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Message: 5625 - Contents - Hide Contents Date: Mon, 25 Nov 2002 19:19:16 Subject: Re: Even more ridiculous 5-comma list From: Gene Ward Smith --- In tuning-math@y..., "Kees van Prooijen" <kees@d...> wrote: I didn't know about it; I think I'll poke around on your site. Your comma factorization is missing powers of 2, by the way.
Message: 5626 - Contents - Hide Contents Date: Mon, 25 Nov 2002 20:09:22 Subject: Re: Even more ridiculous 5-comma list From: wallyesterpaulrus i don't know what to say to pierre, other than that some may wish the theory to cover more ground, instead of less, than any practical application would require -- why not? -- that way you'll never fall "off the edge", and given more examples, you can more easily ponder the mathematical relationships, a process which can sometimes offer insight applicable even on the most "worldly" scale. that said, none of these "ridiculous" lists included commas of clear practical import, the blackwood 256/243 and the negri 16875/16384. so gene did not answer my question.
Message: 5627 - Contents - Hide Contents Date: Tue, 26 Nov 2002 03:08:00 Subject: Re: Adaptive JI notated on staff From: monz hi George,> From: "gdsecor" <gdsecor@xxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Monday, November 25, 2002 9:24 AM > Subject: [tuning-math] Re: Adaptive JI notated on staff > > > --- In tuning-math@y..., "monz" <monz@a...> wrote:>> i added Dave's graphic and a MIDI-file of it to my >> "adaptive-JI" definition: >> >> Definitions of tuning terms: adaptive JI, (c) ... * [with cont.] (Wayb.) >> >> -monz > > Monz, >> We appreciate your doing this. > > Just one problem: the graphic is out of date. We've changed three > of the symbols in the 217-ET standard set since that it was made. > This includes adoption of the alternate 8deg symbol as the standard > one. You should use this graphic instead: > > Yahoo groups: /tuning- * [with cont.] > math/files/secor/notation/AdaptJI.gif done. thanks. -monz
Message: 5628 - Contents - Hide Contents Date: Tue, 26 Nov 2002 14:55:08 Subject: Re: A common notation for JI and ETs From: gdsecor Correction to my message #5057: --- In tuning-math@y..., "gdsecor" <gdsecor@y...> wrote:> ... I took > some time to look at the 7:17 comma problem. I thought the problem > might be a matter of requiring the //| symbol to represent all of the > roles ranging from ~42.0c (for the 7:17 comma) to ~43.8c (for the > 5:13 comma), but I see that there are a number of divisions above 217 > in which //| is valid for all of these: 224, 270, 282, 342, 388, and > 612. Those in which //| is not valid for all of these are 306, 311, > 364, and 400, and curiously, in most of these the 7:17 comma is the > same number of degrees as the 7:17 comma, but different for the 5+5 > comma. So I think that we just ran out of luck with 494.The next to the last sentence should have read: "Those in which //| is not valid for all of these are 306, 311, 364, and 400, and curiously, in most of these the 7:17 comma is the same number of degrees as the 5:13 comma, but different for the 5+5 comma." The point I was trying to make is that the smallest and largest comma roles are the same number of degrees, while it is the mid-sized 5+5 comma role that differs. So the problem is not that we are trying to represent too large a range of comma sizes by a single symbol. --George
Message: 5629 - Contents - Hide Contents Date: Tue, 26 Nov 2002 15:22:10 Subject: Re: Even more ridiculous 5-comma list From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote: >>> that said, none of these "ridiculous" lists included commas of clear >> practical import, the blackwood 256/243 and the negri 16875/16384. so >> gene did not answer my question. >> You asked for a list based on log-flat badness, and I gave you one.i said "i'd like to know what is missing, based on some log-flat badness measure." i didn't say "i'd like to know what to eliminate, based on some log-flat badness measure." at least, there's no way i'm eliminating negri and blackwood.
Message: 5630 - Contents - Hide Contents Date: Tue, 26 Nov 2002 16:28:32 Subject: Re: Even more ridiculous 5-comma list From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:> i said "i'd like to know what is missing, based on some > log-flat badness measure." i didn't say "i'd like to know what to > eliminate, based on some log-flat badness measure." at least, there's > no way i'm eliminating negri and blackwood."If we used weighted or geometric badness and upped the cutoff a little these would be included. You'd then need to explain what you mean by "missing"--obviously, at some point you need to close off the list!
Message: 5631 - Contents - Hide Contents Date: Tue, 26 Nov 2002 16:34:36 Subject: Re: Even more ridiculous 5-comma list From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote: >>> i said "i'd like to know what is missing, based on some >> log-flat badness measure." i didn't say "i'd like to know what to >> eliminate, based on some log-flat badness measure." at least, there's >> no way i'm eliminating negri and blackwood. >> If we used weighted or geometric badness and upped the cutoff a >little these would be included.that's what i was trying to get you to provide.>You'd then need to explain what you mean by "missing"just the above -- no more, no less!
Message: 5633 - Contents - Hide Contents Date: Tue, 26 Nov 2002 17:23:12 Subject: Re: Paul's new names From: wallyesterpaulrus --- In tuning-math@y..., "Paul G Hjelmstad" <paul.hjelmstad@u...> wrote:> > Could someone give me the formulas that are used to calculate complexity, > rms error and badness? I'll also check monz's dictionary. > > Thanks > > Paulthere are several different versions of complexity. rms error is simply the root-mean-square error of the distinct consonant intervals in the odd limit in question (in this case, it's 5-limit, so it's the root-mean square error, in cents, of 3/2, 5/4, and 5/3). badness has different versions, but in general it's a product of complexity (to some power) and rms error (to some power).
Message: 5634 - Contents - Hide Contents Date: Tue, 26 Nov 2002 18:02:14 Subject: Re: Even more ridiculous 5-comma list From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:>> You'd then need to explain what you mean by "missing" >> just the above -- no more, no less!I guess Yahoo groups: /tuning-math/message/4554 * [with cont.] is a step in the right direction, at least.
Message: 5635 - Contents - Hide Contents Date: Tue, 26 Nov 2002 18:15:07 Subject: Re: Even more ridiculous 5-comma list From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote: >>>> You'd then need to explain what you mean by "missing" >>>> just the above -- no more, no less! >> I guess Yahoo groups: /tuning-math/message/4554 * [with cont.] > is a step in the right direction, at least.sure -- i just wouldn't want to cut it off before the monzisma, out of admiration for the Monz.
Message: 5636 - Contents - Hide Contents Date: Tue, 26 Nov 2002 19:16:56 Subject: Re: A common notation for JI and ETs From: gdsecor --- In tuning-math@y..., David C Keenan <d.keenan@u...> wrote [#5021]:> At 07:32 AM 15/11/2002 -0800, you wrote:>> From: George Secor, 11/15/2002 (#5015) >> ... >> Here I've taken the single-shaft symbols of 132b and used their >> rational complements: >> >> 132c: ~|( /| |) |\ (|~ /|\ /|| ||) ||\ (||( /||\ (RC) >> >> But I'm beginning to wonder if we should allow /|\ to exceed (|), which >> would give us a more meaningful 5deg symbol: >> >> 132d: ~|( /| |) |\ (|) /|\ /|| ||) ||\ (||( /||\ (RC) >> >> This might be justified on the same basis that we have allowed /| to >> exceed |) and even |\ in a few instances. After all, we are already >> used to seeing either sharps or flats higher in pitch in different >> octave divisions. >> Yes. I approve of allowing (|) to be smaller than /|\ in the larger > multiples of 12-ET. It's what I had earlier but only starting with 204-ET. > However, I think I was using /|) in its place as the 5+7 comma for the > smaller multiples, which I've now agreed we should only do if it's also the > 13-comma. > > I can accept either 132c or 132d. You (or your spreadsheet) should decide. > I'm mentally too distant from such details at present.I vote for 132d, because it makes the 5 and 6deg symbols rational complements of each other. --George
Message: 5637 - Contents - Hide Contents Date: Tue, 26 Nov 2002 20:15:12 Subject: Re: Paul's new names From: Carl Lumma>there are several different versions of complexity.Has there been any discussion on where we disagree on complexity? What are the main formualtions, and how desirable is it that we pick one? -Carl
Message: 5638 - Contents - Hide Contents Date: Tue, 26 Nov 2002 00:43:41 Subject: Re: Even more ridiculous 5-comma list From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:> that said, none of these "ridiculous" lists included commas of clear > practical import, the blackwood 256/243 and the negri 16875/16384. so > gene did not answer my question.You asked for a list based on log-flat badness, and I gave you one.
Message: 5639 - Contents - Hide Contents Date: Tue, 26 Nov 2002 20:23:09 Subject: Re: Paul's new names From: wallyesterpaulrus --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:>> there are several different versions of complexity. >> Has there been any discussion on where we disagree on > complexity? What are the main formualtions, and how > desirable is it that we pick one? > > -Carli'd be happy with an unweighted complexity measure for the purposes of these graphs, if that's what people prefer. ultimately, though, to repeat myself, i'd like to figure out a complexity measure that agrees with the size of the numbers in the comma (at least in the 5- limit case). it seems kees's lattice does this, but . . .
Message: 5641 - Contents - Hide Contents Date: Tue, 26 Nov 2002 20:24:54 Subject: Re: Paul's new names From: wallyesterpaulrus --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:> What are the main formualtions,we have graham's (unweighted minimax), unweighted rms, weighted rms, geometric (both unweighted and weighted??) . . .
Message: 5642 - Contents - Hide Contents Date: Tue, 26 Nov 2002 20:39:38 Subject: Re: Paul's new names From: Gene Ward Smith --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:> --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:>>> there are several different versions of complexity. >>>> Has there been any discussion on where we disagree on >> complexity? What are the main formualtions, and how >> desirable is it that we pick one? >> >> -Carl >> i'd be happy with an unweighted complexity measure for the purposes > of these graphs, if that's what people prefer.I like geometric complexity because it is a uniform system applicable to any regular temperament.
Message: 5643 - Contents - Hide Contents Date: Tue, 26 Nov 2002 20:41:40 Subject: Re: Paul's new names From: wallyesterpaulrus --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:> --- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:>> --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:>>>> there are several different versions of complexity. >>>>>> Has there been any discussion on where we disagree on >>> complexity? What are the main formualtions, and how >>> desirable is it that we pick one? >>> >>> -Carl >>>> i'd be happy with an unweighted complexity measure for the purposes >> of these graphs, if that's what people prefer. >> I like geometric complexity because it is a uniform system >applicable to any regular temperament.including equal temperaments? can you give a sorting of ETs in some limit? does GC reduce to something simpler for ETs?
Message: 5644 - Contents - Hide Contents Date: Tue, 26 Nov 2002 20:44:00 Subject: spiral lattices From: wallyesterpaulrus these were part of a big exhibit in the greenhouse that my girlfriend showed me: Spiral Lattices | Phyllotaxis * [with cont.] (Wayb.) applicable to MOS scales . . .
Message: 5645 - Contents - Hide Contents Date: Tue, 26 Nov 2002 21:36:03 Subject: Ultimate 5-limit comma list From: Gene Ward Smith Not that any list is really ultimate, but with rms error < 40, geometric complexity < 500, and badness < 3500, it covers a lot of ground. 27/25 3.739252 35.60924 1861.731473 135/128 4.132031 18.077734 1275.36536 256/243 5.493061 12.759741 2114.877638 25/24 3.025593 28.851897 799.108711 648/625 6.437752 11.06006 2950.938432 16875/16384 8.17255 5.942563 3243.743713 250/243 5.948286 7.975801 1678.609846 128/125 4.828314 9.677666 1089.323984 3125/3072 7.741412 4.569472 2119.95499 20000/19683 9.785568 2.504205 2346.540676 531441/524288 13.183347 1.382394 3167.444999 81/80 4.132031 4.217731 297.556531 2048/2025 6.271199 2.612822 644.408867 67108864/66430125 15.510107 .905187 3377.402314 78732/78125 12.192182 1.157498 2097.802867 393216/390625 12.543123 1.07195 2115.395301 2109375/2097152 12.772341 .80041 1667.723301 4294967296/4271484375 18.573955 .483108 3095.692488 15625/15552 9.338935 1.029625 838.631548 1600000/1594323 13.7942 .383104 1005.555381 (2)^8*(3)^14/(5)^13 21.322672 .276603 2681.521263 (2)^24*(5)^4/(3)^21 21.733049 .153767 1578.433204 (2)^23*(3)^6/(5)^14 21.207625 .194018 1850.624306 (5)^19/(2)^14/(3)^19 30.57932 .104784 2996.244873 (3)^18*(5)^17/(2)^68 38.845486 .058853 3449.774562 (2)^39*(5)^3/(3)^29 30.550812 .057500 1639.59615 (3)^8*(5)/(2)^15 9.459948 .161693 136.885775 (3)^45/(2)^69/(5) 48.911647 .026391 3088.065497 (2)^38/(3)^2/(5)^15 24.977022 .060822 947.732642 (3)^35/(2)^16/(5)^17 38.845486 .025466 1492.763207 (2)*(5)^18/(3)^27 33.653272 .025593 975.428947 (2)^91/(3)^12/(5)^31 55.785793 .014993 2602.883149 (3)^10*(5)^16/(2)^53 31.255737 .017725 541.228379 (2)^37*(3)^25/(5)^33 50.788153 .012388 1622.898233 (5)^51/(2)^36/(3)^52 82.462759 .004660 2613.109284 (2)^54*(5)^2/(3)^37 39.665603 .005738 358.1255 (3)^47*(5)^14/(2)^107 62.992219 .003542 885.454661 (2)^144/(3)^22/(5)^47 86.914326 .002842 1866.076786 (3)^62/(2)^17/(5)^35 72.066208 .003022 1131.212237 (5)^86/(2)^19/(3)^114 151.69169 .000751 2621.929721 (3)^54*(5)^110/(2)^341 205.015253 .000385 3314.979642 (2)^232*(5)^25/(3)^183 191.093312 .000319 2223.857514 (2)^71*(5)^37/(3)^99 104.66308 .000511 586.422003 (5)^49/(2)^90/(3)^15 74.858154 .000761 319.341867 (3)^69*(5)^61/(2)^251 143.055244 .000194 566.898668 (3)^153*(5)^73/(2)^412 235.664038 5.224825e-05 683.835625 (2)^161/(3)^84/(5)^12 100.527798 .000120 121.841527 (2)^734/(3)^321/(5)^97 431.645735 3.225337e-05 2593.925421 (2)^21*(3)^290/(5)^207 374.22268 2.495356e-05 1307.744113 (2)^140*(5)^195/(3)^374 423.433817 2.263360e-05 1718.344823 (3)^237*(5)^85/(2)^573 332.899311 5.681549e-06 209.60684
Message: 5648 - Contents - Hide Contents Date: Wed, 27 Nov 2002 19:27:15 Subject: Re: Paul's new names From: wallyesterpaulrus --- In tuning-math@y..., "Carl Lumma" <clumma@y...> wrote:>> What are the main formualtions, >> >> we have graham's (unweighted minimax), unweighted rms, >> weighted rms, geometric (both unweighted and weighted??) . . . > > For complexity?yup, doze R dem.> What are they? dem. doze.
Message: 5649 - Contents - Hide Contents Date: Wed, 27 Nov 2002 19:28:13 Subject: Re: Even more ridiculous 5-comma list From: wallyesterpaulrus --- In tuning-math@y..., "Paul G Hjelmstad" <paul.hjelmstad@u...> wrote:> > Thanks for the explanation. I'll admit I am a little stuck on how there can > be negative numbers (for generators).can you give an example of where you're getting stuck? i'm sure we can hold your hand and walk you through this . . .
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