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A Possible Intro To Permutation
Imagine you are the greatest baker in the kingdom, and the king says bake me a cake, for my favorite daughters wedding using five layers. One being, Chocalate, Devils, Angels Food, Velvet, and Strawberry, and you better get it right or else you are dead. However the king leaves before telling you what order the layers are supposed to be in. So do you guess, or do you bake multiple cakes using as many combinations as possible to get it right, I guess the best way would be to bake as many combinations as possible, so as to hedge your bets. This is what this lesson is about, its about hedging your bets through the art of choas. In a sense, get a hat, and some paper and play cards. This is permutation, in a simple sense, it is drawing cards out of a hat, and hope you hit. Please if any one has more insight into this complex subject, please write me, for this concept seems to mathematically border on calculus, and I am not Newton, however was Bach Newton? Anyway This lesson has no real musical quality, rather it is playing with combinations. Simply put look at the first measure. We have nothing but the first five notes of a cmajor scale-c,d,e,f,g. Now look at the second part it is g, f, e, d, c. It is a mirror image, but in reverse. So mathematically it is 12345, turned backwards to 54321. Then the first line, in the second measure goes 23451, and the second, 15432. Or d,e,f,g,c to c,g,f,e,d. It is a backwards image of the first line run in repetiion, and you can seemingly do this in infinitum, using all combination of the five notes. I am just beginning to sort the mathematics of permuation out, and sadly enought I am not a great mathematician so much study will be needed, however it is well worth it, for behind the math, lies the music. For it is a great aid in understanding cannonical writting, and of course fugues. So please expound.