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Talk:Pythagorean tuning

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This is an old revision of this page, as edited by Camembert (talk | contribs) at 12:04, 2 November 2002. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

I'll expand this further in time, but this will do for now. I'd appreciate it if people could let me know if it makes sense - it makes sense to me, but I've studied all this stuff, and a list of unannotated numbers and cent values would make sense to me, so that doesn't mean much. Oh, and if anybody wants to prettify the table, please do so - my html skills are not up to the task. --Camembert

As I've thought about this since I wrote it, I've come to think that I'm really trying to write two or three articles in one here; one on Pythagorean tuning, one on what should be at Mathematics of the Western music scale, and one on tuning ratios generally (what a 9:4 is, and why it is equivalent to a 9:8). So I regard this as something of a work in progress, and one that might get broken up into bits in the future. --Camembert

I've added a note on number theory. I think modular arithmetic comes in to this too, because in tuning up in fifths we yank notes down to stay within the range of an octave. I am planning to make a PNG of the piano keyboard at some point. Maybe a long version of that would be good here, to show graphically the circle of 5ths stretched out, with the clash in the middle. -- Tarquin

Something like that would also be very useful for the articles I'm writing on small intervals like the syntonic comma. --Camembert

Okay, I'm talking rubbish: removed "Put in terms of number theory, no multiple of 1.5 is a power of 2." because it's completely wrong. 1.5 ^ 12 = 129.746337890625 , and 2^7 = 128. I think it's that. (note: "think"). Will ponder some more. -- Tarquin 11:26 Oct 30, 2002 (UTC)

Camembert, I had a look like you asked, and I don't think you're spending too much time on the basics here at all. There's only one slight sticking point for me where there's talk of all twelve fifths being tuned and the D's not being a perfect octave. I know what you mean, but I had to read it a couple of times. I'd have fixed it, but I'm not sure how else to say what you're trying to say there. Good job though, this tuning stuff is still a tricky subject and I'm impressed with the work you folks have done.JFQ

Thanks - I think I'll leave this article as is for now, and maybe come back and try to polish it a bit when I've done the other tuning systems articles (gulp). --Camembert
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