I've had an idea now for a while but I'm struggling with the potential size of the project, just wandered if you guys think I'm barking up the wrong tree and wasting my time. Basically assuming that all modulation and harmonization points are rooted in mathematics would it be possible to right a formula or algarithm that would define all potential branches from a fixed point, a little book of sums as it were that could define all potential key changes that work. A universal set of rules that could be applied to any starting note/key?
I know for this I 'd have to not only work out the modulation points with in each mode of the major scale but the harmonic minor, but what about melodic minor or any of the other exotic scales? is a universal modulation theory possible? Thoughts anyone?
While I'm sure you can codify tonal functional harmony into math, I'm not sure using scales is the right way to go about it.

In purely musical terms, orienting harmony around scales is a loser's game.

...modes and scales are still useless.

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Music is an art. It uses patterns and can be analysed mathematically but I think a person is misguided when they start thinking that a mathematical analysis of what has gone before can be used to predict or determine the possibilities of future art.
-Unless of course the math that is being done, is itself, a stand alone work of art with no practical application intended.

...what is the point? It sounds like a lot of work that would ultimately be of little to no practical value. But if it's simply because you enjoy the beauty of seeing things explained mathematically then go for it.
I'm just one of those weirdo's that like to quantify and understand things, but I can see it lacks little practical application other than to maybe keep me busy for a few months You have convinced me not to waste my time.
Nothing "weirdo" about wanting to know how things work. You're definitely asking the right questions.

'Where to from here?' Is probably one of the most common questions that a composer will ask themselves. Exploring that is an excellent idea. It's just a matter of finding the right method of discovery.
It would probably improve your understanding of the theory behind it as you'd really need to understand the subject to get the calculations correct. However I don't see the benefit to anybody else. Rather than learn the theory i'll just learn some formulas.

So just spend the time learning the theory
I don't think there would be any benefits from it and also if you figured out all the possibilities, people would just stop using their ears and start composing just using maths (OK, maybe not because there would be so many different options).

But the thing is, you can modulate from any key to any key if you want to. And you can use whatever chords you want to. Just let your ear guide you. Maths won't really help at this kind of things.

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Forget nay-sayers, I like the idea. Though I don't know enough music theory or math to help with it.


On second thought, I may have to do a 180 on this one. I suddenly recalled "Ken's Theory on Dance" (well, one of my theories, there may be others) The theory is this: Any "error" in dance, like an awkward trip, slip, off-time move, can be transformed into a ""good" dance if you add appropriate symmetrical movements at the right time. Dance is basically about rhythmic patterns of movement, so if you make an unintended "glitch," it only remains a glitch if you fail to rhythmically work it into your patterns of movement by coming back to it or some variation of it.

This may not work for falling down a flight of stairs, but for minor, unintentional movements it seems to do okay. I've applied this theory in my own casual dancing at festivals, clubs, raves, parties, whatever.

The point is, any movement that would be perceived in isolation as a "wrong" movement is salvageable and can be transformed into a "right" dance move. I've seen plenty of professional dance routines that were built around the notion of having dancers "play" fall, "play" trip, or just play at being clumsy, but then it artistically resolved in a way that those moves wound up being the start of an exquisite dance.

I guess if I apply this theory to music, I have assume that if you take some seemingly dis-chordant notes, there IS a way to ultimately take that starting point as a challenging introduction to music that would come back to those dischordant aspects, perhaps piece by piece, and play with them, and harmonize them, till by the end a rich musicality is developed. I mean, just as a relative novice noodling, I played with starting off with a tri-tone chord change (E to Bb) just to see if I could "resolve" it into a musical piece, and I could rather easily. I've done the same with some longer series of dischordant notes or chords, and found ways to use them to launch into a particular "Mood" piece that seemed to work. So, I guess my conclusion is that ultimately there may not be any "wrong" notes, if you are up to the challenge of working on how to salvage and develop and harmonize them. And so the notion that there will only be certain chords that can follow other chords, or only certain chords you can use to pivot between keys...well, I am not sure there is any validity to such limitations.

I'm sure you can take a child randomly striking a piano for 5 minutes and say, "Now harmonize that!" and I'll have to concede defeat, but it is not because it is objectively impossible to do so, but it is that the human animal has finite patients and would not, at least at this stage of evolution, have the patients to settle in and listen for the time it would take to go back, work through, and harmonize such a lengthy series of dischordant notes, it is NOT that it is objectively impossible to do so.

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Last edited by krm27 at Apr 25, 2014,
Music Theory is the system of quantified relationships you're looking for. It covers everything you're asking about and more.

Trying to shoehorn mathematics into music is pretty worthless, and really just misses the point of music as a whole, which is aural cognition. It's all about movement between different sounds, and there aren't really any mathematically emergent situations. There is no natural law that a series of sounds has to progress in a certain way. All you have are a tendencies of tradition, which are entirely up the whim of the composer.
Last edited by cdgraves at Apr 25, 2014,