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 Forum index » Discussion » Composition
magic squares, serial techniques and playing sudoku...
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Alexander



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PostPosted: Wed May 09, 2007 1:40 pm    Post subject: magic squares, serial techniques and playing sudoku... Reply with quote  Mark this post and the followings unread

Good evening everybody,

I am reading this very indepth and inspiring essay:

"An essay on patterns in musical composition
transformations, mathematical groups, and the
nature of musical substance."


It's a pretty long read and I am almost through, why I opened this discussion is because the magic squares and sudoku puzzles are piling up on my desk and I have a lot of ideas and questions.

I'm reading into the basics of Messiaen's serial techniques and I want to try and apply some and combine them with other methods and rules.
I would love to just start and writing down scores based on transformations of series obtained from all those wonderful squares, but I could also write a patch to read from a matrix and apply all the data directly from the software to the sound synthesis, which saves me the time of programming all the notes and or playing parts after i compose them. Both options will give me different results, but using a program will give me more ways to explore the variations.

I am still thinking of doing both, but I don't have that much time and patience.

To stay on point, I would really enjoy comments and or discussions on serial techniques, using algorithmic software, writing out scores, why sudoku is so addictive! Very Happy

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Alexander



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PostPosted: Thu May 10, 2007 6:29 am    Post subject: Reply with quote  Mark this post and the followings unread

First problem..


Rhythm structures. The approach mentioned by Messiaen has three main rules:

a) adding smaller rhythmic values
b) augmentation and diminishing values, by multiplying or dividing the total pattern by 1, 2, 3, 4, 5, 6, etc.
c) symmetrical structure.

Very clear except that I haven't found a way to determine these structures. I concluded from my data that I can easily apply series to dynamics, pitch (and timbre or envelope), but for Rhythm it's not so easy.

In a letter from Pierre Boulez to John Cage, there are these great examples and suggestions, but the whole thing is en francais, and I don't parle francais enough.
What I did get out of it, is that he didn't use the diminishing of rhythmic values, but started with the rhythmic patterns in there shortest form and then augmenting that by the number obtained from the series!

This last thing seems a beautiful solution and makes me wonder what parts were predetermined and what were based on series.

I am running in that last part. mostly through applying the techniques to max. I would love the patch to just render the number squares into all parameters necessary and restrain myself from using random values. The main problem in this is to 'hear' the magic (latin, sodoku, or whatever) square in the generated structures.

Does anybody know of an english (or dutch Wink ) translation of the letter (from Pierre Boulez to John Cage in 1950).
And maybe tell me more about creating Rhythm structures in predeterministic using serial techniques?

thank you.

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Alexander



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PostPosted: Thu May 10, 2007 7:35 am    Post subject: Reply with quote  Mark this post and the followings unread

To make things even more clear, I am also thinking about not using tones at all in the patch. I could easily assign the numbers to frequencies. One of the reasons is that latin squares, unlike magic squares are never to a power of 2. For chromatic scales this is difficult to obtain atonality. In the example of a sudoku, I would get 9 pitches:

eg:

C - D - Es - F - Ges - As - A - B - (c')

I enjoy this scale and would like to implement it, but the only way to do it, I think, is to either include the octave, making c the fundamental pitch.
Or using the number 9 as a switch, so that every time I obtain a 9, I transpose the scale, move up an octave, or something like that???

I could also use use a three octave range and apply 4 rows to it, giving me 36 unique pitches. this could work, but is also not making things easier.

Frequencies would make things less complicated, but would remove me even further from the traditional set of rules and the characteristics of serialism I'd wish to explore.

suggestions?

Very Happy

( I found some nice 12x12 sudokus and pan-magic squares to tackle, I am loving it, should've studied math Wink )

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PostPosted: Thu May 10, 2007 1:47 pm    Post subject: Reply with quote  Mark this post and the followings unread

Another day is almost done and I have made a lot of progress. I finally created a way to structure a form from a 12 x 12 sudoku grid.

I applied a few patterns to it to obtain a train of 2 x 8 x 2 x 12 (= 384) notes without repetition using the outer 4 rows of a magic square. The next thing to do was figure out a way to obtain rhythmic values as well as the structuring of rhythmical patterns from the square.

I used the same technique as for the note rows, obtaining 4 x 12 x 12 (= 576) values without repetition.

But how to combine the two is where it got, difficult, interesting and challenging at the same time!!

Starting with a sixteenth note value I created a row adding one of it's smallest value. So a sixteenth, an eight, a dotted eight, a quarter, etcetera.
I repeated the procedure using an eight and a quarter note as initial values. The result is 36 durations ranging from a sixteenth to 3 whole note lengths.

Ofcourse there are overlappings and thus the 36 durations are not unique. I replaced the duplicates with rests of equal values and now have a set of 24 unique durations and 12 rest values.

The remaining problems are:

- how to apply rows of 12 values to 36 duration/rests? I could apply an ABC grid to my square, but haven't thought of this yet.
- the twelve rest values are still not unique (two quarter rests, two halve rests, two dotted halve rests) and using the set as I have it now will determine all of the rhythmical character of the music.

Less and less options and I feel I am coming closer to a system where all I need is a magic square to start either writing out the notes or creating a patch that will generate structures based on that square. And it feels good to spend some days focussing on a certain technique and browsing the web for information.
All I do now is keep my fingers crossed for the final results Wink !

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PostPosted: Thu May 10, 2007 3:54 pm    Post subject: Reply with quote  Mark this post and the followings unread

That's an interesting article you limked Alexander. It's a bit a of slow read though for me as I have to look up even the simplest things like "inversion". Which also means that your questions are way over my head unfortunately, but I read it all with interest. And it did give me some ideas for a nice, I think, Nord Modular patch Very Happy
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also .. could someone please turn down the thermostat a bit.
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PostPosted: Thu May 10, 2007 5:41 pm    Post subject: Reply with quote  Mark this post and the followings unread

Since we last talked about this (a long time ago) I've been solving Sudoku's as well and occasionally thinking about this.

Maybe it's ChucKian of me but what I wonder about is time and progression. Specifically; I find a solved Sudoku perfectly boring but the way it develops from a minimal given (I don't like the easy ones so much) to a finished and stable state are more interesting to me.

Typically a Sudoku starts out as a pattern that's incomplete (this is apealing musically already, to me) but it contains in itself one or several options for added elements. From there on a few paths could be taken and the end result is a stable and harmonious whole.

The question -in that perspecive on it- would be how to make solving them automated (not so hard in -say- Prolog but probably quite hard in MAX?) and how to hook that process up to sonification in a way that makes aesthetic sense.

Oh, well, that's what I came up with in the meantime... Not so much :¬)

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PostPosted: Thu May 10, 2007 6:29 pm    Post subject: Reply with quote  Mark this post and the followings unread

Great idea, I have also thought about that process a lot. I am also only working with self resolved squares to view the structure and catch any recurring patterns. Especially the way I keep shifting from strategy and sometimes just use a trial and error method to obtain anything, is very interesting.

I already made some rough patches where I can read in an array and obtain various rows, but there are no real algorithms used there yet.

(*thinking out loud* Writing a algorithm that actually follows the patch as the puzzle is solved, would be amazing. The output would be non-serial, though. But that was never the main goal. There are a few sudoku/magic square algorithms online and some don't look all that hard too implement, but it's still a little over my head, math wise. *end of rant*)

The thing is, I am combining this with serial techniques, so I take paths through the matrix and use the values in a linear way. Applying them to the smallest elements in the composition. The whole function of the matrix is to provide me with 12 horizontal, 12 vertical and (in the case of sudoku) 12 cubed rows of 12 values, which could be inverted, mirrored, reversed, etcetera. The end result is a lot of data that is at this precise moment more interesting than generators and applying chaos algorithms (which over the course of some patches, I hardly understand) to my work.

I have almost reached the point now, obtaining the numbers, solved the duration problem, where I can sit down and write this piece down. It's going to be a lot of work, but I first want to see how this works out.
The greatest thing about this work, is that all the work and rules I set now, result in a pretty long piece which is completely determined by one (or more) number squares. I guess I'll sharpen my pencil in the morning and have a go at it this weekend.

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PostPosted: Thu May 10, 2007 8:30 pm    Post subject: Reply with quote  Mark this post and the followings unread

Alexander wrote:

(*thinking out loud* Writing a algorithm that actually follows the patch as the puzzle is solved, would be amazing. The output would be non-serial, though. But that was never the main goal.


Clearly, yes, but what *would* the output be?

I was imagining looking at it as a series of states, maybe phrases to be repeated. The amount of repetition and the sort of transition could be based on the way of (and dificulty of) determining the next known number.

I have no doubt at all that this kind of thing can generate a lot of data and that that data can be sonified, likely with some results being pleasing. What would be harder is figuring out what sort of magic square or Sudoku results in what sort of end result. Obviously there is more to music then just a lot of notes that follow rules, plenty of uninteresting fugas are testament to that....

To me much rule-based music lacks direction so a possible angle to that would be to encapsulate direction in the structure of the rules used.

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PostPosted: Fri May 11, 2007 5:47 am    Post subject: Reply with quote  Mark this post and the followings unread

Quote:
Clearly, yes, but what *would* the output be?


Probaly a stream of numbers with a lot of repetition, a good and often used strategy in solving sudoku, is solving it number by number. Offcourse you'd have to change your strategy often, but I find myself returning to working with just one number and checking the whole grid.

Quote:
I was imagining looking at it as a series of states, maybe phrases to be repeated. The amount of repetition and the sort of transition could be based on the way of (and dificulty of) determining the next known number.


The weight of the output is, in the situation of solving the puzzle, very interesting, since as you mentioned above, the grid becomes more and more stable and the answers become more logic.
There has been a lot of research (google) and they are almost certain that with 17 given values on a 9x9 regular sudoku, there is only one possible outcome, that would be a starting point for some very interesting experiments.

The way I approach this right now, is to have no weight, or equal weight on every single output (note, duration and velocity), leaving all the choices I have to paths across the matrix, combining phrases in a horizontal and vertical way and structuring the main composition.

But what about rule based music applied to a timbre free soundsource like for instance a synthesizer or samples? I think a lot of the ambient pads I created using random-based generators, sound good because of their sound qualities, not their musical properties. And traditional serial and post modal music had only traditional instruments to work with , which were already well known and understood timbres. Still you could be amazed how strange and often very emotional (this could be personal) some of the rule based works can sound.

Quote:
What would be harder is figuring out what sort of magic square or Sudoku results in what sort of end result.


That's the whole reason it grabbed my attention, how can certain algorithms be pleasing. For some it's fulfilling to simply look at number logics, for a lot of people puzzling with them is a fun thing to do. So my guess was creating patterns and music out of them would be at least a lot of fun! And up until now, that part of the experiment is successful!

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