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Message: 10325 Date: Tue, 17 Feb 2004 19:30:17 Subject: Re: top23 From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote: > This looks reasonable. Let's go back to the top 23 from Gene's >114... Gene was using the L_infinity norm of the wedgie there, but never explained why. I used the L_1 norm because that gives you the (hyper) taxicab cross-sectional area of the periodicity unit of the temperament in the Tenney lattice. I'll assume that Gene had some reason for using L_infinity . . . It seems that in all the cases we've looked at, only 7-limit linear's wedgie is "rich" enough so that L_infinity and L_1 don't give virtually identical results . . .
Message: 10326 Date: Wed, 18 Feb 2004 18:04:34 Subject: Re: top23 From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote: > --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: > > --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote: > > > > > This looks reasonable. Let's go back to the top 23 from Gene's > > >114... > > > > Gene was using the L_infinity norm of the wedgie there, but never > > explained why. > > It was one of the two obvious choices, and since a linear temperament > is always two vals wedged together, I picked a val-based definition. I don't get it. Why would a val-based definition lead you to use the L_infinity norm?
Message: 10347 Date: Sat, 21 Feb 2004 02:54:35 Subject: JIP From: Paul Erlich /root/tentop.htm * If the JIP is not a point in the original space it operates on, then it probably shouldn't be referred to as a point. Rather, it seems to measure pitch, so why not refer to it as PITCH or something? (You probably asked me if I preferred that already but I had even less idea what it meant then.)
Message: 10348 Date: Sat, 21 Feb 2004 03:06:03 Subject: Who's Val, anyway? From: Paul Erlich I sympathize with the confusion over the term "Val". You have named its dual after our friend Monz. Graham's approach has always been, I think, to work with these directly, so why not refer to them with the term "Breed" (which happens to be descriptive as well!)?
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