This is an Opt In Archive . We would like to hear from you if you want your posts included. For the contact address see About this archive. All posts are copyright (c).
- Contents - Hide Contents - Home - Section 1110000 10050 10100 10150 10200 10250 10300 10350 10400 10450 10500 10550 10600 10650 10700 10750 10800 10850 10900 10950
10200 - 10225 -
Message: 10200 - Contents - Hide Contents Date: Thu, 12 Feb 2004 04:15:37 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote: >>> If you mean, log-flat with no other cutoffs, then no. I don't think >> this was ever on the table, even from Gene. There is an infinite >> number in the increasing complexity direction. I understand this would >> be a single straight line on the log-log plot parallel to the apparent >> lower left "edge" of the populated region. >> It would in particular be the line which is a lim sup for the slope, > and hence containing an infinite supply of temperaments. > > Limit superior and limit inferior - Wikipedia,... * [with cont.] (Wayb.) >>> If you mean log-flat badness in conjunction with error and complexity >> cutoffs then it can stay on the table if you like, but I don't know >> how you can psychologically justify the corners. >> Can you specifically cite when an obnoxious temperament turned up in a > corner, and you couldn't get rid of it without losing something good?No. I can't, but it may have happened and I wouldn't have known since we only started plotting things very recently. However, it may well be possible in some cases to find a wide enough moat in the right (subjective) ballpark that can accomodate both a smooth curve and a tri-linear (bad, comp, err) cutoff giving the same list. That's the beauty of moats.
Message: 10201 - Contents - Hide Contents Date: Thu, 12 Feb 2004 04:31:53 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>>>>> Dave doesn't seem to want the macros which would >>>>> be necessary for the scale-building stuff. >>>> To me, in the context of the current highly mathematical discussion, >> this said to me that you think macros are necessary (i.e. you can't do >> without them) for scale-building stuff. >> >> I think this is obviously wrong since you can show how to build a >> scale using meantone which is not a macrotemperament. >> >> But since I now learn that you apparently only meant "desirable" >> rather than "necessary" in the strict logical sense, >> Hate to nitpick now that we understand each other, but it has > nothing to do with strict logic, but rather *what* one wants to > do. Try this again: >>>> Do *what* without them? Build any decent scale (the above sense)? >>> Or run any kind of decent scale-building program (the sense in >>> which I said "necessary")?By "scale-building stuff" I assumed you mean "showing readers how to take temperaments and build scales from them, complete with several examples". This corresponds closely to the second option above. I don't think our difference of interpretation has anything to do with that. But the words "any kind of decent" did not appear in your original statement. If they had, there would have been no problem. So continuing the nitpicking: "necessary for <whatever>" does not mean "indispensable for any kind of decent <whatever>". But I agree that "necessary for any kind of decent <whatever>" would have been just as good as "desirable for <whatever>". But of course I still disagree with your opinion on this.>> you should note >> that I long ago agreed to neutral thirds and pelogic being on the >> 5-limit list. Surely they are macro enough for your purposes. >> Herman just got through posting on tuning how beep is a great > temperament for scale-building.It may be good for scale building, but it isn't a temperament in the sense of approximation of JI. Herman agrees.
Message: 10202 - Contents - Hide Contents Date: Thu, 12 Feb 2004 02:31:59 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>>>>>> It is well known that Dave, for example, is far more >>>>>> micro-biased than I! >>>>> >>>>> ? >>>>>>>> What's your question? >>>>>> What does micro-biased mean, on what basis do you say this about you >>> vs. Dave, and what is its relevance here? >>>> I'd like to know what you mean by micro-biased. It may well be true, >> but I'd like to know. >> Of all the amazing things I've seen on these lists, the failure of > both you and Paul to understand the meaning of "micro-biased" is > possibly the most amazing.You misjudge. It wasn't failure to understand, it was carefulness in checking for possible misunderstandings, rather than immediately telling someone they are wrong. Something that surely we'd all like to see more of.>>> At the moment I fell you should be calling me "centrally biased" or >> some such. >> Obviously you did understand it!Yes, as it turns out (but might not have).>> I don't want to include either the very high error low >> complexity or very high complexity low error temperaments that a >> log-flat cutoff alone would include. >> Yes, you are apparently centrally biased. You should like circles > in that case. :)Yes, I do, so far. Haven't you read that? For me there are three candidates on the table at the moment. log-log circles or ellipses, log-log hyperbolae, and linear-linear nearly-straight-lines. I'm guessing that one can probably make any one of these fit within any given moat. If so, a major reason to prefer one over another would be the number of free parameters and the simplicity of the expression for the cutoff relation in terms of error and complexity. What happens to the curve once it is free of the pack (sorry, reading about too many antarctic sea voyages lately) doesn't much matter, although I guess you could still argue psychological plausibility from the curve's behaviour in regions that don't happen to be populated.
Message: 10203 - Contents - Hide Contents Date: Thu, 12 Feb 2004 05:47:00 Subject: Bye for a while From: Dave Keenan That's it from me for a while. I'm a tuning list addict. I don't know how to moderate my list use, so I'm going cold turkey. I'm happy that my position is now understood (but not agreed with) by all concerned, re this temperament list cutoff business. Sometimes I think it's all so unimportant, and no one but us is terribly interested in it anyway. The idea of worrying about priority makes me laugh. Also, when you read stuff like this [off topic] Life After the Oil Crash * [with cont.] (Wayb.) I feel like we're just fiddling while Rome burns. You know how to email me. Tamam Shud
Message: 10204 - Contents - Hide Contents
Date: Thu, 12 Feb 2004 08:39:19
Subject: Shells of 7-limit note-classes
From: Gene Ward Smith
If we say a note-class belongs to shell n if its symmetrical lattice
distance from the unison is sqrt(n), then the first nine shells are
listed below. At shell nine, a new phenomenon emerges--there are two
geometrically distinct (and algebraically distinguishable, using
invariants) kinds of notes in shell nine. At shell 14, we get another
interesting phenomenon--there are no notes in shell 14. In fact, it is
a moat! We also get moats at shell 46, shell 56 etc. If we regard what
shell a note belongs in as a measure of its complexity, note that
126/125 and 225/224 (which together generate meantone) are less
complex by this measure than 81/80--and in fact, 2401/2400, lying in
shell 11, is less complex than 81/80 in shell 13.
Shell 2 is interesting because of the special intervals 36/24, 21/20
and 15/14 which are so important when looking at the lattice of chords.
Shell 7 has both 64/63 and 126/125 in it, a fact I exploited in a
piece which progressed from 126/125-planar (Starling) to 64/63-planar
and back again.
Shell 1: 7-limit consonances
{12/7, 3/2, 5/3, 7/5, 8/7, 7/6, 6/5, 5/4, 4/3, 7/4, 8/5, 10/7}
Shell 2: tetrad lattice generators
{48/35, 21/20, 28/15, 40/21, 35/24, 15/14}
Shell 3: conjugates of 9/7, as well as 10/9, 16/15, 25/24, 36/35 and 49/48
{32/21, 28/25, 42/25, 48/25, 64/35, 49/40, 80/49, 35/32, 25/24, 16/15,
36/35, 49/48, 9/5, 9/7, 10/9, 25/14, 96/49, 21/16, 14/9, 60/49, 35/18,
15/8, 25/21, 49/30}
Shell 4: squares of consonances
{32/25, 64/49, 49/32, 49/25, 25/16, 25/18, 50/49, 9/8, 72/49, 16/9,
49/36, 36/25}
Shell 5: conjugates of 9/8 and 50/49
{147/80, 200/147, 75/56, 288/175, 63/50, 288/245, 63/40, 56/45,
175/96, 45/28, 90/49, 192/175, 80/63, 75/49, 245/144, 147/100, 100/63,
175/144, 49/45, 112/75, 98/75, 384/245, 160/147, 245/192}
Shell 6 conjugates of 105=3*5*7
{125/84, 480/343, 105/64, 168/125, 54/35, 35/27, 128/105, 343/240}
Shell 7: conjugates of 28/27, 64/63, 126/125 and 27/25
{384/343, 125/72, 54/49, 27/14, 147/128, 28/27, 256/245, 224/125,
196/125, 343/288, 640/343, 126/125, 216/175, 245/128, 64/63, 576/343,
360/343, 63/32, 147/125, 256/175, 400/343, 343/200, 175/128, 27/25,
40/27, 245/216, 144/125, 250/147, 125/96, 432/245, 45/32, 27/20,
125/98, 128/75, 49/27, 125/112, 343/300, 50/27, 343/320, 175/108,
125/63, 64/45, 192/125, 343/180, 600/343, 75/64, 256/147, 343/192}
Shell 8: squares of tetrad lattice generators
{2304/1225, 441/400, 800/441, 1225/1152, 225/196, 392/225}
Shell 9: there are two varities of shell-nine note-classes
9a: cubes of consonances, including 128/125
{432/343, 27/16, 128/125, 216/125, 32/27, 343/216, 343/250, 512/343,
343/256, 125/108, 500/343, 125/64}
9b: conjugates of 225/224
s92 := {1152/875, 441/250, 225/224, 1600/1029, 1225/768, 375/196,
1728/1225, 189/100, 392/375, 1225/864, 200/189, 343/225, 135/98,
500/441, 875/576, 640/441, 1715/1152, 196/135, 2304/1715, 441/320,
1536/1225, 1029/800, 450/343, 448/225}
Message: 10205 - Contents - Hide Contents Date: Thu, 12 Feb 2004 21:35:28 Subject: Re: Symmetrical complexity for 5 and 7 limit temperaments From: Carl Lumma>>> >he symmetrical complexity for codimension one (5-limit linear, >>> 7-limit planar) is the symmetrical lattice distance for the >>> comma defining it. >>>> Is this the same as the "n" in your "interval count" message, >> then? That was what I've been calling "taxicab distance to >> the comma". >>No, it's the symmetrical Euclidean lattice distance.Ok, let's take a look...>To get to a note-class in what I called shell n^2 from the unison >in 7-limit, you need at minimum n steps because a straight line >path of 1-step intervals takes you only out to a distance n.Oh yeah, here you're squaring n, even though the 7-limit is 3- or 4-dimensional. So what the hell is a "step" in a "straight line path"?>For 81/80 this is ceil(sqrt(13))=4 steps, and for >2401/2400 it is ceil(sqrt(11))=4 steps also.Where do 13 and 11 come from?>In fact, both can be reached in four steps in only one way, up >to commuitivity; we have > >81/80 = (6/5)(3/2)^3 (1/4) >2401/2400 = (7/6)(7/5)^2(7/4) (1/4)This sure looks like taxicab, but what are the "(1/4)" terms? -Carl
Message: 10206 - Contents - Hide Contents Date: Thu, 12 Feb 2004 02:40:08 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>>> Dave doesn't seem to want the macros which would >>> be necessary for the scale-building stuff. >>>> What are macros? >> Again, I'm amazed that this well-worn terminology isn't effective > here. AKA exos?Again, just being careful since my current understanding did not agree with them being necessary for scale building. It wouldn't be the first time we both thought we understood the meaning of a term and eventually discovered we were poles apart. (Damn those Antarctic stories :-)>> Why can't you do scale-building stuff without them? >> I don't know that it can't, but they're certainly fertile for > scale-building.Carl, "necessary" means you can't do without them. Please be careful about your use of hyperbole (as opposed to Gene's use of hyperbolas :-), particularly since frustration is running high in all quarters at present.
Message: 10207 - Contents - Hide Contents Date: Thu, 12 Feb 2004 08:42:58 Subject: Re: Shells of 7-limit note-classes From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> Shell 2 is interesting because of the special intervals 36/24, 21/20 > and 15/14 which are so important when looking at the lattice of chords.35/24, 21/20 and 15/14--5*7/3, 3*7/5 and 3*5/7.
Message: 10208 - Contents - Hide Contents Date: Thu, 12 Feb 2004 23:51:50 Subject: Pelogic and "hexidecimal" From: Herman Miller From the big 7-limit temperament list: Number 19 Pelogic [1, -3, -4, -7, -9, -1] [[1, 2, 1, 1], [0, -1, 3, 4]] TOP tuning [1209.734056, 1886.526887, 2808.557731, 3341.498957] TOP generators [1209.734056, 532.9412251] bad: 39.824125 comp: 2.022675 err: 9.734056 Number 94 Hexidecimal [1, -3, 5, -7, 5, 20] [[1, 2, 1, 5], [0, -1, 3, -5]] TOP tuning [1208.959294, 1887.754858, 2799.450479, 3393.977822] TOP generators [1208.959293, 530.1637287] bad: 84.341555 comp: 3.068202 err: 8.959294 The 5-limit Pelogic has this TOP tuning: [1206.548265, 1891.576247, 2771.109114] The 7-limit temperament labeled "Pelogic" has a better 7:1 approximation at -5 generators (3383.96 cents in the TOP tuning). Worse, the 7:4 with the +4 mapping is way too flat. In short, the mapping [0, -1, 3, -5] is better even with the TOP tuning given for "Number 19 Pelogic". It also works better with the traditional pelogic ET's 16 and 23. The TOP tuning for "Hexidecimal" is closer to the 5-limit Pelogic TOP tuning than Number 19's TOP tuning is. I suggest that the name "Pelogic" would be more appropriately applied to Number 94 than Number 19.
Message: 10209 - Contents - Hide Contents Date: Thu, 12 Feb 2004 00:49:25 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> It's a non-subjective musical result. The number of intervals >> involved, >> Not the only valid measure of complexity.Who said it was?> Why should I only care about major tetrads?The same applies to minor tetrads. As to why you should care about tetrads, the only 7-limit JI harmony there is is tetrads or subsets of tetrads.> Then something like the Kees lattice should be used, but this > assumption would add a new chapter to our paper that would probably > make it too long.I wasn't suggesting adding it to our paper, I was hoping to add it to our thinking.> In C major, the progression between C major and D minor triads > doesn't use any shared notes. Is that a problem?It's not a problem, but it does mean that it is less organic than from C to a or e; it is well-known that ii relates to both IV and V, and this *does* involve shared notes. iii is sometimes hardly regarded as a separate tonal presence, since it ties so closely to both I and V.>> We can start from chords and then get back to the notes. >> I don't want to assume any particular chord structures; that would > make this whole enterprise far less general and might doom it to > being nothing more than an academic curiosity.I hope you have not become allergic to thinking about theory except in terms of a paper. As for chord stuctures, in the 5 and 7 odd limits, with no tempering, you don't have a lot of choices.
Message: 10210 - Contents - Hide Contents Date: Thu, 12 Feb 2004 09:42:14 Subject: A Hemiwuerschmidt scale From: Gene Ward Smith If I combine shell 0, the unison, with shells 1, 2 and 3, I get a symmetrical scale of 43 notes which turns out to be an excellent candidate for tempering by the hemiwuerschmidt temperament (covered by 68, 99 and 130.) This has 41 notes since the two steps of size 2401/2400 in it are nuked. Here it is in TOP tuning: ! hemw.scl Hemiwuerschmidt TOP tempering of 43 notes of septimal ball 3 41 ! 36.757436 46.792679 73.514873 83.550115 110.272314 120.307552 157.064988 183.787187 193.822429 230.579866 267.337302 304.094739 314.129981 350.887417 387.644854 434.437533 471.194969 497.917168 544.709847 581.467283 618.224720 654.982156 701.774835 728.497034 765.254470 812.047149 848.804585 885.562022 895.597264 932.354701 969.112137 1005.869574 1015.904816 1042.627015 1079.384451 1089.419689 1116.141888 1126.177130 1152.899324 1162.934567 1199.692000
Message: 10211 - Contents - Hide Contents Date: Thu, 12 Feb 2004 00:52:06 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote: >>> I don't see how the fact that x/612ths of an octave is a fine way to >> tune the ennealimmal generator has any bearing on the musical >> usefulness of 612-ET _as_an_ET_. >> Try thinking like a computer composer, who could well desire to keep > track of things more easily by scoreing in terms of reasonably small > integers.OK. I'll grant that that is a form of musical usefulness for 612-ET but it is not derived directly from the n-limit properties of 612-ET itself, but only indirectly from the properties of ennealimmal (which are themselves of dubious utility). Even if we want to include _this_ kind of derived usefulness in our considerations I think an ET should only inherit a tiny fraction of the usefulness of an LT it supports. The other way of approaching this (which I favour at present) is to say that the support of LTs should have no such impact on the inclusion or otherwise of an ET _as_an_ET_, because the ET will get it's due in this regard when the LTs are listed since we would include a column giving the ETs that well support each ET.
Message: 10212 - Contents - Hide Contents Date: Thu, 12 Feb 2004 01:51:25 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma>>>> >an you name the temperaments that fell outside of the top 20 >>>> on Gene's 114 list? >>> >>> Yes. >>>> Eep! Sorry, I meant the ones that you want that fell outside >> Gene's top 20/114. >>Oh. Sorry. I just don't have any enthusiasm for working this out now. >I just know that I like Paul's latest list (which I can't easily find) >because it has the ones I want plus a few more that bring it up >against a reasonable moat.And which list is that? -Carl
Message: 10213 - Contents - Hide Contents Date: Thu, 12 Feb 2004 02:54:02 Subject: Re: ! From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>> You know what a moat is right? >> Obviously not! :( >>> You have the castle (the circle is its >> outer bound) with people (temperaments) inside. >> Then it's the same as a circle!No. A circle is infinitesimally thin. A moat has real thickness. If we're talking circular cutoffs then we'd say the moat is annular. The circle is only one edge of the moat. Of course it doesn't have to be circular, but continuing in that vein ... You could draw the smallest circle that encloses all the lucky temperaments and then you could draw another one outside that which is the largest circle that still encloses the same ones and no others. The space between them is the moat. You can then give a quantitative measure of the size of the moat as the percentage difference between the radii of the two circles. The term "moat" came to mind because the temperaments sometimes look like constellations and in the Niven and Pournelle books "The Mote in Gods Eye" and "The Moat around Murcheson's Eye", "the Moat" is a vast region of space with no stars.
Message: 10214 - Contents - Hide Contents Date: Thu, 12 Feb 2004 01:59:25 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma>So continuing the nitpicking: > >"necessary for <whatever>" does not mean "indispensable for any kind >of decent <whatever>". But I agree that "necessary for any kind of >decent <whatever>" would have been just as good as "desirable for ><whatever>".I'm sorry, I can't parse this.>But of course I still disagree with your opinion on this.I think you understand me, but ultimately I'm not sure since I couldn't parse the above.>>> you should note >>> that I long ago agreed to neutral thirds and pelogic being on the >>> 5-limit list. Surely they are macro enough for your purposes. >>>> Herman just got through posting on tuning how beep is a great >> temperament for scale-building. >>It may be good for scale building, but it isn't a temperament in the >sense of approximation of JI. Herman agrees.But if you view it as a "temperament in the sense of 'approximating' JI" it still works. The point is that temperament, in whatever sense, is useful for all sorts of reasons. -Carl
Message: 10215 - Contents - Hide Contents Date: Thu, 12 Feb 2004 02:55:29 Subject: Re: Rhombic dodecahedron scale From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" <paul.hjelmstad@u...> wrote: In>>> analytic terms, the generating function for the above problem is a >>> series (1+2q+2q^4+2q^9+ ... + 2q^n^2 + ...)^3 = >> 1+12q+6q^2+24q^3+..., > >> *I get 1+6q+12q^2+8q^3+6q^4... am i missing something?*Sorry, I wrote down the generating function for the number of tetrads, not notes. Define th(q) = 1+2 sum(n=1..infinity) q^n^2 = 1+2q+2q^4+2q^9+... th01(q) = th(-q) = 1+2 sum((-1)^n q^n^2) = 1-2q+2q^4-2q^9+... th10(q) = 2 sum q^((n+1/2)^2) = 2 q^(1/4) (1+q^2+q^6+...) Then the generating function for 7-limit note-classes is (th(q^(1/2))^3 + th01(q^(1/2))^3)/2 The generating function for balls centered on tetrads is (th10(q^4)^3)/2 = 4q^3 + 12q^11 + 12q^19 + 16q^27 + ... For balls centered on hexanies is (th(q)^3 - th01(q)^3)/2 = 6q + 8q^3 + 24q^5 + 30q^9 + ... This leads to scales of 4, 16, 30, 46 ... notes for the tetrad-centered scales, which can be centered on either a minor or a major tetrad, and 6, 14, 38, 68, ... for the hexany-centered scales. th(q)>>> where the coefficient on the q^n term is the number of 7-limit >>> note-classes at a distance of sqrt(n) from the unison. Similar >>> generating functions can be defined for distance from the center > of>>> tetrads, hexanies, or the midpoint of the 1-3 interval, with >>> corresponding scales.
Message: 10216 - Contents - Hide Contents Date: Thu, 12 Feb 2004 00:58:12 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:> We have a choice -- derive badness from first principles or cook > it from a survey of the tuning list, our personal tastes, etc.What first principles of the human psychology of the musical use of temperaments did you have in mind?
Message: 10217 - Contents - Hide Contents Date: Thu, 12 Feb 2004 03:00:50 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>>> We have a choice -- derive badness from first principles or cook >>> it from a survey of the tuning list, our personal tastes, etc. >>>> What first principles of the human psychology of the musical use of >> temperaments did you have in mind? >> Since I'm not aware of any, and since we don't have the means to > experimentally determine any, I suggest using only mathematical > first principlesBut badness is clearly a psychological property, what have mathematical first principles got to do with it?> , or very simple ideas like... > > () For a number of notes n, we would expect more dyads in the > 7-limit than the 5-limit. > > () I expect to find a new best comma after searching n notes > in the 5-limit, n(something) notes in the 7-limit.These sound reasonable, but I don't see how to use them to determine psychologically reasonable cutoff for lists of the temperaments most likely to be musically useful. I think we have no choice but to "cook it from a survey of the tuning list, our personal tastes, etc.". Some of us have been doing informal surveys of these questions on the tuning list for a decade or more.
Message: 10218 - Contents - Hide Contents Date: Thu, 12 Feb 2004 11:10:26 Subject: Symmetrical complexity for 5 and 7 limit temperaments From: Gene Ward Smith The symmetrical complexity for codimension one (5-limit linear, 7-limit planar) is the symmetrical lattice distance for the comma defining it. For a 7-limit linear lattice, we have Symcomp( <a b c d e f| ) = sqrt(3 (a^2+b^2+c^2) - 2(ab+ac+bc)) which is the symmetrical mapping lattice distance for the first three components of the wedgie, considered as a note-class mapping. It might be interesting to compare the lists of temperaments we get using this definition of complexity with, L1 TOP, etc. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service * [with cont.] (Wayb.)
Message: 10219 - Contents - Hide Contents Date: Thu, 12 Feb 2004 01:00:52 Subject: Re: acceptace regions From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> >> wrote:>>> We might try in analyzing or plotting 7-limit linear temperaments a >>> transformation like this: >>> >>> u = 4 - ln(complexity) - ln(error) >>> v = 12 - 4 ln(complexity) - ln(error) >> In the terms Paul, Carl and I have been using, this is a cutoff relation > > max[ln(complexity)/4 + ln(error)/4, > 4 * ln(complexity)/3 + ln(error)/12] < 1Only if you choose to use it for one. It's a coordinate transformation, primarily.> It seems we may be moving towards some kind of agreement. :-)I've been *trying* to help you and Paul here, with all of this stuff about convex hulls and what not which I have been told is useless. I hope I am finally communicating *something*. This idea, by the way, is an old one but not much heed was paid to it by anyone, including me, and I proposed it. The new aspects are to use it as a coordinate transformation in a loglog context, and to draw hyperbolas if you want to smooth corners.> OK. But I don't think it will help to do a u v plot. Why not?I'd prefer to see> it on the existing log log plot,Why not both? and I'd really like to see if you can> come up with one of these hyperbolic-log beasties that gives the same > list as Pauls red curve. This is exciting. :-)Probably that can be done, but what is special about Paul's red curve? I didn't like it, and in any case Paul tells us that the reason it drops off so fast at the end is not because he was trying to nuke ennealimmal, but because he ran out of things to plot. The massive subjectivity of it all is what I'm hoping to avoid.
Message: 10220 - Contents - Hide Contents Date: Thu, 12 Feb 2004 03:06:05 Subject: Re: acceptace regions From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:> Well log(error) and log(complexity) are already so far away from any > reasonable kind of pain(error) and pain(complexity) that I fear this > will just make it worse. You convinced us to humour you with the > log-log thing, but this seems to be going too far.One posting you use the word "exciting" and in the next you aren't even willing to look at a plot, because doing that might be to go too far in humoring an obviously confused person. Which is it?> What is the point of putting all the math-complexity of the cutoff > relation into the coordinate transformation just so the cutoff > relation looks simple. The math-complexity is still there.It's to make clear what and how I am doing. An objection to clarity and simplicity, which is what this amounts to, seems to me to be very misplaced. And Paul and you both tbink *I* am making spurious excuses!> Sure. I'd like to see it on linear-linear too. But since I'm not doing > it, I figure I can't ask for too much.People ask me to do things on this list all the time. Sometimes I even do them.> OK. So long as its something close to Paul's list, otherwise we're > just wasting our time.Does this mean you didn't even *look* at my lists??> We're not trying to _avoid_ subjectivity, we're trying to _model_ it.The best model for total subjectivity is simply to pick any temperametns you like for any reason you like. We could try that.> And we're trying to do so in such a way that > (a) the model has only a small number of parameters, preferably no > more than 3.Moving the origin of my uv stuff is two. Adding a hyperbola gives you three.> (c) we have agreement from as many people, as possible.Has this last been attempted? It seems to me it's got to be whatever you and Paul want, lately.
Message: 10221 - Contents - Hide Contents Date: Thu, 12 Feb 2004 01:02:45 Subject: Re: Rhombic dodecahedron scale From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul G Hjelmstad" <paul.hjelmstad@u...> wrote:> Interesting. What's the 1-3 interval?Twelfth, fifth, etc. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service * [with cont.] (Wayb.)
Message: 10222 - Contents - Hide Contents Date: Thu, 12 Feb 2004 03:08:01 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:> I don't understand why you think log-flat is a magic bullet in this > regard. If you use log flat badness and include the same number of > temperaments as Paul and I and Gene are considering (around 20), then > exactly the same scenario is possible, only this time it will be > temperaments with moderate amounts of both error and complexity that > are omitted and the objecting musician won't be fictitious, he'll be > Herman Miller.Now explain why my list of 22 is no good, please, and what you think should be on it that isn't, or off it that is. ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service * [with cont.] (Wayb.)
Message: 10223 - Contents - Hide Contents Date: Fri, 13 Feb 2004 13:32:08 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma>> >ragnabbit, we've already been through this. I do *not* mean >> *diatonics*, I mean *scales*, YOUR definition, pitches. >>A discrete set of notes? Pitches, yes. -Carl
Message: 10224 - Contents - Hide Contents Date: Fri, 13 Feb 2004 20:00:57 Subject: Re: loglog! From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:>>>>>> The complexity measures cannot be compared across different >>>>>> dimensionalities, any more than lengths can be compared with >>>>>> areas can be compared with volumes. >>>>>>>>>> Not if it's number of notes, I guess. >>>>>>>> What's number of notes?? >>> >>> Complexity units. >>>> It's only that (or very nearly that) in the ET cases. >> Your creepy complexity is giving notes, clearly.Hmm . . .And what do you propose to use for the 5-limit linear and 7- limit planar cases?>> So it the below >> still relevant? >> Yes! It's a fundamental question about how to view complexity. > I'd be most interested in your answer.Again, I view complexity as a measure of length, area, volume . . . in the Tenney lattice with taxicab metric. We're measuring the size of the finite dimensions of the periodicity slice, periodicity tube, periodicity block . . .>>>>> I've suggested in the >>>>> past adjusting for it, crudely, by dividing by pi(lim). >>>>>>>> Huh? What's that? >>>>>> If we're counting dyads, I suppose higher limits ought to do >>> better with constant notes. >>> If we're counting complete chords, >>> they ought to do worse. Yes/no?Still have no idea how to approach this questioning, or what the thinking behind it is . . .
10000 10050 10100 10150 10200 10250 10300 10350 10400 10450 10500 10550 10600 10650 10700 10750 10800 10850 10900 10950
10200 - 10225 -