I know I'm being too long-winded, okay, but this is my last message on this topic anyway, because I want to come home in the evening and relax and not spend my time getting pissed off in front of the monitor, so make an effort to read and understand everything. If before I used to play and have fun through bursts of ideas—believe me when I say I used to post my convictions with a smile plastered on my face—now things are getting heavy and I'm not having fun anymore because I would like to seek a dialogue that is as civil as possible, even if colored with swear words (we are all adults; those who are minors probably know them and use them more than we do), but on the contrary, I am realizing that people here are taking things too personally. As I repeat, I don't give a damn about the Herma, but I love the "battle" of ideas because I am convinced that one learns much more from someone who thinks the opposite of you rather than from someone who thinks like you, as you can discover insights and points of view that you have never noticed before and maybe, why not, in some cases embrace a theory completely different from the initial one if well-argued and motivated. But if someone has to feel bad because of my words or the words of others, then there is no more fun in this clash and I prefer not to continue out of respect for others first and foremost, and also for my own personal peace: I want to go home knowing that I haven't hurt anyone, verbally and/or physically; at least that is what I hope for in my life.
I expressed an opinion: harsh? Not harsh? Off Topic? If you want, I'll issue a warning to myself, but honestly, as you may have noticed, I rarely report Off Topic if the flow of the discussion is somehow related to the topic. Of course, if we are talking about teaching and end up talking about cattle farming... Okay, that's off topic. Check around and see for yourself how many OTs I have reported. Here, Stellina asked for a little help studying the Herma, and we ended up arguing pro-Herma and anti-Herma; in any case, it's always about the Herma being discussed. Okay, how much are we OT? It is true that Stellina herself, who opened this topic, instead found the subject very interesting in one of her posts and thanked us for the information we provided. In some way, even listening to other people's debates is useful when you want to study a piece. Topics can evolve, and unless the subject changes drastically, I don't feel like reporting Off Topic, not even when the discussion becomes uncomfortable... At most, I avoid responding.
I only said what I thought, and I am not angry with any of you; I repeat this, so I don't understand this animosity of yours towards me, Claudio; perhaps you will explain it to me in private.
As far as I'm concerned, you can listen to and study the Herma for 20 hours a day, but for me, the Herma remains useless, as already stated a few posts above. I don't consider it useless only to the ear (as your friend told you, Claudio, who judged it musically)—that would be reductive because this work is based on principles that are not musical; I also gave an analysis based on mathematical sources as to why I consider it useless, I provided citations that supported my theses, and as for stochastics, during that period Xenakis was specifically dedicated to that. With these data, I don't want to convince anyone to hate the Herma, I only want to motivate my choice so that I am not told the classic phrase: "You don't like it because not everyone is allowed to understand," as Boesendorfer textually insinuated. Well, that is an insult! But I continued with my convictions without paying too much attention to that phrase. My choice is based on a lifetime of study (I am referring in this case more to the scientific rather than the pianistic field) and a deep understanding of this work, and I do not accept being snubbed by being told that I am not allowed to understand. Am I perhaps an idiot? This is proven by the fact that in 6 pages of topic, no one has been able to answer a very simple question that I will pose again later. In any case, I have not raised criticisms against anyone, but now that we are talking about criticism, well, maybe I was the first to receive the insult! But one stays silent for the sake of peace, or perhaps they are unfortunate phrases that come out without realizing it, or at least I like to think so...
You know well how much I respect you as a person, Claudio, and how much I value your interventions (which in my case can be recognized by the likes), always very precise and rich in content. You are without a doubt more knowledgeable than me in Musicology—after all, how could it be otherwise, it's your degree—but if you allow me, I believe I am more knowledgeable than you in mathematics and physics, which concern me more closely and which I find myself working on side-by-side almost every day. In this sense, in the Herma, we approach this duality. A composition that
it is generated precisely from a mathematical basis; to approach Xenakis's nature as an architect, we could say that these mathematical bases represent the "foundations" of this composition, and its organization in time (which you rightly referred to) also belongs to a well-defined mathematical construct which, to stick with the construction theme, we could compare to load-bearing pillars. I can appreciate one thing about Xenakis, namely the idea of giving order to randomness, because it is stochasticity that is being discussed here. In theory, from a distance, it isn't bad, but unfortunately, then it doesn't work. If we are talking about mathematics, things must be formal. In physics, less so; in mathematics, the corridor is straight and narrow. There is never a duality; everything must be exact, there is no propagation of errors, and there are no measurements contained within a certain interval. Mathematics is univocal, clear, and unambiguous; first-degree equations always return one result, second-degree two results; if in the first case more than one occurs, we have made a mistake, if in the second more than two, we have made a mistake. Any ambiguous theorem in mathematics ceases to exist, it cannot be... Mathematics admits no ambiguity.
To give an example in the physical realm, everyone will remember when a researcher seemed to have proven that the speed of neutrinos was greater than the speed of light. Everyone knows at least by name special relativity, which is based on the concept of absolute velocity and relative space and time. Relativity has been demonstrated in various situations, some of an experimental type in the laboratory, others in nature: within accelerators, during solar eclipses, in the explosion of supernovae, in the observation of space, etc., etc. In the end, it turned out to be a hoax (thank goodness)—I say thank goodness, because if the experiment had actually been true, more than half of the physics we know today would have collapsed and it would have been impossible to explain certain paradoxes, why? Simply because pure mathematics, upon which physical theories are based, does not accept dualities. If it is one thing, it cannot be another.
Now, Xenakis wants to base Herma on mathematical concepts, and this is clear and obvious; he even writes it in the score and describes phrase by phrase the membership sets of those particular groups of notes that belong to very precise regions of the keyboard, while basing them on stochastic sequences. Now, even if one wants to bring order to randomness, the result remains random. It would be like saying: I take 3 groups of markers; in the first group, I randomly put markers ranging from red to orange, in the second markers ranging from aqua green to dark green, and in the third from light blue to ultramarine. Now I order them using set theory, making intersections and arranging the elements contained within them randomly for each group. The idea is the orderly organization of sets, but if the elements of each respective set are not ordered, the result is still stochastic; I hope I have explained myself better now; I cannot find more trivial examples to explain what in mathematics reflects one of the most important topics of the entire analysis course, namely that which concerns set theory, which is master of all fields of study: complex field, real field, natural field for sequences of natural numbers... etc.
Now, if the basis of a composition is mathematics and mathematics proves that the results are ordered groups of elements in stochastic order, one can assume that the content is stochastic and therefore random notes. If we are talking about random notes, setting aside the mathematical idea and focusing only on the acoustic result—that which the ear perceives—I really cannot see the difference between Herma and the notes of my 5-year-old cousin. I am serious... Stochastic for stochastic's sake, what would be the difference? Illustrate it to me. In other posts, I wasn't so direct, but the fundamental question I have posed is exactly this: I am writing it in bold not to shout, but to highlight it...
Random for random's sake, what would be the difference?
If I ask Claudio for a sequence of random numbers and then we ask Frank for one, how can we establish which of the two is more beautiful? What would be the procedure to follow to define the most beautiful within a random sequence of "events" that can then be numbers, notes, ingredients, or any other class of sets you know in nature.
We might get lucky and generate stochastic notes that sound nice in the melodic line, but it is unlikely considering that on 88 keys, taking all possible combinations without permutations of only 8 notes, we would have with the following formula:
"only" 64,276,915,527 combinations, which is just over 64 billion combinations.
So, as I repeat, I appreciate the mathematical philology behind Xenakis's thought, namely the attempt to order the unorderable; excuse my wordiness, but the acoustic result remains nonetheless random... and I don't like it. The fact that I don't understand how others can enjoy it is a matter of interest to me, but I do not judge those who tell me 'I like Herma'; however, I would like them to motivate me as to why they don't like my cousin for the reasons I just expressed above...
For Xenakis, the '60s were precisely the years in which he dedicated himself to stochastic music, to which Herma belongs in terms of genre.
What more can be said?
Does Stellina want to play Herma? What annoyance should it cause me? I wouldn't waste my time on it, but if it is important to her, she should put in the effort, and here is how:
@ Stellina
In any case, to answer Stellina, having taken the score in hand and having analyzed it repeatedly over these past few days due to this discussion that has gradually developed, I will answer your initial question:
The score is very complex, both rhythmically and at the level of notes. It presents many leaps, which requires great mastery of the keyboard and great self-confidence toward one's own inner image of the keyboard to facilitate the execution of the movements required (I am referring to the ability to hit the right leaps with eyes closed, trusting one's instinct).
The technical level required to complete such a reading must therefore be high, no question about it.
We find sudden dynamic excursions: moving from pp to fff, and in leaps, this complicates things.
My advice is to equip yourself with a pencil and read Herma without worrying about the rhythm at first. Read only to note the measures and the most complex leaps.
Once you have found the most complex measures, I advise you to start studying the leaps, slowly, without worrying about the rhythm; this will be necessary to find your own security in executing the most difficult leaps.
Listen carefully to all the interpretations you find on the internet and learn Herma by heart without dwelling too much on listening to one in particular. This will facilitate reading since the rhythm will become natural to you having learned it from interpretations (otherwise, you would waste so much time decoding groups of 6 notes in a quadruple pattern in simple time in 5/16 time, just as an example); by listening, it comes naturally, but above all, by varying the interpretations greatly, you will not be subjugated by one interpretation rather than another. (This applies somewhat to everything when deciding to prepare a piece)
The difficulty of execution lies in learning stochastic sequences that therefore have no rule of succession, neither from a harmonic nor a melodic point of view (vertical line for the former, horizontal line for the latter). The eventual formation of 'standard' or so to speak 'canonical' harmonic elements is a purely random event—or perhaps not, given that we are talking about stochastics and the 'slipping pen'; this cannot help us understand if certain harmonic lines are the author's choices or random events, just to stay on theme.
It is also useful to study the sets indicated by Xenakis above each group because, barring rare exceptions (those I mentioned where ambiguities are found), a set A always contains the same elements.
To 'facilitate' your task, if F is a set that can be written as the sum of subsets A, B, C, then F = A + B + C.
In certain cases, to obtain more complex combinations of sets and expand the number of elements within the musical period, Xenakis uses combinations of negated subsets or, at the extremes (towards the end of the piece), negations of combinations of negated subsets.
The negation is expressed with a small horizontal bar above the name of the set, as in this example:
If A (a, b) = {true, false}, then the negation of A (a, b) = {false, true}; practically, one takes the negated elements of A.
In the case of Herma, knowing that F (which is the set of 88 keys) = A + B + C, saying that we take set A is equivalent to saying that we will use the elements of set A; negating A is equivalent to saying that we will use all the elements that do not belong to A and therefore we will take the elements of sets B and C, while always remaining within a subset F which, mathematically speaking, being restricted to 88 natural numbers, is a subset of N, which in turn is a subset of R.
In the extreme case, we witness set-based compositions like this one, in the final pages of Herma:
which reads (A intersection B, sum (or union), negation of A intersection negation of B, all negated intersection negation of
by C.
In other words, we will have all those elements that do not belong to: the elements of A in common with the elements of B, the result added to all those elements that do not belong to: the common elements that do not belong to A and that do not belong to B; from the total result of this, one then extrapolates the common elements with all those that do not belong to C.
In this way, Xenakis tries to find a large number of combinations in order to combine a great multitude of sets together.
As I repeat, innovative experimentation but which is not guaranteed to bring satisfactory results; on the contrary, in my opinion, it is a completely useless and unlistenable acoustic result.
With this post, I'll move on and close... And please try not to slaughter each other over this nonsense... It is well known how it ends when talking about contemporary music: everyone goes home with their own opinion. However, I felt the need to step on the gas for the sake of personal culture. A little something that tells me, 'I like it because... blah blah blah,' so that one day, if a debate on Herma arises, I can also express the convictions of those who support it, even though for me it has no meaning in existing.
