> I indicated epimericity with the sizes of the numbers in the ratios,
> in case you didn't know that. My brain is tired -- if you can express
> epimericity in terms of the quantities on the x- and y-axes, I can
> probably show contours for it.
If u = log2(n) and v = log2(d), then the x and y axes of your graph show
x = u + v
y = (u+v)/(u-v)
Solving for u and v in terms of x and y gives
u = (x + xy)/2
v = (x - xy)/2
This now gives us
n = 2^u = 2^((x + xy)/2)
d = 2^v = 2^((x - xy)/2)
From this, e = log2(n-d)/log2(d) would be
e = (2/x(y-1) log2(n-d)
which is a function of x and y. Fixing an e, you can find y in terms
of x by Newton's method.
... I indicated epimericity with the sizes of the numbers in the ratios, in case you didn't know that. My brain is tired -- if you can express epimericity in...
... If u = log2(n) and v = log2(d), then the x and y axes of your graph show x = u + v y = (u+v)/(u-v) Solving for u and v in terms of x and y gives u = (x +...
... y = (u-v)/(u+v) ... (2/(x*(y-1))) * log2(n-d) ... Yes good. I expressed them as functions of x and y, after all n(x, y) = 2^((x + xy)/2) d(x, y) = 2^((x -...
... You mean (2/(x*(y-1))) log2(n(x,y) - d(x,y)), right? I did that and the signs seem wrong . . . I then extended the contours into negative values and at...
... Whoops--I'm having problems looking at things sideways, I guess. Should be x = u + v y = (u-v)/(u+v) However I used the right values for y in when I solved...
... I think they are not only poetic, but mnemonic and nice&short - additionally - for some of them, somehow appropriate. ... and before I even get done with...
... my former classmates! ... That's the spirit. And (off topic) I, an avid reader of Scientific American, had to wait 6 months for that freakin' rag Discover...
... At first meeting of the TLA (Tuning List Anon): Hi my name is ____ and I am a microtonal list addict. So baaadly to the point I forgot the music... ... ...
... scientist worth his salt... I once got arrested for it, too...Imagine now what could and can happen to a crazy Asian male "armed" with drumsticks and...
... these peculiar times... & luckily I only got psych monitoring/probation for 5 yrs (5 yrs max w/o parole in the Huntsville Hole otherwise... skipped outta...
... Sorry I hadn't caught up. ... I'm afraid I find these difficult to read because I don't know very many LTs by their vanishing commas, but rather by their...
... gradually ... with ... because ... blue 'badness ... and ... data ... Because they agree exactly, for the Tenney-weighted minimax over *all* intervals!!...
... I don't see what distinction you're trying to make. By "bicomma" I meant a wedgie of any pair of commas forming a basis for the kernel of the temperament,...
On Fri, 09 Jan 2004 05:53:36 -0000, "Gene Ward Smith" <gwsmith@...> ... I'm pretty much in agreement with Paul's original list, with the addition of the...
... http://groups.yahoo.com/group/tuning/message/51208 ... Gene, ... disagreement ... things ... with ... faith ... we're ... this ... to ... both ... agree ...
... made of >them (if at all) by using purpose-built extremely inharmonic timbres. [. . .] ... Big favs with me - recently I have been "collecting" tons of...
... I thought at the time it was better to write something up instead of spending all that time deciding which temperaments should be listed or not. And the...
... choice ... possibly ... the ... by the ... position. ... How about teaching a man how to fish *and* giving him trout plus 12 or so other kinds of fish?...
... Yes, but the poor man's been waiting for a couple of years now and he still doesn't have either! Whereas he's had plenty of opportunities to further his...
... Paul's 5-limit database constitutes 5-limit fish, with a little explanatory stuff that's mostly been written. The teaching-how-to-fish, however, is...
... fish, ... What did you have in mind? ... Yes, it seems that the XH era is ending, and even 1/1 always got more circulation anyway. I'd like the co-authors...
... A 'for-dummies' how-to identify, search for and optimize temperaments and turn them in to scales. Definitions of epimericity, epimorphic, how to use...
... to- ... temperaments ... Ouch -- I think you're talking about a book, not an article. I see no reason for most of this stuff. ... published ... XH has been...
... Most? The Grassman Algebra primer is the only part I see as optional. And perhaps "working with matrices" would be a better title for the scope I had in...
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