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Thank you very much for analyses. You gave some very interesting insights into these compositions.

But I was honestly not thinking about the Notations when I mentioned Boulez. The notations always seemed very different from most of Boulez output, probably due to their use of literal repetition.

When I was talking about random sounding tone patterns I was thinking about later compositions such as Le Marteau sans Maitre. In this piece Boulez partitions a 12-tone row into multiple sets and multiplies them with each other. The order of the multiplications in the piece is afaik determined by drawing diagonal lines in a matrix.
I have a hard time seeing how this approach relates meaningfully to anything the listeners hears in the piece, especially given that the notes in each multiplication may appear in any order.

But if you could provide a similar analysis for Le Marteau sans Maitre, that may be illuminating!
Sure, I can give my thoughts on that. I am going on vacation from work and will not have time for about 1 to 2 weeks as I will also be taking care of some medical things as well. But can reply after that.

In the meantime, are you familiar with "free atonality"? In particular, why and how it came about (and led to serialism), and how someone like say, Webern, wrote it it so well? And are you familiar with Boulez being considered in the "Webern School"? (He does not write strictly Webern "pastiche". He has actually expanded on Webern's ideas and techniques). Do you understand Webern's style to begin with and what separates it from the others? These are the starting points and I was just wondering how familiar you are with them.
 

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To get started on my "dissertation", I will have to start with the Webern style/school and thought, then compare Boulez to this same style to which he is a direct successor.
This is just the first part.

The first thing to understand is that the Webern school constructs the series in its own unique way. Contrary to popular belief, not all 12-tone rows are created equally. Berg’s rows hint very closely at tonality. I cannot analyze them at this time, due to time and space constraints. Schoenberg’s are sort of a happy medium, mostly. His can span the full gamut depending on what he is going for. Usually they are “blurred tonality”. Webern’s however, are strictly atonal and make no hints whatsoever at any tonal centers, scales, keys, etc. at all.

How does he do this? By mostly sticking to contiguous major and minor seconds that cannot possibly occur in a tonal scale or key together. Take the pitches D, Eb, and Db, for example. These pitches do not occur in any tonal scale or key all at the same time. He will make similar patterns from there on out (sometimes including tritones as well). This helps ensure that the music has no chance at all for being mistaken as tonal.

He actually led up to this line of thinking from his pre-serial, atonal writing, such as his Bagatelles. In that piece, you can witness how meticulous he was in going through and trying to make sure each note was new that was sounding and that it’s relation was in no way related to the previous one or two notes. This was all done without constructing any row (12-tone theory had not been developed yet).

This is the type of goal Boulez attempts to accomplish as well, and I will continue to discuss later…
 

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One of the ways in which Schoenberg carried this idea further, was by introducing the idea of permutations. It is important to discuss this now as it is my belief this has something to do with what Boulez is doing with the whole multiplication of pitches (so this is why I'm mentioning this in this Boulez discussion), which is: 1) ensuring that complete chromaticism and cycling of pitches stays consistent and new, and 2) groups of chromatic pitches are easily and quickly accessible; 3) the use of the row and its transpositions have become tiresome either to the ear, to the composer, or 4) the new pitches that are needed need to purposely be unrelated to the row.

A permutation is taking the original form of the row and constructing a completely new 48x48 matrix in the following order:

1, 3, 5, 7, 9, 11, 2, 4, 6, 8, 10, 12
1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12

And so on until you have the new matrix. As you can see, you take the row order and make a new row with odds first, then evens. Then take THAT row and do the same. Then you keep doing that.

If you don't mind me doing so, I am attaching a score for one of my own compositions in which I used permutations and will explain why I did it. This is a short 12-tone piece for Mezzo Soprano and Alto Flute (written for a contest). I knew I was going to use the row and all of its transpositions throughout the piece (1 statement of each transposition) and where they were going to go. I wanted new material in the section in which the musicians play together (just in the middle part). But I purposely did not want the main melody which is based on the original row to be accompanied by a transposition of the same row. So, instead of spending forever and a day picking notes at random, I was able to quickly get notes from a permutation. The rhythms, dynamics, articulations, and where notes repeat and go together must still be decided (it made a triadic outline in the flute part at two points, but I was only looking for pitches to go well with the soprano. The row in its other forms is completely atonal).
 

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To really get into the nuts and bolts of what’s going on in Le Marteau, we need to move on to understanding how the Webern school looks at the elements of music differently than what came before, and why.

Let’s look at melody and harmony in the past and how atonal music (including 12-tone) compares. In the music of the past, tension and release/drama/emotions/etc. were conveyed through the means of a hierarchy of consonance and dissonance in relation to a tonal center, yes? This carried the listener through the music in whichever direction the composer wanted to take them.

But without tonality, that all went away, right? There is no tonic chord anymore, no tonic pitch, no hierarchy of one note or group of notes above another, no forward or backward direction to move the listener towards and away from any goal.

This didn’t stop composers like Berg, however, from writing in old styles, but with serialization of those styles. Take the Violin Concerto. There is serialization of Baroque homophonic and polyphonic styles. Like a melody in half and quarter notes in a “classical” phrasing accompanied in a “classical” texture. Just the notes are changed (but since the row has tonal implications, it’s not all that jarring).

Schoenberg would most often be the same way (until much, much later). He would have a classical chamber music and symphonic style not at all unlike Mendelsohn, Brahms, Mozart, or even impressionist textures. But the notes are from 12-tone rows.

To reiterate, you might have textures such as the following (as in Schoenberg and his followers, not Webern though): melodies with simple, classically phrased rhythms accompanied by sustained chords; a similar melody as just described over an accompaniment of ostinatos; a similar melody as previously described accompanied by arpeggios. And so on…

Later composers felt that that sort of thing did not always fit well with atonality and serialism (for reasons stated previously). They felt more that in atonal music, what makes the music expressive/dramatic etc. are the interval relationships, the rhythm, silences, dynamics and phrasing, formal design, and most importantly (especially in pieces like we will see in Le Marteau) the tone colour and texture.

For interval relationships, you’ve heard me preach here on this site about the difference between the expressive qualities of each of the intervals and their direction (ascending/descending). Also, now when an atonal composer wants to get from say, relaxation to tension in 16 bars or so, since he doesn’t have tonal chord progressions and scales to rely on anymore, he knows now he might try:

Start with tranquil movement, weak pulse (“vague” rhythms), mid registers, weaker intervals, low contrasts, legato articulations, etc. etc. then progress to more rapid movement, stronger pulsations, irregular rhythms, stronger intervals, more extreme registers, contrasting silences (perhaps), staccatos and accents, louder dynamics, etc. etc. etc.
So, the music no longer looks “classically phrased” anymore, however, it CAN’T be or else it wouldn’t be as expressive as it is in this new way of writing.

So, you will see this kind of writing from time to time with Webern and Boulez. However, it is still not the majority of what you see in Le Marteau.

Let’s look again at what I mentioned earlier with tone colour and texture. I will not comment on the instrumentation being inspired by ethnic music as that has already been done to death.

Le Marteau is a composition in the Webern school. Not pastiche, of course. As it is completely Boulez’s own, but its core foundation is clearly Webern. Let’s take a look.
Watch and listen to the following video. This is Webern’s Symphony, Op. 21. Tomorrow I will analyze it (to a certain degree) and compare it to Boulez's Le Marteau.
(More later)…

 

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The first thing I wanted to mention about the Webern Op. 21 is the rhythm and the orchestration. Oddly enough, the way he has composed the piece, these features go hand in hand.

The main thing to notice about the rhythm is that Webern is using a very limited number of note and rest values. Notice that the first section only uses half, quarter, and whole note/rest values; then later he moves on to dotted quarters, dotted halves, and eighths.

The pitches, BTW, as the video mentions, are a double canon (although this is not really noticeable on an audible level unless you are extremely familiar with the piece, and it is still extremely hard to tell).

The articulation is also limited. He is restricted to tenuto, staccato, and legato.

What you want to notice about the texture is that there is no harmony/accompaniment. You just have counterpoint in which the single lines are segmented and dispersed between the multiple instruments, each one getting a portion of the “melody” in their turn. Some instruments might play 1 note of the “melody”, some might play 2, some might play 3, etc. In jazz scoring, this technique is called “hocketing”. It’s one line that looks like it’s multiple lines.

In a way, the ensemble sounds like 1 unique instrument where all the tone colors combine in unique ways at different times to state their portion of the texture. It’s like playing a piano, but where the two hands are equal, not where one hand accompanies the other.

You know how in looking at a score, you can always tell which part is the clarinet part, which part is the violin, the tuba, the flute, the horn by HOW it is WRITTEN? The WAY the music LOOKS? Notice how that is obscured here. You can’t tell. All the lines look the same. That is on purpose.

This does not mean he is not writing idiomatically. He is. But he has taken into account what the instruments can do similarly. Like a Vinn Diagram. The instruments are in idiomatic range. But notice how each line, no matter what instrument, usually has wide leaps? He’ll have grace notes in all instruments that can execute them. There is still idiomatic things in the strings like double stops and pizzicato. But if you didn’t see the first page of the score, it would almost be impossible to tell what instrument is playing what line just by how the line is written.

(Keep in mind the reason for why he might be doing this was explained in previous posts).

The lines imitate more around the climax at bar 61. More regular note values with longer phrases.

We will review these points again when we look at Le Marteau.

Webern did these things in other pieces too, btw. Like the Concerto for Nine Instruments.

More later…
 

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The second movement is similar. Limited rhythmic values (quarters, eighths, dotted quarters, eighth rests). And this time utilizing many of the values in pairs.
The variations use similar rhythms in instruments grouped in similar ways as before. And it again, is hard to tell what line is written for what instrument do to their similarities.

I’ll be able to begin looking at the video of the score to Le Marteau (with audio) tomorrow/this week so we can compare with what I’ve been explaining so far. Hopefully it shouldn't take but just a couple of posts...
 

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So, here now is the score and audio for Le Marteau sans maitre


Notice now the similarities to the aforementioned Webern pieces.

Look at Mvt I. Right from the start we see that there is the restricted use of limited rhythmic values (notes and rests). The first section with quarters, eighths, dotted eighths, dotted quarters, eighth triplets; and the second section utilizing more irregular groupings of 5-tuplets in eighth and quarter groupings and quarter note triplets, as well as a half note here and there. That’s actually not very much. Just compare to a Ferneyhough, or even some Stravinsky for that matter and you’ll see it’s limited.

The articulation is a bit more varied in the first movement, but legato, tenuto, and marcato dominate the majority of it.

The #1 thing to notice about this is that he has maintained Webern’s concept of no foreground, no middle-ground, and no background in the texture. There is no “melody with accompaniment” as in some “classical” forms/textures, Schoenberg and Berg as was mentioned earlier. It’s all “hocketing” mentioned previously with all the lines segmented and dispersed equally among multiple instruments where each one will get 1, 2, 3, 4, etc. of the “melody”/texture.

So, it still holds true that “In a way, the ensemble sounds like 1 unique instrument where all the tone colors combine in unique ways at different times to state their portion of the texture. It’s like playing a piano, but where the two hands are equal, not where one hand accompanies the other.”

Notice that all the lines look practically the same/very similar again. This is of course, on purpose. It’s just like the Webern. Again, all within the instruments’ ranges, and with wide leaps, grace notes, but with some idiomatic things thrown in for each instrument too (like pizzicato and multiple stops for strings, harmonics for flute, and so forth).

Also take note of the great lengths he went to in order to maintain this idea. What I mean is take a look at the vibes and guitar part especially. If I was writing a piece with guitar and vibes, serial or otherwise, I would utilize strumming patterns on the guitar along with arpeggio accompaniments, fingering patterns of chords, and the list goes on. For vibes I would utilize the keyboard qualities like a piano, such as 2 or 3 part writing, rolled chords, sustained chords, the sustain pedal, the motor “on” for vibrato (or “off” when not needed), arpeggio accompaniments, and on and on.

But Boulez doesn’t do any of that, because none of those things would work with what he is doing. But he is still keeping within the instruments’ idioms (like utilizing the open strings in guitar chords, for example, or widely-spaced chords you can only get on mallets).

Look at the following movements and notice similar things. Keep in mind that the note values he works with change, etc. but the concepts are basically the same (they are limited in number). What I find interesting, and this goes for Webern as I believe he got the idea from him, is that he has constructed a longer piece by putting together a succession of short ones. It’s almost as if 12-tone music seems to lend itself best to smaller forms as it seems to be taken in and digested easier this way. Further, I think it works best with this style as these two composers are masters (along with Schoenberg, who is probably the best at it) of creating disparate pieces of musical character in 12-tone technique (look at Notations for these qualities as well (And Schoenberg’s piano pieces especially).

Mvt III starting at 6:26 is also worth mentioning. The first thing to mention about this is the vocal part. Notice that it is NOT sprechstimme, like how Schoenberg and Berg would most often write for the voice. It’s just standard bel canto, like how Webern writes vocal music. The rhythms are freer and in an “atonal”/Webern style of melodic writing, but note how the lines still favor each other? What I mean is that the vocal part is “flute-like” isn’t it? Starting at bar 6, they are practically identically written straight to the end. So much so, that if I were conducting this, I would ask the players to listen very close to each other and match as much as humanly possible. The flute should sound like a vocalist, and the vocalist should sound like a flute, creating one single “flute-voice” sound for the piece.
 
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