>Ahh ... so then it's not 12-*tET* centric, but it *is*
>12-*tone* centric, because the Pythagorean comma is
>("8ve"-invariant) 3^12.
Yup.
>Thanks, Manuel, good idea ... but what's "p"?
Symbol for the Pythagorean comma.
If v is the size of the fifth, and a the size of the
octave, then p = 12 v - 7 a.
For example in 31-tET, v=18 and a=31, so p=-1.
My Dictionary entries
http://www.ixpres.com/interval/dict/positive.htm
http://www.ixpres.com/interval/dict/negative.htm
define positive and negative tuning...
It's correct. The interval of 12 fifths minus 7 octaves (the Pythagorean comma) defines whether a system is positive or negative. So with a fifth of 3/2 it's...
In-Reply-To: <003f01c19866$03a02e80$af48620c@...> ... That's correct. ... You remember when we were at the Huygens Fokker Institute in Amsterdam, and I...
... to ... could ... articles ... extends ... This is a rich and deep literature we're referencing. Your arrogance has won you few fans on the other lists, and...
... To you, perhaps. I would imagine other people might come to a more correct impression, namely that 12-et-centric thinking in my estimation makes no sense...
... One can, of course, turn this around--if Bosanquet looked at things relative to the 12-et, then he was *not* looking at them purely as temperaments, but...
... conclusion ... giving. ... estimation makes no sense in this context, In what context??? We're talking about a _definition_ of "positive" and "negative"....
... I wasn't referring to the context in which it's been used, in fact I don't know what that is; for my guesses see my previous posting. I was referring to...
... it's ... But look at your posts again -- YOU were the one who brought up "context". What other context is there? ... What do you mean, the context in which...
Well, now the tuning-math list has 58 members instead of 57. And I might not have even signed up had it not been for reading, for the past week or so, a couple...
... Hi Monz. The accepted usage, not in some imagined "context" that Gene may wish to dream up as his ego inflates to the point where all existing tuning...
... I'm not sure why you keep attacking me--in what way have I injured you? So far as this "positive" and "negative" business goes, my suggestion would be to...
... (which would include the 12 et) would have a flat fifth. This set of definitions is independent of the "positive" and "negative" definitions. The...
... Your proposal is that 700 cents is the border between meantone and schismic, if I understand correctly, since the third you get by going round each way on...
... different ... This is not "my proposal", Gene, this is the _established definition_. Monz is not producing a dictionary of Gene-and-Paul- tuning-terms --...
... systems "meantone" ... as ... the ... approximation to ... to ... approximation ... and ... definitions ... could ... wrong ... a ... relevant ... positive...
... I have some of the original Bosanquet papers . . . I'll try to bring them in. ... Well, let me put it this way. For meantone systems, the meaning of ...
Paul, Gene, Joe, You've missed or ignored my answer to Joe's question, which was the most concise I could give. The borderline is the point where the...
... Yup. ... Symbol for the Pythagorean comma. If v is the size of the fifth, and a the size of the octave, then p = 12 v - 7 a. For example in 31-tET, v=18...
Offline 
Send Email
