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Message: 375 - Contents - Hide Contents Date: Mon, 25 Jun 2001 22:05:01 Subject: Re: Hypothesis revisited From: Paul Erlich --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote:> --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:>> --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote:>>> Actually, with the 10-note 369c MOS, I was looking for a MOS scale >>> that Paul would have difficulty finding unison-vectors for, that > are>>> anything like unisons. i.e. This one was meant to have _big_ UVs, > and>>> not to contain any good approximations to SWNRs. >>> >>> Are you asking us to find a linear temperament that treats those >>> unison vectors (49/40 and 4375/4096) as commas, and to tell you > how>>> "good" it is relative to the usual JI criteria. >>>> I think Dan just found unison vectors for your example, Dave! >> If that's the case, then it makes my point quite well. Isn't it just a > little ridiculous to refer to intervals of 351c and 114c as "unison" > vectors or "commas"? >Only if you think of the scale as existing _initially_ in JI. Some of my favorite scales, such as the 14-out-of-26-tET 7-limit scales, involve very large unison vectors. Since they are tempered out over a large number of consonant intervals, the fact that they are very large in JI doesn't bother me.
Message: 376 - Contents - Hide Contents Date: Mon, 25 Jun 2001 22:05:49 Subject: Re: 41 "miracle" and 43 tone scales From: Paul Erlich --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote:> All that means is that Partch wasn't intentionally using Miracle You bet! > and > that Wilson missed the fact that Partch's scales imply it."Imply" is a little strong. I'd say "suggest".
Message: 377 - Contents - Hide Contents Date: Mon, 25 Jun 2001 22:08:35 Subject: Re: 41 "miracle" and 43 tone scales From: Paul Erlich --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote:> It's interesting that Miracle distinguishes all three of these ratios, > as Partch did. > > 11:12 is -9 generators > 10:11 is 22 generators > 9:10 is -19 generators > > -- Dave KeenanPartch distinguished them because they're all in the diamond. Early on, his scale was _just_ the diamond. 10:11 and 9:10 (and their octave complements) are the _only_ pair of notes in the diamond that fall in the same place in modulus-41 . . . that's why Partch ended up with 43, rather than 41, notes . . . he was not willing to compromise the diamond . . . he built many instruments around it!
Message: 378 - Contents - Hide Contents Date: Mon, 25 Jun 2001 22:15:22 Subject: Re: 41 "miracle" and 43 tone scales From: Paul Erlich --- In tuning-math@y..., "monz" <joemonz@y...> wrote:> But Graham's speculations are intriguing, and I'm fairly convinced > by them that Partch *intuitively* understood the MIRACLE concept > and perhaps was indeed guided in constructing his 43-tone scale > by some of the additional "senses" in which the 14 new (and > original 29) pitches could be taken in MIRACLE.I will continue to take the (partly devil's advocate) stance that this is not the case at all and Partch was really just feeling out modulus-41 while steadfastly maintaining the diamond intact.> > Partch's 14 additional pitches are, as Graham correctly states, > primarily an expansion of the Tonality Diamond in the prime-factor-3 > dimension, which Graham notes is *not* a feature of MIRACLE.Good evidence for my position -- note how well 41-tET approximates prime-factor-3.> About Yasser's proposal, Partch emphasizes that its goal is > not the betterment of intonation, but simply an expansion of > scalar resources. He notes the improved approximations to > 5- and 7-limit ratios, and also that "The ratios of 7 are somewhat > better also, but still with a maximum falsity of 21.4 cents > (33.1 cents in twelve-tone temperament). The ratios of 11 are > not represented at all". Actually, 19-EDO's closest approximations > to the 11-limit ratios are all between +/- 17.1 and 31.5 cents, > significantly better than 12-EDO's.Perhaps Partch *intuitively* understood that 19-tET was not consistent in the 11-limit :)> > [3] Paul (or anyone else in Boston): It still says in the 1974 > edition of _Genesis_ that White's harmonium was housed in a > practice room at New England Conservatory, and that Partch > examined it in 1943. I've found page references in _Genesis_ > that should have been renumbered from the 1st edition and weren't, > so perhaps this is a story that also should have been updated. > Please... go take a look and let us know! >Hmm . . .
Message: 379 - Contents - Hide Contents Date: Mon, 25 Jun 2001 22:25:19 Subject: Re: pairwise entropy minimizer From: Paul Erlich --- In tuning-math@y..., "M. Edward (Ed) Borasky" <znmeb@a...> wrote:>At some point in the > not too distant future, I'm going to see what adaptive simulated annealing does > with the Sethares dissonance function for up to 5 simultaneous tones, each > consisting of 11 harmonic partials. This is the test case I've been using.It would seem that you would want to construct an octave-equivalent version of the Sethares dissonance function for these sorts of exercises. Because if you're interested in scales that repeat themselves every octave, you're really interested in the _interval classes_ from 0 to 600 cents, with octave inversion and/or extension not affecting the dissonance value. You can probably construct such a curve by considering each tone to be a large chord of octave- equivalent notes, equally "loud" in every octave from the lowest registers on up to the highest registers. If you then assume 12 or more harmonic partials for each, you should have no problem obtaining Partch's 29-per-octave diamond as the set of local minima of dyadic dissonance (if you tweak the parameters in a suitable way).
Message: 381 - Contents - Hide Contents Date: Mon, 25 Jun 2001 23:25:02 Subject: Re: Hypothesis revisited From: Dave Keenan --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:> --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote:>> --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:>>>>>> 2. Masses of people over centuries have effectively given > us a >>>>> short>>>>>> list of those they found useful. >> ...>>> I am [objecting to the above sentence]. >>>> I mean the ancient scales that are still in popular use today in >> various cultures. eg. "meantone" diatonic. Arabic scales. Various >> pentatonics. Gamelan scales. >> There are a lot of cultural accidents that lead to "popular use". And > those Gamelan scales . . . you'd need some large unison vectors for > those, wouldn't you?Yeah. Dammit. :-) So neither PBs nor JI seem relevant there, except possibly in a Setharian sense.> Doesn't the 19/72 > generator work as well for Partch's scale as the 7/72 generator?That's a JI minor third, so kleismic, generator. You tell me. How many holes in a chain that encompasses it? How big are the errors?. Maybe on the main list. -- Dave Keenan
Message: 382 - Contents - Hide Contents Date: Mon, 25 Jun 2001 23:28:42 Subject: Re: 41 "miracle" and 43 tone scales From: Dave Keenan --- In tuning-math@y..., Graham Breed <graham@m...> wrote:> Be careful you don't get carried away with these speculations. It seems > plausible that he was feeling for something like 41-equal but with improved > 11-limit harmony.Oh yes, that's certainly still worth considering.> In that case, you'd expect the result to look something like > a 41-note MOS of a good 11-limit temperament. The scale he ends up with does > fit schismic better than Miracle.Please give details. How many holes in a chain that encompasses it. How big are the errors? Are there any overloads? Maybe on the other list. -- Dave Keenan
Message: 383 - Contents - Hide Contents Date: Mon, 25 Jun 2001 23:40:12 Subject: Re: 41 "miracle" and 43 tone scales From: Dave Keenan --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:> I will continue to take the (partly devil's advocate) stance that > this is not the case at allYes. Please do.> and Partch was really just feeling out > modulus-41 while steadfastly maintaining the diamond intact.But Partch did compromise the diamond in the 39 note "Ur" scale, and in just such a way as to reduce its width on a Miracle chain, i.e. deleting the 11/10 and 20/11. -- Dave Keenan
Message: 384 - Contents - Hide Contents Date: Mon, 25 Jun 2001 23:30:55 Subject: Re: pairwise entropy minimizer From: carl@l...>>> >mmm ... multi-dimensional optimization isn't a particularly >>> difficult problem, as long as the function to be optimized is >>> reasonably well behaved. >>>> IIRC, that's the problem with harmonic entropy. >> > Huh? You wrote...>John's spring model works because the objective >function (the function being minimized) is >quadratic in all the input parameters. The full >harmonic entropy curve is clearly not quadratic; >hence this wouldn't work. Based on my education >as a physicist and my profession as a statistician/ >financial engineer, I can tell you that global >optimization of functions with many local optima is >a very icult problem to attack rigorously and is >typically approached with Monte Carlo methods. -Carl
Message: 385 - Contents - Hide Contents Date: Tue, 26 Jun 2001 00:31:32 Subject: Re: pairwise entropy minimizer From: Paul Erlich --- In tuning-math@y..., "M. Edward (Ed) Borasky" <znmeb@a...> wrote:> On Mon, 25 Jun 2001, Paul Erlich wrote: >>> It would seem that you would want to construct an octave- equivalent >> version of the Sethares dissonance function for these sorts of >> exercises. Because if you're interested in scales that repeat >> themselves every octave, you're really interested in the _interval >> classes_ from 0 to 600 cents, with octave inversion and/or extension >> not affecting the dissonance value. You can probably construct such a >> curve by considering each tone to be a large chord of octave- >> equivalent notes, equally "loud" in every octave from the lowest >> registers on up to the highest registers. If you then assume 12 or >> more harmonic partials for each, you should have no problem obtaining >> Partch's 29-per-octave diamond as the set of local minima of dyadic >> dissonance (if you tweak the parameters in a suitable way). >> 1. I'm using Sethares' formulas as given in the book, specifically the Matlab > code version, since there are errors in the Basic code in the book(but not on> his web site.) Rather than break things up as "intrinsic" dissonance, > "interval" dissonance, "triad" dissonance, etc., I combine thepartials in a> list first, and then evaluate the dissonance of the combined "sound". Naturally. > > 2. I started with 7 partials with 1/n scaled amplitude and was unable to > reproduce Partch's scale. I replaced this by 11 partials, all with unit > amplitude, and now I have nice minima at many points of the Partch scale. The > curves have been posted to the files area of this list (I thinkit's this list> :-). When I retain the 11 partials but scale their amplitudes by 1/n, the > whole curve becomes lower -- less dissonant throughout the 1/1 -2/1 range --> and all those nice minima disappear.Exactly the kind of behavior I found with the Sethares stuff.> > 3. I'm interested in the Sethares algorithm essentially as written, with the > built-in adjustments for the spectrum of the tones and the actual physical > frequencies, not in "octave-equivalent" measuresWell, Partch's scale and most other scales are conceived in octave- equivalent form . . . I'm just pointing out that it would be more theoretically consistent to use tones doubled and tripled at multiple octaves for the Sethares calculation when evaluating Partch's "consonances".> or measures based on "small > integer ratios".Huh? What are you referring to here?> Since I'm doing algorithmic composition, I have the "luxury" > of fairly complex processing -- I don't need to deliver a note inreal time at> the command of some MIDI source. Even so, I think I can code the Sethares > dissonance measure to operate at the *control* rate of a digital synthesizer, > given that the amplitudes and frequencies needed for input are also available > at the control rate.Why would you need to do that? Also, keep in mind that Sethares/Plomp dissonance (due to critical band roughness) is only one component of the sensory dissonance we perceive (as amply demonstrated by our listening experiments on the Tuning Lab). This will become very noticeable when you compare otonal hexads with utonal hexads.
Message: 386 - Contents - Hide Contents Date: Tue, 26 Jun 2001 00:33:09 Subject: Re: 41 "miracle" and 43 tone scales From: Paul Erlich --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote:> --- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:>> I will continue to take the (partly devil's advocate) stance that >> this is not the case at all >> Yes. Please do. >>> and Partch was really just feeling out >> modulus-41 while steadfastly maintaining the diamond intact. >> But Partch did compromise the diamond in the 39 note "Ur" scale, and > in just such a way as to reduce its width on a Miracle chain, i.e. > deleting the 11/10 and 20/11. >I replied to this view on the tuning list.
Message: 387 - Contents - Hide Contents Date: Tue, 26 Jun 2001 00:35:02 Subject: Re: pairwise entropy minimizer From: Paul Erlich --- In tuning-math@y..., carl@l... wrote:>>>> Hmmm ... multi-dimensional optimization isn't a particularly >>>> difficult problem, as long as the function to be optimized is >>>> reasonably well behaved. >>>>>> IIRC, that's the problem with harmonic entropy. >>> >> Huh? > > You wrote... >>> John's spring model works because the objective >> function (the function being minimized) is >> quadratic in all the input parameters. The full >> harmonic entropy curve is clearly not quadratic; >> hence this wouldn't work. Based on my education >> as a physicist and my profession as a statistician/ >> financial engineer, I can tell you that global >> optimization of functions with many local optima is >> a very icult problem to attack rigorously and is >> typically approached with Monte Carlo methods. > > -CarlOh, come on, Carl. Name a dissonance function that does _not_ have many local optima.
Message: 388 - Contents - Hide Contents Date: Tue, 26 Jun 2001 01:46:18 Subject: Re: pairwise entropy minimizer From: carl@l...>>>>> >mmm ... multi-dimensional optimization isn't a particularly >>>>> difficult problem, as long as the function to be optimized is >>>>> reasonably well behaved. >>>>>>>> IIRC, that's the problem with harmonic entropy. >>>> >>> Huh? >> >> You wrote... >>>>> John's spring model works because the objective >>> function (the function being minimized) is >>> quadratic in all the input parameters. The full >>> harmonic entropy curve is clearly not quadratic; >>> hence this wouldn't work. Based on my education >>> as a physicist and my profession as a statistician/ >>> financial engineer, I can tell you that global >>> optimization of functions with many local optima is >>> a very icult problem to attack rigorously and is >>> typically approached with Monte Carlo methods. >> >> -Carl >> Oh, come on, Carl. Name a dissonance function that does _not_ have > many local optima.Sounds like you're reading me to say there was a problem with harmonic entropy. Maybe I should have said, that's a property of harmonic entropy which makes the optimization problem difficult. Either way, I wouldn't know. I was simply recalling something you had said in response to my asking why the Monte Carlo approach was necessary, why something like John's approach wouldn't work. Hopefully, this won't obscure the two questions I asked originally, which were... (1) Are there results for scales with numbers of tones other than five? (2) Are there runners-up for the 5-tone case? Generally, are there many significantly-different scales close to the global minima at each cardinality? I think the fact that meantone pentatonics won is fairly interesting, but IIRC they didn't win by very much. In the long run, I'd be interested in finding scales where the total entropy is low and the entropy of the modes are nearly the same. -Carl
Message: 389 - Contents - Hide Contents Date: Tue, 26 Jun 2001 01:53:36 Subject: Re: pairwise entropy minimizer From: Paul Erlich --- In tuning-math@y..., carl@l... wrote:> > Sounds like you're reading me to say there was a problem > with harmonic entropy. Maybe I should have said, that's > a property of harmonic entropy which makes the optimization > problem difficult.Again, can you name a dissonance function which would make the optimization problem easier?> > (1) Are there results for scales with numbers of tones > other than five?Yes . . . see the archives.> > (2) Are there runners-up for the 5-tone case? Generally, > are there many significantly-different scales close to > the global minima at each cardinality?Yes . . . see the archives.> > I think the fact that meantone pentatonics won is fairly > interesting, but IIRC they didn't win by very much. > > In the long run, I'd be interested in finding scales where > the total entropy is lowMeaning total dyadic entropy, or entropy of larger chords?> and the entropy of the modes are > nearly the same.How could they not be the same?
Message: 390 - Contents - Hide Contents Date: Mon, 25 Jun 2001 22:02:19 Subject: ET's and unison vectors From: Herman Miller You've probably seen or made charts of equal tunings sorted by the size of their fifths and major thirds. http://www.io.com/~hmiller/png/et-scales.png - Type Ok * [with cont.] (Wayb.) What's interesting is that the tunings on this chart are lined up in a neat interlocking set of rows, and that the slopes of the lines correspond to 5-limit unison vectors! The row along the top consists of scales that share the unison vector 128/125 (0 -3). They all have 400 cent major thirds, with fifths ranging from small to large: 21, 32, 12, 39, 27, 42, and 15-TET. The line continues off the chart, with 9-TET to the left and 18-TET to the right. Now look at the triangle with 12, 19, and 22-TET at its corners. Outside this triangle is a handful of scales arranged in a pattern of interlocking lines. Inside the triangle is a swarm of scales that fall mainly into the "near-just" category, with all intervals within 5 cents of just; a few of them have minor thirds slightly farther than 5 cents from just, and one (101-TET) has a major third a bit more than 5 cents away from just. The left edge of the triangle consists of meantone scales, with unison vector 81/80 (4 -1). From top to bottom: 12, 67, 55, 98, 43, 117, 74, 105, 31, 81, 50, 69, 88, and 19-TET. Continuing onward, 45 and 26-TET lie along the same line. The right edge of the triangle consists of diaschismic scales, with unison vector 2048/2025 (-4 -2). There's actually a pretty good number of scales in this family: 12, 70, 58, 46, 126, 80, 114, 148, 34, 124, 90, 56, 78, 22-TET on the edge of the triangle, plus 54 and 32-TET if you continue the line to the lower right. The bottom edge of the triangle, from 19-TET to 22-TET, consists of scales with slightly narrow major thirds, sharing a unison vector of 3125/3072 (-1 5). Five major thirds up equals a fifth plus an octave. The sequence goes: 19, 79, 60, 41, 104, 63, 85, 107, 22-TET. Also along the same line are 35-TET, to the left, and 25-TET, to the right. The schismic temperaments, with unison vector 32805/32768 (8 1), are collected on a line that goes straight through the middle of the swarm of near-just tunings. There seem to be quite a few of these. 53-TET lies on a major 3-way intersection near the center of the chart. Scattered around the outside of the triangle are a number of small groups of tunings in an interlocked pattern of lines; here are a few of the more obvious ones. (-4 -5) : (12) 73 61 49 37 (25) (8 7) : (12) 95 83 71 59 (4 -4) : (12) 64 52 40 28 (3 4) : 28 47 19 48 29 (-2 7) : 26 29 32 (5 -3) : 37 59 22 51 29 Off the chart to the left is the tiny series 11, 9, 16, 23-TET, with the unison vector 135/128 (3 1). Below the chart is the even smaller series 13, 10, 17-TET with the unison vector 25/24 (-1 2). 7-TET sits at the intersection of these two lines, on a vertical line together with a few other multiples of 7-TET, with 14-TET above the chart. 5-TET and 8-TET are way off by themselves up and to the right of the chart. 6-TET is so far off to the right that it might as well be on another planet. -- see my music page ---> ---<The Music Page * [with cont.] (Wayb.)>-- hmiller (Herman Miller) "If all Printers were determin'd not to print any @io.com email password: thing till they were sure it would offend no body, \ "Subject: teamouse" / there would be very little printed." -Ben Franklin
Message: 391 - Contents - Hide Contents Date: Tue, 26 Jun 2001 02:24:18 Subject: Re: ET's and unison vectors From: Paul Erlich --- In tuning-math@y..., Herman Miller <hmiller@I...> wrote:> You've probably seen or made charts of equal tunings sorted by the size of > their fifths and major thirds. > > http://www.io.com/~hmiller/png/et-scales.png - Type Ok * [with cont.] (Wayb.) > > What's interesting is that the tunings on this chart are lined upin a neat> interlocking set of rows, and that the slopes of the lines correspond to > 5-limit unison vectors!You're so cool, Herman! This chart looks almost exactly like the plots I did of the triads within the early part of the harmonic series . . . spooky.> > The bottom edge of the triangle, from 19-TET to 22-TET, consists of scales > with slightly narrow major thirds, sharing a unison vector of 3125/3072 (-1 > 5). Five major thirds up equals a fifth plus an octave.Apparently, this is called the small diesis. This must me one of the unison vectors of the 10-note chain-of-major-thirds scale that comes up from time to time.> (-4 -5) : (12) 73 61 49 37 (25) > (8 7) : (12) 95 83 71 59 > (4 -4) : (12) 64 52 40 28 > (3 4) : 28 47 19 48 29 > (-2 7) : 26 29 32 > (5 -3) : 37 59 22 51 29 > > Off the chart to the left is the tiny series 11, 9, 16, 23-TET, with the > unison vector 135/128 (3 1). Below the chart is the even smaller series 13, > 10, 17-TET with the unison vector 25/24 (-1 2). 7-TET sits at the > intersection of these two lines, on a vertical line together with a few > other multiples of 7-TET, with 14-TET above the chart. 5-TET and 8- TET are > way off by themselves up and to the right of the chart. 6-TET is so far off > to the right that it might as well be on another planet.Herman, you rock!
Message: 393 - Contents - Hide Contents Date: Tue, 26 Jun 2001 02:40:51 Subject: Re: pairwise entropy minimizer From: Paul Erlich --- In tuning-math@y..., "M. Edward Borasky" <znmeb@a...> wrote:> The general plan is to do more or less free stochastic music as Xenakis > defines it, except that all the tones will be constrained to the Partch > 11-limit JI. What I want to do is define a musical space in terms of the > Partch concepts of Monophony -- 11-limit JI, the 28 tonalities, the > one-footed bride (this is where Sethares comes in -- I'm using the Sethares > algorithm because I understand it), etc. Then the algorithm will explore > that space. If the algorithm produces utonal hexads that sound worse than > otonal hexads, I'll tweak it.Couldn't you decide whether utonal hexads sound worse that otonal hexads _before_ you implement or even decide upon any algorithm? But actually this may be a moot point for your artistic goals, since Partch himself put otonal and utonal on an equal footing, so if you're trying to emulate Partch, you may wish to retain that status.
Message: 395 - Contents - Hide Contents Date: Sun, 25 Jun 2000 20:20:42 Subject: Re: 41 "miracle" and 43 tone scales From: monz> ----- Original Message ----- > From: Dave Keenan <D.KEENAN@U...> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Monday, June 25, 2001 10:25 AM > Subject: [tuning-math] Re: 41 "miracle" and 43 tone scales > > > --- In tuning-math@y..., "monz" <joemonz@y...> wrote:>>>> It was Erv Wilson who hypothesized that Partch was intuitively >>>> "feeling out" a version of 41-EDO where two of the pitches could >>>> imply either of a pair of ratios (12/11 and 11/10, and their >>>> "octave"-complements). >>>>>> Actually, the pair was 11/10 and 10/9 . . . you don't get a >>> PB or CS the other way. >>>> OK, I understand that *theoretically* this is the elegant >> comparison. >> >> But we had a discussion about this around two years ago... >> >> Didn't Daniel Wolf present cases in Partch's actual compositions >> where either pair could be interchangeable? That's what I remember. >> It's interesting that Miracle distinguishes all three of these ratios, > as Partch did. > > 11:12 is -9 generators > 10:11 is 22 generators > 9:10 is -19 generatorsYes, Dave, exactly! This is another reason why I tend to agree with Graham's speculations (and yours?) that Partch was intuitively "feeling out" MIRACLE even moreso than 41-EDO. (BTW, I made a webpage out of that post I sent earlier today ... unfortunately, didn't finish it before I had to go to work. Coming soon, to a web-browser near you...) -monz Yahoo! GeoCities * [with cont.] (Wayb.) "All roads lead to n^0" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 396 - Contents - Hide Contents Date: Sun, 25 Jun 2000 20:25:35 Subject: Re: 41 "miracle" and 43 tone scales From: monz> ----- Original Message ----- > From: monz <joemonz@y...> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Sunday, June 25, 2000 12:58 PM > Subject: Re: [tuning-math] Re: 41 "miracle" and 43 tone scales > > > ... Actually, 19-EDO's closest approximations > to the 11-limit ratios are all between +/- 17.1 and 31.5 cents, > significantly better than 12-EDO's. > > Partch had mentioned in "Chapter 15: A Thumbnail Sketch of the > History of Intonation" that King Fang (in China) and Mersenne, > Kircher, and Mercator (in Europe) all proposed this tuning.Sorry... I had shifted some text around and left this bit unedited by mistake. That last clause should read "... all proposed 53-EDO". -monz Yahoo! GeoCities * [with cont.] (Wayb.) "All roads lead to n^0" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 397 - Contents - Hide Contents Date: Tue, 26 Jun 2001 03:36:00 Subject: Re: 41 "miracle" and 43 tone scales From: jpehrson@r... --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote: Yahoo groups: /tuning-math/message/329 * [with cont.]> Sorry about the previous message, sent by mistake. > > --- In tuning-math@y..., jpehrson@r... wrote:>> I'm getting a little confused here... Did Harry Partch use a >> 41-tone scale in addition to his 43-tone scale?? >> Sure. There are two in the Scala archive, But that's not what I meant. >>> He never actually used "Miracle 41" did he?? >> No. I didn't say that either. But he might not have noticed if someone > had substituted a scale which was MIRACLE-41 plus a couple of extra > notes from MIRACLE-45. > > Read: > http://www.anaphoria.com/secor.PDF - Type Ok * [with cont.] (Wayb.) > and > Lattices with Decimal Notation * [with cont.] (Wayb.) > and then tell me what you don't understand. > > Regards, > -- Dave Keenan Hi Dave...I guess what I'm understanding is that some of the "fill in" notes that Partch used to complete his 43-tone scale could be described by the "miracle generator..." Am I on the right track?? ___________ __________ _______ Joseph Pehrson
Message: 398 - Contents - Hide Contents Date: Sun, 25 Jun 2000 20:36:53 Subject: Re: 41 "miracle" and 43 tone scales From: monz> ----- Original Message ----- > From: Paul Erlich <paul@s...> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Monday, June 25, 2001 3:15 PM > Subject: [tuning-math] Re: 41 "miracle" and 43 tone scales > > > --- In tuning-math@y..., "monz" <joemonz@y...> wrote: >>> But Graham's speculations are intriguing, and I'm fairly convinced >> by them that Partch *intuitively* understood the MIRACLE concept >> and perhaps was indeed guided in constructing his 43-tone scale >> by some of the additional "senses" in which the 14 new (and >> original 29) pitches could be taken in MIRACLE. >> I will continue to take the (partly devil's advocate) stance that > this is not the case at all and Partch was really just feeling out > modulus-41 while steadfastly maintaining the diamond intact.OK, Paul... I can see your point of view as well. But I find it *more* than very interesting that Partch knew about 31-EDO's good approximations to a significant percentage of his scale, and chose to say *nothing* about it!> Perhaps Partch *intuitively* understood that 19-tET was not > consistent in the 11-limit :)Yes, that's a very good suggestion. And in an earlier post, Paul wrote:> --- In tuning-math@y..., "Dave Keenan" <D.KEENAN@U...> wrote: >>>> All that means is that Partch wasn't intentionally using Miracle >> and that Wilson missed the fact that Partch's scales imply it. > >> "Imply" is a little strong. I'd say "suggest".Hmmm... I think you have a very good point there, Paul. "Suggest" is more likely what I mean too, when I said "imply". -monz Yahoo! GeoCities * [with cont.] (Wayb.) "All roads lead to n^0" _________________________________________________________ Do You Yahoo!? Get your free @yahoo.com address at Yahoo! Mail - The best web-based email! * [with cont.] (Wayb.)
Message: 399 - Contents - Hide Contents Date: Tue, 26 Jun 2001 04:07:04 Subject: Re: pairwise entropy minimizer From: Paul Erlich --- In tuning-math@y..., "M. Edward Borasky" <znmeb@a...> wrote:> >> -----Original Message----->> From: Paul Erlich [mailto:paul@s...] >> Sent: Monday, June 25, 2001 7:41 PM >> To: tuning-math@y... >> Subject: [tuning-math] Re: pairwise entropy minimizer > >> Couldn't you decide whether utonal hexads sound worse that otonal >> hexads _before_ you implement or even decide upon any algorithm? >> >> But actually this may be a moot point for your artistic goals, since >> Partch himself put otonal and utonal on an equal footing, so if >> you're trying to emulate Partch, you may wish to retain that status. >> Well ... I'm trying to emulate both Partch and Xenakis ... I was in fact > planning to give otonal and utonal equal status.Well then dyadic consonance measures will be fine.> Now that I think about it > though, aren't utonal and otonal hexads identical? There's only one hexad -- > 1:3:5:7:9:11 -- right???No -- that, along with its many octave-equivalents (such as 7:8:9:10:11:12) is an otonal hexad. The utonal hexad is 1/11:1/9:1/7:1/5:1/3:1/1, along with its many octave equivalents (such as 1/12:1/11:1/10:1/9:1/8:1/7). Why don't you listen to various voicings of these and tell us what you think.
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