Question about Polytonality and pillars...

Hi, I was wondering if anyone knowledgeable on the subject, could answer the following:

When composing polytonal music, do both keys have to be established in the same way? I understand the ultimate goal, is the V pillar to the I pillar, however leading up to that point, say one key is established through a

iii-vi-ii-V-I progression, would the other key have to progress in the same way, at the same time? In other words: do one of the pillars have to be present, at all time?

Thank you

Short answer: No.

Long answer: depends on how you use the pillars, how the context causes one to be more prominent over another or if they're equal, etc.

Short answer: No.

Long answer: depends on how you use the pillars, how the context causes one to be more prominent over another or if they're equal, etc.

Very clear to me now, thank you!

When composing polytonal music, do both keys have to be established in the same way?

It also depends on the keys. Keys that are close together have a different level of dissonance than keys that are further apart. Think C major + G major vs C minor + B major. You have the choice of making the dissonances more intensive the closer you put the cadences in relation to eachother.

Writing in bitonality is kind of tough given it doesn't exist and all.

Writing in bitonality is kind of tough given it doesn't exist and all.

Bitonality exists just fine, but who mentioned this at all in the thread? I thought he was asking about polytonality.

Bitonality exists just fine, but who mentioned this at all in the thread? I thought he was asking about polytonality.

Well, I don't even really believe 'bitonality' exists. At least, in any sense that it would be justified being called under that label. And if even the superimposition of two keys isn't possible, then I don't see how it'd be possible to superimpose anymore than that and do anything that could be justified having the label 'tonality' in it.

Given the context in which he is talking, I think it's a fairly safe definition (if somewhat ambiguous in practice) to define tonality as a system of pitch hierarchies whereby the full chromatic is all related functionally to a central tone. It's been my experience that a superimposition of any two keys (even in very simple functional contexts) does not work at all at producing the effect of tonality. One of two things tends to happen: Either one key is allowed to dominate and that is heard as the fundamental tonic ultimate (i.e. the Rite of Spring where even blatant juxtapositions of keys do still yield a prevailing tonal center) or, by the own complexity of the material and saturation of the full chromatic, essentially comes out sounding without any prominent center whatsoever; a lot of Ligeti comes to mind.

Not to mention that, in most famous cases of 'polytonality' that I'm aware of, all of the harmonic materials tend to be controlled by an external mode that allows for implications of multiple keys; the octatonic mode being the most popular example which helped to control a lot of Bartok's and Stravinsky's 'bitonality'

Plus, because of the complexity of a lot of the harmonic aggregates as a result of the juxtaposition of multiple keys, there tends to be an obligation to keep the contrapuntal layers restricted entirely to the diatonic notes of that key. In effect, I think this really should be called 'polymodality' since I think it gives a more accurate description of the effect and processes involved. I've yet to hear a single, convincingly function 'bitonal' piece of music. And I know the term's relevance whatsoever has been contested by more than a few musicologists.

If you want to seriously put in doubt poly-tonality or bi-tonality as a term, you'll need to do a lot better than that.

The terms refer to the method of composition, not the end product. Hence, simply using two keys simultaneously in a function-harmony way yet isolated from eachother can lead to all sorts of sound formations. It's however much easier to explain it by noting the use of tonal parameters that operate independent from eachother according to a differing axis.

It also generates the problem of now having to find a new term to describe the above process. Unless you have a better suggestion, I think there's absolutely nothing wrong with bitonal or polytonal as descriptions of composition method. Again, the end result isn't important and just as well since otherwise any given term will fall in the same trap.

And if even the superimposition of two keys isn't possible, then I don't see how it'd be possible to superimpose anymore than that and do anything that could be justified having the label 'tonality' in it.

The label tonality is used due to the restrictions applied. In other words, again, it has nothing to do with what it sounds like in the end but it has to do with construction (chords in 3rds, hierarchies within the same axis, etc.) That is, cadences, voice movement, etc can all be observed by all parallel keys independent from eachother. It is using the major/minor tonality system and construction principles and mixing it with itself. The only possible description of such an specific technique is that of referring to multiple keys (in the traditional sense) that move parallel to eachother. It's obviously not going to sound "tonal," and that was never the point.

Poly/bitonality doesn't really say anything about specific usage concerning what's important or what isn't, just the building blocks, so whatever your criticisms are they are piece-specific and can't apply to the technique itself as it doesn't dictate how many keys must be parallel to eachother or how they must interact with eachother (or if they must interact what so ever.)

I'd like to see the actual musicological arguments against the terms, if you got them handy since if it's got anything to do with what you're saying they're utter nonsense but I want to see for myself.

I had a longer message typed but it ended up going out on a tangent regarding general philosophy of music and how I think there will be a fundamental tension between us because of it. In the interest of not wanting to derail this thread, I'll try to keep things as concise and on-topic as possible.

I'll concede that there are some pieces in which 'polytonality' is justified. Many of the stereotypical 'polytonal' pieces that I know of, however, do not justify this label at all and, to the best of my knowledge, I've never encountered a piece where the label was justified. Of course, this could be my own ignorance and I can still respect the theoretical possibility of what you're saying.

That being said, I still feel there's a flaw in the term. That is, it privileges only horizontal relations without any regards global vertical structuring (between the various axises.) This gets to be a problem for various reasons. I had a whole list of them typed out but I feel the most pervasive is one of perception. If you're going to write a piece with independent, tonally governed axises, you're likely going to have to resort to some mean of vertical structuring which will govern the relations between them. Otherwise, the term allows for so much ambiguity that, even while writing under completely sound horizontal logic, the result could be a incomprehensible, incoherent mess. It is very likely the composer (even if not entirely consciously) will still resort to some global structuring between the various layers. And while this isn't a big enough flaw in itself to discount the use the term 'polytonality,' I think it should largely be qualified with references to how the global harmony between layers is structured.

But again, there is also the question: If the harmonic materials reach such a complexity that any impression of a tonal center in the individual layers becomes lost, then what exactly is the point of writing with functional tonality whatsoever? Functional tonality is written under the assumption that a tonic is the 'goal' (ideally) and when you reach such density of information that the tonic no longer becomes perceptible, then really, you may as well not be writing functionally anyway since, obviously, whatever is controlling the harmony isn't traditional function. It's the same problem Schoenberg ran into with writing his late tonal pieces. Writing in layers of even perfectly defined, simple functional harmony is going to guarantee no consistency of sound in terms of larger structure and if the result remains consistent or logical at all, it's likely going to adhere to different means of structuring with the 'polytonality' being merely a means to the end (but far from the only.) Unless, of course, you believe in the absolute integrity of purely horizontal listening.

There are two angles you can look at this from:

1) Analysis of historical pieces like Bartok's Bagatelles, where you can describe the usage of two keys simultaneously in rather plain simple terms.

2) The ability to use tonal parameters to create things beyond a tonal-only scope (by virtue of layering.)

For the first the term bitonality (and by extent polytonality) makes plenty of sense, as it's a handy way to describe what's going on. It's accurate as well within it being just one single label.

For the second, the term polytonality or bitonality is probably much harder or impossible to infer from analysis alone. I can come up with all sorts of music that I can trace back entirely to tonal harmony and voice movement principles but when layered ontop of eachother produces something entirely different. I don't think the label is wrong however, but it's a description of the method rather than of the result.

So to narrow it down, the only possible definition that makes any attempt to describe both things is one that only talks about the layering of the keys, and not in which way they are layered or how they're organized. Simply using keys against eachother qualifies, as well as building clusters of out five or six different keys layered together.

For a more elaborate description, I would avoid using the term altogether really, as I would avoid using any general technique term to describe anything if I'm going for detail.

On 5/13/2011 at 6:18 PM, Nirvana69 said:

I had a whole list of them typed out but I feel the most pervasive is one of perception. If you're going to write a piece with independent, tonally governed axises, you're likely going to have to resort to some mean of vertical structuring which will govern the relations between them. Otherwise, the term allows for so much ambiguity that, even while writing under completely sound horizontal logic, the result could be a incomprehensible, incoherent mess. It is very likely the composer (even if not entirely consciously) will still resort to some global structuring between the various layers. And while this isn't a big enough flaw in itself to discount the use the term 'polytonality,' I think it should largely be qualified with references to how the global harmony between layers is structured.

Even though this is an 11 year old topic, I can't help but insert my opinion on this.  So the 'problem' you address here is perception, but I think that a big part of something being perceived as tonal, atonal, bitonal or polytonal is memory.  Does the composer establish the say, two key centers being used sufficiently on their own before then juxtaposing them?  I can very easily imagine (and have actually used in my own compositions) the technique of sustaining a previously established tonality (with a reduced dynamic level) in the background while a melody in a foreign tonality plays above or below it - a technique which I think can very effectively give the impression of two distinct tonal centers being perceived at once.  I think you are assuming that both tonalities must move through their harmonic rhythms at the same time and be constantly and actively establishing their individual key centers at the same time which would mostly likely be overwhelming to hear.  The keys do not have to be at war with each other.

Another thing I wanted to mention is that the farther apart in range the layers of tonalities are set at the less likely that they will be perceived as dissonant.  There is even an aural illusion having to do with the harmonic series (I forgot what this particular illusion is called) that says that if you have a tuba play it's lowest note and a piccolo a note 8 octaves and a half step higher - because of the enormous distance between them, they will be perceived as the same pitch class even though they are technically a flat 9th.

5 hours ago, PeterthePapercomPoser said:

Another thing I wanted to mention is that the farther apart in range the layers of tonalities are set at the less likely that they will be perceived as dissonant.

This is exactly what I said... 11 years ago.

On 5/9/2011 at 3:14 PM, SSC said:

It also depends on the keys. Keys that are close together have a different level of dissonance than keys that are further apart. Think C major + G major vs C minor + B major. You have the choice of making the dissonances more intensive the closer you put the cadences in relation to eachother.

 

lol.

But honestly the point Nirvana was making is that he didn't like the label because it didn't describe, to him, what the end product sounded like, and I argued that the label is a label of the method of composition, not a description of the end result. If you layer 6 keys on top of each other (ie, C C# D# E F F#) you end up with a bunch of clusters that, if you were to ask anyone, wouldn't be really defined as "polytonal" or "tonal" anything, it'd be just a wall of sound. IF you then started to separate them so that each key had different hierarchies and so on, you can start to bring out a "tonal" character out of it which is audible. None of this has any bearing on the technique per se, only on the execution, which is where the real distinction lies.

I found the aural illusion I was talking about earlier.  It is referred to in this video as the "Consonance Calibration Effect" and is used in Stretch Tuning: