You shouldn't be talking about a traditional C major triad or a V-I cadence in 5tET!

About the remapping partials, we are absolutely not compromising anything. In fact it is a requirement if one wants to play in some alternate tunings. Cultures who's traditional music employs tunings other than ones close to the tunings ideal for harmonic partials do so because the traditional instruments of their culture, by chance, are odd enough shapes and designs that they emit non harmonic partials, which causes the consonant intervals of those instruments to be of different sizes than our just intervals, and the applicable scales to be of different number of tones per octave than ours.

What about gamelans in Bali in which instruments are tuned apart specifically for the beat frequencies that I seem to recall you defining as a "dissonance"?

So when we remap the partials, we are just imitating the series of partials required to make that tuning sound "in tune". For example, if you played in 5-TET with a cello like instrument (or any that emits harmonic partials) it would sound terrible, not because of the players skill, but because what sounds in tune on an instrument it defined by the sound it emits, its partials. The same goes for the odd shaped eastern instruments that are used to play in the alternate tuning of their traditional music. If they tuned these same instruments to play the fundamentals of our tunings based off of harmonic partials, it would sound equally terrible, because the partials of the instrument would not line up with the tuning.

30tET and 24tET don't line up with the "harmonic partials" of stringed instruments. Does that mean that Haba's string quartets, for example, sound out of tune or terrible? Because last time I checked, neither was the case. In fact, it was quite far from it.

Check out the two sounds here. They show you how you can change the partials/overtones of an instrument without changing the character of the timbre much.

This is a gong, regular:

http://homepages.cae.wisc.edu/~sethares/Sounds/Gong.mp3

And this is the gong with all of its partials mapped to multiples of (I think) 64 Htz:

http://homepages.cae.wisc.edu/~sethares/Sounds/Gong65.mp3

Notice how although the second one is obviously different and has pitch, it is still recognizable as a gong.

And here is a "song" where a (nice coincidence) clarinet of electronically altered partials performs.

http://homepages.cae.wisc.edu/~sethares/Sounds/Legend.mp3

This is what it is like to remap the partials. The timbre will sound a little different and this new sound will fit the different tuning while still retaining its character.

As you mentioned the timbre is different. Therefore, it does not retain its character.

That's true, and any change to the character or timbre is manipulating partials as I understand it, but my point was that you can not map every partial specifically to fit any tuning like dynamic tonality allows, on any acoustic instrument.

Hence my "not exactly what you're talking about".

So its not "worth exploration" without an isomorphic keyboard?

I tend to deal too much in absolutes and that's my fault. It is less worth it because it requires more work per likelihood of satisfaction or professional result due to the difficulty inherent in production. Not completely un-worth-it, but less so worth it than most would prefer, therefore leading to less production and playing.

And if you're using combinations of intervals, aren't you still using pitches to define tunings?

Well I see what you mean, but thats not really what I meant. I mean that instead of defining tunings by pitches which are defined as certain increments in cents along an equally tempered scale that can fit on a keyboard, this method defines them as the tones that fall in as the most related intervals to the tonic in the tuning, therefor nullifying the need for tunings that even have a definite number of tones per octave. If you choose a size of the fifth that produces an infinite number of tones per octave, only the 19 tones defined by that tuning (the tonic and the 9 fifths above and below) are applicable in tonal music. So here with dynamic tonality and an isomorphic 2-D keyboard one can play in a tuning completely inapplicable to a linear representation of pitch where it is required to have a set size for each increment from one key to the next.

And to your statement about "theoretical intervals", that's the problem with many microtonal compositions and a lot of the thinking! Trying to force a hierarchy upon a tuning that it doesn't work in! A tuning will dictate its own hierarchies based on the intervals that can be found in it. You shouldn't be talking about a traditional C major triad or a V-I cadence in 5tET!

But each tuning does have it's applicable major and minor triads, the size of their intervals will just be defined by the overtones of the timbre one uses to define the tuning. The actual fundamentals of the pitches of these applicable chords will obviously not be the same as your C major triad and different patterns of modulation will arise, but chords are still tertian in all tonal music's tunings, that is, are created by combinations major and minor thirds. And the terms major third or minor third ARE applicable in other tunings, granted you are speaking tonally (which I have said before: this is only applicable to tonal/modal music). That is because these terms are actually defined by certain combinations of the fifths and octaves defined by that tuning. The major third, in any tuning, is the tonic combined with the note 4 stacks of the given fifth upwards, and two octaves reduced downward. The minor third can be derived similarly with combinations of the fifth and the octave.

So no the actual hierarchy of chord progressions and such should not be and is not imposed on alternate tunings, but the terminology of theoretical intervals is always relevant (in tonal music).

What about gamelans in Bali in which instruments are tuned apart specifically for the beat frequencies that I seem to recall you defining as a "dissonance"?

There I go again with my absolutes. If that dissonance is intended, that absolutely doesn't mean it doesn't sound really freaking cool (I youtubed those gamelans :-]), and it for sure doesn't mean it sounds terrible (sorry for using that word). It just means that by definition that music is not tonal, because tonal music relies upon the basis of the fundamentals of ones pitches on the method of stacking and reducing important intervals in a timbres partials. Although it is almost never defined directly as so, when one uses this aformentioned method to create and play any tuning, one always ends up with the characteristics of tonality, that is a tonal center, resting and leading tones, and triadic harmonies/tertian chords, whereas if one does not and uses instruments that also do not, one ends up without these characteristics. Doesn't mean it's bad, and it can be very good. This simply means that dynamic tonality is not applicable to the type of music that these instruments play, seeing as it is not technically tonal.

30tET and 24tET don't line up with the "harmonic partials" of stringed instruments. Does that mean that Haba's string quartets, for example, sound out of tune or terrible? Because last time I checked, neither was the case. In fact, it was quite far from it.

I think I addressed this above; I don't mean to say that any music that doesn't not line up the partials of ones instruments with the tunings sounds terrible. I know thats pretty much what I said, and I'm sorry. Music like that can sound great. I just mean to say that it is then not technically tonal because tonality is defined by certain characteristics that are created with methods of tuning not employed by these micro tuned/performed instruments playing outside their "tonal range", and therefor are not applicable to dynamic tonality.

As you mentioned the timbre is different. Therefore, it does not retain its character.

But you could still tell it was a gong couldn't you? That's my point, it will change slightly, but still be recognizable as that instrument's original character and have similar, if not the same, applicational possibilities in music.

John

I see this thread has moved to a more interesting teritory...

Several months ago I wasn't aware of dynamic tonality, but I've thought about the concept long ago - to manipulate the overtones in order to fit certain tunings or even to use it as tension-release tool, but as time proves, there are lots of things already discovered and explored. David Cope's approach to interval strength is one more example - I was unaware someone has already explained them that way, but I did use the same explanation myself.

I don't like calling the tuning systems from the past defective. They have been useful and continue to be useful thanks to their specific features. When they fit your needs, they are certainly not defective, but effective. Defective is something that is intended to serve you in a certain way but fails to do it.

Manipulating / moving the overtones doesn't mean they are not overtones anymore. This isn't true - they obviously don't become undertones and don't disappear. Don't forget that 'overtone' doesn't imply it is necessarily harmonic - it is just over the tone, that's all, and there are harmonic and inharmonic overtones. But I suspect charliep123 simply used the word 'overtones' instead of 'harmonics'.

There are lots of tunings available (considering also those which are foreign to the western world) and I am not sure if anyone knows them all by heart in details, but you can always explore. The important thing is to understand the principles.

But each tuning does have it's applicable major and minor triads, the size of their intervals will just be defined by the overtones of the timbre one uses to define the tuning. The actual fundamentals of the pitches of these applicable chords will obviously not be the same as your C major triad and different patterns of modulation will arise, but chords are still tertian in all tonal music's tunings, that is, are created by combinations major and minor thirds. And the terms major third or minor third ARE applicable in other tunings, granted you are speaking tonally (which I have said before: this is only applicable to tonal/modal music). That is because these terms are actually defined by certain combinations of the fifths and octaves defined by that tuning. The major third, in any tuning, is the tonic combined with the note 4 stacks of the given fifth upwards, and two octaves reduced downward. The minor third can be derived similarly with combinations of the fifth and the octave.

Whoa! Did you even read what charliep posted? He mentioned 5tEt. Are you seriously saying there are "major and minor triads" in 5tet? You constantly speak of "any" tuning, but your posts clearly show that you're actually thinking of only a very narrow set of tunings. Tunings aren't necessarily based on stacking fifths. Tunings aren't necessarily based on picking out intervals from the harmonic series. Interval names like a "major third" only make sense in specific contexts and even more so names like "major triads".

And where did you get that a major third is "defined by 4 stacks of the given fifth upwards"? That's a way of describing it in the diatonic scale, with some traditional tuning systems (but technically only in equal temperament, since any other of these traditional tuning systems doesn't have one "given fifth" but at least two), but I don't think it's how it's "defined". Interval names are derived from diatonicism and not from a mathematical size either in semitones or stacked fifths (even if you can retroactively use this to describe them) - otherwise major and minor thirds wouldn't be sharing the same basic name. And there also wouldn't be any thirds in the harmonic series, if you defined them as stacks of fifths (because obviously the harmonic series isn't built by stacking fifths…).

Oh yes, you said "in tonal music". But it sounds like with that you mean "traditional, western tonal music" or something. Because obviously tonality can very well exist without major thirds, triads, tuning systems built of stacked fifths, and all that stuff. And it should have been pretty obvious that charliep wasn't talking about traditional western tonality when he mentioned 5tet. Unless a new discovery showed that Beethoven used this…

There are lots of tunings available (considering also those which are foreign to the western world) and I am not sure if anyone knows them all by heart in details' date=' but you can always explore. The important thing is to understand the principles.[/quote']

Well, since there are theoretically infinitely many tunings systems, I'm pretty sure nobody knows all of them by heart. :P