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And that's also what I was alluding to with the pictures of directed graphs back there a few posts ago.

In which the hero sketches something, for he hath not the strength to venture, unbidden, into more detail. Gerbes? He thinks not.

Hmm. This is going to be harder than I had initially thought now that I think of it. Basically, given three melodies that work in counterpoint they are written on three staves, one above the other. And we have the identity that the interval between the lower and middle voice added to the interval between the middle and upper voice will give the interval between the lower and upper voice. And we have rules that relate how these voices should interact with eachother.

However, one can still apply most of the rules quite well if we make things a little bit abstract and no longer require the above relationship [a,b]+[b,c]=[a,c] to hold, but rather that it hold only up to a certain constant interval I.

And what’s the sense in this? Well with this you still have three melodies, only now instead of all three being contrapuntally amenable, we have that any two of them are. I haven’t seen this expounded elsewhere, and given how practical it seems I thought I’d mention it here.

And why the devil did I want to mix up Fuchs with cohomology? Well, I was trying to figure out an easy example of a Gerbe :) (I failed, as it happened, but it’s quite teasingly close!).

And why this rambley ramble here as opposed to something more deliberate? Because I’ve been meaning to post this since November last year, that’s why. So this means I get to relax about it now. Chill, you know? And if anybody should wish for any explication I would be Only Too Happy to provide it.

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