Polytonality becomes Atonality: Gustav Holst, Mars

I have heard several atonal works, and I have found what basically amount to 3 types of atonality. There is the atonality because of lack of harmony(12 tone music for example). There is the atonality because of meandering harmony that lacks a tonic(Satie Gymnopedies). And then there is the atonality from what I call "Tonic competition". This third type of atonality is what I hear in Mars from Gustav Holst's The Planets suite and is very closely related to polytonality.

Polytonality is where you have multiple keys at the same time. Most of the time, this is 2 keys, but it can be more than 2 keys, like for example 5 keys in the ending of Divertimento in F, Ein Musikalisher Spass(Sorry if I butchered the German spelling there, but at least I'm getting the pronounciation out clear) by Mozart. 

Here is an example of some dissonant but obviously polytonal music:

Eb major and E major is certainly a dissonant combination, especially the way Stravinsky uses it here. There are much less obvious examples of polytonality such as C minor and Eb major(these 2 keys together just sound like C minor and the polytonality only becomes obvious on paper). And even with 2 major keys at the same time, there are much more consonant combinations than 2 major keys a half step apart such as having them a sixth apart. Heck, even C major and C minor at the same time is much more consonant than Eb major and E major at the same time.

In Gustav Holst's Mars from The Planets, it feels to me as though this polytonality is taken to the max. I hear all these keys competing for the place of tonic:

• G major
• C major
• C minor
• F minor
• Bb major
• D major
• A major
• A minor

And there are probably even more competing for tonic than what I just listed. Because all these keys are competing for tonic instead of cooperating, it goes from feeling polytonal to feeling atonal. Even as it ends, it still feels atonal. This is what those last few chords sound like to me:

G major on top of a C minor chord base -> F minor -> Diminished harmony -> Pattern gets repeated multiple times -> GM/Cm continues until the very last chord -> C major

And the C major doesn't feel like a resolution any more than Bb major or D major would. The only sort of resolution I hear is dissonance -> consonance. I don't hear anything close to even a polytonal cadence.

This is actually the way Gustav Holst originally wrote it is for a piano duet. He orchestrated this piano duet version, but hopefully you can hear what I mean by "Tonic competition" going on here in the piano duet. Even when it gets to the G pedal, there are still multiple keys competing for tonic. No wonder this piece sounds like 2 pianists warring against each other, they can't even agree on the key, the tonic for one measure. Combine that with the octave rhythm of Triplet, quarter, quarter, eighth, eighth, quarter and the melody rhythm of Dotted quarter, eighth constantly and you really have a piano duet with the 2 pianists warring against each other, both harmonically and rhythmically. I'm actually surprised that this harmonic and rhythmic war doesn't sound any worse.

Basically what I am getting at with Mars by Gustav Holst, is that it feels like the polytonality has been taken so far that it becomes atonality. Do you agree with this assessment of mine? Do you feel as though it is multiple tonalities competing and in the process collapsing into no tonality?

On 1/10/2020 at 1:39 AM, caters said:

There is the atonality because of lack of harmony(12 tone music for example). There is the atonality because of meandering harmony that lacks a tonic(Satie Gymnopedies). And then there is the atonality from what I call "Tonic competition".

Wow, I think this is too risky.

Atonality means no tonal center, but not lack of harmony. There is harmony in every kind of music. Other thing is that the harmony you hear is not tonal and hierarchical according to classic standards.

In the Gymnopédies there are tonic centers. Again they are established in different ways. Most parts of Gymnopedies are modal. Modal music have also "centers", call them tonic center or whatever, but the music runs around the center.

Atonality and politonality is not the same. In bitonality you have TWO tonal centers, and in true bitonality you need full development of each tonality with dominants and tonics. In politonality, it's the same but with more tonalities. When there are no tonal centers at all, you have atonality. It was the progressive "obsession" of those composers, first Schönberg was not convinced of free atonality because it could have "hidden" tonal centers, and he developed atonal dodecaphonism. Serialism was a step further.

What happens in Mars is not politonality. For that, tonalities must happen simultaneously, not one after the other. I think Holst used bitonality here in some parts with centers on G and C#).

This piece by Ives is truly polytonal:

12 hours ago, caters said:

I have heard several atonal works, and I have found what basically amount to 3 types of atonality.

What a way to start an argument.

28 minutes ago, Monarcheon said:

What a way to start an argument.

 

This method is Socratic maieutics

I don't know if you're being sarcastic, but I definitely am. Trying to categorize the entirety of a sound type while only having listen to several of its members? Why go into an argument leading off with an admission of lack of sufficient evidence? 

There's just a lot of short term analysis in generating your argument. The slow section, for example, is based off parallel major triads as a harmony of an extended chromatic enclosure to a prolonged tonic that was previously established and is implied. It may not be tonal in the common practice way of thinking, but it's tonal in many, many other aspects that have extended from it. Without the aid of a computer, musical things are embedded in time; not everything is vertical. 

@Monarcheon . Yes, I was sarcastic, of course. I'm sorry.

I think many fields in modern harmony are mixed in real composition. But we need to have clear what is atonality and what not. And what it politonality and what is a tonal center, etc... 

I don't understand how polytonality can be taken far enough to become atonality.

In my experience, they are different things.

1 hour ago, aMusicComposer said:

I don't understand how polytonality can be taken far enough to become atonality.

In my experience, they are different things.

 

Well, polytonality can certainly be unstable. And in general, the more tonics you have on top of each other in polytonality, the less stable it gets, even if say you have the tonics in fourths, giving a quartal sound(ex. Bb major over F major over C major is going to be less stable than either F major over C major or Bb major over C major, because it is 3 tonics instead of 2). 5 is the maximum number of tonalities that I have seen still sound polytonal. The closer the tonalities are physically, the more unstable it gets. Most unstable open interval for polytonality is the fifth, because that extra sharp or 1 fewer flat leads to a lot of dissonance. That's how come G major over C minor sounds as dissonant as it does, because of the major seventh and augmented fifth intervals between Eb and 2 of the notes of G major. F major on the other hand and you have a much more stable polytonal platform. Fourths and sixths are much more stable intervals between keys when you are dealing with polytonality in general. Thirds however are perhaps the most stable of intervals between keys in polytonality. So stable, that in some cases it may sound like just a single key(for example, a polytonal piece with 1 key being Eb major and the other being C minor is just going to sound like C minor, and it only becomes obvious on paper that it is polytonal).

If you layer polytonality on top of polytonality and combine it with supposed modulations, it really becomes unstable. Now, what if the rhythm gets involved, causing a rhythmic and harmonic war? For example at 1:13 in the Mars Piano Duet, I hear the second pianist on a C pedal, which combined with the dissonance I have already heard, tells me that this is most likely C minor. A second or 2 later and I hear F minor in the melody played by the first pianist. Even at the very beginning of that piece, I am hearing what sounds like D major over G major polytonality, with the melodic tritone sounding like C#°, the leading tone triad of D major. And the melodic rhythm is Dotted quarter, eighth in quite a few sections, whereas the rhythm of the harmony, that pedal point, is triplet, quarter, quarter, eighth, eighth, quarter. These 2 rhythms alone don't work together, not even if the aim is for syncopation. Instead, these rhythms war against each other. Even the dotted half, half melodic rhythm at the beginning while working better, still sounds like 2 warring pianists because of the harmonies

At some point, the modulating polytonality becomes too much and like a tall tower toppling over, it doesn't just fall leaving tonality in it's wake, it instead collapses leaving behind no intact bits of tonality. This is how come, while I hear sections that could be described as polytonal in Mars by Gustav Holst, and the way the piece is written suggests modulating polytonality, the piece isn't actually polytonal, but is instead atonal, is because this rhythmic and harmonic war collapses all involved tonalities into atonality(when the rhythms work together, the harmonies get more unstable, when the harmonies are a more stable combination, the rhythms don't cooperate).

I don't think that politonality can become atonality. Most polytonal works are separated in voices or parts, and if you hear a part or voice by separate the tonality is still there.

But in atonality no matter what you do, the tonality doesn't exist.

Even in modal music there's some tonality.

I think the real atonality comes when you compse something in serialism, where every note is the same, and none is more important than the others.

54 minutes ago, Tortualex said:

I don't think that politonality can become atonality. Most polytonal works are separated in voices or parts, and if you hear a part or voice by separate the tonality is still there.

But in atonality no matter what you do, the tonality doesn't exist.

Even in modal music there's some tonality.

I think the real atonality comes when you compse something in serialism, where every note is the same, and none is more important than the others.

 

You're right. There are "opposite" concepts. In politonality there is tonality. In atonality there isn't.

@caters

I suggest to read the part about polytonality by Vincent Persichetti.

What you say above is a mess.

When you talk about stability what do you mean? Each tonality is stable in itself. The whole can be more consonant or more dissonant.

He establishes this order of intervals between two tonalities from more consonant to more dissonant BUT FOR MAJOR TONALITIES, not major plus minor.

On the other hand, he explains that the most resonant (not consonant) interval for bitonality is the tritone.

He talks about combining minor-major or viceversa, too.

And also what intervals are more consonant when there are more than two tonal centers.

It's all in his book.

I think the ideas of extended tonality sort of shattered the core concepts of your argument here. You can use chromaticism, for instance, to make a D major 11 chord with a 1/2 diminished 7th and diminished 9th interval sound consonant -even though it is nothing more than a c minor triad superimposed onto a D Major triad (yes, very close to a cluster: C, D, Eb, F#, G, A). 

One thing I want to mention -and this is strongly related to the topic- is that dissonance is a funny beast. For instance, in my example chord mentioned above... spacing of the notes plays a significant role in determining whether it is dissonant or consonant. Also playing a significant role is whether your playing the full chord at once or via arpeggiation. Playing those notes together within the same register and range would make it sound dissonant and harsh to the ear. Yet, when I place the notes within different registers.. the results vary. Further, when I arpeggiate that chord out D F# A C Eb G... it is much more pleasing to the ear. And, even more important to you tonalists… it does provide a means for resolution within the key of D Major that is theoretically sound. 

The point? Polytonality -and even atonality- aren't without harmony or attempts to fully negate the importance of harmony. Polytonality did, historically, lead to the supposed 'collapse of the tonal system.' The reason wasn't, though, that it lead to direct atonality. But, instead, it was due to the realization that the concept of dissonance and consonance was thrust into full upheaval. If a polytonal chord comprised of two remotely superimposed triads could sound consonant... then what exactly is dissonance? Debussy is an excellent study into extended tonality and polytonality. His works greatly exemplify my points. This was something that Hindemith -despite being an awesome theorist- just couldn't do.

Add On: One thing I think is a good question is whether or not you sit at a keyboard and try different combinations of notes? Like have you ever tried playing a cluster and then displacing notes in that cluster to other registers? This is a good way to explore these types of discussions with your ears. Or play some of these chords in different ways..  you'll see why it had such an impact on the trajectory of musical development in the west.

I don't think Democracy in music (serialism) is a good thing. I'm not so sure that Democracy in general is not without serious flaws. But that's another subject. Simple repetition is sometimes all you need to make the wrong sound right in music. That in itself and with a little artistry makes it not atonal, . Analysts and historians of Sravinsky refer to his "tonal centers" as key to his modernism.  Not a mode, as in your Satie, and perhaps not a full fledged methodology but only a mannerism or technique. Repetition is key though. In the last analysis doesn't it come down to the artist's sense of aesthetics? @jawoodruff is right. Dissonance is a funny beast.

I think the way to atonality was not politonality. In politonality, the tonalities must be well defined, opposite that what happens in atonality.

In my opinion atonality has the antecedent of using passing notes and added notes as principal, not secondary. As Wagner did. Taken it further there was a period of free atonality until Schöngber, who created an "imperfect" method to override the tonal hierarchy. Which was taken again to the limit with serialism.

I totally agree that atonalism is strongly based on harmony. Many people think atonalism = lack of harmony, but it's impossible.

Also, atonalism is not the same as dissonance all the time... It's a relative issue. A piece where dissonance is continuous (or consonance) is unbalanced and uninteresting.

I don't think you quite understand the meaning of atonality (which is a very abstract term that you need to define more in this post). Atonality is generally absence of tonality, so thus this simple definition rules out polytonality due to the fact that there is... multiple tonalities. Also this idea that there is no harmony in atonal music is a little ignorant to the definition of harmony, not all harmony has to be a cadential figure, in fact harmony can be more than just vertically aligned, and interval series could be considered harmony as well. Also just because something sounds unstable and dissonant doesn't mean it is atonal, there are plenty of key centers in Mars and the Gymnopedies despite their RELATIVE dissonance.

Tldr- using a lot of tritones and minor 2nds doesn't make something atonal if there is still a key center.

9 hours ago, Luis Hernández said:

I think the way to atonality was not politonality. In politonality, the tonalities must be well defined, opposite that what happens in atonality.

In my opinion atonality has the antecedent of using passing notes and added notes as principal, not secondary. As Wagner did. Taken it further there was a period of free atonality until Schöngber, who created an "imperfect" method to override the tonal hierarchy. Which was taken again to the limit with serialism.

I totally agree that atonalism is strongly based on harmony. Many people think atonalism = lack of harmony, but it's impossible.

Also, atonalism is not the same as dissonance all the time... It's a relative issue. A piece where dissonance is continuous (or consonance) is unbalanced and uninteresting.

 

If that's the case, you could argue that Beethoven is the antecedent to atonality, since he often emphasizes non-chord tones by putting them on the downbeat and uses a lot of non-chord tones, both melodically and harmonically. That just doesn't sound right to me. He is the composer who mapped out the entire tonal landscape and he frequently modulates to distant key areas. As an example, take Rondo a Cappricio. How do you think you would pull off a G major to Bb major modulation? Beethoven pulls it off with a single G minor chord which then leads to 2 very typical sequences, first a circle of fifths sequence in Bb:

Quote

Gm -> Cm -> F -> Bb

vi -> ii -> V -> I

and then a very typical cadence to Bb:

Quote

I64 -> V -> I

12 hours ago, Luis Hernández said:

I think the way to atonality was not politonality. In politonality, the tonalities must be well defined, opposite that what happens in atonality.

 

I think the problem here is a lack of understanding of these concepts. Polytonality doesn't have to be well defined at all. Extended tonality -i.e. the use of extended chords, superimposed triads, etc.- expands the bounds of what is possible in the framework of traditional tonality. Thus, you can literally take any two triads... and manipulate them with chromaticism... and it will work to the ear. This concept smacked the bounds of the tonal framework thru which composers had worked in the west for centuries. The early 20th century saw some of the giants of late romanticism: Vaughn Williams, Strauss, Mahler... all of whom dabbled heavily in the use of extended tonality. What was tonal? What was consonant? Why am I able to play basically a cluster of notes and it fits comfortably into my progression...even when convention would tell me it doesn't? These were the questions that lead to the rise of atonality -the complete and utter absence of tonality. 

2 hours ago, LayneBruce said:

 Atonality is generally absence of tonality, so thus this simple definition rules out polytonality due to the fact that there is... multiple tonalities. Also this idea that there is no harmony in atonal music is a little ignorant to the definition of harmony, not all harmony has to be a cadential figure, in fact harmony can be more than just vertically aligned, and interval series could be considered harmony as well. Also just because something sounds unstable and dissonant doesn't mean it is atonal, there are plenty of key centers in Mars and the Gymnopedies despite their RELATIVE dissonance.

Tldr- using a lot of tritones and minor 2nds doesn't make something atonal if there is still a key center.

 

This is a little bit more correct. However, I disagree slightly with some of what Layne is saying. First, a mere intervallic series isn't going to be considered harmonic in nature. I could randomly chose an intervallic sequence and say it is harmonic in nature -but, that would be wrong to say. The sequence would have to work within some sort of structural, harmonic framework where the particular interval serves a functional sense -which, wouldn't be the case since the intervals were just chosen at random. See my point? Second, Layne lays out exactly how polytonality and the use of extended tonal techniques lead to atonality: multiple key centers playing simultaneously. This was exactly what the collapse of the tonality was all about. A complete breaking of the tonal system where it became possible to play multiple key centers at one time... chords stacked high to the heavens with superimpositions over superimpositions.. and melodic fragments that reflected this type of extreme harmonic freedom. Finally, from Layne's reply... the use of quartal and secundal harmonies also contributes to the loss of function within the tonal framework. That's a different conversation though.

The point of all this... the simple, boiled down point... is that all of this lead to the fundamental question of what can be considered consonant and dissonant. What is close to and far away from any respective tonal center? What causes tension and provides the release? Can there be tension without release? Are there degrees of it?

The tonal system used for 300 years in the west couldn't provide a fundamental, clear answer to composers at the dawn of the modern era. The prevailing thought is that if something doesn't work... you got to throw it out. Thus, it was thrown out.

I disagree.

 If the different tonalities are not well defined in polytonality, you don't have it...., it'll be another thing.

Persichetti:

6 hours ago, Luis Hernández said:

I disagree.

 If the different tonalities are not well defined in polytonality, you don't have it...., it'll be another thing.

Persichetti:

 

That's not what I meant at all -sorry if you got that impression. What I'm referring to isn't that the technique of polytonal composition is not well defined -that's not the case at all. Interpreting the overall composition produced using the technique is what I'm referring to. The bigger impact of polytonal works -along with other techniques and processes- is what led to atonality. Take the Ives piece, for example, do you know which key the piece is in? Do you get a 'tonal' sense of closure from the piece? Does the piece make sense to your ears? You can listen to the individual parts of it -solo- and get an idea.. but how about the whole? How do you classify the final chord played in the piano? What structural functions does the harmony of the piece served? Finally, the last question you need to ask... how would you take the impact of such a piece when all you've ever heard up to the point of listening to this piece was music built upon iterations and variations of T-S-D-T progressions? 

This was the impact of extended tonality, polytonality, and heavily chromatic music. All of it lead the way to the final 'emancipation of dissonance' as Schoenberg were to eventually called it. After all, if you're going to compose music where each part is in a different key... why have keys at all? In many ways, Ives was very much a sign of the times -albeit an often ignored composer by the establishment. Ives is a good, early example of an 'American' composer -in that he personifies the experimentalism that came to define 20th Century American Classical Music. That's a digression though. To sit at your computers and say that polytonality had no part in the lead up to atonality makes no sense at all. No matter how organized the system of creating this type of music was... it lead to a serious questioning of the fundamentals of the western tonal tradition (for obvious reasons). 

That said, does this back up Caters' post? No. I'm just stating that Caters isn't exactly off the track (she isn't entirely on the track either). Polytonal music isn't atonal by definition... but it certainly blurs the lines of what exactly defines tonal music. And that is what Caters noticed -in a way similar to those who first heard this type of music. It doesn't seem to have a tonal center -even though it has many.

Yes. It's the way I think @jawoodruff

We can't separate what happened in those same years and had influence on what was coming next. As a concept and in practice, polytonality is different than atonality, but no doubt the development of any sort of extended harmony are needed to understand the origin of atonality.

Tonality is a galaxy, atonality is another galaxy, polytonality is the ship going from tonality to atonality, but the one travels in the ship is tonal, the real atonal is the alien waiting for the traveler, in other words, polytonality is the way tonality becomes more and more advanced until it could eventually leave entirely all tonal traces, but it's in that direction, not in the other direction.*

Serialism is a black hole takes you straight to the atonality galaxy.

*There is always an exception, like Berg.