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Muzikale omgeving Metapontum

Muziek uit het spelen van metapontum

This is the music of Metapontum as transcribed by prof. Garrith Lloy from the State University of Southern California in San Diego, California, U.S., faculty Musicology, in may 1982.

Het componeren

Er is een bandopname van mei 1982 bewaard gebleven waarin de musicoloog Garrith Lloy uitlegt hoe de analogie werkt bij het vertalen van de zetten van Metapontum in harmonische muziek. Hieronder de Nederlandse vertaling.

De muziek

Beluister de originele bandopname, waarin Garrith Lloyde zelf twee keer de melodie speelt die hij via zijn model aan een Metapontum spelvariant heeft onttrokken.

Report from prof. Lloy

Following is an explanation of how the analogue worked of transcribing the the moves of Metapontum onto music.
Prof. LLoy: "Concerning the method I used. These here are my observations. So what I did was after reading this article of this example game, which is such an elegant game, really, to accomplish here in 40 moves a complete reversal of pieces, it is astonishing. What I did was, I played it on the board a few times to get a feel for it, and then you know, I sort of let my imagination wander to see what will come out.

So the very first thing I did was, to just take take all the pieces from left to right across the board, and assign, well I had a choice, I could either assign pitches to the board positions, or I could assign them to the pieces themselves.
The first scheme was to just number the pieces left to right, assuming these are white and these are black, likewise from here over I found that the numbering scheme used for this game was, as you described it here, from left to right 1 to 8 and 9 to 16, which is fortunate that some numbers agree to the board, and I could figure it out. And I also discovered some errors in the positions, and I think I found them all.

I also have a couple of questions about things but I did not have a chance to focus on while I was concentrating more on the music.

While it appeared that you had moved a white piece whereas you were supposed to have moved a black piece initiative.

Any way, all of that not withstanding, so what i did was, which (attempt) I think was not very successful, was to just take the numbers left to right 1 to 8 like the notes on the music scale 'do, re, mi, fa, sol, la, ti, do, like that from left to right, a complete octave and then for the black, I did the same but an octave lower so they would not overlap in pitch, and likewise for the pawns did the same thing for the pawns; they have exactly the same octave as the major pieces, so i had accomplished together two octaves with white on top and black below.
And then I simply went through and observed what piece was being moved.
I actually wrote numbers on the bottom of the chess pieces so that after the game had moved quite a bit, I turned the piece over to see what piece was moved and find the analogous note. And then simply I wrote down that that pitch was used at that point, and I came up with what I call is example A which has a lot of problems. There was one which corresponds to this move here and I subsequently figured out it should have been a twelve. But I did not feel that it was worth to patch up for here was a missing note there. since they are the outer pieces

Essentially, on the first moves, using the administrators (renamed templars) and their associated pawns since they are the outer pieces so for instance the administrators (templars) and the pawns (pioneers).

I had the first...two pieces so I had do, do, so I had the first two notes. This and this are the two notes that correspond to the two administrators (renamed templars) and their associated pawns.

Essentially every one and every place This and this are the two notes that correspond to the administrators (templars). So essentially every one and every space corresponds to a note so I have two notes here. C ........I am using the syllables Do, Re, Mi, Fa, Sol, La, Ti, Do, and Do corresponds to the note C that is the note C and that is white going into the place of black; ... so those two notes sound simultaneously and so because two pieces move simultaneously, you have two notes for every move, which gives a two part counterpoint that is you have note against note style which is the natural outcome of METAPONTUM which is counterpoint, a note against note style which is a kind of species counterpoint which is developed in the middle ages as an outgrowth of Gregorian chant.

There is something right there which suggests that and that is a good analogy of Gregorian chant. About these analogies, depending on the rules that I chose to transcribe them in the game of yours, and if I could have if I were very sophisticated in choosing these rules take this game of yours, and come up with a double specific, if I were to make an arbitrary set of rules that says there are some arbitrary mappings of rules and I can create a set of arcane rules that come up with this note of this piece and the next move in the game comes up notes and so with all these relationships put together and so I can create a set of rules that says that I can translate anything into just about anything else.

It is just the nature of building rules. I could also make a set of rules and turn it into a donkeys brain, hopelessly unmusical, but given that range of possibilities of building rules. So I have this kind of range in building rules, This means that there are appropriate and inappropriate analogues. So when I say this is a good analogy, this is what I really mean, that there is a suggestion in the game, nothing more than a suggestion in the game, but still a good suggestion and I think appropriate a suggestion as well.



So the ones I say that have a good analogy suggestion as well and the style of game is very very reminiscent of games that have existed in past ages that corresponded to certain styles of a Statehood and of Nationhood, the idea of a kingly ruler and his minions and associates having a strict hierarchy that like a tree, that has a king as the root and all the branches in the rest of society that is reflected inside chess, metapontum and in music.

So, what I really was trying to do was avail myself of that grand analogy in so far as I possibly could. And it is not surprising that in pursuing that analogy that I came up with music which is vaguely reminiscent of the music that was being written for the cultures that used those principles of organizations that resulted in such games as chess and such nation states with kings and kingly nations. So with that let us move on. Anyway, so we now have what I am showing you, how I have this note against note style as a result of the movement of the two players. And the fact that we have 8 pieces suggests that we have 8 notes and of course the most natural thing to associate 8 notes is with the 7 notes of the octave plus the 8th note which is the supervening octave and those are all things which come out of a period of musical history from about 500 to 1500 AD which I think correspond to, and ran up to the development of modern nationhood and kingly nation states and games like chess and also metapontum.

So the next thing that happened is what I call move 1 B which is again another administrator and artisan (renamed pioneer) which exchanges places and so we have the same notes again. Well this is very appropriate to have chosen these outer limits as octaves because they start the game off. Typically, a piece of music begins by mentioning the tonic, the principle note of the piece of music . The tonic is not the key, it is just the root of the scale. So the next note is from move 2a which is an scientist and administrator ( templar) swap places; the scientist is 7 and the Templar is 8, because anything on these notes are taken as the same. So this is one column as you will and this is another column. In any case these numbers that are assigned to the bottom of the pieces and these that will be translated into notes. So the scientist and administrator are notes 7 and 8 respectively, so we have a white scientist which is note 7 is C and note 8 is, a B C and the administrator which is a C and we have then this note against this note. But this is not so good, because this is an interval of a second degree there is a one note difference between these which is in the music in these ages appearing to be a dissonant, having a raw sounding note simultaneously against each other. So here the analogy begins to stray.

This is a perfectly appropriate and good move in the game, but it is not an appropriate note musically. This is where the mapping is shown to not being perfect. So we cannot look too closely at this to look for its musicality, and we have to stand back from it and listen to some higher levels of it. You cannot make a concrete analogy that the music, according to the rules of music is going to sound musical if it is derived from a game which is based on a good exposition of the rules of the game.

The point is that you can have a beautiful game which your example is of elegance and high style which is going to translate by pretty much any set of rules into music which is good in some places and misses in other places because the rules that determine what is good music are substantially different to the rules that determine what is a good game.

Non the less, it is evident for anybody looking at it, that there is a quality to how you play the game which is similar to the quality which you are using of how you are composing music,
that is to say within a complex body of rules which you can strain in various ways against making certain rules like. You know for instance,
you cannot make certain rules in your board game that violate the rules because in in terms of music that would be considered a dissonant. Because the rules are there to keep you from doing certain things which would violate the sense of the music and there are certain rules in your game to keep you from violating the sense of the game if you violated the rules. So there is no one to one mapping between the rules of the game and the rules of music by any set of rules that I was easily able to discover. It would be quite an arcane sort of effort to come up with a set of rules which would in fact translate the rules of the game into the rules of music in a way that would produce beautiful music. But it could be done with enough effort; you could come up with a set of rules, but it does not string out dramatically from the game.

Question: "There are no sharps and flats?"

A. Well, you can, but that is one of the things that you can do. However, the reason why I did not explore that, is that would introduce even more the possibility of even more dissonances. So the strategies which I adopted at that point was to say: what rules do I make for translating between the game and the music that would try and cover for 6,37 as much of the asymmetrical nature 6,33 of the rules of Metapontum and the rules of music as I could. In other words, you have the rules of Metapontum and the rules of music composition and you have the set of transformational rules, But how can I adjust the transformation of the rules 6,18 so that pretty much anything that comes through from metapontum is going to sound musical. I did not come up with a really good answer, but I came up with a coupe of solutions which I think are in fact better than other sets of rules that in fact. So I came up with this piece here which is based on the same kind of procedure which I used than this, but a more sophisticated model that was better at, as you will, with covering over the rough edges where the rules of the game translated into non-rules of musical composition. So let us leave this one, which was my first attempt, as I have said, which was strictly note against note and it showed up some problems, and now I talk about what I did subsequently.
I went back and and decided to do slightly more abstract mapping between the moves and the music. Instead of directly going from a move to notations, I first of all went to writing down the numbers associated with the moves; we have administrators administrators (Templars), there is for that move and for this move we have another administrator and artisans (pioneers) moving, so there are more 8th and here the scientist and templar swap. So I went through, and where there is only one piece that moves, I noted what piece moved.

And again I used a straight a mapping from left to right. but then I introduced the idea of a key for black which would take the note and I took the number and associated it with some keys and then also with some note, and this would allow me more flexibility by going to the sale, to do it in a way which would optimize the moves so that it would reduce the amount of dissonance in the number of times where voices would be speaking next to each other in a way which was not agreeable. And I started off with what I call the most reasonable analogy for associating pitches with notes other than using a scale which was the Regent that is associated with Do and that would make sense because that is the tonic and the guardians Te associated with the Do above. Then I thought who stands next to the guardian and the regents. They are the minsters and their positions correspond to a 7th, a second degree, so the regent and the guardian are the tonic and the notes which stand on either side of them are the second degree in the scale.

The next notes which are the third 3rd and 6th degree and finally the administrators, appropriately, ended up as the furthest notes from the top of which are the other most important notes of the scale, the forth degree below.

So then they all fit around the guardian and regent we have the octave positions and the other notes. Then I went back and applied this mapping, and where I would see an 8th, I would write a Do. Also this gave me a set of notes to use and I went through in a similar vein to the first and try to do a simple note against note style. Where only one note was sounding I doubled the time in other words these take two beats and these would only take one when there was only one note sounding, I went back to the previous note for that voice and take it from a half to a quarter notew and then introduce the single note as the quarter note that was to follow.

This is also very characteristic of modern counterpoint. that is a second species counterpoint. and there is a note against note style first species .and two notes against one note introduces. the notion second species counterpoint, and so on ... But that becomes more complicated. So the note against note style did pretty well ...

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