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There's a great interview online where Glenn Gould talks about Stravinsky and Schoenberg (circa 1960). His comments about Stravinsky certainly haven't aged well but nonetheless, he does make some rather good points. And on Schoenberg too. All of these aside, he does make one remark (see below) that confuses me tremendously.

He says Schoenberg once said to him:

A great deal of music remains to be written in the key of C major

What he goes onto say next (his two things regarding the above) go straight over my head.

I must confess a lot of this will be down to the system where Schoenberg spent a majority of his time constructing and Richard did do his best to explain this to me some time ago but I find the two comments Glenn Gould makes rather verbose.

Would someone be able to translate his points? Does Schoenberg have a point? Is there still a lot of music to be written in C?


I did have a small pause before composing this as to whether or not this is likely to be closed for being too opinionated. Professionals would be able to agree (or disagree) as a consensus what Glenn Gould is saying here so it is not just down to opinion. Had the interview not been provided above, quite possibly, yes. I am merely asking for someone with a much better sense of the history and terminology to translate his two points he goes forward to explain.

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    Seems to me that he meant 'diatonic' - or if you like 'non-serial' music still had plenty of mileage to go - C major being a blanket term for it. Only surmising! – Tim Dec 30 '20 at 12:39
  • I don't think there can be a definitive answer to your question. We can only discuss it. But that applies to a lot of questions about any art form such as music! It says something about Gould that he found Schoenberg's tolerance for musical paths other than Schoenberg's own remarkable. Textbooks often speak of the 'rejection' of tonality by the '12-tone' composers. This doesn't mean they were disgusted by tonal music! Just that they chose to explore a different path. I haven't a clue what Gould means by 'quasi-mathematical'. – Laurence Payne Dec 30 '20 at 13:05
  • Michael Curtis and I wrote very similar answers, and I feel like his is the clearer one. Hopefully between the two of us you can better. understand Gould's comments and also some more about Schoenberg's context and the larger point about whether C major is exhausted or not. – Todd Wilcox Dec 30 '20 at 16:21
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    Historically, Schoenberg has of course proven to be correct - since he made that statement, a great deal of music has indeed since been and continues to be written in C major. In fact the vast majority of music written since then has been tonal (and C major is still the most commonly used key at least in western music, though that's kind of beside the point). – Darrel Hoffman Dec 30 '20 at 20:54
  • Sounds like hero-worshipping. – Beginner Biker Dec 30 '20 at 21:13
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The two points I heard him make were:

  • the 12 tone system was not a refutation of tonality or diatonicism.

  • serial composition techniques need not be restricted to atonal music.

The first point is about the development of art styles up until post-modernism. In a nutshell new artistic styles were championed as superior to older styles. The attitude is one of artistic evolution from primitive to sophistication. That attitude is particularly true of various types of modernism. Those folks liked to write manifestos rejecting the old and outdated and championing whatever the new style was.

This was true about atonal music. Some felt tonal music had progressed along lines of increasing chromaticism to the inevitable conclusion that all 12 tones were equal and the tonal style had exhausted itself. Tonality must be abandoned so music could be progressed via the 12 tone style. Schoenberg's comment "a great deal of music remains to be written in the key of C major" was explained by Gould to mean Schoenberg actual felt tonal music had not exhausted itself.

The second point about serial technique is a bit harder to explain. I think it starts with the idea of a hierarchy of tones in tonal music. Not all tones are equal, the tonic is most important. Not all combinations are equal, tertian harmony is preferred. In that sense not all options of rhythm and pitch are equally available in tonal music. Choices are limited to give prominence to the tonic.

Serial music takes a palette of musical elements - at the very least pitch in 12 tone music - and treats any series of those elements as available options. There are various procedures for creating series - this is the aspect which I think Gould calls "quasi-mathematical" - but an important aspect was to give equal important to all 12 tones. With equal importance of all tones, no tonic can be defined, hence the music is atonal, without a tonal center.

Equal treatment of all 12 tones means no preferential treatment of select tones. Any series of tones melodically or harmonically can be combined. When you do that will all 12 tones you can get a lot of "chords" which are dissonant by tonal standards. Remember, tonality gives preference to certain combinations, like major and minor triads. 12 tone music actively avoided such preferences and the result is a lot of "chords" with seconds, sevenths, and diminished or augmented sounds.

In tonal terms those 12 tone chords are very dissonant. But, 12 tone music was supposed to be the natural conclusion of the increasing chromaticism of the tonal style. Remember too the attitude of refuting the old when championing the new style. 12 tone music was supposed to emancipate music from the restricted old attitudes about consonance and dissonance. But that didn't happen. Most people feel 12 tone music is very dissonant.

One of the main reasons 12 tone music is dissonant is because it uses a palette of all 12 chromatic tones. Mathematically speaking there are many, many combinations which will be dissonant. If you reduce the number of tones, and especially if you limit the specific relationship between the tones of the palette, you will reduce the number of dissonant combinations.

If you reduced the palette to just C major (surely meant to mean any set of 7 diatonic tones,) you eliminate a great deal of dissonance. In fact if you play the whole set, all 7 diatonic tones, you get a thirteenth chord which while certainly sounding modern, it can also sound consonant.

Let's get back to Gould and Schoenberg. Gould is explaining Schoenberg's comment "a great deal of music remains to be written in the key of C major" to mean serial technique could be applied to a diatonic tone set. I don't know exactly what Schoenberg envisioned, but based on Gould's comment I imagine the idea was music without a strong tonal center - atonal in that sense - but much less dissonant that 12 tone music, because the number of dissonant combinations and types of dissonance would be greatly reduced.

I don't know how much of this is actually Schoenberg's ideas or Gould's ideas about Schoenberg. But what I've written is how I understood Gould's comments.

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Would someone be able to translate [Gould's] points?

Gould is assuming familiarity with Schoenberg's compositions and composition techniques on the part of his audience. Hopefully you have at least some understanding of those. The important thing to know about Schoenberg with respect to Gould's comments here is that Schoenberg's music would not generally be considered to be in any key, in the traditional sense of the word. In other words, Schoenberg himself was not striving to write music in C major, which could make one think that Schoenberg disdained or at least did not value music written in traditional keys like C major.

So Gould's first comment about Schoenberg's tastes being "catholic" (small c) despite his compositions is really saying that Schoenberg valued all kinds of music that was different from the kinds of music that he composed. Just because Schoenberg was into 12-tone as composer doesn't mean tonal music is dead to him.

Gould's second point is a little more involved. The word "quasi-mathematical" almost certainly refers to the way that 12 tone composition is somewhat formulaic in a way. There are rules for how it is done. I think Gould's use of the word "dissonance" might be a bit confusing, especially from any point of view that consonance and dissonance only exist in the context of a theoretic and aesthetic framework for music. Let me try to put that more simply: Some people would say that consonance and dissonance are completely subjective, so one listener might be trained find 12-tone music consonant and C major music dissonant, while most listeners in the world today would say that C major music has more often consonant intervals and 12-tone music sound more dissonant.

I think Gould is at least partly in the other camp, that believes consonance and dissonance have at least some objective basis. Usually the acoustic and psychoacoustic basis for the objectivity of consonance and dissonance is the harmonic series and how different intervals evoke or conflict with the harmonic series. Generally 12 tone music is written with no regard to the harmonic series, so from the objective view of consonance and dissonance, it is somewhat "randomly" consonant or dissonant, which leads to sense of general dissonance on the part of listeners. Either way, since the vast majority of listeners in Gould's world were "trained" on tonal music, some of which was written in C major, they would find 12 tone music dissonant, and we can suppose that at the very least, Gould found 12 tone music to be dissonant.

So with that in mind (12-tone = dissonant), we can unpack what his second point is about. What he's suggesting is that perhaps Schoenberg saw ways to bring some of the influence of 12-tone composition into a tonal compositional framework, and allow for new and/or different patterns of consonance and dissonance than had been explored in the key of C major up to that time. We could easily suppose that a composer could develop a 7-tone system based on the 12-tone system and start with the 7 tones of the C major scale and otherwise compose with a serialist approach, which has in fact been done in some ways. Serialism (a broader concept than 12-tone music) has definitely influenced modern composition, even compositions that are otherwise very tonal (e.g., definitely written in a key).

So it seems clear that Gould has a positive view of Schoenberg's view of music, and I want to note that he doesn't call Schoenberg's comment "surprising", he calls it "revealing". As in it's something that many people wouldn't know or think about Schoenberg but is nonetheless true.

For the larger question about "Is there more music to be written in C major?" we can turn it around and ask "Has all the C major music possible already been written?". History tells us that the answer to that question is always "No". That question has been asked and/or discussed over the last two millennia and any answer of "yes" has always been very quickly disproved. That said, there are always people who are ready to believe that all music has been written or that all music will soon be written or that all music in a certain category or with certain restrictions has been or will soon be written. That they have always been proved wrong in the past doesn't seem to deter these people, and I expect some may comment on this very answer that we can't say for certain whether it's possible to write all the music that could be written in C major. History strongly supports the assertion that all the music will never be written, and that there is no category of restriction we might place on music such that all the music that fits that category will ever be written.

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  • Thanks for the very nice answer---I'm intrigued by your hint that Schoenberg's suggestion (or Gould's Schoenberg's suggestion) about using serial techniques in a diatonic context has indeed been taken up by contemporary composers. Could you give some examples? I'd be very keen to listen to them. – stefano Dec 31 '20 at 7:30
  • @stefano I can't speak for Todd directly, but serialism has been such a major movement in modern "classical" music that it's had an influence on just about everyone's thought in one way or another. As far as specifically diatonic serial music goes, Ligeti's "White on White" piano etude is not truly serial as far as I can tell but has kind of a similar attitude. Although some may well be out there, I don't know of any strictly serial diatonic music, so I'll go write some and get back to you. :P – Zoë Sparks Jan 3 at 14:32
  • @stefano One aspect of serialism that has penetrated deeply in several forms of music is the extension of serialism to rhythms. Rhythm serialism can be as simple as taking a set of rhythms and using them in a predetermined order. But I argue that rhythmic serialism has been somewhat deconstructed and has influenced hip hop and EDM in the form of evolving hi hat rhythms that are ubiquitous in those genres, to say nothing of the clear influence of serialism on 20th century classical and soundtrack music. – Todd Wilcox Jan 3 at 15:02
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...in the last years of his life he said what to me is a very revealing statement: he said that a great deal of music remains to be written in the key of C major. But that means to me two things: first of all it means that he was a man of some catholicity of taste—he didn't automatically assume that because he had espoused a certain system of composing music which came to be called, not too accurately, the twelve-tone technique, that all music not composed in that system or not harmonious with it or not in some way acquiescent to it was false or wrong...That's one thing it represents.

I think this is probably pretty easy to understand. Basically, Schoenberg and others had put forward a new strategy for composing music. Some composers who had come up with a system like that would be very dogmatic about it and insist that everyone who didn't follow them was on the wrong track (which was an attitude that some later serialists did take). Gould is suggesting that Schoenberg himself wasn't so dogmatic as that, but rather that he saw his approach as one reasonable possibility among many.

EDIT 2: If you're wondering what his "not too accurately" comment is about, my guess is it's because serialism came to be understood as a much more general idea than simply relating to the 12 tones of the traditional chromatic scale—so general that you could even apply it to other art forms aside from music. Read on for more. :P

The other thing that it represents, I think, is the feeling that comes very strongly from Schoenberg's compositions and from his writing about those compositions in his last years, and that is that he begins to see that the very highly dissonant forms of twelve-tone music, of serial music...aren't necessarily a concomitant of this music. That one could apply some of the quasi-mathematical (never more than quasi-mathematical) formulas that he worked out and apply these to sound formations that were really quite consonant, that were triadic, that were in fact precisely the sound formations that every composer from the Renaissance onward had worked with. So that what you find in the late years of Schoenberg is this extraordinary coalescence of ideas that were extremely radical, in the sense that he was saying, "I do not believe the arithmetical components of music as it's been practiced in the generation or two before my own. I do not believe that these are any longer serviceable," and at the same time extremely conciliatory in that he was saying, "Look, there is a way to take very old sound formations, very consonant ones, totaly undissonant ones if you like, and organize them in a mathematical relationship that gives them maximum expressivity and minimum debate against each other," which was the formation of tonality. So I see Schoenberg more as a man affecting a conciliation than as a man overturning things.

Obviously this is a little more technical and I wouldn't be surprised if this is more of a sticking point for you, so I'll get into this in more detail.

First: serial music is really not so complicated, essentially speaking. The basic idea is that you take a set of possible musical actions and arrange all of them in some order. Then when you're composing, you use those actions in that order. So, if the musical actions are the 12 tones of the traditional Western chromatic scale, you would arrange all 12 of them in some order (called a "series"), and then every time you wrote a note you would follow it with the next note from the series. Like, if A was followed by C#, then whenever you wrote an A in a certain voice, you would make sure C# came next in that voice. They don't have to have the same note value and they can even be in different octaves and such, but just in terms of pitch class, they should follow the series.

The idea behind this is to make sure that you use all 12 tones equally much, instead of giving prominence to any one of them. Before Schoenberg devised this technique, he was writing "freely atonal" music, which had no key signature but also no overarching formal principle akin to tonality or the like (this was his first piece in that idiom, specifically the fourth movement). Music written in this manner can still end up kind of tonal in one way or another, so the 12-tone technique is a more rigorous approach to atonality.

However, that technique, in and of itself, says nothing about consonance or dissonance, or even passing moments of tonality. Note that I never said, "Make sure you can't form a major triad by lining your series up against itself a certain way," or something like that. However, many following serialist composers became very adamant about avoiding even the faintest whisper of tonality in their music, and even moved to serialize other aspects of music like rhythm and dynamics (see Boulez's Polyphonie X for an extreme example of this). The result was music that was very suspicious of consonance, rhythmic pulse, repetition of any idea smaller in scope that the series, etc.—a much more extreme break with the musical past than plainly-stated serialism requires. These composers generally felt that they were being true to the spirit of serialism, but of course that's a matter of perspective.

Schoenberg himself did not really share that perspective, and in fact he became rather unfashionable in mid-late-century serialist circles in favor of his pupil Webern, who pioneered this more "pure" or "severe" (depending on your outlook) approach to serialism. This isn't surprising considering how Schoenberg arrived at atonality to begin with: he started out as a well-regarded late Romantic composer, and said he moved to atonality because total chromaticism was the only place left to go after composers like Wagner and Mahler pushed the boundaries of tonality so far. He wasn't necessarily trying to be an iconoclast, nor was he driven by some sort of all-encompassing abstract ideology about music.

Gould is making the case that he was even more like this in his later years than in the decades prior. As an example of the sort of music of his Gould might be referring to, you could check out Ode to Napoleon Buonaparte, which has a pronounced tonal character despite its serialism, even ending on an Eb major chord that's approached in a manner recalling his late Romantic period. There's a lot of classicism in it, not just in terms of its harmony but also some of its rhythmic figures and so on. That might be the sort of thing Gould is getting at, that he found ways to use this novel and math-ish (lots of terminology from set theory in serialism) composing strategy to get at very traditional ideas in Western music.

In terms of his general attitude around that time, he even returned to that late Romantic style with stuff like his Chamber Symphony No. 2, which he had started writing a couple years before his first atonal pieces. Also, he was a music professor in his later life and wrote some very good textbooks covering the styles of the common practice period—at least of what I've read of his output, he spent far more words discussing the techniques of composers like Mozart and Beethoven than he did describing how to write serial music.

So, in a way, he's not such an enfant terrible as he's made out to be. That reputation might be more reasonable to confer on some of his successors, like Babbit, Boulez, Stockhausen, and so on, who were more determined to totally upset the Romantic apple cart.

EDIT: As a postscript, I figure Gould says "quasi-mathematical" because serialism is not truly mathematical, in the sense that it lacks axioms and proofs and what have you. It has quantitative procedures for constructing and manipulating series, but there's nothing unusual about Western music theory having a quantitative flavor even going back hundreds of years. what maybe distinguishes serialism is that it also lifted a fair amount of terminology and a handful of ideas from set theory, since the elements used to construct a series (like the steps of the chromatic scale) can be thought of as a set, and a series as an ordering of the set. That still doesn't make it math, though, just "math-inspired". :P

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