How am I to take this statement, Million? What radical idea are you trying to convey?There are good reasons I do not see eye-to-eye with proponents of CP tonality.
For example, the fourth is considered a dissonance in CP tonality, and it is.
I'm having problems with my posts being erased, so I'm having to post in small increments. You may want to read my whole post before responding. Sorry for the inconvenience.How am I to take this statement, Million? What radical idea are you trying to convey?
Bach was not a proponent of CP tonality, he simply accepted its framework and produced the works he did. And I believe he considered the 4th as a dissonant interval and treated it according to the "grammar" of the time (that lasted at least until Bruckner). What is your point, bon sang!?
I'm saying that all function derives from the vertical relationships of the harmonic model. All horizontal relations came later, and are cerebral constructs, and arbitrary.How am I to take this statement, Million? What radical idea are you trying to convey?
Bach was not a proponent of CP tonality, he simply accepted its framework and produced the works he did. And I believe he considered the 4th as a dissonant interval and treated it according to the "grammar" of the time (that lasted at least until Bruckner). What is your point, bon sang!?
I really don't have the time for this, but I will indulge you for the moment.I'm having problems with my posts being erased, so I'm having to post in small increments. You may want to read my whole post before responding. Sorry for the inconvenience.
But perception as you speak of it takes place over spans of time. This does not represent sound, it represents perception.Well, I do hope so!
No. Why should we hear "C as tonic" if the note is played in isolation? It's just a note in isolation. It's as you suggested before, we can be walking down a road and hear an air-con unit from an open window in the street and hear a pitch (could be a C, could be micro-tonally just above a C) - why call that a "tonic"? Calling notes tonic or subdominant and so on is already going to condition how you listen to and process those sounds. If you then hear an F below, we may well (as classically-trained musicians) perceive that as a fifth below but why hear that as the root if there is no 3rd to confirm? Are you thinking and hearing sounds in CP terms? You are making big assumptions about the ways other people hear and respond to sounds, Million.But perception as you speak of it takes place over spans of time. This does not represent sound, it represents perception. For example; if we hear middle C, we hear it as "tonic" in isolation.
Sure, the F below the C becomes a fifth (in CP and aural analysis) but not that F is the root as in F major; and playing the G after the C also makes a fifth but that does not confirm any root or tonality.If we then hear the F below that, C suddenly becomes a fifth, with F as the new root.
If we hear C, then the G above that, C still retains its rootedness.
Or function (in C major) as a 7th in VI6. Its vertical pitch function (out of time) as "V" will be diluted by its horizontal role as a secondary 7th. But you said before you are not interested in CP harmony, so again I don't see where you are going with all this.G will always be the fifth in a C scale.
Sure, on paper 'F' will always be the 4th of the scale but could be a fifth or a fourth as an interval.F will always be a fourth in C.
Harmonic context can change, for sure. The relations within a scale are fixed only in terms of stylistic grammar, they are not all set in stone for all time. Function, in the grammar of CP, can only be heard within the context of the vertical and horizontal, the y and x axes.Context can change; it is arbitrary. The relations within a scale are fixed. Function is determined, and given meaning, by the vertical.
I'm just using musical nomenclature out of habit when I say "tonic." I should have said "tone center."But there is really no difference; the isolated C functions as a "tonic" or tone center.No. Why should we hear "C as tonic" if the note is played in isolation? It's just a note in isolation. It's as you suggested before, we can be walking down a road and hear an air-con unit from an open window in the street and hear a pitch (could be a C, could be micro-tonally just above a C) - why call that a "tonic"?
I disagree, since I see the various functions (tonic, dominant, etc.) as being derived from the harmonic hierarchy, which is the model of one note and its harmonics. The functions are already "inside" this note, as inherent relations to the fundamental. No perception or processing through time is necessary. The function is built-in to the scale hierarchy, whatever that scale may be, as a harmonic model.Calling notes tonic or subdominant and so on is already going to condition how you listen to and process those sounds.
I always back up this 2-note interval perception theory by referring people to the book I got it from, Schoenberg's Structural Functions of Harmony, which explains root movement and progression in terms of interval perception. You want the details? I can paste a previous explanation, but I'm tired of going over and over it.If you then hear an F below, we may well (as classically-trained musicians) perceive that as a fifth below but why hear that as the root if there is no 3rd to confirm? Are you thinking and hearing sounds in CP terms? You are making big assumptions about the ways other people hear and respond to sounds, Million.
That's what the perception of tonality is based on; the way things sound to our ears.Sure, the F below the C becomes a fifth (in CP and aural analysis) but not that F is the root as in F major; and playing the G after the C also makes a fifth but that does not confirm any root or tonality. You are just taking notes in isolation and applying possible basic tonalities according to the habits of your ears.
You're trying to stuff a horse into a suitcase. All I've really said is that tonality is a potentiality which is self-contained in its vertical relationships to "1" or the root fundamental. I never said that this could not be elaborated on, or that it invalidates the horizontal activity which results, or that the horizontal invalidates the vertical. I don't really see a conflict with the two views. Whatever works for you.It just so happens that when I hear a 'C' I hear it as the third of A-flat major, so when I next hear an 'F' I am hearing the subdominant, and when I hear the 'G' I hear the leading note. In your argument, you need someone to tell you what is the referent "key" for your argument to hold water.
You need to think about it some more, then, because I have all the source material and confirmation of these ideas that I need.Or function (in C major) as a 7th in VI6. Its vertical pitch function (out of time) as "V" will be diluted by its horizontal role as a secondary 7th. But you said before you are not interested in CP harmony, so again I don't see where you are going with all this.
I'm talking only of the key scale, and its functions.Sure, on paper 'F' will always be the 4th of the scale but could be a fifth or a fourth as an interval.
I disagree. Tonality, and function, are potentialities which are self-contained in their vertical relationships to "1" or the root fundamental. I never said that this could not be elaborated on, or that it invalidates the horizontal activity which results, or that the horizontal invalidates the vertical; but only assert that the vertical relationships are primary, and came first. The horizontal is simply an elaboration of these functions, and can bee seen as "playing" with them.Harmonic context can change, for sure. The relations within a scale are fixed only in terms of stylistic grammar, they are not all set in stone for all time.
Then stay within that paradigm, if that works for you, but don't attempt to invalidate my truth with your CP truth.Function, in the grammar of CP, can only be heard within the context of the vertical and horizontal, the y and x axes.
I know it's hard to keep threads airtight, but I'm a little dismayed that I need to go to another thread to be able to fully understand where you're coming from. I'm going to have to address your post #49 at a later date.http://www.talkclassical.com/38920-serialism-move-forward-backward-11.html
I refer you to this thread, starting on page 11. This stuff has already been hashed-out.
I'm sorry for the inconvenience, TalkingHead.I know it's hard to keep threads airtight, but I'm a little dismayed that I need to go to another thread to be able to fully understand where you're coming from. I'm going to have to address your post #49 at a later date.
I sort of agree with you to a point. (And I really like your way of thinking, as always, even when I think differently.) "All horizontal relations are cerebral constructs and arbitrary", this is the key. But I tend to think that it is indeed these cerebral constructs that may indeed be arbitrary, that make up what music is to us as human beings. I don't believe that music is sound. Music is what sound points towards, it's an arbitrary and necessary cerebral construct. Sound is the appearance of music. Sound is being, but being lacks meaning. Music is the meaning. And meaning may be an arbitrary construct. A castle in the air that is nonetheless necessary.I'm saying that all function derives from the vertical relationships of the harmonic model. All horizontal relations came later, and are cerebral constructs, and arbitrary.
CP tonality is an arbitrary procedure of dealing with music, and should be seen as arbitrary. Tonality is derived from the vertical, not the horizontal. The horizontal can reinforce a sense of tonality. but tonality in its essence is vertical, as are all functions.
This is also extremely clarifying. I realize that I'm indeed in the camp that is averse to too much receptiveness, prefering a controlling thought process. Music is not instantaneous, natural and universal to me. That's sound. And sound is not music. I don't want to "be", I want to "mean". But I'll grant you that a certain degree of "being" and receptiveness is needed lest we desiccate into mummies (or petrify into Greek statues, which is much more beautiful!). Wagner was into this "being", this refreshing receptiveness, I think. But I think that this idea of "being" must be told to us in the terms of "meaning". I.e. we need an artist-philosopher-hero to tell us by language and concepts that we could actually be human beings every once in a while.The sum of it is that perception of music is instantaneous, natural, and universal. This opinion is at odds, apparently, with those who assert that, for one example, tonality is not perceived except as a long, involved thought and perceptual process of the conscious mind, which makes connections and relationships over spans of time, only. I disagree with this, and with the entire way of thinking this embodies. To me, the perception of any art involves a certain posture of receptiveness, not a controlling thought process.
Well, I'm certainly glad we've cleared that up! But I never said 'all sounds are harmonic' in that sense. That would be stupid, wouldn't it?Firstly, to clear up the point about whether all sounds are harmonic or not - the answer is: not all sounds are harmonic. In fact most sounds are correctly described as inharmonic. White noise is an inharmonic sound whether or not you decide to ignore large parts of its energy profile to find a pitch. A harmonic sound is is sound more or less conforming to the harmonic series - for example a violin string or the human voice. The further the sound diverges away from the harmonic spectrum (for example by including a much denser or less evenly distributed pattern of frequencies) it becomes less and less harmonic. That is the definition.
No, I don't claim that.Secondly, I will discuss the idea that all musical pitch relationships are inherent in the harmonic series. You don't seem to claim this...
I never said "the harmonic series" was anything but a model for scales....but I thought I should make it clear - the harmonic series doesn't play out for a great deal of contemporary music (spectralism somewhat excepted).
It's based on an hierarchy of ratios to "1" or tonic, like the harmonic series. All scales are models of this. It reeaaly is that simple. You can make it complicated if you wish, but you will be misinterpreting this general truth....If you are referring to tonality (you seem to claim this though I am unclear as to what you think tonality is) there is a relationship between harmonic ratios and tonality, but it is nowhere near as straight forward or 1-1 as you are making out.
I disagree. All that follows is the elaboration of the initial harmonic model, so, yes, it has"precedence" after that because there is nothing left to do but elaborate on that model, using thought-up musical ideas and mechanisms. It's called "composition," and it takes place horizontally in time....The consonance of a sound is often measured by beats. Simply put, the more near misses in the aligned spectrums of two or more sounds the more beats. A sound will be more grainy the more near misses in the spectrum we hear within the audible range. That is why a low piano note sounds so inharmonic and grainy, it is because so many of the overtones that are very close together are within audible range. As a general rule when it comes to harmonic sounds, they will have less beats the lower the epimoric ratio of their fundamental frequencies are. So, a 3:2 relationship generally has no audible beats if it is between two harmonic sounds. For this reason, when music started to include simultaneous voices, harmonic consonances were preferred. In the medieval era, 5ths and 4ths were perfect consonances to be freely used, while 3rds and 6ths were treated as imperfect consonances which had to be treated carefully. This also has a practical dimension - it is simply easier to tune 5ths and 4ths than 3rds or 6ths. As more and more voices began to be stacked together, the triad became an important unit. This is because it is the most consonant spacing of three pitches within an octave. I believe it is for this reason that 3rds and 6ths began to be treated freely, demoting 4ths to their position of consonant dissonance. To put it plainly, a 4th against the bass implies a lower virtual fundamental than the 5/3 or 6/3 positions of a triad as well as later becoming associated with the rhetoric of cadential suspension. From these starting points (8ve, 5th, 4th, 3rd as consonances) tonality grew. That is as far as the harmonic series relates to tonality. From then onwards it is the ordering of counterpoint to lead to logical successions of consonance and dissonance that takes precedence.
When music is scored, it has a vertical axis and a horizontal axis. This doesn't cause me any problem....Thirdly, a niggle of mine is when people use the terms horizontal and vertical. Music is not a spacial art (generally) and we should all be careful of taking the score as a literal map. Speak in time instead, there are simultaneities and there are successions.
Harry Partch backs this idea, and I'm sure Terry Riley and Philip Glass would as well. This is an ancient truth....On a more general note - this idea that all function springs from the harmonic series is very old fashioned...
I beg your pardon! If you feel that way, why am I even bothering to communicate with you about this?...and pretty useless theoretically.
That's irrelevant to the idea of a harmonic model from which arises all function....Of course, any sound art will take note of the way that multiple sounds work together, but that is not to privilege one spectrum above another, it is just a practicality of performance. Take a tonal piece and play it on a succession of large bells - it sounds pretty rubbish. That is because the bells aren't tuned harmonically so they do not fuse in harmonic ratios.
You're thinking very literally....The links of some human music to the harmonic spectrum is an accident of evolution, and not even reflected in all cultures, and not reflected in a great deal of western art music since 1945.
So why did you literally say "all sounds are harmonic"? And then argue with people when they pointed out that they are not? You know words mean things right?(I explain the not all sounds are harmonic) Well, I'm certainly glad we've cleared that up! But I never said 'all sounds are harmonic' in that sense. That would be stupid, wouldn't it?
Oh so your whole point was that notes have frequency ratios? I just had tried to read something extra into it because that would be a hugely asinine comment and a waste of everyone's time to point out.It's [tonality] based on an hierarchy of ratios to "1" or tonic, like the harmonic series. All scales are models of this. It reeaaly is that simple. You can make it complicated if you wish, but you will be misinterpreting this general truth.
What does that even mean?? How can something take place 'horizontally' in time? That is a meaningless phrase.it [composition] takes place horizontally in time.
So much to mention here:Plus, you forget that CP tonality has always been a compromise, from as far back as Pythagoras. He stacked 2:3 fifths, and closed the circle with error, to get an octave. Consonant triads are just an ideal which was never realized.
So you are saying harmony came before melody right? That is your basic premise? Except of course that ,historically, melody came before harmony. Ancient Greek theorists were speculating on a melodic practice. There is no good reason to believe that the precise tuning of the intervals to harmonic ideals had anything to do with Ancient Greek performance practice. Indeed, there is no evidence to suggest that they ever played notes simultaneously at all.(I write that consonance and disonance is related to harmonically but also other features of music) But my whole point is that harmonicity came first, and defined all the functions beforer any of the rest of it occured. Expectation, line, voice, and rhetoric is secondary.
It does mean you end up saying pretty nonsensical things though... Plus, I hope you realize that music can happen without a score?When music is scored, it has a vertical axis and a horizontal axis. This doesn't cause me any problem.
I doubt Philip Glass would have any opinion on this at all. As for Partch and Riley I don't think they are really the go to guys for understanding history, theory and history of theory.Harry Partch backs this idea, and I'm sure Terry Riley and Philip Glass would as well. This is an ancient truth.
Perhaps because you aren't totally close minded and are actually interested in learning about music theory. I thought that is what this forum is for?(I claim that function does not spring purely from the harmonic series)I beg your pardon! If you feel that way, why am I even bothering to communicate with you about this?
I think you think it is irrelevant because it really clearly contradicts something you have read recently. Also, you must think gamelan is irrelevant since that uses inharmonic instruments and doesn't use harmonic tunings. There is a whole world of practice out there!(I mention other cultures that don't tune intervals harmonically)That's irrelevant to the idea of a harmonic model from which arises all function.
No, I am trying to think about the real world and how music actually happens. If you have used language that was misleading, then I suggest you try harder to use terms like 'harmonic' and 'model' as they are properly defined.You're thinking very literally.
(I explain the not all sounds are harmonic)
Well, I'm certainly glad we've cleared that up! But I never said 'all sounds are harmonic' in that sense. That would be stupid, wouldn't it?
You keep referring back to the harmonic series, and that is too literal; it does not apply to what I am saying. 'Inharmonic" is defined as sound which departs from the whole-numbered harmonic series, and my model does not use the harmonic series literally, but as a model. You seem to have a problem with "abstracting" this principle out from the actual, literal harmonic series.So why did you literally say "all sounds are harmonic"? And then argue with people when they pointed out that they are not? You know words mean things right?
Tonality is based on an hierarchy of ratios to "1" or tonic, like (not literally) the harmonic series. All scales are models of this. It reeaaly is that simple. You can make it complicated if you wish, but you will be misinterpreting this general truth.
Not only do notes have frequency ratios, but these ratios are derived from their relation to "1" or the tonic. This gives them "function" which is manifest in degrees of sonance to "1". This creates an hierarchy, gradated on those ratios.Oh so your whole point was that notes have frequency ratios? I just had tried to read something extra into it because that would be a hugely asinine comment and a waste of everyone's time to point out.
No, the hierarchy is "hard numbers."Also, the harmonic series doesn't imply any hierarchy whatsoever. Any will to impose hierarchy resides in human conceptualization, not in the phenomena itself.
I disagree that no hierarchy is implied. All that follows is the elaboration of the initial harmonic model, so, yes, the horizontal has"precedence" after that because there is nothing left to do but elaborate on that model, using thought-up musical ideas and mechanisms. It's called "composition," and it takes place horizontally in time.
You will have to start thinking of a "time line." Apparently you have no experience with computer-based recording sysyems. Everything takes place on a time line. This visual way of depicting music in time is elementary. I'm beginning to think you are just disagreeing for the sake of it, or you enjoy "invalidating" other people's ideas.What does that even mean?? How can something take place 'horizontally' in time? That is a meaningless phrase.
Plus, you forget that CP tonality has always been a compromise, from as far back as Pythagoras. He stacked 2:3 fifths, and closed the circle with error, to get an octave. Consonant triads are just an ideal which was never realized.
Yes, but he invented our 12-note scale, basing it on fifths. To deny his influence is ridiculous.So much to mention here:
1) Common practice music stretches from 1720ish through to 1880ish in the main. Pythagoras lived thousands of years before that.
Wow, I never heard anybody completely invalidate Pythagoras like that. That's hubris to the nth degree.2) We have no idea what Pythagoras did with intervals. We have literally nothing written by him or anyone immediately around him. Some theorists from the Pythagorean school stacked 5ths and were interested in the tetractys. I think it is pretty outlandish to claim a musical procedure for someone we know next to nothing about. The myths surrounding Pythagoras are just that: myths.
CP tonality is based on an unrealized, imperfect, compromised model of perfectly consonant triads. Pythagoras stacked his 2:3 fifths in an attempt to get this. The "Pythagoran comma" is the compromise, in order to close the circle and preserve the octave. Major thirds (4:5) suffered greatly, hence, all of the tempered tunings like "mean tone" which attempted to get better M3rds.3) If you want to hear a consonant triad go and see a good choir. Whenever they hold a chord for a long time they will lock into a consonant triad. Or listen to a meantone organ. Or a good quartet. Or a barbershop quartet. Or an orchestra. Hardly an unrealized ideal.
(I write that consonance and disonance is related to harmonically but also other features of music)
But my whole point is that harmonicity came first, and defined all the functions beforer any of the rest of it occured. Expectation, line, voice, and rhetoric is secondary.
No, that is not my basic premise.So you are saying harmony came before melody right? That is your basic premise?
All I can tell you is that Pythagoras wanted those 2:3 fifths. Why he stopped at 12 is our problem now. Harry Partch calls it a five-limit system of octave division.Except of course that ,historically, melody came before harmony. Ancient Greek theorists were speculating on a melodic practice. There is no good reason to believe that the precise tuning of the intervals to harmonic ideals had anything to do with Ancient Greek performance practice. Indeed, there is no evidence to suggest that they ever played notes simultaneously at all.
When music is scored, it has a vertical axis and a horizontal axis. This doesn't cause me any problem.
Watch out. Don't get rude, or there will be a report.It does mean you end up saying pretty nonsensical things though... Plus, I hope you realize that music can happen without a score?
Harry Partch backs this idea, and I'm sure Terry Riley and Philip Glass would as well. This is an ancient truth.
What are your sources, then? You refute mine, yet you have cited nothing!I doubt Philip Glass would have any opinion on this at all. As for Partch and Riley I don't think they are really the go to guys for understanding history, theory and history of theory.
(I claim that function does not spring purely from the harmonic series)
I beg your pardon! If you feel that way, why am I even bothering to communicate with you about this?
I've given up on "teachers" who do not grasp their ideas in depth.Perhaps because you aren't totally close minded and are actually interested in learning about music theory. I thought that is what this forum is for?
That's irrelevant to the idea of a harmonic model from which arises all function.(I mention other cultures that don't tune intervals harmonically)
I think you think it is irrelevant because it really clearly contradicts something you have read recently. Also, you must think gamelan is irrelevant since that uses inharmonic instruments and doesn't use harmonic tunings. There is a whole world of practice out there!
Don't presume to tell me what you think I am thinking.
You're thinking very literally. Besides, Balinese Gamelon music is essentially melodic, not harmonic.
If you can't use more general definitions of "tonality" and "harmonic," that's not my problem, although I suspect that this "specific definition and meaning for everything" is the biggest part of your argumentation strategy.No, I am trying to think about the real world and how music actually happens. If you have used language that was misleading, then I suggest you try harder to use terms like 'harmonic' and 'model' as they are properly defined.
