How Would One Approach Studying A Piece Like This

Shall we say "The Beatles"?

but I don't understand... are you trying to "prove" that Xenakis didn't make music? That his composition method is "non-musical"?

I'm not the one saying it, he is, Thallo. In this piece, the method is mathematical (ergo not musical) ... it's not a secret.

ttw wrote:

I'm not the one saying it, he is, Thallo. In this piece, the method is mathematical (ergo not musical) ... it's not a secret.

This argument is absolutely inconsistent. A musical piece is not the proof of a mathematical theorem. Xenakis knew mathematics: if he had wanted to proceed with the proof of a mathematical theorem, he would have used the means of mathematics.

HERMA is constructed through the application of a mathematical principle, but it remains a musical piece. You can construct a musical piece by applying a serial, narrative, architectural, mystical, etc., paradigm, but the object will always and anyway remain a musical piece.

Maybe it depends on who, RedScharlach

ttw wrote:

Maybe it depends on who, RedScharlach

Not at all.

RedScharlach wrote:

This argument is absolutely inconsistent. A musical piece is not the proof of a mathematical theorem. Xenakis knew mathematics: if he had wanted to proceed with the proof of a mathematical theorem, he would have used the means of mathematics.

HERMA is constructed through the application of a mathematical principle, but it remains a musical piece. You can construct a musical piece by applying a serial, narrative, architectural, mystical, etc., paradigm, but the object will always and anyway remain a musical piece.

Forgive me RedScharlach, if with this response I might seem haughty to you, I assure you that this is not the tone, but I do not understand how you can tear down those participating in this discussion by saying: "what you are saying is inconsistent". I could say the same about what you are saying, but instead, I try to argue my hypotheses in light of documents and proofs beyond my simple thought, which I no longer believe is a secret. Thus, in this sense, I try to use the documentation I find in my favor. And I have written 7 pages of arguments. Now, I do not believe that such arguments, mine and others', can be knocked down by 4 lines where, on one of the 4, it reads: "this argument is inconsistent".

You quote: "A musical piece is not the proof of a mathematical theorem. Xenakis knew mathematics: if he had wanted to proceed with the proof of a mathematical theorem, he would have used the means of mathematics."

First of all, one must debunk the myth that Xenakis was a mathematician by profession... He was not at all! Moving on...

It is true that a musical piece is not the proof of a mathematical theorem, but if you base your composition on a mathematical theorem, its result cannot be independent of it; otherwise, why would he have used it? If one does not want to receive criticism in this sense, then one should simply not use mathematics. It's like saying... "Yes, I based Herma on a mathematical procedure, but don't pay attention to it, think about the music". No, no and no again. All choices must be analyzed just as is done with the scores of Bach, Chopin, Mozart, Beethoven, Cimarosa, and whoever else—certainly with different premises, since we are in different fields, but always asking ourselves: why did he adopt this choice in this phrase? Why shouldn't we do it in Herma?? Xenakis himself writes the set-theoretic operations used in the score; the author himself therefore encourages the reader to research the logical-mathematical choices of the piece... If you continue to tell me no here, I will immediately ask you the following question... "If Herma is to be understood only as a musical piece, then why does Xenakis himself write for every phrase the set operations that compose the subsequent phrase?"

All this discussion for what reason? For the simple reason that, for my artistic taste, Herma communicates nothing musical to me, and if, as you say, the object will always and anyway remain a musical piece, then the discussion ends there. But if there are other premises, then why not exploit these to see if, beyond the result, there were reasonings that instead reward this work? That is why I went to research what the reasons were that drove Xenakis to compose Herma, and there, indeed, I saw good intentions. Flawed from a mathematical theory point of view, but it doesn't matter much since the field is musical... Therefore, if before, after listening to Herma, I said: "What a crazy piece of sh*t" (Fantozzi-style), after having studied it, analyzed it, and learned the author's premises, I now say: "Yes, okay, I still don't like the music, but there are excellent thoughts behind Herma; there is the author's will to bring order and combine random elements, and thus, philosophically speaking, Xenakis attempts to bring order to the chaos of numbers and therefore of random notes".

I quote a piece of text from Wikipedia in the paragraph "Stochastic Music" in the lemma Iannis Xenakis:

"Chance becomes in this context much more than simple 'randomness'; contrary to what happens with Boulez (Third Piano Sonata, or other contemporary 'open' works), or with John Cage and his 'renunciations', for Xenakis probability is entirely calculated, the rules are made explicit (see Achorripsis or ST/10-1 in 1961). The global process is entirely predictable, even if the events that compose it are aleatory."

This excerpt is extremely interesting because it says in just two lines what I have said in six pages. Predictable global process (which Xenakis obtains through divisions of set elements and operations between sets), aleatory events that compose it (the elements that compose each set); this is how he attempts to order the unorderable. Philosophically speaking it is right, it is not right at the level of"

result, Ligeti tells us this by using the example of Plastilina. Everything mixes together and the colors can no longer be distinguished.

Interesting developments in the topic

TheSimon wrote:

after having studied it, analyzed it and learned the author's premises, I now say: "Yes, okay, I still don't like the music, but there are excellent thoughts behind Herma; there is the author's will to bring order and combine random elements, and thus, philosophically speaking, Xenakis attempts to bring order to the chaos of numbers and therefore of random notes".

Finally we made it, after 9 pages we have arrived at bringing the discussion back to the level of taste (I like it, I don't like it) and evaluating this work on a conceptual level, as it is.

Xenakis has produced his trademarks... things that if you (re)do them, after 3 seconds they tell you: This is Xenakis... so there is no doubt about his artistic depth... regarding the musicality of this piece we were right to talk about it... is that what matters or was he truly interested in it?

"If one does not want to receive criticism in this sense, then one should simply not use mathematics."

Boulez would be nothing more than a conductor then!

Let's make an example:

If I were to write a piece in which I have a section of 55 bars, then one of 34 bars, then one of 21, then one of 13, and then instead of having one of 8, I put one of 10, would that not be okay?

Or: I decide to use a random number generator; to each of these numbers I will assign a pitch and then have these sounds performed by, say, a quartet. Everything is going according to plan, this is what I wanted, I have established a rhythm (let's assume it is all homorhythmic for the sake of simplicity) but then at a certain point I hear vertically a C major seventh chord, something that I absolutely would not want (it's not that I don't want it, I am speaking in the abstract). I do not have permission to change it because I started from a pseudo-random process and therefore - for consistency - must keep the result intact?

Of course! If you start from a mathematical concept that you define as coherent, you must be coherent, but are we joking? Try writing a theorem that only works sometimes and see how the scientific community responds to you... You can't put 10 but 8 if you want to be coherent, just as you could also start from 89 but not from 88 instead of 54. If you put 88 nothing happens, but then I arrive, notice that you started from a mathematical concept and say that you are not coherent! And you'll have to live with it. You will tell me: "I know, I did it on purpose" and I will tell you okay, then you didn't base yourself on a mathematical series.

If the series you are basing yourself on is this Fibonacci one 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... as long as one of these elements is different, the series is different or even non-existent.. And why shouldn't I point it out to you?

You tell me: the composition is mine, I postulated it on the Fibonacci series but I modified one step... I tell you... Well then it is not coherent with the Fibonacci series because if you exclude one step, that is not the Fibonacci series.

Sometimes in logic tests I have had to complete series. Some elements of the series were compatible but the subsequent ones did not match those of the exercise -> the series was not what I thought it was..

Aside from this, I did not judge Herma in a malicious way for the mathematics behind it, which I instead appreciated, so I don't understand why you want to convince me of something that I have demonstrated is not mathematically correct but that I nevertheless appreciate philologically, but regarding the musical point of view which conveys absolutely nothing to me!

TheSimon wrote:

Forgive me RedScharlach if with this response I might seem haughty to you, I assure you that this is not the tone, but I do not understand how you can tear down those participating in this discussion by saying: "what you are saying is inconsistent".

No problem! But my criticism was not at all aprioristic: the argument was perhaps too synthetic, so I will clarify with an example.

Nuper rosarum flores is an isorhythmic motet written by Dufay on the occasion of the consecration of Santa Maria del Fiore. According to a musicological interpretation - which is moreover disputed - the proportions of the motet reflect the proportions of Brunelleschi's project. The paradigm is therefore architectural. However, the measurements of the transept of Santa Maria del Fiore deviate by about 3% from the proportions indicated by the motet. If we were to apply the proportions indicated by the motet with "rigor," Santa Maria del Fiore would not stand up. The architectural paradigm is not followed with rigor (with the rigor due to the laws of statics, I might say). Ergo, should we deduce that Nuper rosarum flores sucks?

I know it, moreover, magnificent in its choral and musical simplicity... However, I was not aware of this dispute regarding the measures. In this case, however, you understand well that the final material on which we find ourselves arguing is quite different from what might be produced by stochastic music...

another example is Metastaseis and the Philips Pavilion in Brussels.

note that the music was born before the architecture in this case!

edit:

also the architectural proportions and Renaissance painting were modeled on the principles of consonance in vogue at the time (fourth, fifth, octave, third... Santa Maria Novella is the emblem of this!)

RedScharlach wrote:

Nuper rosarum flores

scelsi wrote:

metastaseis

....are they listenable? Suggested links (and eventual score)?

TheSimon wrote:

the final material on which we find ourselves arguing is quite different from what might be produced by stochastic music...

Without a doubt! Nuper rosarum flores is magnificent (although I wouldn't define it "simple"), I would gladly listen to it in the morning when I wake up and in the evening before falling asleep, whereas Herma gets on my nerves after a while.

As for the pleasantness/stochastic connection, however, one could attempt an experiment: composing a piece that applies a stochastic principle, but restricting the field of available sounds (what Xenakis calls "R class," if I remember correctly) to a diatonic scale, in a central register, with dynamics ranging from pp to mp, and with a very wide arrangement of rhythmic impulses (a very, very slow metronome, to be understood).

Probably something quite boring would result, certainly not exciting, but certainly not exasperating and unpleasant like Herma ... it could be interesting!

Of course, for simplicity I meant at the level of instrumentation since it is practically all a cappella except for some cases where the voice is supported by wind instruments...

Stellina wrote:

....are they listenable? Suggested links (and eventual score)?

metastaseis (this is a truly "beautiful" piece, eh... moving I would say... )

a couple of links where you can listen to it:

http://www.youtube.com/watch?v=uLW0q3De9HY

and here is the score:

http://en.scorser.com/S/Sheet+music/xenakis+metastaseis/-1/1.html

Open content (youtube)

Open content (youtube)

http://en.scorser.com/S/Sheet+music/xenakis+metastaseis/-1/1.html

Guillame Dufay - Nuper rosarum flores

The score is http://erato.uvt.nl/..._flores_PML.pdf

http://www.youtube.com/watch?v=5P0ti5ULyD8

http://erato.uvt.nl/..._flores_PML.pdf

Open content (youtube)

That is an excellent and relevant quotation from Dufay!

In mathematics, a theorem has its validity when it is correct. Music can run parallel to mathematics but it is not mathematics...(at least in my opinion). If Bartók used the Fibonacci sequence and then deviated from it, I have no problem with that, the same goes for Debussy (La cathédrale engloutie), Boulez with his permutations, etc.

Music was not made to describe Brownian motion, or game theory, or who knows what else... But it can happen that these elements can be a remarkable starting point. Ligeti, I don't remember for which of his compositions, said he was inspired by chlorophyll... It goes without saying that one must always consider composers in whom these elements represent the structure and not the beauty of the piece. I have never tolerated those who say "Listen to this piece, it is Cantor's diagonalization".... But who knows.....

And anyway, even if someone wanted to achieve those results, it would be enough to use algorithms!

Yes, I remember that in Debussy's prelude 10 from the first book there was a structure that followed the golden ratio. I read it, I don't remember in which book... I think in that case, however, the music came first and then the mathematics. As I have been repeating for about 100 posts now, in my opinion, one should always observe the premises...