On Wed, Sep 4, 2013 at 8:17 AM, Edward Lilley <[email protected]> wrote: > I don't consider myself to have much of a head for mathematics, but > having read up on the relevant bits, I decided that -- given that it was > simple enough for me to understand -- there was no reason not to at > least write down the relevant formalisation (and formalising things > mathematically is The Haskell Way, right? :-)).
True, and I should probably also make the effort to learn some basic vocabulary about sets and groups, since those seem to come up a lot in programming. > The main thrust is that, quite apart from tuning systems being > representable as groups with one generator (equal temperaments) or two > generators (meantone temperaments) (or more generators), the *notation* > of intervals in common musical practice defines a two-generator group > regardless of the tuning system in use[2]. Indeed, and even in equal temperment, enharmonic spelling communicates important information. And even post-Baroque European music is mostly not equal tempered! As far as I can tell, only small ensembles involving a keyboard are. And electronic music, of course. By "generator" you mean a starting pitch and a way to modify it to get the next pitch? I can see how equal temperment then only has one, e.g. just add 100 cents repeatedly. I don't know enough about meantone to know how that would apply, but I expect it wouldn't work for a just scale, unless you want to say there are 7 generators :) > You're completely correct about what I have "in mind" -- I'm currently > only really concerned with what I consider to be "essential" to the > music theory -- pitches, intervals and durations. This represents a bit > of early music-bias (and general arrogance) on my part, so sorry about > that! There's another tradeoff where the more opinionated a notation is, the more powerful and concise it is within its area, though less general. So it's entirely appropriate to choose an area and focus on it! >> Also, it seems like you're focusing on scales with 7 diatonic steps? >> The Name type with its A-G implies that it's hardcoded that way. > > That's correct. It always seems like a nice idea to say things like > "this package is not limited to Western classical music, and, in fact > only implements it as a special case" (most of the music-related > packages on Hackage seem to make some variant on that statement), and I > think such attempts are laudable, but I'm not currently claiming any > such generality -- it's not like there's a shortage of Western classical > music to play around with. I doubt those packages actually *are*, I think they just say that :) > That said, it might be nice to implement some scales from the Arabic or > Indian traditions, to demonstrate some of the more exotic tuning systems > in Tuning.hs (cf. TET17 and TET22). Also, I'm considering adding a > hexachord-based pitch representation, to more accurately write down > pre-1500 music. Indian music is generally understood to be a just 7 tone system. However, in practice you never hear a single tone in isolation unless it's the 1 or 5, as they are all embellished with microtonal variations. So as far as I can tell, the concept of intonation doesn't really apply. For instruments with frets or sympathetic strings, you'd probably have to go do a survey to see what people seem to think "in tune" is, but I'd guess people wouldn't feel the need to tune that precisely, or it would basically be 5 or 7-limit just. Arabic and Turkish music I believe does have a concept of intonation and a scale with a set number of degrees. Though as usual this is probably just a theoretical approximation of a pre-existing system and you'd need to know more about the music to know how useful it is outside of a textbook. With regard to pre-1500 European music (church I assume, nothing else seems to be written down), I'd be quite interested in seeing what your experimentation yields, I think there's probably a lot of poorly explored territory in there. You might also try to get some nicer sounding samples or csound patches, having a nice timbre is at least as important as having the proper intonation. > Hope that answers some of your questions! Sorry for the interminable > essay. Not at all, thank you for the interesting discussion. _______________________________________________ haskell-art mailing list [email protected] http://lists.lurk.org/mailman/listinfo/haskell-art
