I also just had some insight into rhythm permutations. Random permutations are not musically meaningful the same way random note permutations end up sounding meaningless, hence the need for some structure such as inversions and retrogrades provide.
I remembered that, in Africa, master drummers cycle through rhythms. So, if you’ve got the one played all over Africa 2+2+1+2+2+2+1, when you want to play something different but related to this, you can play through one of it’s rhythmic modes. For example starting on the second rhythm event and using that as the beginning aka 2+1+2+2+2+1+2. This is musically meaningful/useful permutations of the rhythm.
Notice also that the first one I gave mirrors the intervals in a major scale M2 M2 m2 M2 M2 M2 m2. Because of this we can say it is the Ionian rhythmic mode. Another interesting thing about this is that the other two most prominant rhythmic modes in Africa are part of the cycle of this one. It shouldn’t perhaps be surprising then that they are in fact the Lydian and Mixolydian modes. I, IV and V. Creepy, I know.
Another more abstract but still musically meaningful permutation is to sort notes in ascending and/or descending order of length or perhaps rhythmic cells sorted in ascending order of probability, just like in my chart on my http://www.myspace.com/gongchime page in the Music Comps folder under pics.
I was looking at the chart in the other post about Probability and was thinking about how that data is similar to a zip file and that every melody used to create it is still stored in the data and we just need to unpack it. That lead me to think about a phenomenon called Automorphs. Maybe you’ve heard of them.
You can take any kind of series melodic or rhythmic and then just continue to expand or contract it so, for example, if you move up an interval of a m2 then the next time you can move up the interval of a M2 and after that a m3 etc...
Rhythmically, it might go a sixteenth followed by an eighth followed by a sixteenth morphed using rhythmic augmentation into an eighth followed by a quarter followed by an eighth and morphed again the same way into a quarter note followed by a half note followed by a quarter. Then played back to back. You can also alternate such as moving UP a m2 DOWN a M2 UP a m3 etc...
I wanted to mention that not every culture thinks about things the same way we do and what they’re thinking about can be very surprising to us. Specifically I’m thinking about the first comment in the article made about Mozart that said he used just a short list of melodic patterns that he composed from. I suspect this may have come from his father Leopold encountered somehow by way of Middle Eastern musicians.
Before explaining, it should probably be pointed out that when Europe was wallowing in the dark ages, all of the mathemtical and scientific advancements were coming out of the Middle East of those regions at that time.
When improvising, many musicians coming from Middle Eastern countries don’t just go up and down the scale or hop around the way we might. They have been taught by a teacher to join fairly short melodic patterns together. There are three kinds for ease of memorization; upper tetra-chord, lower-tetrachord and one’s that bridge the tetrachods.
You can start on any pattern that you learned at any position, it doesn’t have to be the first pitch and you can end on any position, then if you want to continue a melodic line you have to either superimpose the last note you played onto another of the basic patterns at the place where it has that pitch or to an adjacent pitch aka conjunct or disjunct respectively. This seems to be similar to what Mozart had done.
Their teacher’s teacher’s teacher going back thousands of years had already worked out the most common solutions and taught improv using this method. And this has become the basis for much of the Middle Eastern tradition. Using my handy dandy chart recently acquired, I’ve made a list of the common solutions through the pitch series that are the most effective in the Western tradition.
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