OMWBWAY

I'd really like to get a handle on 12-tone rows' date=' and 12 tone technique. Building a matrix, etc. We covered it in class, years ago, but I never quite got a hold on it, and my teacher (a concert organist), wanted to get out of that topic as quickly as possible. I'd like to just start from scratch with it, though I've got a general idea about the whole thing. I'd like this to be my first step into 20th century composition and a-tonal and whatnot, so I can then incorporate it at will into my own style when I see fit.

My major medium for composition is Musical Theater based works. I have done a few other compositions for random assortments of instruments, but piano and a vocalist are where I'm most comfortable. However, I do feel that atonal/12 tone/microtonal music is completely appropriate, since Musical Theater and Opera are so full of emotion, that musical thoughts and thus emotions don't always have to be organized in Major, minor, diminished, and augmented thought patterns. Perhaps sometime, I'd like my character to be so confused that he doesn't know what key he's in while he sings, or so angry, that there is no definite structure to the song. Yet, I don't want to go into that mindset just by writing random notes on the page and having the vocalist learn it, I want there to be structure in the discord, for ease of learning. This sort of music is something non-existent in musical theater because it's usually so abrasive to the average audience that is used to classical and romantic period music. I think Sondheim(if you're familiar with musical theater at all) began to pave the way for what is absolute dissonance and discord in theater music, but I think it can be taken even further and still be enjoyable if set perfectly. I'm rambling...

I hope you'll accept me as a student. Hope to hear from you soon.[/quote']

Well, I'll warn you now, I'm not much of a musical theater person (or at least the "Broadway" kind of musical theater), so I may not be able to help you too much with that side of your craft, however I will certainly be able to help you with the contemporary techniques!

You mentioned that you have experience with 12-tone technique, so my question is, how much? Would you like to start from the very beginning or somewhere towards the "middle"? Are you looking for just an explanation of 12-tone technique or also a lot of analysis? Are you only looking for Schoenbergian serialism or also Boulez or Babbitt type integral serialism?

You also mentioned microtonality... this is quite a large filed, how in depth are you looking to go?

Are you looking for just theory instruction or composition as well?

This sort of music is something non-existent in musical theater because it's usually so abrasive to the average audience that is used to classical and romantic period music.

Oh, and by the way, check out Peter Maxwell Davies' Eight Songs for a Mad King (or here if you can't do FLAC). Also some of the musical theater works of Kagel, etc. It's not completely non-existent! ;)

Thanks for accepting me as a student. I've been a bit apprehensive of this style of music, but I have given it a chance. Some things I'm slowly warming up to, the more I listen to them. I find 12-tone music, in it's absolute mathematic properties, to be absolutely intriguing. I think this is where I'd like to start. Sooo.....

I don't need help with musical theater. Well, I do, I'm far from perfect, but I don't expect such from you, so that's fine if you don't like it. As far as 12-tone tech.... I think it might be best to start from the beginning, and I'll just tell you when I can no longer understand you. :) I think both explanation and analysis is the best approach.The better I understand it, the better I can implement it myself, at any time down the road. Once I know it well, I'll have it in my 'composer's toolbox' for use when appropriate. I'm familiar with Schoenberg serialism, but a refresher is always nice, so I can get re-familiarized. I've never even heard of 'integral' serialism(or I don't remember). I'd love to learn all of the above, please!!!!! Obviously, 1 step at a time, but a complete coverage would be SWELL!

I think microtonality can go back in the toybox for now. I'm not ready to play in that playground.

I think we should do theory as well as some composition practice, as it will help me get accustomed to it more quickly.

I will most definitely look those up. I didn't mean to be so infinitive in my words. I know it exists. But the average theater goer, or performer, either doesn't know it, or doesn't like it. (I don't know it, so I don't know if I like it, lol. Both?) I just want to fuse it with music that is 'pleasing' to the average theater goer. I don't mean to start up that debate on pleasant dissonance and atonality, but it's a fact that more people (at least in theater) prefer to hear 'normal', tonal music. I think they just don't know what they're missing. Anyway, I'm rambling.

THIS WILL BE FUN!!!!

I'm happy to do it! What I meant was that I won't be able to critique your music as well from a "musical theater" point of view (if that makes sense), but I'll still be able to give you lots and lots of comments.

We'll start with tone rows and then work are way up. Sound good?

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Great, lets get started:

So in Schoenberg's 12-tone system, our basic building block is our tone row. Traditionally speaking, the tone row is a non-repeating arrangement of the 12 chromatic tones. Within the 12-tone system we have 4 "versions" of the row. We have the prime form (P), which is the tone row, unaltered, and its permutations, retrograde (R) (presented in reverse order), inversion (I) (intervals inverted, so if we have an ascending major second, we now have a descending major second, if we have a descending fourth, we now have an ascending fourth), and retrograde inversion (RI) (the inversion presented in reverse order). These forms are also transposed to give us even more permutations of the row.

Permutations of the tone row are typically indicated by their form (P, I, R, or RI) and their transposition/starting pitch, (C♮ = 0, C♯ = 1, D♮ = 2, D♯ = 3, E♮ = 4, F♮ = 5, F♯ = 6, G♮ = 7, G♯ = 8, A♮ = 9, A♯ = 10, B♮ = 11), so if we have the inversion of our tone row starting on D, we would call it I2 or a transposition of the prime form starting on G♯, P8. (Keep in mind though, that they can be and are labeled in a couple of different ways, which I'll get to when I explain matrices. This is the way I prefer to do it, and I think it's the most straight forward, so its what we're going to use.)

This tone row is then used to create all of the melodic and harmonic material within a work. Schoenberg's "rules" say that the rows should not suggest or incorporate tonal elements and that there should be a preference for "dissonant" intervals, such as seconds and sevenths. This is a rule that's been broken many times though.

So lets take a look at the row from Schoenberg's Suite, Op. 25:

Intervalically speaking, we have a minor second, major second, tritone, perfect fourth, minor third, perfect fourth, tritone, minor third, minor second, minor third, and a minor second (he doesn't use a major third).

Our Inversion would be:

Our Retrograde would be:

Our Retrograde Inversion would be:

So thats your basic, "traditional" tone row.

There are many ways of constructing a tone row. For example, Schoenberg's row from Op. 25 can be viewed as 3 groups of four notes, with the first 2 groups ending in a tritone and the last group being a retrograde of the Bach motif.

And speaking of the Bach motif, lets take a look at the row from Webern's String Quartet, Op. 28 (which is built entirely on the motif):

You'll see we go down a minor second, up a minor third, down a minor second, up a major third, up a minor second, down a minor third, up a minor second, up a major third, down a minor second, up a minor third, and down a minor second.

Lets look at it in terms of 4 note sets:

Now you'll notice that the second set is an Inverted and transposed form of the first, and that the third set is a transposed version of the first.

Because of this our Inversion also becomes our Retrograde:

This is a form of combinatoriality known as invariance, which is when a segment of one permutation of the row can be found in another, unaltered. It is the result of a "derived" row, basically when a row is constructed from permutations of a smaller set as seen in the Webern row.

Another example can be found in Webern's tone row for his Symphony, Op. 21:

If we were to take our first hexachord (six note set) and present it in Retrograde and transpose it a tritone then you'll notice that we get the second hexachord. That would mean for a Retrograde of the original row, starting on the same pitch, we would get the following:

Notice that P9 and R9 are exactly the same.

There is also what's known as hexachordal combinatoriality which is when the pitches of the first hexachord can be found in the pitches of the second hexachord of another permutation, in an altered or "jumbled" order. An example of this can be seen the tone row of Schoenberg's Piano Concerto, Op. 42, in which the combinatoriality can be seen between the Prime form and the Inversion.

As you can see, the first hexachord of P3 is the same as the last hexachord of I8 and the last hexachord of P3 is the same as the first hexachord of I8.

Another example can be seen in the tone row of Berg's Lulu, in which the combinatoriality occurs between different transpositions of the Prime form:

I suppose one can cite the untransposed Retrograde of any row as hexachordal combinatoriality, however this would be inherent to any tone row. The tone rows above are special in that they have the characteristic of having these same hexachords with permutations other than the untransposed Retrograde.

Combinatoriality can be thought of or used, I suppose, as a non-tonal form of emphasis on particular pitches, or as a kind of modulatory device from moving from permutation to permutation.

Also, keep in mind that the Retrograde of either of the rows I listed as being examples of hexachordal combinatoriality when in Retrograde means that hexachord one and hexachord two are the same with both. This is still combinatoriality. It really doesn't make a difference if you line up one and one and two and two or one and two and two and one. The point is that the row has combinatorial properties.

Now, this can be a tricky topic, so I'm going to direct you to the following articles for a more thorough and detailed explanation and analysis:

Segmental Invariance and the Twelve-Tone System by David W. Beach

Combinatoriality without the Aggregate by Robert Morris

A General Theory of Combinatoriality and the Aggregate (Part 1) (Part 2) by Daniel Starr and Robert Morris

Another form of tone rows would be the all interval row, in which, as the name suggests, every possible interval is used in the construction of the row.

For example:

This row consists of a minor second, a major third, a minor third, a major second, a perfect fifth, a tritone, a perfect fourth, minor seventh, a major sixth, a minor sixth, and a major seventh.

Getting a bit outside of traditional 12-tone technique, you could also have a row that does not use all 12 chromatic pitches or one with repeated pitches (or both!). In addition, microtonal tone rows are also possible, as in some works by Boulez, Ben Johnston, etc.

Another form of the row that can be used is the diagonal row. While this is something that can be used only when working with a matrix, and thus not part of traditional serialism (Schoenberg didn't use matrices, he wrote out every permutation of the row), it has been used by some "post Schoenbergian" composers. One example could be found in Penderecki's Threnody to the Victims of Hiroshima (but we're getting ahead of ourselves here).

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If you have any questions, post 'em! I'd like you to create your own tone row and post it. We'll then construct matrices, both of existing rows (which you'll use for analysis) and of the one you create (for composition), discuss the applications of the tone row, analyze some pieces, and then you'll write a nice little 12-tone piece or two. After that we'll move into integral serialism.

Actually, as I'm thinking here, I think it would be good to do, say, a little suite for piano or something (a "musical theater"ish song cycle if you prefer?) with each movement using a different serial technique that we discuss.

EDIT: I confused myself a bit this morning when I wrote this and skipped over some ideas, so some of the info (particularly the combinatoriality section) has been revised and/or expanded.

So, a few questions....

With Schoenberg serialsm, must you always approach the row by intervallic relation? Or could you, technically, just choose the random notes, but in the inversion of the Prime, you must use intervallic relations, and not just change the order? That was a jumbled question. For instance.

If P(1) is: C#-E-A-B-etc , then I must observe the intervalic relationships of...minor third, perfect fourth, major second. Therefore making P(4) E-G-C-D-etc? I was always under the impression that the Prime stayed the same....making P(4) E-A-B, and continued on, leaving it in the same order, but beginning on a different pitch. Sorry, my thoughts are jumbled, therefore making my speech(text) jumbled as well.

Also...the number system....C is always 0? etc etc up to B is always 11? Another misconception I had was thinking that the numbers were simply the order, so P(4) meant E was the 4th pitch of the row. If that is the case, why is it necessary to include the number, when indicating your series. For instance, if G is always 7, then what is the purpose of writing P(7): G, etc etc, if G is understood to be 7. Is it not just as informative if you see P: G-A-C#, etc etc. This way you would know that it is the prime series, or some transposition of the Prime series, and that is starts on G, which is understood to be 7. I just want to completely understand.

I'm glad you caught the point that any retrograde series hexachord, when not transposed would be an example of combinatoriality. I was just thinking that while reading, and then you answered my question and I laughed out loud.

I don't understand why it's called the "Bach" Motif. Is it from a particular piece he wrote? or is it stylized after him in some way?

Does the 'invariance' combinatoriality only work if you're using each pitch once? Is it possible to map out such a happening? Does it only work by following a certain formula? For instance, in the first example you gave (where R(7)=I(7)). Would that have been possible using any other combination of intervals. Obviously several intervals are repeated, so I know that's one factor. Also, would it be possible for the second set of four notes to be transposed by anything other than a perfect fourth, and the third set of four notes transposed down by a major third from the original four, and still only use each pitch once? I've been experimenting trying to figure out if there is a definite formula for such.

Enharmonics- I think this is all just preference. Sometimes, it's jumping from Db to G#, which is just odd to read, initially, whereas other times, it is an even Db to Ab. The enharmonic doesn't change the interval, or the pitch number, so what is the purpose for haveing different spellings? What's to keep a person from using all flats and naturals, and no sharps at all?

Thanks so much so far. This is already really interesting. I'm keeping up, but it's almost too much to take in. So many questions...

Forgot the assignment....

P(0): C-Ab-G-D-Bb-F-Db-A-F#-Eb-B-E

up m6, down m2, down P4, up m6, down P4, down M3, up m6, down m3, down m3, up m6, down P5

So, I liked the way it sounded, but didn't realize I was favoring an interval until I wrote it out, which I'm glad I did for my own good. Is this ok?

With Schoenberg serialsm, must you always approach the row by intervallic relation? Or could you, technically, just choose the random notes, but in the inversion of the Prime, you must use intervallic relations, and not just change the order? That was a jumbled question. For instance.

If P(1) is: C#-E-A-B-etc , then I must observe the intervalic relationships of...minor third, perfect fourth, major second. Therefore making P(4) E-G-C-D-etc? I was always under the impression that the Prime stayed the same....making P(4) E-A-B, and continued on, leaving it in the same order, but beginning on a different pitch. Sorry, my thoughts are jumbled, therefore making my speech(text) jumbled as well.

What you're discussing is Rotation, not Inversion. Rotation comes in to play a bit "post-Schoenberg". We'll discuss it when we look at Stravinsky's 12-tone pieces and some others.

So, to clarify, what you're describing -- moving the first pitch to the end of the row -- is Rotation. Inversion is when "flip" the intervals. So your minor third up, is now a minor third down, your perfect fourth up is now a perfect fifth down, and your major second up is now a major second down.

In creating your row, you don't necessarily have to think about it in terms of intervals. Some composers do, some don't. You will need to think about it that way to create the inversion.

Also...the number system....C is always 0? etc etc up to B is always 11? Another misconception I had was thinking that the numbers were simply the order, so P(4) meant E was the 4th pitch of the row. If that is the case, why is it necessary to include the number, when indicating your series. For instance, if G is always 7, then what is the purpose of writing P(7): G, etc etc, if G is understood to be 7. Is it not just as informative if you see P: G-A-C#, etc etc. This way you would know that it is the prime series, or some transposition of the Prime series, and that is starts on G, which is understood to be 7. I just want to completely understand.

As I said, there are multiple ways to number the row. But the one I use and the one that I think is the simplest and makes the most sense is the system I described. So yes, C is always 0, etc. up to B which is always 11.

Numbering it based on the row like you describe is something that's been done, and I'll get into the other numbering systems when I explain matrices (as it'll be a lot easier to get). But the reason I like to use this system is because every time you see P7 you know that it's the Prime form transposed to start on G. As opposed to other systems, where it could be the Prime form transposed to F or B or A or something.

You're right to an extent about P7 being pretty much all the information you need, and in an analysis, its perfectly acceptable to write just the names of the rows, without actually writing out the row. I wrote out the full rows here to show you everything and make it clear.

I don't understand why it's called the "Bach" Motif. Is it from a particular piece he wrote? or is it stylized after him in some way?

B♭ in German notation is spelled B♮ and B♮ is spelled H. So the pitches actually spell out Bach. It was also used by Bach, in the unfinished fugue from The Art of the Fugue, BMW 1080. It was also used, transposed, in a number of his other works. Its been used by many composers since (as you saw in both the Schoenberg and Webern rows).

Does the 'invariance' combinatoriality only work if you're using each pitch once? Is it possible to map out such a happening? Does it only work by following a certain formula? For instance, in the first example you gave (where R(7)=I(7)). Would that have been possible using any other combination of intervals. Obviously several intervals are repeated, so I know that's one factor. Also, would it be possible for the second set of four notes to be transposed by anything other than a perfect fourth, and the third set of four notes transposed down by a major third from the original four, and still only use each pitch once? I've been experimenting trying to figure out if there is a definite formula for such.

I'm sure you could create a row with repeating pitches that is invariant. I've not seen any examples of it, nor have I tried it, so I'm not really certain. I don't know why it wouldn't be do-able.

Okay, perhaps I should have been a bit clearer on invariance. In order for it to work, your second 6 pitches must be a permutation of the first 6. The Webern row from Op. 28, which is constructed on four pitch sets, also works this way. The second six pitches are the Retrograde Inversion of the first. So basically, the key is some form of symmetry in the row.

Enharmonics- I think this is all just preference. Sometimes, it's jumping from Db to G#, which is just odd to read, initially, whereas other times, it is an even Db to Ab. The enharmonic doesn't change the interval, or the pitch number, so what is the purpose for haveing different spellings? What's to keep a person from using all flats and naturals, and no sharps at all?

It is all preference to an extent. I mean, you will often find sharps going up and flats going down. Or a D♭ instead of a C♯ if the preceding pitch is C♮. Sometimes to show the intervals clearly, but this can't always be done.

Thanks so much so far. This is already really interesting. I'm keeping up, but it's almost too much to take in. So many questions...

Its what I'm hear for! I know its a lot of info, and feel free to ask more questions, this is so that you understand it. But to keep from completely losing you, I'm going to give you a few days before I post my lesson on matrices.

Your row looks good, most rows tend to favor specific intervals (hey, unless its an all-interval row, its gotta have at least one repeating interval, right?), now give me the Inversion, Retrograde, and Retrograde Inversion.

I mixed up my words. I meant transposition? that is starting the row on a different pitch. And now, I realize the proper name is rotation. I will keep that in mind. Also, you said, in the first paragraph of this response....inversion....up by a fourth inverts to down by a fifth. That's a mistake right? Or am I missing something?

And the invariance is clearer now. I understand the concept of the permuted second hexachord. That all makes sense. When it got divided into 3 groups of 4, I suddenly panicked, lol. All clear.

Prime

P(0): C-Ab-G-D-Bb-F-Db-A-F#-Eb-B-E

Inversion

I(0): C-E-F-Bb-D-G-B-Eb-F#-A-Db-Ab

Retrograde

R(4): E-B-Eb-F#-A-Db-F-Bb-D-G-Ab-C

Retrograde Inversion

RI(8): Ab-Db-A-F#-Eb-B-G-D-Bb-F-E-C

Yup, that is a mistake, good catch! Yes a fourth up inverts to a fourth down.

That was my fault, I should have been a little clearer and provided a better explanation with that first row. But it is important, when looking at that particular row, to see how he manipulates the Bach motif. Which does result in that "symmetry" in the row.

If there is still any confusion regarding combinatoriality and/or invariance let me know. As I said, it can be a tricky topic, so if anything else wasn't completely clear in my explanation, I'll be happy to clarify.

Your permutations all look good.

I'll give ya' matrix stuff in the next couple of days.

Awesome. In the meantime, I will be listening to all those Schoenberg/Webern pieces you referenced. And I'll try to read a bit of those articles you linked as well.

Great, listen to Schoenberg's Suite, Op. 25 in particular. After we go over matrices, I'm going to have you do some analysis of that one.

Okay, so Matrices.

While not actually necessary with serial music (I think I mentioned that Schoenberg wrote out every permutation on a staff), have become an important tool in both the composition and the analysis of 12-tone music.

So you start with your tone row:

C♮ E♮ F♮ D♮ G♮ A♮ F♯ G♯ B♮ A♯ D♯ C♯

Then down the left side, you add your inversion:

C♮ E♮ F♮ D♮ G♮ A♮ F♯ G♯ B♮ A♯ D♯ C♯

A♭

G♮

A♯

F♮

D♯

F♯

E♮

C♯

D♮

A♮

B♮

And then you fill in the rest, transposing your row to start on each of those pitches.

C♮ E♮ F♮ D♮ G♮ A♮ F♯ G♯ B♮ A♯ D♯ C♯

A♭

G♮

A♯

F♮

D♯

F♯

E♮

C♯ F♮ F♯ D♯ G♯ A♯ G♮ A♮ C♮ B♮ E♮ D♮

D♮

A♮

B♮

C♮ E♮ F♮ D♮ G♮ A♮ F♯ G♯ B♮ A♯ D♯ C♯

G♯

G♮

A♯

F♮

D♯ G♮ G♯ F♮ A♯ C♮ A♮ B♮ D♮ C♯ F♯ E♮

F♯

E♮

C♯ F♮ F♯ D♯ G♯ A♯ G♮ A♮ C♮ B♮ E♮ D♮

D♮ F♯ G♮ E♮ A♮ B♮ G♯ A♯ C♯ C♮ F♮ D♯

A♮

B♮

(I fill in each prime form, one could certainly go by the inversion. I also find it easiest to just go up by half step, as above, however there is no order you need to do this in, just so long as you're transposing)

C♮ E♮ F♮ D♮ G♮ A♮ F♯ G♯ B♮ A♯ D♯ C♯

G♯ C♮ C♯ A♯ D♯ F♮ D♮ E♮ G♮ F♯ B♮ A♮

G♮ B♮ C♮ A♮ D♮ E♮ C♯ D♯ F♯ F♮ A♯ G♯

A♯ D♮ D♯ C♮ F♮ G♮ E♮ F♯ A♮ G♯ C♯ B♮

F♮ A♮ A♯ G♮ C♮ D♮ B♮ C♯ E♮ D♯ G♯ F♯

D♯ G♮ G♯ F♮ A♯ C♮ A♮ B♮ D♮ C♯ F♯ E♮

F♯ A♯ B♮ G♯ C♯ D♯ C♮ D♮ F♮ E♮ A♮ G♮

E♮ G♯ A♮ F♯ B♮ C♯ A♯ C♮ D♯ D♮ G♮ F♮

C♯ F♮ F♯ D♯ G♯ A♯ G♮ A♮ C♮ B♮ E♮ D♮

D♮ F♯ G♮ E♮ A♮ B♮ G♯ A♯ C♯ C♮ F♮ D♯

A♮ C♯ D♮ B♮ E♮ F♯ D♯ F♮ G♯ G♮ C♮ A♯

B♮ D♯ E♮ C♯ F♯ G♯ F♮ G♮ A♯ A♮ E♮ C♮

You'll notice that the diagonal from the top left row to the bottom right are all the same pitch. This will always be the case with traditional matrices, so you can use it as a guide when you do it.

So if we attach names:

I0 I4 I5 I2 I7 I9 I6 I8 I11 I10 I3 I1

P0 C♮ E♮ F♮ D♮ G♮ A♮ F♯ G♯ B♮ A♯ D♯ C♯ R1

P8 G♯ C♮ C♯ A♯ D♯ F♮ D♮ E♮ G♮ F♯ B♮ A♮ R9

P7 G♮ B♮ C♮ A♮ D♮ E♮ C♯ D♯ F♯ F♮ A♯ G♯ R8

P10 A♯ D♮ D♯ C♮ F♮ G♮ E♮ F♯ A♮ G♯ C♯ B♮ R11

P5 F♮ A♮ A♯ G♮ C♮ D♮ B♮ C♯ E♮ D♯ G♯ F♯ R6

P3 D♯ G♮ G♯ F♮ A♯ C♮ A♮ B♮ D♮ C♯ F♯ E♮ R4

P6 F♯ A♯ B♮ G♯ C♯ D♯ C♮ D♮ F♮ E♮ A♮ G♮ R7

P4 E♮ G♯ A♮ F♯ B♮ C♯ A♯ C♮ D♯ D♮ G♮ F♮ R5

P1 C♯ F♮ F♯ D♯ G♯ A♯ G♮ A♮ C♮ B♮ E♮ D♮ R2

P2 D♮ F♯ G♮ E♮ A♮ B♮ G♯ A♯ C♯ C♮ F♮ D♯ R3

P9 A♮ C♯ D♮ B♮ E♮ F♯ D♯ F♮ G♯ G♮ C♮ A♯ R10

P11 B♮ D♯ E♮ C♯ F♯ G♯ F♮ G♮ A♯ A♮ E♮ C♮ R0

RI11 RI3 RI4 RI1 RI6 RI8 RI5 RI7 RI10 RI9 RI4 RI0

Another way to number this would be to keep the Primes and Inversions the same, but note the retrogrades to match them, so R1 above, for example, would be R0, RI4 would be RI5. You could also number 0-11 down each side. So P8 above would be P1. As I said, this way of numbering is how I'd like you to do it.

Unless you have any other questions, I would like you to make a matrix for your rows, as well as Schoenberg's row from Op. 25. I would also like you to label the rows in the first movement of Op. 25.

Questions or comments, let me know. If you need the score, let me know.

Then we'll discuss other matrices (rotation matrices and Stravinsky's vertical arrays, Boulez matrices, etc.) and eventually other ways to apply this stuff (eventually integral serialism).

Just letting you know, I recently started the Fall semester at school, so my responses will be a bit slower. I have read this. I'll discuss questions/comments later when I have more time.