Then I find MOS of sizes 3 (4 7 10 13 16) 19, all to be CS.
It's only when we set the generator to precisely 6/19 oct that we find
that 13 and 16 are not CS (but 16 is proper).
Agreed?
That makes Erv's definition of CS (as relayed by Kraig and Monz)
pretty useless. Are CS only defined for scales embedded in EDPs (Equal
Divisions of the Period)? Did they leave that bit out? Or are we
supposed to parameterise the definition of CS with some allowable
error whereby two slightly different intervals are to be considered as
instances of the same interval?
... It seems from http://www.ixpres.com/interval/dict/constant.htm that Carl Lumma was briefly seduced into thinking that all MOS are CS, or rather that a CS...
Dave Keenan
D.KEENAN@...
Jun 2, 2001 1:47 am
Ok. Try this: All MOS whose generator is an irrational fraction of their period, are CS. If I take the generator to be say 1 + 6*phi ... 3 + 19*phi Then I...
Dave Keenan
D.KEENAN@...
Jun 2, 2001 2:18 am
... I'm having a great time replying to my own posts. Thank goodness you guys aren't in the same time zone or I'd never get anything else done. ... Notice that...
Dave Keenan
D.KEENAN@...
Jun 2, 2001 2:37 am
... http://groups.yahoo.com/group/tuning-math/message/106 ... Hi Dave, I'm glad you're asking these questions, because I've long been unhappy with my...
monz
joemonz@...
Jun 2, 2001 2:50 am
... It's not useless -- most scales characterized as CS are not MOSs. ... Nope! ... Nope! ... Nope!...
Paul Erlich
paul@...
Jun 2, 2001 8:50 pm
... This isn't very helpful Paul. Can you give a definition that we can turn into a recognition algorithm for the case of MOS, such that, when considered as a...
Dave Keenan
D.KEENAN@...
Jun 2, 2001 10:56 pm
... Why? I think you guys are right that almost all generators lead to MOSs that are CS. So the non-MOS scales for which the term CS is used, which don't have...
Date: Fri, 01 Jun 2001 21:21:24 -0700 To: David C Keenan <d.keenan@...> From: Carl Lumma <carl@...> Subject: Re: Constant Structures? Howdy Dave! ...
Dave Keenan
D.KEENAN@...
Jun 2, 2001 11:02 pm
... Amazing, Daniel! This is just what I guessed CS was, before the correspondence from Kraig. See monz's web site reffed earlier in this thread. ... On the...
carl@...
Jun 3, 2001 4:15 am
... Kraig also thought that CS meant something different before Wilson gave him the definition on Monz' web page. ... Daniel Wolf didn't post directly to this...
Paul Erlich
paul@...
Jun 4, 2001 3:46 am
... Nope. ... Not a family of scales, but a family of scale cardinalities common to MOSs with the same ie but different generators. This was simply my guess at...
carl@...
Jun 2, 2001 7:05 am
... Ok. Monz, you might want to delete that bit from your dictionary. ... Thanks Carl. But the above definition means that I can make an infinitesimal change...
Dave Keenan
D.KEENAN@...
Jun 2, 2001 7:22 am
... Hate to say it Dave, but I don't think CS is that useful a property anyway. Or, maybe I should say, I can almost hear Wilson crying out, 'Of course! It's...
carl@...
Jun 3, 2001 4:04 am
... Actually, Dave, if you're only interested in CS, I think you can just use the size of L/s. The stuff I gave in my last message is good for any scale (not...
carl@...
Jun 3, 2001 4:21 am
In-Reply-To: <9f8ggf+60hs@eGroups.com> ... Looks like it. ... Dunno, it's Dave's formula. I'm not sure why you only get one MOS there: it should have given...
graham@...
Jun 1, 2001 4:56 pm
... What do you mean by this? Do you mean you want to find MA errors at an N+1 integer limit instead of N odd limit when the octave is tempered too?...
Dave Keenan
D.KEENAN@...
May 26, 2001 9:44 pm
... I mean taking an arbitrary set of intervals and finding some generators and periods that fit them. Graham...
... On that page it says, "I've written a Python script to systematically find equal temperaments consistent within a given prime limit." You mean odd limit,...
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