Contour in Serialism
I've recently been attempting to teach myself how to compose serially. I've found sufficient material on the internet to understand tone rows with x number of pitch classes and how to build matrices for permutations. I cannot, however, find enough material to help me understand how to apply contour to a tone row (is this only applied to integral serialism?). I've ran across short number sequences for contour to which one may apply permutations (ie. A B A') but I still do not understand the number sequences, and if I did I wouldn't understand how to use multiple parameters.
Could somebody explain how to go about writing integral serialism? Or direct me to the right resources?
Man. I didn't realise serialism was THAT mathematical. That's like linear algebra with a couple of group theoretic terms there!
Other than that, sorry. :D
There's a thread in this forum on dodecaphonics so if you do a search for that term you may find something useful in there.
Other than that, if you give me a link to any of these mathematical methods of construction I'll have a look and see if I can help you out.
Yeah dude, every single facet of integral/total serialism is controlled mathematically, even something as small as timbre, like the vibrato on a stringed instrument. It sounds horrible in my opinion, but I want to know how to do it, maybe I can pull off an acoustic guitar fugue in total serialism that sounds decent, people wouldn't know what to think.
I can't find any in depth information only a syllabus.
It begins talking about my confusion after  where it begins:
Length: 30 seconds to one minute
Directions: The A and A' sections use this contour 21043. The B section uses its inversion, 23401
Contour can represent anything - notes, motives, phrases, durations, dynamics, register, etc.
Inversion makes sense. Where they pulled 21043 out their ass doesn't.
I think the numbers are the intervals from the first note of the row. I'm not entirely sure of this, however, as one would then assume that the inversion of the example in  would be 34012 rather than 23401 (which would only make sense if the first two-tone interval was indicating the starting point of the row from some universal note, e.g. middle C).
In terms of applying contour to a given row (taking duration as the contour, for example) I read this as creating another set (i.e. the contour) of each possible duration (e.g. whole beat, half beat, quarter beat, eigth beat, etc...) and then serialising these durations with respect to the row. I then read this to mean that each duration must appear once before the contour is repeated.
This would then imply that a simple application of this idea would be the case where the row and contour consist of the same number of elements. I'm not sure whether it would be classed as strict serialism (as my understanding of the subject is not great) but you could then keep the row sequence constant while permuting the contour set.
As for the mathematical side of this, I think this is probably limited to multiplication and transformation of matrices. Combinatorical analysis would simply lead to the number of permutations within a row or contour of a given number of elements.
Well, that's my take on it anyway; without specific examples of the mathematics behind the constructions it's difficult to know whether that answers your question.
You can create OK-sounding rows with serialism. Just split the row into subsets of diatonic or 'nice'-sounding sequences then begin applying all the other stuff.
I think an interesting idea would be to determine the orbit of a single permutation, and apply the different powers of the permutation to different musical elements or facets (rhythm, pitch, dynamics...). You could maybe even apply the same permutation to the powers of the permutations, so the orbit would also change the musical aspects each power of the permutaton applies to.
At our university, there is a public lecture by one of our professors, Dave Benson, on Music and Math's coming on November 17th. Although I am making the worthy skip to go and see Cynic in Glasgow on the same day. :D
by the way does anyone know of a book that uses examples of real serialistic pieces with an analysis of the music?
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