What are the real characteristics and function of a Tonal Center ?

[m19834]

The other day I had kind of a major thought about this and I would like to try to articulate some of what I am thinking, so as to better move forward.

I realized that a "Tonal Center" acts as kind of an "axis" of sound, that in my mind is best described as horizontal.  So, if we just take a scale, Do is home and acts as the X-axis of sound (or sound memory).  Every other tone of the scale relates to Do in their own particular ways, creating a second axis of sound that is perpendicular to the first axis (Y-axis) :


 
Though, it seems that these axis are not straight lines, but rather spherical planes (that extend forever) :




And, I wonder what fills in the spaces between the characteristics of the planes ?  Is it just the sound waves themselves since they don't actually exist on just one plane ?  It seems to me that the experience of sound overall should actually create a circle, since sound waves actually move from their source in a spherical fashion.

Also, it seems that the entire thing would be moving ... forever (it is considered to be the fourth dimension ??).

My thoughts though are, perhaps within a single piece of music, the concept behind modulation is, or was originally, meant to be a kind of experience in an aural land that is still relating to the original tonal center.  I remember the Walter Ramsey (I think !) posted something about this in a thread that I started over a year ago as I was working to analyze a score.  I wonder if I am on the right track ?

Along these lines though, I wonder again now about the idea of "fixed do" vs. "moveable do" and if there is actually, truly, one that is more "true" than another.  In fixed do, for example, there is not truly a modulation and then everything that exists in sound is maybe still compared to C as do ?  Which would require a crazy kind of consciousness of "do" (perfect pitch) for a piece written in an entire other key to make sense.

Okay.  I KNOW that I am not making sense but I had to start these ideas and I will come back at some distant time to work a bit more on it  . 

I think I ought to go practice now 

[db05]

Just a thought, if you don't mind.

https://www.aruffo.com/eartraining/research/phase7.htm
Scroll down to June 18, 2003. Lattice and Tomatoes. What do you think of WA Mathieu's harmonic lattice?

[javacisnotrecognized]

While an in depth response will have to await my fully processing this idea, have you heard of or seen the "Music animation machine"? It is a program that creates a visual representation of music that could, for example, use a different color for every voice in a fugue. There are some videos uploaded here: https://youtube.com/smalin.

[m19834]

I read through the lattice and tomatoes thing.  I will need to go through it again to get exactly the ideas about how he builds the lattice (as in, "adds two" and whatnot), but I think it very much relates to what I am basically trying to express.  This is the basic concept of music (or harmony and tonal center anyway) that I currently have :

"(...)the nature of this lattice is not to go up in distance like the relative scale, but to expand outward into harmonic complexity.  As Mathieu describes it, "[music] is made... from the center out, more like the concentric forces of an atom (...)" WA Mathieu

On top of all of it, I know that the overtone series has to have some kind of connection in all of this.  I guess my biggest question right now is, if "fixed do" could be considered forever the starting point, as though "C" is the permanent constant, and every other tone that exists in tonal music is just further or closer away to it.  And, I am curious how things work in other cultures where they have either pentatonic scales, or where they have quarter steps and these things.  I don't know how they think of "tonality" or tonal centers there.

The thing is, this is somehow a concept I have had of the piano and of tonality since I was a child... hmmmm.

I looked at the animation machine thing, and it's interesting.  I don't know, I need to think about all of this more.

I guess another element that is on my mind with all of this is how it all relates to time, especially since it is generally accepted that Western music is strictly temporal, which I have struggled with in terms of concept as the years have gone on.  If you consider something like this lattice, or if you approach the concept of increasing harmonic function by working outward, it kind of changes the concept of "time" and all of these things existing linearly, which actually makes MORE sense to me.  Instead of time, per se, it would seem there is more just a matter of harmonic and tonal "goals" ... where our experience in music is just some sort of lattice work of outward growth from (or inward movement towards) the tonal center, whose complexity is perhaps somehow complimented by time, but not necessarily ruled by it ... though they are interwoven.

To me, music is (or to me "should be") a kind of kaleidoscope experience.

[javacisnotrecognized]

I think it may be instructive to think of it as more of a process. Say you have a graph, like the first picture in the OP. For each change in tonal center you would figure out how all the the notes being used are from this tonal center, and it could be added to the graph as a line. Thus it forms a map of the relations between the tonal centers themselves, and the way the music is organized around each center. Is this kind of what you are talking about? (I think I saw this on an episode of Star Trek once)

[m19834]

Yeah, let me see if I can better relay what I am thinking.  So, you say about thinking of each tonal center as kind of a graph, where I would find out how each note relates and these things.  Let me try to show what that would look like in my head if I were to kind of graph it (each "plus" sign = x and y axies) :

So would I think of it as strictly this way (a piece of music modulating up a fifth, let's say)

                  V (G)     + (an actual new tonal center with its own graph)
     
I (C)  +                            I (C)  +


Or would I think of it this way :

           V (G)  ------------- (more of a plane as part of the original key/graph)
     
I (C)  +.......(forever keeping "do" in mind).... I (C)  +


hee hee ... I don't know if that explains it any better.  But, maybe that's because I didn't see the particular Star Trek episode  :-

[m19834]

I want to find the tonal center of the Universe  .  There is, in my mind, some kind of lattice for all of existence, everything originating from one source.  And, that is the level I want to know music on, and that is how I want to express music.  I would like to express music from there.




Universal Tonal Center, Universal "DO", from which all of musical existence originates and emanates.  Everything on one, grand "grid" ...

*daydreams*

[javacisnotrecognized]

If searched the entire universe, you would not find it. Do you know why?









It's inside you.

[db05]

I want to find the tonal center of the Universe  .  There is, in my mind, some kind of lattice for all of existence, everything originating from one source.  And, that is the level I want to know music on, and that is how I want to express music.  I would like to express music from there.

I don't think there is ONE tonal center for everything, but different personal centers. Or maybe centers for different universes entirely. Imagine if we could map out the C major lattice and connect it to the different keys and extend that to infinity... that is just the 12 tones we use in Western music (assuming A around 440 Hz), in infinite octaves...

What about the other Hz that we don't use? What makes them out of tune? It's just because of the arbitrary A = 440 that we only hear these musical vibrations as "out of tune" or "strange". I think my tonal center is one of those.

Have you ever heard the band Mineral (coincidentally, my signature is from their lyrics)? A lot of rock bands are out of tune, but it seems that these guys are decidedly out of tune. I would try to sing along, but it sounds awful since my voice naturally gravitates to the "normal" scale. One of my favorites, yes, because I am "decidedly out of tune" myself. It just so happens that I got a practice piano 1 1/2 tones out of tune. But maybe it is destiny (law of attraction?). The piano gives a harsh sound, much like the bands I enjoy listening to. Somewhat "darker" than most pianos.

[m19834]

If searched the entire universe, you would not find it. Do you know why?









It's inside you.

 

[Petter]

https://en.wikipedia.org/wiki/String_theory any help?

[javacisnotrecognized]

If searched the entire universe, you would not find it. Do you know why?









It's inside you.

That wasn't some kind of metaphorical statement. There are actual physical locations inside your body that mirror aspects of your music. Try to locate them.

[db05]

Ma'am Karli, you might be interested in this book: https://www.amazon.com/Compose-Yourself-Awakening-Rhythms-Life/dp/0738704180

I have a copy I got from a sale that I read once, but didn't make much of the exercises. I'm too lazy for that LOL. It relates the seven elements of music to the seven chakras and includes exercises for developing personal resonance. There is also an appendix of recommended listening at the end for the different styles = different chakras.

[m19834]

That wasn't some kind of metaphorical statement. There are actual physical locations inside your body that mirror aspects of your music. Try to locate them.

Yes, good, I am glad it wasn't a metaphorical statement because, sometimes I get tired of some of those when they are supposed to stand alone.  I believe I know what you are talking about, and probably I will actually take some time to do this when it seems right.  For now, I need to be more strict with myself ... hee hee, I think, and stay focused on some specific things.

Ma'am Karli, you might be interested in this book

Thanks, DB, for the book reference.  Similarly to my above statement, I will check it out at some point (and I believe I read once something by Bernhard regarding some of this), but maybe not right at the moment.

*goes back to work*

[m19834]

I came back to this section to post in a thread about fixed do vs. moveable do, but found this thread (that I had forgotten about) and decided -- after reading through the tread -- to post here, instead.  As of this morning, I have officially decided that I am deeply a fixed do girl.  I have been ever since I was born (), but didn't have names for it way back when and got confused somewhere between then and now.

I am posting now mainly as a way to organize my thoughts on the subject as I see it at the time.  Firstly, I plainly like fixed do because it gives each tone (not just note, but tone) a fixed name.  Within the system of solfege, these fixed names have implied relations to each other, far beyond any relationship I have ever been able to grasp between letter names (such as "C").  The system of solfege in general implies tonal polarity, and this kind of tonal polarity can be found in many places within the tuning system of the piano.  What I like better about fixed do vs. moveable do -- aside from fixed names -- is that I believe it actually holds deeper secrets, implies deeper meaning, and lends itself to a deeper understanding.  For example, I find it very interesting and much more informative that the same kind of tonal polarity can be found between ti -- do, as can be found between fi -- sol, given the right contexts.  Fixed do keeps the context of how all of the tones work together, and when the same tonal polarity between fi-sol is achieved as the affect one would get from ti-do, this affect is indicative of a kind of movement without losing the original barings.  Whereas, moveable do is, it seems to me, a kind of surface-level way to address the sense of tonal polarity that can be achieved in different scales, and leaves behind the context of how all tones on the piano interact and relate to one another simultaneously.  As though we can take one scale out of the context of the tuning system, or out of the context of the rest of the tones.

Well, I have no idea if that makes sense to anybody.  I think that somewhere, in some heart either near or far, it makes sense or means something to the right person(s) anyway.

[m19834]

Okay -- Just further clarifying my thoughts.  Fixed Do, as I see it, represents the Principles of tuning that the instrument is built upon.  Its name is even indicative of its behavior in the sense that it respresents something which is "fixed" about tone and sound and how pitches relate to one another.  Moveable Do is an aural affect; it is basically something that we experience as a result of Fixed Do.  Moveable Do is basically a "mode" and one of several. I think that is important to grasp, and in a sense, it is beneficial to "know both" and how/why they exist as they do.  Moveable Do wouldn't exist without Fixed Do, and I don't think the inverse is true.

[prometheus]

I don't think it makes sense to adopt some complex way of looking at something unless it adds something or explains something new.

I don't see a good way to relate every tone in 2 or 3 dimensions to the tonic. One thing makes most sense, imo and that's to give each tone a value on how strongly it want's to resolve to the tonic.

And this is incomplete information. Each note can be followed by each other note in the context of a certain tonic. If you keep it strictly tonal there's 6 values for each tone. And measuring this objectively is not easy.

As for tonal center. Each frequency is just as good as any other to be a tonal center because each tone has all the overtones and possible intervals every other tone has.

As for the function of a tonal center. It's function is to make music interesting by establishing the tonal center, weakening the tonal center, then strengthening and then reconfirm it. It is very analogies to how story plots develop.

[m19834]

Thanks for your post, prometheus.  I read it initially and have been further clarifying my thoughts and questions, and now I have read it again and I see it a little differently than before (it's funny how that happens !).

Firstly, I am definitely not "adopting" anything, per se, but simply organizing my mind.  There were certain elements to my understanding of tone that were somehow (luckily ?) established when I was extremely young and was just working at the instrument all on my own.  These days for me invovle large quantities of going back in time, so-to-speak, and organizing many aspects of my musical upbringing (which was nearly entirely without a teacher until my 20's).  So, for me, this is not a matter of trying some kind of conceptual clothing on to see how it fits, exactly, but rather a case of finally finding some kind of order and organization for very deep experiences, in a way where I can hopefully much better call upon and use certain informations that I had in what seems like another lifetime.  For me, it is a very strong sense of coming home.

Each of your points helps me further clarify my thoughts, but overall I realize that most of what I think you are saying is based in a form of tonal relativity, which is what I am currently thinking of as "moveable Do."  Moveable Do is "all about" the experience of tonic and dominant and how each tone wishes to resolve to what we call tonic.  This, I don't argue with and can now more plainly "see".

What I am thinking of in terms of fixed Do is a bigger concept, though something which envelopes the experience of relative Do (etc.).  There is a much different kind of Tonic, for example, involved with it in a way that I can't currently put my finger on, exactly.  I can say though that as a child, I could inwardly feel these pitches and movements away from and towards others, I could feel intervals -- they were more than sounds and pitches, it was something much, much more, and I specifically remember so much of that "revolved" around C (and I don't think this is simply because that's what I was originally "shown" by my Mom).

So, where this leaves me right now is that I am just working to better understand pitch itself.  Yes, I 'get' that there are overtones and such.  I 'get' that a single tone is not exactly what it seems.  Actually, that is part of why I am continuing to dig -- there just must be some kind of basic value or basic concept that I just don't have words for yet.

I was reading a theory book just moments ago, even going back to the beginning where it is "explaining" pitch and such, and it gave a little historical background to some of the concepts.  I found something which I didn't know in that, apparently, from about 800-1430 and in the Renaissance (roughly  1430-1600), musical relationships were understood in hexachords in a standard pattern of W-W-H-W-W, and apparently (?) first started on C.  Apparently the first ever accidental came as a result of wanting to allow the hexachord to start on F instead of C, and then what followed was a hexachord beginning on G.  Firstly, this is crazily significant to me -- as in it causes everything within me to sound all alarms !  But, secondly, there is SO much that is unexplained in that and which is being taken for granted (because there are parameters to the book and most people probably don't want to know what I want to know about it).

I finally started being able to articulate my questions.  Aside from the fact that these early hexachords reflect the tonal movements from I, IV, V (as we could think of it today), they also called the hexachord built on C the "natural" hexachord, the one built on F the "soft" hexachord, and the one built on G the "hard" hexachord.  That may not seem like much, but WHY do they name them like that, and also, WHY did they ever start with C, and WHAT was the natural flow which led them from there to the IV and V ?  And, even beyond that, I was finally able to articulate my deepest question regarding tone itself.

How did a "single" tone every become distinguished in the first place ?  To me, it seems that all tones are actually some form of being indistguished as individual tones.  This is not as reflected on something like the piano, because we visually see that each tone has an individual key and it is very easy to take that at surface level.  But, on something like the violin, for example, or in singing, where pitch can audibly "bend" and all of the distance "between pitches" can be explored in greater depth, I think illustrates part of where my questions currently lay.

To me, it's as though tone exists as one great sound (though it's more than sound) -- as though there is just this huge bog of mud.  How did somebody originally EVER distinguish that there was in fact a grain of sand (or so) within that bog of mud ?  I don't get that.  How did we ever decide that the whole bog of mud was in fact made of individuals particals ?  AND, what made somebody distinguish C first ?  What in the freaky french fry does it represent

Now I'm angry ... haha.  I need to go practice and calm myself down.  

[m19834]

aaaaaahhhh ... (HELP !) ... me can't stop !!!!!! 

Okay, Okay, Okay ... so, my thoughts just leaped into somewhere crazy and I am currently overwhelmingly and completely obssessed by this, DESPITE the fact that I have many other things to be doing.  I HAVE to write this down here ... I'm possessed !!

Okay.  So, here is my current theory/hypothesis and I need to try this out --

Firstly, the hypothesis and theory starts with a fundamental idea which I can't claim to scientifically know as fact, though I SUSPECT it could actually be scientifically proven (or has been or whatever).  In that, I think there IS, in a very real sense, just one, giant, great sound ... one, giant great utterance from the Universe (and even just as the Universe as we know it).  I think that all of this sound, its essence lay in great depth beyond "sound" as we humanly think of it, but even as we do humanly think of it, it envelopes every, single, sound and even includes silence as one humungous ... well, concept, really.  The perception of there being breaks in sound (ever, at all), there being specific pitches, even, is only perception born of a limited view and the seeming inability to comprehend the entire "picture" -- that perception is relative though, and doesn't erase the bigger concept.

So, let's say that is true (which to me, right now, it most certainly is).  My next step is that the CONCEPT of "DO" in a fixed way, actually represents this HUGE, SINGLE sound (which envelopes all sound that ever existed and exists and will ever be) -- it's like the SUN, it's like light -- it's just everything at once -- even an entire symphony, even multiple symphonies enveloped all at once.  Even all of creation ... hee hee hee.

BUT, IF that's true (?), what is to be said for something/somewhere like SOL ?  If it's true, everything else could only be a concept in relativity -- if it weren't true (but it is), then the existence of an actual Universe of SOL outside the context of a Universal DO (not necessarily thinking in pitches anymore, but entire universes and everything that ever existed ... haha), would negate the entire idea of Do.

hmmmmm .... But, a Universal Do HAS to be true !!! 

[m19834]

hmmm ... yes, any moment I will go back to the piano forever (haha).  But, I just went up the thread a bit and read my post where I posted the Sun.  Yep, that's a representation of Universal Do, and I see that now nearly two years later I actually on some level truly understand what I suspected then.  What I realize today in articulate terms is what I was looking for then.  What I didn't expect, exactly, was to feel as though the only thing that can possibly exist is Do and nothing else.  I mean, I sort of thought that could be, but I didn't expect it in conscious terms.  Life is crazy.

Now, this is all fine and dandy, but how to make anything like this practical ?  I know, practice, study, research.  But, does anybody in the world see that I simply can't just stop being a musician ?  That this is something very deep to me ?  That ... that ... that ... I also need YOU ?  Does that even count for ANYTHING ??  bah.  I love that this thread is hiding in some secret place in some secret, barely used, barely noticed child's board.  Entire lifetimes are living themselves out in my head right now ... so what ?

Okay.  Now I really go.

[pianowolfi]

Karli, fireheart


(This emoticon is supposed to represent a rib crushing Thalhug  )

I think you might want to explore "Harmonia mundi" (or Harmonices mundi) by Johannes Kepler (1571-1630)

https://www.keplersdiscovery.com/Harmonies.html

I haven't read that yet but stumbled on it when I was doing a google search on "skeleton" "intervals"
after having read your last posts here. I'll definitely read that someday

P.S. I found a very interesting comment on that book here:

https://www.amazon.com/Harmony-Memoirs-American-Philosophical-Society/dp/0871692090?ie=UTF8

Today's scientists of all disciplines would do well to study Kepler's original work. This is not only a seminal work in the history of astronomy, but a case study in the creative process of discovery. By rejecting empiricism and sense certainty, Kepler used his mental instruments, geometry and music, to investigate the harmony which orders all fundamental physical processes. The same mental processes which make humans unique must be coherent with the principles of creation and development of the universe as a whole.

which, as I think, represents the essence of it. Music not only as random creativity but as a creative force and a "divine joy of creating a world".

 

[pianowolfi]

bah.  I love that this thread is hiding in some secret place in some secret, barely used, barely noticed child's board.  Entire lifetimes are living themselves out in my head right now ... so what ?

It's the price and the advantage of being here incognito.  

[m19834]

Well, there is certainly one thing that is very evident through this, it is that I really know how to get my undies in a bunch  .  Thanks for posting those links, Wolfi, as it is helpful and I have read about the Kepler stuff before -- at least the part about the string producing a tone and such (I guess that's pythagoran, too) -- and it just didn't quite organize for me before.  I know there is more to it than that and I will read, but it does take some of what seemed so mysterious to me out of the equation (which is mostly a good thing).

In the meantime, thanks for those links and for the vicarious Thalhug .

[pianowolfi]

I hope it can be more to you than only some links, as to me it is something that I feel deeply inside, music (the Logos) constitutes the world, dynamically. As I said before I haven't read it yet, except some little excerpts and these little excerpts have electrified me.

[m19834]

Well, it is, of course.  It's just that sometimes I reach these states of emergency and complete agitation over these ideas, and it's very ... seemingly pointless sometimes, in the end.  I'm just this silly person, sitting in this silly house, and barely a soul has any idea who I even am, and even fewer people even care.  I don't mean that in a belittling way, either.  It's just, I know how the world works, or at least a little anyway.  I also know that it's just not possible, or at least not actually productive for me to try to live in a perpetual state of emergency and agitation about all of this.  I mean, my mind takes me into these far out regions and then the reality is that I simply have to "come back" (and this is a good thing, too) and put anything of any value into real use.  The reality is that I must keep working very hard, and that's okay, I accept that.  Sometimes it just ... I don't know.

Anyway, projects beckon.

[pianowolfi]

When you go beyond emergency and complete agitation and keep your track there will be (burn) still enthusiasm

[m19834]

When you go beyond emergency and complete agitation and keep your track there will be (burn) still enthusiasm

You're right, Wolfi, thank you .  Very much. 

[pianowolfi]

You're right, Wolfi, thank you .  Very much.  

Glad it helped
Regarding the subject, I think that there is a whole huge metaphysical idea involved which is difficult to discuss and might go beyond the scopes of this board.
A music-theoretical approach to it might be possible though. Perhaps you can develop it?

I just had the idea to start at the difference between something so basic as F# and G^b
There is something in us that "corrects" the well tempered tuning and we hear actually a difference between these two notes, if they are played on the piano within two different harmonic contexts.
Likewise I think that what we hear as music might be actually all like this. The physical sounds just stimulate us to hear the *real* thing, the *real* music, and this music happens actually "inside". But this "inside" in itself has two aspects, the "inner" and the "outer" inside. I mean, our inside experience of the ideal sound is not only in us, but leads to an "inner outer" world which is not only subjective but as objective as our outer physical world. Like in the physical world exists such a thing as the difference between our body and other objects/subjects which belong to the outer world, there must be a difference between our inner self and the outer "inner world".
Lol maybe I'm getting really complicated here...

[m19834]

Well, I think that ultimately the "discussion" takes place in music itself, and it is a wonderful thing if more than one individual experiences it simultaneously, which is why I ever have a notion of performance, btw (however, it will obviously not easily be achieved every time ... at least, I am very much still in training here).

I will tell you of something quite interesting though (imo), sometimes, as I am just quietly and very deeply "contemplating" the world (what could perhaps be called a kind of prayer), I get this glimpse of a kind of universal harmony, a kind of univeral principle of harmony, and its domain.  And, lately there comes with it a kind of tangibility which I can "hear" with some sense, and actually sing a pitch of "do" (as middle C) and be correct -- and, I am getting to where I really know that I am correct before I check it. hmmmm ... 

In any respect, that is very much along the lines of my childhood experiences .