SSC

Excellent. Well, now that you've listened to these pieces, let's leave serialism a little to the side and go a little over how they work.

Penderecki's Threnody was written almost as a reaction to the 50s serialism, in a sense that the way it's written allows for some freedoms of interpretation. The score is written in a graphical manner in sections with the goal of uncertainty.

Both Atmospheres and the Threnody use a technique which comes from Henry Cowell (and to a lesser extent Charles Ives), which is that of Clusters. There's a common misconception about what clusters are and how they work, so let's fix that. The effect you heard as "wall of sound" in Atmospheres is caused by the moving cluster textures across the orchestra, and in Penderecki's case, the clusters are used in a different way (which brings the frightening-like character to the piece since horror movies and such have used these techniques extensively. However, the sound is much more jarring than Atmospheres.)

Let's define a regular "chord" in a sense of intervals. You can tell a major from a minor, a diminished from an augmented chord because of the differences between the intervals between the notes that make up the chords. Chords are built in the norm by distances of 3rds, small or big 3rds, in a row. So, in essence, a cluster fills up the holes between each note and the next, so that you can't really hear which notes are being played individually.

Indeed, a cluster is an attempt to unite the sound of more than a single note, as a "single sound" rather than a combination of sounds. The way it does this is by eliminating intervals between the notes, though there are many other things that can be done. There are many types of clusters, and as you heard in these two pieces, they can have wildly different uses.

What defines a cluster is:

Size - How many notes you have going.
Dynamic - If the same dynamic is applied through the entire cluster, or not.
Sparsity - How far apart the notes are.

The last one is particularly important. For example, if you take a tiny 3 note cluster, C - Csharp - D, and play those notes right next to eachother, you get a very compact cluster. However, if you play these three notes across 3 octaves so they are far apart, the effect is entirely different, while retaining the texture from the first cluster.

Ligeti's piece, Atmospheres, has entire groups of clusters that move through each orchestra section, across sections. The clusters become narrower, louder, more sparse, softer, and so on as the piece goes.

Curious fact: the score for Atmospheres is written in regular notation, and in fact it's in 4/4! Ligeti probably went for the easiest way to write it, and used 4/4 only as an organization metric, since the piece's rhythm is very difficult to determine to say the least. This tendency to use time signatures only as an organization aid comes far back from examples such as Stravinsky's "Sacre du Printemps" (Rite of spring) where the orchestra is accentuated outside of metric-beats, so that the time signature isn't defining the rhythm of the piece, but rather just keeping it readable for the musicians.

You can also see how different the implementation of the orchestra in Ligeti's piece is compared to what we usually have as "orchestration" for Romantic, Vienna Classic, and so on periods. The parameters such as Rhythm, Melody, harmony, and so on are so blurred that you don't perceive them in the traditional sense, despite their existence regardless.

This tendency to uncertainty is largely part of a quasi-revolt to the super-strict and exacting character of Serialism. To put it a little into historical context, in Europe there major turmoil with the 2nd world war, and in Germany (which was before the war one of the leading nations in the avant-guarde, modern music, and so on) was basically all beaten down. Composers who did not write in certain "aesthetics" (Like Wagner) were either forced into leaving the country (Hindemith, etc), stop composing (Webern, etc) or worse. And overall, there was a general "backwards" tendency in the 40s with Richard Strauss (Who had success during Nazi germany due exactly to his Romantic/Wagnerian-aesthetics) and the general Neoclassical trend.

I've said before that the only reason composers have generally looked to the past, was to find new inspiration, to try new things, and to understand where they are and what they can do to move "forwards" in a sense. Hindemith and Stravinsky (early Bartok) were composers who took this approach, and their Neoclassical/Neoromantic compositions are not just reviving old techniques or styles, they did a lot of things which were very different, new, and explored far deeper than just recreating or imitating something.

With Strauss a similar tendency can be seen ever-so-slightly but due to political pressure it never got that far. The 4 last Lieder ("Vier Letzte Lieder") from him can be considered a compact portrait of everything that has happened in music history until then, harmonically, and so on. Then there were composers such as Hans Pfitzner who were a lot more interested in political reasons (in his case, it's argued that he tried to gain popularity following Strauss by writing music the Nazis found acceptable. The outcome wasn't so bright for him, though, and he ended up being just a footnote in what otherwise was a terrible period of music history.)

Then, came the end of the European war, and people began flocking back to Germany, establishing festivals for new art in an attempt to make up for all the lost time during the war. From this attempt, came such festivals as the Documenta (Kassel) and the festivals/summer courses for new music in Darmstadt (where people such as Xenakis, John Cage, Stravinsky, Stockhausen, would meet with young composers of the time, do seminars, concerts, etc.)

The actual start of Serialism as "The serialization of all musical parameters" (opposed to 12 tone, which is just pitches, and there are other aesthetic principles beyond just that, making both rather different in practice.) can be traced to a piece from Messiaen. Messiaen himself was a teacher during the Darmstadt summer courses/festivals in 1949 and 1950, and his piece from this time "Mode de valeurs et d'intensités" marked the start of the tendency towards serialism in new compositions of the time.

The 50s was also a period where Electronic music made its debut, though electronic instruments and electro acoustic experiments were not new, total-electronic music was something unexplored. Part in due to the technological impediments, and of course the fact it was extremely time-consuming and required a healthy budget (Hence Stockhausen worked closely with the West German Broadcasting (Westdeutscher Rundfunk) station's studio, and so on.)

The leap to pure electronic music can be said to have two origins. The first, was the necessity to have performances that don't depend on real people, so that pieces of enormous complexity can be created and always flawlessly played each time.

The second and more important for later, was the search and understanding of sounds. Composers such as Milton Babbitt warned that nothing grows older faster than "new sounds," yet that did pretty little to stop people such as Pierre Henry and Pierre Schaeffer from taking the electronic compositions to extremes (but that's a whole different story, so we'll go back to them later on.)

With the coming of electronic music, not only could composers compose the literally unplayable, but they could from this build entire techniques it had never occurred to them to try in real instruments. And here is precisely where, later in the 60s, Penderecki debuted his Threnody piece which caused a lot of waves in the music world due to it's usage of techniques pioneered in electronic music, but with actual instruments and people.

Not only that, but Penderecki also coupled it with elements of uncertain notation (such as a symbol that means "Play the highest note possible" rather than specifying the highest note himself), so the piece would never really come out "the same" each time it was played.

Ligeti, Iannis Xenakis, Luciano Berio, and other composers from the 60s were focused very much on the manipulation of actual sound and its consequences than a "system of composition" so to speak, and their work began showing possibilities to produce new sounds out of classical instruments (which in itself was not something new, but this new usage had a lot more depth than previous attempts, generally speaking.)

There's a lot more to say, and to show, but I think for now this should give you an idea of what the hell was going on and what people were actually doing at the time.

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Now, let's actually do some work shall we~

First, a correction. To make an "inversion" of a 12 tone row, you need the same starting note (1) as the prime(original) row. That is to say, you invert the intervals from there on. Let me give you an example:

Say your row starts like this:
F-Sharp, F natural, E flat, C sharp, C natural.

The inversion would look like this:
F-Sharp, G natural, A natural, B natural, C natural.

It's really the opposite interval. If from F sharp to, F natural there's a semitone down, in the inversion it will go a semitone up (G natural). And so on. In your case, the inversion to your row will look like:

C sharp, D natural, F natural, and so on. You had the right idea, but keep the starting tone the same, or row is going to be different. After all, inversion only works with a tone of reference, otherwise how do you determine the interval of a note against nothing? You need two notes to have an interval, and so you need the first note in the row as anchor so you can manipulate the rest (likewise in the retrograde, where the first note is the last note.)

So, now that we've cleared that up (I hope!):

I want you to actually write me a little sketch, or tiny piece, or fragment using the 12 tone system. Let me elaborate:

In practical terms, the 12 tone system dictates that you have a specific order in which tones come around, so that you can't freely use any tones you want but rather you must use the row you created. However, HOW you use the row is very relative.

We'll be working with free rhythm, and also free choice of register/instruments. If you want you can try your hand at writing for string quartet, or a wind trio.

the thing about the row is that, like our variations exercise, you can build chords out of calling a bunch of row tones all at the same time. IE, if you have a row where 1 2 3 4 are C E G B (flat), you could play them all at once and end up with a C major + 7th chord, if you don't you'd end up with an arpeggio of the same chord.

The notion that 12 tone music is "atonal" is not only wrong, but rather misleading. You can also manipulate rhythms so as to cause tonal harmonies between different rows going on at the same time. Depending on how you handle the rows, you can obtain entirely different results.

Now, we're not going by Schoenberg standards, and certainly even he questioned the validity of his system in his later years. However, let's try to keep it at least within the restrictions such as:

You must always use the rows, even if you're using inversion, retrograde, and so on (techniques discussed in the previous post.) You are allowed to make pauses instead of a note in any given row, but the pauses count as the note + row number, so the next sounding note will be the next number after the pauses. IE: if 1 2 3 4 is A B C D, but B is a pause, it'd look like A (pause) C D. Got it?

Again, you're free to do with the rhythms as you want, as well as pick where in the octave the row notes come (since a row ONLY defines WHICH (names), not exactly WHERE (register, octave) they are.)

So, have fun and as always, feel free to ask if you got any doubts.