... Clearly you need to use different notation or something. You said "Taking the Tenney height of this gives the square of the Kees expressibility" (I think...
... I think I know what you mean (despite the unfortunate notation), but I think in general there are *three* different things you need to compare the error...
... Well, Paul, I'm glad you're understanding what Gene means, because although I'm trying to follow the thread, it's not making much sense. Gene, is there...
... It's easier if you take the idea and convert it into an alternative formula for expressibility. If |e2 e3 ... ep> is a monzo, then take ... fixed base....
... That the commas are of size zero, but the easier way is to convert this to another formula as in my previous post. Then you can find the unit ball, and...
... Right. You get the hexagon which in polar coordinates is r = 2/(|cos(theta)|+|sin(theta)|+|cos(theta)+sin(theta)|) which has corners at [+-1,0], [0,+-1],...
... Sorry, I put u2 in this formula, which is nonsense. It should be ... The Kees metric being a metric on pitch *classes*, which gives us a (non-Euclidean)...
I'm thinking I should make a web page for this business, and wonder what's already there. This doesn't seem to be it: http://www.kees.cc/tuning/perbl.html ...
... <gwsmith@s...> ... <perlich@a...> ... below, I ... but I ... compare ... Not to me either. But the one thing I think I did manage to understand above was...
... And if you take the Kees norm, you get ... Why don't you tell me what you are plotting? What are the verticies of the hexagon? For ... Shouldn't that be...
Wow, amazing to find this huge thread with my name on it. The only thing I can think of to help you Gene, is that I think I wasn't to clear with the links from...
... Thanks, I recalled those but didn't know where they had gotten to. I'm in the process of writing up a different lattice geomery, based on the definition of...
I have been working with Paul Ehrlich's Zoom diagrams (The 2 dimensional diagrams that have temperaments as points and 5-limit commas as lines). I am trying to...
... I don't get it. Why would you do that? ... saying ... I'm plotting "vals" in a 2D projective space, using tricentric coordinates. The three "axes" (at...
Sorry -- I replied to this incorrectly before. Here's the correct reply. ... That's Erlich :) ... I ... to ... each ... Hi Paul, Good talking to you on the...
... wrote: ... This differs from Rami Vitale's Byzantine superset in only two notes. I think that this is clearly superior from the point of view of numbers of...
Gene, And thank you for this! Yahya ... OK ... are you happy with the notation "3" for "a tempered 3", or can we do better? I suggested 3' to Paul in my...
Paul, Thank you for this. Yahya ... Thank you! Much better! Writing your "tempered 3" as "3" is one way to go about it; how about writing t(3), or even 3',...
... Kees, Just shows you what happens when you think out loud ...! :-) ... I never saw these, so will explore, in "Kees" they help reduce my confusion. ... ...
... No. What I mean by Kees error (hey, I didn't start calling it that) is similar to TOP damage in my paper. The difference is that octave- equivalence is...
... that) is ... I would think so, but I think it's a good idea to talk the stuff over for a while. Why haven't you responded to any of the latest posts here...
Hi Gene, ... Clicking your name on the home page of this group, in an attempt to find this old page of yours, doesn't work. But when it reappears, I think the...
... Gene, DNS from xenharmony.org is apparently not working. But Paul, a Google search quickly reveals... http://66.98.148.43/~xenharmo/ ...from which "Theory"...
... The link no longer depends on the DNS server working. Let's hope no one changes the IP address. Here's the start of a Kees tuning page, but without...
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