> > But of course there are an infinite number of ways to do it,
> > for example one could use the golden angle times the ordinal
> > number of the prime. Any one-to-one mapping of primes to
> > angles will do, and any set of lengths will do too (as long
> > as no overlaps result).
>
>
> I understand the second sentence to be true, but am pretty
> foggy about what you describe in the first. Can you elaborate?
>
The idea would be to mirror the way many plants and flowers grow.
First, a single "bud" pops out of the center. After the first bud has
grown a bit, the next "bud" pops out at the golden angle (222.49
degrees). Then the next bud pops out at the golden angle relative to
that. And so on. Each bud would represent a different prime. This
would ensure that, if you used a lot of different primes in your
lattice, their lines would stay as far as possible from one another
and near-overlaps would be avoided.
... http://groups.yahoo.com/group/tuning/message/22059 ... http://groups.yahoo.com/group/tuning/message/22060 ... OK... I see we're online at the same time,...
monz
joemonz@...
May 3, 2001 9:24 pm
... The idea would be to mirror the way many plants and flowers grow. First, a single "bud" pops out of the center. After the first bud has grown a bit, the...
paul@...
May 3, 2001 9:38 pm
... http://groups.yahoo.com/group/tuning/message/22058 ... Well... there's also the variant of my formula that is based on 180 degrees instead of 360. So I...
monz
joemonz@...
May 3, 2001 9:07 pm
... As you now know, there are an infinite number of ways to do it. Here's what I would do. First, the 5-limit lattice would be represented exactly as in the ...
paul@...
May 3, 2001 9:15 pm
... http://groups.yahoo.com/group/tuning/message/21894 ... Well, this is really important, so I'd better be sure I have the right scale, ahem (!!) It's the...
jpehrson@...
Apr 30, 2001 9:26 pm
... Nope -- there's no 31-tone scale mentioned in that message. The scale in question is the following degrees of 72-tET: 0 2 5 7 9 12 14 16 19 21 23 26 28 30 ...
paul@...
Apr 30, 2001 10:03 pm
... http://groups.yahoo.com/group/tuning/message/21909 ... Whoopsie! Where did Keenan hide that one?? THANKS, PAUL!!!! ... _________ _____ _ _____ Joseph...
jpehrson@...
May 1, 2001 12:27 am
I was about to mention that. It's the one in this message: http://groups.yahoo.com/group/tuning/message/21805 I couldn't help fooling around with the unison...
Kees van Prooijen
kees@...
Apr 30, 2001 10:12 pm
... more ... That almost works, Kees, but the parallelopiped produced by these unison vectors, when mapped to 72-tET, has four changes relative to Dave's...
paul@...
Apr 30, 2001 10:44 pm
... http://groups.yahoo.com/group/tuning/message/21911 ... Thanks Kees! THAT'S WHY I missed it! That post was BASICALLY about a 19-tone scale that Dave made...
jpehrson@...
May 1, 2001 12:44 am
... Don't stop what you do. It really is inspiring for composers like me (and Joseph if I might speculate) who humbly admit to being novices in the field of...
Alison Monteith
alison.monteith3@...
Apr 30, 2001 10:34 pm
... http://groups.yahoo.com/group/tuning/message/21913 ... principles. ... me (and Joseph if I might speculate) who humbly admit to being novices in the field...
jpehrson@...
May 1, 2001 12:49 am
Paul, I guarantee that if you looked around for more 'more consonant structures than M' type maximally even scales you'll find them. Though nice enough, I...
D.Stearns
STEARNS@...
Apr 30, 2001 10:49 pm
... Though ... Well, I've looked around quite a bit . . . do you have any suggestions? ... This refers, I presume, to the 7/72 oct. generator?...
paul@...
Apr 30, 2001 10:51 pm
Yeah, well that's basically 'punishment' for using 'non-dissapearing' unisons in a certain ET environment. And I never associate a periodicity block with the...
Kees van Prooijen
kees@...
Apr 30, 2001 11:12 pm
... dissapearing' ... Well, Kees, I'm going to flaggelate myself now, because the parallelopiped formed by Dave's unison vectors doesn't exactly give his scale...
paul@...
Apr 30, 2001 11:23 pm
Paul Erlich wrote, <<Well, I've looked around quite a bit . . . do you have any suggestions?>> It's not really an interest of mine, so no, no suggestions. I'd...
D.Stearns
STEARNS@...
Apr 30, 2001 11:54 pm
Oh, Paul! You really made my day. Never in my wildest dreams could I have imagined to accomplish that :-) Kees ... From: <paul@...> To:...
Kees van Prooijen
kees@...
May 1, 2001 12:09 am
I wrote, <<It's not really an interest of mine, so no, no suggestions. I'd have to get in there and look around first. (The 17-out-of-58 that I've used before...
D.Stearns
STEARNS@...
May 1, 2001 2:23 am
Paul, I'm starting to try and take a look at this a bit but I had a few questions to try and make sure that I'm clearly understanding everything... You wrote, ...
D.Stearns
STEARNS@...
May 1, 2001 6:36 am
72er! For the record Hanson Keyboard can be considered as having a generator of 19. Also his keyboard can have 15 ranks as opposed to 19. see...
Kraig Grady
kraiggrady@...
May 1, 2001 10:43 pm
I wrote, <<I'm starting to try and take a look at this a bit but I had a few questions to try and make sure that I'm clearly understanding everything>> Okay, I...
D.Stearns
STEARNS@...
May 2, 2001 2:16 am
... right? 41-tET wouldn't make much sense. In 41-tET, the maximum 7-limit error is 6 cents and the maximum 11-limit error is 11 cents. But in 31-tET, the...
paul@...
May 2, 2001 11:38 pm
... Actually, 19-out-of-22 is not a CS scale -- big disadvantage....
paul@...
May 2, 2001 11:56 pm
... Paul, I don't think Dan was claiming that this was a very useful scale in general, but merely that it has the property that you described as miraculous in...
Dave Keenan
D.KEENAN@...
May 3, 2001 1:35 am
I wrote, <<I went ahead and started poking around a bit for M-out-of-Ns where consonant identities are greater than M. [SNIP] Anyway, this is the sort of thing...
D.Stearns
STEARNS@...
May 3, 2001 12:45 am
Paul Erlich wrote, <<41-tET wouldn't make much sense. In 41-tET, the maximum 7-limit error is 6 cents and the maximum 11-limit error is 11 cents. But in ...
D.Stearns
STEARNS@...
May 3, 2001 3:02 am
Well, Dan,when I looked at these ME M-out-of-N scales a while back, I was looking for CS scales that both improved the harmonies quite a bit over M-tET, and...
paul@...
May 3, 2001 5:17 am
Paul! Well said. One of the important features of microtonality are new structural possibilities! ... -- Kraig Grady North American Embassy of Anaphoria island...
Kraig Grady
kraiggrady@...
May 3, 2001 5:15 am
... I guess this is very similar to what I discussed in my brief thread with Paul two weeks ago about multidimensional scaling solutions. I hope to post more...
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