Is there a direct mathematical equation?

[m1469]

I'm obsessed by something at the moment.  I know that it's been said always that there is at least some relation between math and music, and I can think of simple ways.  But, is it theoretically possible to actually directly translate a piece of music into one, giant(?) mathematical equation?  It seems like it would have to be possible - it's like I can just feel my mind/body doing math while I'm playing and digesting the music.  What kind of math would that be?  I kind feel like I'm staring at it but don't recognize what it is, exactly.  Well, right now and other times, I feel like the whole world is a math and that we are always staring at it.  It's making me burny  .

[richard black]

No, not an equation. An equation, by definition, says that something equals something else, and in the case of a piece of music there's no something else to equate it to.

But you can represent a piece of music mathematically, as a matrix or vector. Then again you can, by suitable choice of definitions, represent _anything_ as a matrix, so, frankly, who cares? It doesn't necessarily get you anywhere.

[m1469]

For me it explains a little bit, in that behind something like architecture, there is mathematics.  And what you get from those mathematics are structures, landscapes, etc..  It's like I can sometimes see structures in my mind and landscapes while playing.  To me, in music, you can get interpretation and language ... and lots of things that are just at the tip of my mind.  There's something really huge ... just over there ... beyond that ... obstacle ... or over the hills?  Or what?

Mozart.  He absolutely ruined me today and I better still sleep tonight!

[chopin2015]

[49410enrique]

https://www.scribd.com/doc/57613470/Acoustics-Basic-Physics-Theory-and-Methods

[chopin2015]

i love you.  i like this book. this is what we used in acoustics class. The funnies thing I've ever heard : if our ears could respond to any transient quieter than 20 micropascals we would hear air particles colliding

[lloyd_cdb]

i love you.  i like this book. this is what we used in acoustics class. The funnies thing I've ever heard : if our ears could respond to any transient quieter than 20 micropascals we would hear air particles colliding

That might ruin music, given that sound waves are vibrations in whatever medium they are travelling through.  It might just add white noise to everything that happens, which would be incredibly annoying.

[m1469]

Thank you for posting that book and the frequency chart!  I do understand that tones have vibrations and frequencies which have unique shapes (though I don't know anything about acoustics), and actually, I "get" that everything in life has frequencies; buildings, people, animals, walls, planets ...   That is definitely something.  What I am thinking about though is not just that (though that wouldn't be excluded, perhaps).  It's about ratios and velocity, I know those two things for sure so far.  I am trying really hard to very calmly think this through and be able to write about it, but it's really, really, really difficult for me and I spent a good portion of the day quite angry and frustrated at having too many thoughts and questions all at once, vs. actually doing more of what I wanted to be doing.  I don't even know how to write a single question yet, even though I can hear all of these ideas going everywhere and I know I have a bunch of questions.  It's just all tangled in there at the moment.

[chopin2015]

That might ruin music, given that sound waves are vibrations in whatever medium they are travelling through.  It might just add white noise to everything that happens, which would be incredibly annoying.

Yep, but isn't it just such a dynamic joke? Ok I am pretty lame.

[lloyd_cdb]

Yep, but isn't it just such a dynamic joke? Ok I am pretty lame.

I think that joke is used at too high a frequency.

Oh god...

[chopin2015]

Teacher: ''there will not be any TT cable questions on the test"
Rich: "If there's no TT's then I'm not coming!"

 

[m1469]

Seriously, that's what has to happen in this thread now?  

[lloyd_cdb]

No, not an equation. An equation, by definition, says that something equals something else, and in the case of a piece of music there's no something else to equate it to.

let y = Chopin's nouvelle etude in A-flat

y= f(A-flat)

let z = Godowsky's study on Chopin's nouvelle etude

z = g(f(A-flat))

[ted]

Turning the thread back to the original question, i.e. is there some sort of  direct invariant mapping between mathematical truth and music in the form of equations, I suggest not in general. Mathematics is about objective truth and music is about subjective meaning. A mathematical truth is not dependent on which particular brain is thinking about it, but the power and meaning of a piece of music vary a great deal among individual brains. On the basis of this fact alone I do not see how such a direct correspondence could exist. Of course many composers use mathematics to create music which many people enjoy and possibly a greater number do not. But that has no bearing on m1469's question.

I could see many other problems with the idea, but that is the main one.

[ted]

Perhaps a second, and stronger argument against the idea, would be go in the opposite direction, to take a truth of mathematics and seek the musical work which corresponds to it. Looked at in this way, the proposition takes on a distinctly fanciful aspect.

[m1469]

Ted, I'm not yet sure how, exactly, but both of your posts help me unwind myself out of knots just ever so slightly!  Thank you!  I still don't know how to ask a question yet.  But, your second one is very interesting to me and I guess that's part of what I'm thinking about.  It seems there would be an inverse relationship and that there could be a mirroring between math and music that way.  

[chopin2015]

Just do Prokofiev toccata

[m1469]

I guess the rest of my questions are related to pieces, style, and composers, rather than just about whether it is possible to represent music in math.  And I need to study more, first, and I think I know how to do the next step.  Haydn got me really mad yesterday  .  I am trying to compare themes and motives (and ultimately forms) between Mozart, Haydn, Clementi, and Beethoven, and there was already such a stark difference between the one Sonata I'm working on with Mozart, and the one Sonata I looked at of Haydn's that it made me crazy in my noggin.  I'm also just involuntarily starting to think in certain ways (listening and looking for certain things) about all the music I'm listening to or playing, and that got me frustrated, too.  

I think I will first just look at only one composer at a time so I get a better feel for patterns and characteristics in how each composer thought in general before I start making comparisons.  So far Mozart is still King though  .  It almost seems there might not be hardly any comparison, except for maybe Bach, actually ... but maybe I'll change my mind when I look at Beethoven anew.  I can't wait to find out more about it all .

[Bob]

How about the golden mean? That's in music.

[m1469]

How about the golden mean? That's in music.

Yes!  Well, from what I understand it CAN be but isn't necessarily, even though it can apparently be there out of the composer's subconscious and not necessarily a conscious decision.  I didn't consciously know I am asking about this, but actually this is probably precisely part of my larger question.  There is the overall arch which makes the golden mean what it is, but in reality there is something happening mathematically on either side of it.   It's not just nothing, nothing, SOMETHING, nothing.  It's framed by somethingness.  And, I'm just wondering if somebody like Mozart, who may have truly had an entire piece of music come at once to him, if within that there are all of these perfect mathematical structures which revolve in this perfect way around a Golden mean.  It seems like each of his phrases and even his motivic material in and of themselves have miniature golden means (aaaahhhhh... I can finally start getting words and questions out!  What a relief), and perhaps even every part of his form does, until it has perfectly framed, in this ultimate, genius, tightly-woven way, the big golden mean.

I still am thinking and need to look and study and explore.  I don't know that it's true what I'm wondering about Mozart (or if it's going to be exactly possible to find (even though I FEEL like I found it), but I might not be able to resist), but I am tempted to think and believe I wouldn't find that almost in anybody eles's works ... well, Mozart would be my first suspect anyway.  

But Rachmaninov may be a certain kind of candidate, as well.

[chopin2015]

I think mathematics can hardly represent music, yet music can be subdivided and analyzed and is logically simplified to make sense to us.   

[goldentone]

So what would it mean if a piece of music can be represented by a mathematical equation, or can be translated into mathematical form?  Would that piece of music, and by extension music itself, have a true weight of existence, a self-existence, if it converts into mathematical form?  As Ted alluded to objective truth.  I'm thinking blueprint now.  Synesthesia comes to mind too as an adducer of your idea.  
When you think of the high vibration of Mozart's music, mathematics would have to be there somewhere, in some relation.

I am trying to compare themes and motives (and ultimately forms) between Mozart, Haydn, Clementi, and Beethoven, and there was already such a stark difference between the one Sonata I'm working on with Mozart, and the one Sonata I looked at of Haydn's that it made me crazy in my noggin.  

That sounds really interesting!  I imagine Mozart's and Beethoven's musical thinking is as different as night and day.

[maczip]

Interesting: you are talking about issues Herrmann Hesse has adressed in his "Das Glasperlenspiel". The problem with it is, it leads to nowhere, it´s just intellectual fun

[m1469]

So what would it mean if a piece of music can be represented by a mathematical equation, or can be translated into mathematical form?

Well, other than timing and organization, I don't know yet, I simply am realizing it can be.  But, on some level I feel like I've always known this, and as I said a few posts up, I think everything we see in the world probably can be.  So far, I don't consider that as thee ultimate truth though, it's just something I observe as part of this existence, and probably which is connected to a deeper truth/layer.

Would that piece of music, and by extension music itself, have a true weight of existence, a self-existence, if it converts into mathematical form?  As Ted alluded to objective truth.  I'm thinking blueprint now.  Synesthesia comes to mind too as an adducer of your idea.  
When you think of the high vibration of Mozart's music, mathematics would have to be there somewhere, in some relation.

Yes, these are all part of what I've been thinking about with this, but also for a long time on some level.

That sounds really interesting!  I imagine Mozart's and Beethoven's musical thinking is as different as night and day.

Yeah, I'm completely fascinated!  But, it's just recently that I can think in more concrete terms about it as I investigate, and I suspect that will change more as I explore more.  I just haven't truly understood until this past little bit what makes one composer's thought process different than another.  I mean, I haven't understood how to really investigate it more concretely and to really see it.  At least I see *something* now which I can try to use as a tool in my investigations ... it's still tricky for me though ...

As a side, something that I am super interested in doing as I continue along is to try to compare selected pieces from these composers where there might be a similarity in material/thought to begin with, if I can find that amongst them, and compare how they individually treat the idea.  But, every second I'm wishing I could take a huge armload of scores to my teachers and ask thousands of questions   ... alas ... some part of me wants to find it by myself though, too.

It all makes me furious, at the same time.  I wish I could just understand it all at once and it seems so big that I have a difficult time approaching it without being furious at every moment (which means I might burst into tears ...  :- ).  But, probably it would be really uncomfortable to suddenly understand the bigger concept all at once.  So, I'll just need to somehow ignore that furious aspect or just put it in some kind of fireplace, and go about my business calmly, despite it.  Honestly, sometimes one of my biggest (gigantic, actually) obstacles has been seeing more (sometimes much more) than I know how to cope with.  As a side, I think that's one argument towards a certain teaching style where it is demanded that the student thinks only of what the teacher is asking and of nothing else.  My mind will always be curious though, I think.

[Derek]

I think the fascinating thing about music is that judgements about it are always simultaneously objective and subjective. That is one of the things that frustrates us most about it. The closest thing I can think of to axioms in music would be: "consonances exist, and there are fewer of them than dissonances." The reason for this is that our brains notice things that have simple relationships. And there are not many simple relationships because as the numbers in the frequency ratios get high enough our inner neural circuits cannot count fast enough to find a dissonant interval "stable." even though for instance a 3rd is actually more dissonant than a 5th. It is still simple enough it sounds stable to us. That these things exist is objective. That time, rhythm and pulse exist is objective.

Which ones we *prefer* to use is subjective. BUT---if we pick some of the more objectively obvious things to start out with---such as a small subset of consonances and perhaps start with nothing but a pulse----then we can objectively approach how to make these (originally subjective) traits stand out.

The objective pursuit of the "completeness" of obvious simple consonances formed the entire common practice period---what we've forgotten today is that it was a subjective judgement that initially led to the pursuit of careful treatment of imperfect consonances. So...it's really tempting to look at great works by Bach, Beethoven, and Mozart and think that they might have derived their most famous compositions from a germinal idea---its a fun analogy, but I personally believe that absolutely every composition that was ever written, by every composer, could each have been written in thousands of different ways. Maybe we could describe music with dry mathematical symbols, but as the music describes itself, I can't imagine what the value would be. We place way too much value on conscious and symbolic reasoning in our culture today!

One topic which really interests me is how cultures *almost* universally have gravitated towards simpler and more consonant intervals as a framework for their music. It's never absolutely precise, and there are definitely some often cited cases of cultures choosing highly dissonant intervals as more interesting. But my recent experience of having played a clavichord for a couple of years and the *startling* difference between imperfect consonances and other intervals and how it feels in the ear---...makes me tempted to think that the beauty of imperfect consonances is ...intuitively objective---paradoxically. In other words, I believe, subjectively, that these intervals may actually be objectively more beautiful than others. I know that doesn't make sense, I just hope some day I can explain why I feel that way.

It's like music is this confounding thing put here by God that has paradoxical traits that cannot be explained or understood in this plane---it literally comes from a higher plane and will forever confound us if we try to explain it verbally---it is something that can only ever be experienced directly by the mind and soul to be understood and enjoyed.

[brogers70]

I'm obsessed by something at the moment.  I know that it's been said always that there is at least some relation between math and music, and I can think of simple ways.  But, is it theoretically possible to actually directly translate a piece of music into one, giant(?) mathematical equation?  It seems like it would have to be possible - it's like I can just feel my mind/body doing math while I'm playing and digesting the music.  What kind of math would that be?  I kind feel like I'm staring at it but don't recognize what it is, exactly.  Well, right now and other times, I feel like the whole world is a math and that we are always staring at it.  It's making me burny  .

Sure, you could, in principle, write down the equations that describe all the frequencies of all the notes and overtone, the beats from dissonances, decay over time etc, etc. But I doubt that's what you feel as the mathematical aspect of music. I think the accessible math of music is most analogous to abstract algebra; groups, rings, and fields, and all that. Transformations or operations acting on a phrase or a key signature which yield a predictable and satisfying result. So a typical Baroque sequence is just taking a phrase and repeating it after it's been transformed down a major second, and then down another major second, with appropriate adjustment to the harmony. Or the circle of fifths is a set of operations such that doing the operation 12 times sequentially is equivalent to the identity function. Or the inversion or augmentation of a subject in a fugue, is a definite, recognizable transformation. To me, these are the aspects of music that feel most mathematical, and are also, I think, the reason why people sometimes say that Bach is the most mathematical of musicians.

[goldentone]

Yes, these are all part of what I've been thinking about with this, but also for a long time on some level.

I caught your vibration, then.

As a side, something that I am super interested in doing as I continue along is to try to compare selected pieces from these composers where there might be a similarity in material/thought to begin with, if I can find that amongst them, and compare how they individually treat the idea.  But, every second I'm wishing I could take a huge armload of scores to my teachers and ask thousands of questions   ... alas ... some part of me wants to find it by myself though, too.

The Diabelli Variations would be perfect for this, but there are really only two big name composers who participated, Beethoven and Schubert.  Czerny and Hummel also participated.  The publisher and composer Diabelli (in case you didn't know) gave the composers a waltz theme for which they were to provide their own variations.  Beethoven's are regarded by Brendel as the greatest piano work, and by Tovey as the greatest variations ever composed.

I just haven't truly understood until this past little bit what makes one composer's thought process different than another.

Well, I think this is a biggie fish.  Can you give anything specific at the moment?

[m1469]

Derek and brogers, Thank you for posting your thoughts, I've read through each post and had ideas, but I'm trying to just focus on more studying before I try to respond about what I think.  So, that may come later.

The Diabelli Variations would be perfect for this, but there are really only two big name composers who participated, Beethoven and Schubert.  Czerny and Hummel also participated.  The publisher and composer Diabelli (in case you didn't know) gave the composers a waltz theme for which they were to provide their own variations.  Beethoven's are regarded by Brendel as the greatest piano work, and by Tovey as the greatest variations ever composed.

Thank you for pointing this out to me, I will very much enjoy exploring these at some point!  I realize that there isn't necessarily an actual theme that was given to each of the composers I'm exploring, where they will all have worked with the same exact idea.  Of course, what I have been thinking about is permeating its way through all of the music I'm playing.

Well, I think this is a biggie fish.  Can you give anything specific at the moment?

Not in a way that explains anything about what I'm trying to clarify in my own mind!  But, Derek mentioned the idea of there not being only one way to write a musical piece, I both agree and disagree with this, and I think this concept and question is important to consider as I investigate further.  

[m1469]

Something I am finding, but didn't anticipate, is that I'm having a trickier and trickier time thinking in solitary ideas.  I had the notion that I could sit down with the scores and figure out even something like a motive, which of course I can in some way, but as of yesterday another idea attached itself to that which hasn't left me alone.  It's like I can't understand a motive or a phrase by itself, it's as though I need to see how it balances out with a larger concept before I am actually understanding the smaller one.  I admit I am not immediately understanding what I am supposed to be understanding about this, I think.  I mean, I'm having a difficult time knowing where to stop in terms of the concept of the piece, in order to balance the one bit against it.  I guess some part of my concept is in fact that the one bit IS balanced within the whole piece and that's the point, but ... I'm not clear yet how to see it as my instincts are telling me to try to see it.  It's a different way of thinking.  It's like the minute I try to "see" a motive, my mind tries to see a subject/theme.  The minute I try to see a subject or theme, my mind tries to see a phrase.  The moment I try to see a phrase, my mind tries to see two phrases at once, like a period, and then my mind tries to see two periods at once.  The minute my mind try to see two periods at once, my mind tries to see an entire section at once (like an exposition), and the minute my mind tries to see the entire exposition at once, my mind tries to see the entire movement ... and the minute my mind tries to see the entire movement, my mind tries to see the entire piece.  And, I promise, there's no end ... it just keeps going.

[Bob]

What about Schenkerian analysis?
https://en.wikipedia.org/wiki/Schenkerian_analysis

[Bob]

Are you thinking actual math, numbers, etc. or patterns present in music?

[m1469]

Are you thinking actual math, numbers, etc. or patterns present in music?

Well, it's more like patterns, but it's also how they relate to each other and the balance that creates.  So, I just realized more of what I am talking about, and this part of it is especially about velocity.  If a group of six notes is played fast enough, or at the right tempo (whatever that is), you can hear it as a group, vs. if you play it so slowly that you lose that ability to hear it as a group but are maybe hearing things more like one note at a time.  But, if you play it in that quicker tempo and you hear the balance of the note-grouping (maybe I should do a little recording), and then you have a next grouping and hear those groupings as they relate to each other, there is a different type of "interaction" between them, a different type of ratio in time, some kind of internal structure, than if you play it slowly (too slow to group them appropriately).  And, I think an entire piece is like that.  There is this certain kind of timing/velocity that is needed in order for the ratios between note-groupings (motives) to be right ... and then in order for phrases to properly relate, and for sections to properly relate, etc., ...  for it to all balance out correctly ... I think somebody like Bach and Mozart knew this maybe intuitively ...

I'll see if I can better clarify it yet ... or find an analogy or something (it's probably partly visual/spacial for me, like a painting or drawing).  That actually is more wording than it's been.

[m1469]

I think I have an idea!

[m1469]

I thought maybe I could draw what I'm talking about because I got a clear visual of part of it for a second, but now I have a few different images in my head overlaying each other and they all want to be represented together and I don't know how to do that (and it's like I can't see "it" or them clearly again).  So I'm going to need to keep thinking.

[m1469]

I think it would be interesting to consider the idea of thought-patterns as having a kind of math to them, and our own unique thoughts as having its own unique math, but maybe things like emotions, as well.  And, those as it reflects the world around us.  Some kind of psychology, and basically, if you want to make a change in your life, or if there is a change, it's a change in the math.  If it were true, I think it would only be one way to look at something and not the ultimate truth.  But, if you think of music as being a direct representation of a composer's psychological math, or emotional math, or of some bigger reflection of these things within the world, I think it's interesting to consider how music does seem to affect living beings in all sorts of situations.  I mean, animals, plants, people who even don't respond to anything but music ... it's like music goes in there and directly deals with the psychological and emotional math and makes something happen.

But, as Marik's math would say to my math ... "But, are you practicing?"    YEP, yep I am.  Here I go some more right now!  *runs as fast as possible*

[m1469]

I'll be back... 

[m1469]

Everything went really far and then really near and then really far and then really near and then ... I got this other idea and accidentally I said out loud to myself ... "OMG" except I said the words and not the letters (but, I was always taught growing up to say "gosh" and not God, OK?)!  And now I have to do actual research some more (which I don't currently know exactly how to do).  I wonder just HOW brilliant Mozart and Bach were?  hmmm?  

Also, would you like to know that I think I start to know how to directly translate certain artworks into a piece of music (and vice versa)?  I think that's true.  And a tighter link between poetry and music ... and art ... and between this all, I think I'm starting to comprehend how I want/must compose something myself, even if I'm wrong about other composers.  I'm sure it's all going to change though in moments ... or days?  or weeks?  Or years?  I don't know ...   :-

Hi     Bye  

[m1469]

Also, I would like to invite anybody to share your thoughts at this point, I don't *think* you're going to ruin anything for me now (but maybe it would ruin it for others?).  More and more is arriving to me at every moment, and I've got a basic idea going that I guess I've been working on for years.  But, I would prefer that it's not just me.  If there's nothing more to say for now then I guess there's nothing more to say!  I do thank you for contributing as you already have, it's all been helpful and interesting!


PS - I'm sure I'll be back  

[Bob]

So what's your big insight?

*Bob is thinking it will be a vague response.... big, something-y, but vague..y... and the m1469 still won't know what she's looking for.*

[Bob]

Everything went really far and then really near and then really far and then really near and then ... I got this other idea and accidentally I said out loud to myself ... "OMG" except I said the words and not the letters (but, I was always taught growing up to say "gosh" and not God, OK?)!  And now I have to do actual research some more (which I don't currently know exactly how to do).  I wonder just HOW brilliant Mozart and Bach were?  hmmm?  

You can read this with a "stoner voice" and it fits.  


More concretely what are you talking about?  What's this math formula that fits music you're thinking about?


*Bob sniffs the air.*


*Bob is aware he has no idea what odor he would be sniffing for.*

[m1469]

Yes, you're right, anything I ever "realize" just kind of sinks into oblivion compared to the new questions it seems to bring ... no matter how exciting it seemed to be when being realized, and no matter how long I had been chewing on the idea(s) before that.  It's already ages ago since I posted last  :-.  That doesn't mean it will not be concretely demonstrable in one way or another, though, and that's what matters.  It's still a very clear for me springboard and idea, but I've got research to do still ... and while that will help, I'm sure it will also get it all plenty mucked up, too.

[goldentone]

It's still a very clear for me springboard and idea, but I've got research to do still ... and while that will help, I'm sure it will also get it all plenty mucked up, too.

Perhaps I can assist you.  You can send me to the library while you stay back pondering.  I'll even bring you back coffee too.

[goldentone]

Everything went really far and then really near and then really far and then really near and then ... I got this other idea and accidentally I said out loud to myself ... "OMG" except I said the words and not the letters (but, I was always taught growing up to say "gosh" and not God, OK?)!  And now I have to do actual research some more (which I don't currently know exactly how to do).  I wonder just HOW brilliant Mozart and Bach were?  hmmm?  

You're cute.

You're thinking about Mozart and Bach, and I'm thinking about Beethoven.  I believe these three are the top three composers, but not sure on the order.  But I've got my top stop reserved for only one.  One only.

[Bob]

Does this help?  







What's the idea?  The short version.  You must have some piece of it you can explain.

[ajspiano]

I hardly have the skills to relate it back to maths but I have a fairly obvious experience when improvising/composing of what simple MUST happen next (what my mind conceives) - and if that is not adhered to even in a minor way it results in a butterfly effect kind of alteration to the music. It doesn't go back on track, it takes a new track.

If im not doing that, the music is effectively not there it just becomes scale patterns and exercises.

That's where I would expect the "equation" to exist, at conception, as if with every new note (or motif, theme etc) the function is run, and there is a variable that my brain sticks into it which alters the general direction. And the variable is controlled by whatever stimulus, emotion, other music, past themes.

I can't really figure this out when looking at how composers string notes together.. Playing their music an studying its constructs increases other potential variables (musical vocabulary) or perhaps the complexity of the mathematical function - but I'm not really sure how to derive what they were doing mentally to conceive the music. I don't know what their function is, only their results.

I guess it's a bit like deriving the function from a pattern of numbers..
From 1 2 4 8 16 we can derive that the function is x2. - music seems a little more complicated and too variable to be able to figure out what someone is doing.. At least not without having an understanding of your own processes - by that I mean that we can not figure out the "x2" function without first understanding numbers in order, their patterns, what multiplication is etc..

[ted]

The next numbers in that series could be 23, 28, 38 .....from the equally simple rule of adding the digits. I actively relish my brain sticking in those arbitrary things which lead to the improvisation taking a new direction. For me that process is absolutely essential to life in music, else I wouldn't bother. Complete predetermination and total randomness seem to me equally destructive of vital improvisation. The question of exactly how we can best attain the magic, intermediary, blissful, mathematically chaotic state has preoccupied me for a lifetime.

[m1469]

Perhaps I can assist you.  You can send me to the library while you stay back pondering.  I'll even bring you back coffee too.

mmmm ... coffee  .  Beware, that hints of a style of living I could not only get used to, but also come dangerously close to completely thriving within   .

You're cute.

Thank you

You're thinking about Mozart and Bach, and I'm thinking about Beethoven.  I believe these three are the top three composers, but not sure on the order.  But I've got my top stop reserved for only one.  One only.

Well, yes, I do agree as much as I can at this point.  I think part of the deal for me right now is that I actually see Mozart and Bach as being somewhat like-minded, I guess I think they have a similar kind of frequency, though they obviously expressed themselves in the ways which were more relative for their respective times, etc..  Beethoven, on the other hand, while hugely "up there", is his completely own guy it seems.  Even though his viewpoints would naturally have *some* kind of influence from the other two, he's on a different frequency and there's something ... different about it that I don't know enough about yet in order to describe.  In order for me to help myself, I feel I need to establish something somewhat clearly about each composer before I start comparing and I've just naturally attached to Mozart and Bach for the moment, as a kind of starting point.  I am extremely interested to find out more about Beethoven though, too, and feel it's right around the corner.  

Here is a (crude) drawing that finally I did this morning:

[Bob]

Still sounds like Schenkerian analysis with those patterns....

[m1469]

Well, it might be, but I didn't truly understand what Schenkerian analysis is upon reading it that once.  I'd have to go back through and read again (which I will do).

Also, I'd love to know people's thoughts on that little drawing I posted, if you feel you wouldn't mind telling about it; I would be most appreciative (even if it's honestly "I haven't got the slightest idea")  .

[ted]

The sort of nested, self-referencing hierarchy in your drawings is what Douglas Hofstadter thinks music, consciousness and almost anything is about, m1469. Might be, might not be, I wouldn't have a clue. You might get a lot out of reading his "Godel, Esher, Bach" though; if you can be bothered wading through two inches of book, the core idea of which he could have written in about three pages.