music21: Visualizing Messiaen’s Mode de valeurs
One of the most influential of Messiaen’s innovation was extending the ideals of twelve-tone music to go beyond pitch. The twelve-tone method, as developed Arnold Schoenberg and his followers, involved arranging pitches in fixed orders so that each note would have equal prominence and the tendency to write music too-mired in the sounds of the past would be eliminated (or at least greatly reduced). While much of the musical world reacted (and still reacts) to Schoenberg by believing he went too far in alienating modern music from the past, Messiaen and a small group of (at the time) young composers believed that he did not go far enough. By not organizing rhythms and loudness (called dynamics or, in French, intensités) similarly to the way he had serialized pitch, Schoenberg’s music could still be rooted in the rhythms and swells of the past.
Messiaen’s 1949 piece “Mode de valeurs et d’intensités” from Quatre études de rythme (“Organization of durations and dynamics” from Four studies in rhythm) was the first European work of “total serialism.” (In America, the composer Milton Babbitt had already made independent but similar creative discoveries). In this piece for piano, three “rows” are used simultaneously. Each pitch in each row is then assigned a particular duration and dynamic that always appears with that pitch (and only with that pitch.) Within each row, the durations get longer as notes get lower.
The precise relationship between pitch and duration is often hard to imagine when looking at the score, but with music21 these relationships become obvious. This code runs a Finale version of the score for the middle row of the Messiaen piece through our graphing tools:
messiaen = converter.parse('d:/desktop/messiaen_valeurs.xml')
notes = messiaen.flat.stripTies()
g = graph.PlotScatterWeightedPitchSpaceQuarterLength(notes,
title='Messiaen, Mode de Valeurs, middle voice', xLog=False)
The 1:1 correspondence between pitch and duration is obvious: each pitch has exactly one quarter length associated with it, and the lengths get longer as the pitch descends. But the non-serially determined aspects of the score are equally obvious. Unlike Schoenberg’s ideal of using each pitch the same number of times, higher pitches appear much more often in the Messiaen piece. But the correspondence is not perfect. For instance, the pitch D 4 appears 11 times while the higher E-flat 4 appears only 10 times. For the most part, the amount of time that each pitch is sounded is roughly constant – at around 20 quarter-notes. But the two shortest notes (G5 and C5) appear as outliers to this theory, appearing only for about 9 and 13 quarters respectively.
What also jumps out in the graph is its shape: it is cubic, that is, it approximates the graph of f(x) = –x3. There are several functions in nature and human society that are modeled by cubic equations, such as magnetic strength, the twisting force of rubber bands (like in wind-up toy planes), and the costs involved with manufacturing. One example from one piece is of course nowhere near enough evidence to suggest that post-tonal pitch and duration relationships could be another place where cubic equations might guide composers. But it does give an idea for further research. As more serial and other post-tonal compositions are inputted into machine-readable formats, I’ll be checking back with whether this relationship holds often enough in Messiaen and other’s music to be significant.
The code for this example has been submitted to the International Symposium on Music Information Retrieval as part of a proposed paper on the system.
performed by Peter Hill, or below by Yvonne Loriod, the composer’s second wife
(please be aware that you can find the specific times for the beginning of each etude in the description of the above video, which I have copied below:
00:00 Ile de feu I
02:06 Modes de valeurs et d’intensités
05:39 Neumes rythmiques
13:01 Ile de feu II)
You know what an étude is, right? The word is French for study (as a noun), and I hadn’t expected we’d talk about Messiaen’s etudes before those of Chopin or Liszt. Now, études (for piano and other instruments) certainly existed before Chopin’s day, but he was the one to compose pieces that were not only challenging to perform and had a pedagogical purpose (training the left hand or some specific technique or whatever), but were also beautiful works in their own right. Many people have since written études for the piano, and they are of high enough musical merit that they’re not just for the practice room but the concert hall too. We have Chopin to think for that, as his two collections of 12 etudes are easily some of the most famous.
Well, we have here a more modern set of etudes, but Chopin’s construct of 24 etudes in all the keys doesn’t apply as much… we have four etudes, as the title suggests, and while I have the score before me now and have listened multiple times, I’m not sure that the individual pieces have any specific technical focus for the performer aside from just being difficult. It seems the concepts laid out in these etudes are more musical or theoretical, rhythmic and harmonic studies and ponderings than they are of execution, although they do seem to be frighteningly virtuosic. But I’m not a pianist.
I talked in the introduction to this series about how learning about the piece at hand, whatever it is, gives us insight into the work that may make it more understandable, easier to appreciate, etc. The first interesting thing to know about this set of four etudes is that they’re not really a set. Let’s look first at the four pieces. From Wikipedia:
The work consists of four movements
- “Ile de feu I” (Fire Island I)
- “Mode de valeurs et d’intensités” (Mode of Durations and Intensities)
- “Neumes rythmiques” (Rhythmic Neumes)
- “Ile de feu II” (Fire Island II)
These four works last in total around twenty minutes, and the real centerpiece and most famous of them is no. 2, Mode de valeurs et d’intensités, and in an oversimplified way, can be stated to be the spark of inspiration behind what Darmstadt represented and/or became, but we’ll get there in a bit.
Or that’s how it is sometimes stated. In Martin Iddon’s book New Music at Darmstadt, he discusses in great detail the political and artistic history of what eventually produced Darmstadt as people think of it, things like Wolfgang Steinecke’s influence and how he came to lead the courses, and why, as well as tons of insightful information about the early days of the courses, where people like Hindemith, Stravinsky, Prokofiev, Kodály, Honegger, Walter Piston, and Britten were featured. Messiaen is often in there, but to be honest, I had to put the book down. It’s beyond the scope of what I’m able to summarize or present in these articles, but is an undeniably great source of information on the topic, so if you’re looking for something to sink your teeth into, I’d suggest that as a great place to start. The main point, though, is that he (and some people he quotes) emphasizes that Messiaen’s stay, presence at, or influence on the Darmstadt school was ‘a brief visit’ and that the association of the Mode de valeurs et d’intensités with what the school later came to do was essentially nothing more than coincidental, having been begun even before the institution as it was known had started. That is to say… dissecting the evolution of a movement like this is hard… so in the interest of simplicity, I think many people pin Darmstadt’s ideas on Messiaen’s work here, but as we shall later see, that’s not entirely accurate (and maybe not at all accurate).
The middle two etudes were composed first, in 1949 (no. 2 actually in Darmstadt), and 1 and 4 (the fire ones) the following year at Tanglewood (in Boston) as some kind of lecture invitation or something. I thought one of them was a commission. In any case, they’re not ‘a set’ like some people may think. (To be honest, Chopin’s etudes aren’t really, either, I don’t think. The preludes make up one long storyline of sorts, but the etudes at least constitute a complete set in all keys). What we have is two quite dense, Messiaen-esque explorations of interesting, rigorous musical ideas bookended by two slightly smaller works dedicated to Papua New Guinea (or just ‘Papoua’). The score that I borrowed from the library contains an “analysis by the composer” in both French and English with score examples and notes, with each piece divided into its respective sections, the first and shortest etude, at just over two minutes comprising “two themes and six sections.” Much of this content is available on the Wikipedia article, although significantly abridged and without score excerpts.
Île de feu I
The score says of the first etude, Île de feu I, that “The first theme is played by the right hand in the lower register… It has four different note values (quarter, sixteenth, eighth, half) and six pitches.” One more little quote and then I discuss:
Contrast is afforded in the third bar by a sudden, brilliant piano passage in the upper register, followed in the next bar by five low chords.
The above describes the first section, from mm. 1-4. What I noticed about these pieces is that they seem to be very episodic. A theme-and-variations work does generally have a progression where it jumps to new ideas all sort of revolving around a common idea, but the feeling I get of Messiaen’s application of themes or figures is more like jump cuts. We’re only two bars in before “contrast is afforded,” and on the surface, there may seem to be no relation to what came before or after, but there is.
Section 2 is bars 5-10; section 3 11-19; section 4 is 20-24; 5 is 25-34, and 6 is 35 to the end (39?). Or at least that’s what I could gather from the analysis. The bars seem to be of arbitrary and constantly-changing lengths, some of 18 sixteenth notes, some only 6 or 7 or 9, and maybe there’s a logic behind this, but I’m not sure. To be honest, I’m satisfied enough with identifying the two themes (or just one) mentioned in the analysis and seeing how it appears and reappears.
Listen to the first ten seconds of the first work. Both staves are notated in the bass clef, and the higher of the two carves out this rhythm that makes up the first theme. After long, low notes, That third bar flourish appears, and the fourth bar gives us what sounds like a cadence that ends the piece, but what comes next is even more intoxicatingly rhythmical. Listen for these kinds of rhythms and how they reappear, notable areas in the music, like two bars of upward glissandi and the very crunchy, rhythmic heartbeat that comes after. While much of this might sound arbitrary and kind of thrown together for a first-time listener, giving it a few listens (do it; this one’s short) and, even better, looking at the score, will show you a bit of what Messiaen’s development and treatment of ideas are like, juxtaposing seemingly unrelated, contrasting content, but actually all coming from familiar, even really identical gestures. Look beyond the apparent chaos and you’ll start to see it.
Mode de valeurs et d’intensités
The second is the (in)famous one. Of no. 2, Wikipedia says:
This movement is the most-discussed of the four, as the first work by a European composer to apply numerical organisation to pitch, duration, dynamics, and mode of attack (timbre) (Toop 1974, 142). Because the treatment of the parameters is modal and not serial (that is, the elements are treated simply as a scale, without any implications for how they are to be ordered), there is no question of the material determining the work’s form (Toop 1974, 148). According to the composer’s own description, there are separate modes composed of 36 pitches, 24 durations, 12 attacks, and 7 dynamics. The duration scale is separated into three overlapping scales, called “tempi” by the composer, which correspond to the high, middle, and low registers of the piano…
So…. it’s not serialist, but modal, but does use “numerical organisation.” While that sounds (obviously) mathematical and even a bit arbitrary, the composer says of it:
…the combination of modes reveals colors of durations and intensity; each pitch of the same name has a different duration, attack and intensity for each register in which it appears; the influence of register upon the quantitative, phonetic, and dynamic sounscape, and the division into three temporal regions imbues the passage with the spirit of the sounds that traverse them, creating the potential for new variations of colors.”
If you say so…
While the idea is a brilliant one, of taking your different variables down and putting them all through their paces, I must say that to me, this is the least interesting to listen to, for me. The analysis in the score gives the 12 listed touches (attacks like accents and staccato, etc.), 7 dynamic levels, 36 notes, 24 durations, as well as an overall analysis of what’s happening play-by-play, listing what’s happening in the top, middle and lower staves (yeah, three staves), with labels like “mode more or less normal”; “abridged retrograde”; “total retrograde”; “arpeggiated inversion”; and so on. “Slight freedom” is even mentioned.
The result of reading all of this, for me, is that it is a compelling argument that what we’re hearing is (obviously) not just random noise, that it’s executed precisely and with purpose. However, I cannot come to hear anything identifiable in it as something that ties the work together. I’m sure there are those who claim they do, but I would never ever be able to come to any of the conclusions I’ve read about by looking at the music on my own. I just don’t hear it. I trust that it’s there, but to me, the end result sounds…. arbitrary.
The Wikipedia article has a section entitled ‘Reception‘ that I’m inclined to copy and paste here…..
The second of the études, “Mode de valeurs et d’intensités”, overshadows all the others for having become the model for composers interested in the serialisation of musical parameters other than pitch. … Pierre Boulez, after a period of estrangement from Messiaen caused by what Boulez viewed as the excessively sensual Turangalîla-Symphonie, belatedly discovered the “Mode de valeurs” in 1951 and composed his Structures, Book I as a gesture of conciliation to his former teacher,…
I took out some enjoyably informative sections of that paragraph to shorten it, but what I mean to say by that is that it was an inspiration for many people to begin moving to a truly serialist method, what really came to be part of the fundamental tenets of Darmstadt. So that’s important.
This was the earliest of the four to be composed, in association with Koussevitzsky’s invitation of Messiaen to some composition course or something. This work is in fifteen sections, but the score mentions the composer’s first three comments:
- “Rhythmic transposition of melodic curves from Gregorian chant”
- “Each neume: fixed dynamic level, upper and lower resonances”
- “Each rhythm is a succession of impetus and rest, or arsis and thesis“.
That last one is particularly interesting, and I get the impression that there are musical things happening in this work that I can finally maybe almost identify. The analysis discusses variations, Messiaen’s ‘non-retrogradable rhythms’, prime numbers, tripartite rhythms, and other things that I’d again be hard-pressed to identify but might actually still be able to hear or feel the result of.
That being said, I have to add that I love this one… despite my inability to analyze it even anywhere near accurately, I can say that it has a feeling.
I speak fluent Chinese, and can read the majority of daily-use traditional Chinese, but I can barely write a small handful of them. I know what my family and friends look like, but I would be hard-pressed to do a sketch of any of them. I can enjoy the local food even if I’m not sure how it was cooked.
What I mean to say is that there’s something about this piece and the repetitive, deeply impressing, unique melodies and rhythms that makes it ‘followable’, exciting, and identifiable. Like I said above, I might not be able to dissect and describe its constituent parts, but I know it when I hear it. There are clearly-defined vibrant ideas that appear throughout these six minutes, and the overall stand-back-and-enjoy effect is a delicate, sensual, but electrifyingly exciting French one, like Debussy and Scriabin taking turns riffing on a piano in a Parisian apartment overlooking some park after a delicious meal and telling ghost stories in front of the fireplace. It’s bristling with energy, nerves, excitement and tension, so regardless of the musical structure and development of neumes (whatever the hell they are), I love this work.
Île de feu II
“This piece comprises nine sections and a coda.” It’s a main theme with five variations. Apparently the work is meant to be indicative of but not related to the first Île de feu…. maybe? Wikipedia says this:
Although Messiaen’s programme note for this étude says that it is, like the first étude, “also dedicated to Papua or New Guinea”, his posthumously published analysis emphatically states that it refers only to the former, not the latter (Messiaen 1996, 165)
I don’t quite get what distinction that is making, but I say we take it as its own independent piece. There are more quotes from the composer in the section about this etude on the Wikipedia article. Go read them.
What I will quote Wikipedia as saying is the relation it does have to the first etude:
The opening strophe from Île de feu I is modified to become the cyclic theme of this étude. As in the other pieces, this alternates with episodes, in this case based on a mode of twelve durations, twelve sounds, four attacks and five intensities (Sherlaw Johnson 1989, 108).
There are more modal treatments of durations and things here, so if there is any kind of… unity to these four works, the fourth in the set calls back to numbers one and two. There’s a ‘duration-row permutations’ chart in the Wiki as well, but it’s Greek to me.
The opening figure is noticeably similar to the opening of number one, and I find this satisfying. While there are definitely identifiable sections (for some pieces of these four etudes, there’s a new marking for interpretation or tempo every bar), that opening figure is riffed on for a while before it seems to move on into ever-increasing excitement, with runs and lots of nonstop sixteenth notes or triplets toward the end. We’re in the same world, orbiting around similar ideas, but it is interesting to see the variance and scope Messiaen can bring to (ostensibly) related ideas. What I find perhaps most significant is the final ending figure of the last etude. It reminds me in a way of some things from the first etude, especially the seeming ‘end’ in bar four of the first etude, about ten seconds in.
Okay, so those etudes are important, some more enjoyable than others, interesting, but musically and historically significant. This is where we’re going, folks, and Messiaen is, as you can see, an important figure in where the next generation of composers went. I say next generation, but Boulez was only a decade or something younger than Messiaen.
In any case, this was a really challenging work to talk about, but I at least had the score on hand. Perhaps that’s what made it longer: I could ramble about things I saw and thought I understood, but for most of what comes next, I don’t even have a score to refer to, so… we’ll do what we can. This sure was a long article for only twenty minutes of solo piano music, but they’re pretty complex works, so… sorry not sorry.
Stay tuned for real Darmstadt stuff coming up next week.