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Message: 9875 - Contents - Hide Contents Date: Sun, 08 Feb 2004 20:44:08 Subject: Re: Jamesbond in 14-et From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> Did you see the horagram I posted?You posted a lot of horagrams. So far I've not seen what you can do with them you can't do with a little algebra, but maybe this horagram will make me see the point of it all. Which one is it?
Message: 9876 - Contents - Hide Contents Date: Sun, 08 Feb 2004 21:32:03 Subject: Re: Beep isn't useless.... From: Herman Miller Dave Keenan wrote:> What qualifies this tune as a good test of a temperament's > approximation of 7-limit JI? It seems the tune was not composed for > 7-limit JI and you are even unsure of how it should be mapped to > 7-limit JI.I don't think of it so much as a test of how well a temperament approximates JI (you can look at the numbers for that). My original thought was that the ambiguity inherent in 14-ET would allow me to choose a different mapping for each temperament that would suit the individual temperament. Then I found a mapping that seemed to work well for a lot of different temperaments, so I decided to use that as a basis for comparison. But I still think I'm going to want to use different JI mappings to illustrate the characteristic features of the different temperaments. A scale that works well in meantone won't be much good for kleismic or magic. If I had an original piece that was unambiguous, I wouldn't have that flexibility. But I need to translate it to some version of 7-limit JI to begin with so that I can apply the temperament. In any case, the point is that a tuning that seemed useless, after a bit of experimentation, turned out to have some attractive features after all.> The Canon was ideal for 5-limit as there was no such doubt. > > Can't we find some "classic" 7-limit-JI piece that demonstrates a lot > of different 7-limit consonances and cadences, and warp that?It's hard enough to find "classic" 5-limit JI! It's not hard to find something that could imply 7-limit harmony, but finding something that doesn't at the same time exploit the meantone comma is going to be tricky. Possibly Beethoven's Moonlight Sonata (minus the second movement) might do the trick. Actually, I've thought about doing a Warped Moonlight page, but never got around to it. I'm sure if I could find some piece that was written with 7-limit JI in mind (assuming that one could be found that's in the public domain), it'd be better suited for tuning comparison than something awkwardly written in 14-ET by a programmer who likes music (not that there's a long tradition of well-written composition in 14-ET to compare with). What I'm more interested in right now is figuring out which temperaments seem the most useful for new music, and the Warped Egress page is a bit of fallout from the sort of experimentation that I'm doing with these tunings to get a general feel for what they sound like (in the same way that Porcupines in the Moonlight was a spinoff of my Zireen kleismic scale experimentation). But then, maybe I'd be better off putting together a page on Zireen music theory, with fragments of actual Zireen music to illustrate the different temperaments......
Message: 9877 - Contents - Hide Contents Date: Sun, 08 Feb 2004 20:48:50 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> > wrote: >> >>>> I>>>> think using log(err) and log(complexity) makes far more sense. >>>>>> I don't think they make more sense practically. >>>> I think they probably will make more sense both practically and >> theoretically, >> As I see it, no way.You've taken me seriously enough to at least looked at it, or are you just blowing the issue off? Example: when you look at the graph with log> (err) as one of the axes, the indication is that JI is infinitely far > away. This is ridiculous.No it isn't. JI has *zero error*! The JI line should be right there, with> some temperaments many times more distant from it than others. > Otherwise, you're operating in the realm of hopelessly impractical > abstraction.It's what we've been doing, in effect, for the last few years, so this argument makes no sense at all to me.>> but you've been ignoring this issue. Are you going to >> think about it, at least? >> Countless hours already spent thinking about it, and discussing it > here.The only one who seems to have thought about it is me. I've been trying to get you to at least think about it, so far with no success. Do you care about convincing the rest of us that what you are doing makes a particle of sense, or is it going to be a committee of two?
Message: 9878 - Contents - Hide Contents Date: Sun, 08 Feb 2004 21:36:15 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Paul Erlich> A bit more concavity still and we include > > 45. BlackwoodFollowing what Dave did for the 5-limit and ET cases, I found that an exponent of 2/3 produces the desired moat, for example when err^(2/3)/6.3+complexity^(2/3)/9.35 < 1. Please look at the resulting graph: Yahoo groups: /tuning_files/files/Erlich/7lin2... * [with cont.] The temperaments in thie graph are identified by their ranking according to the badness measure implied above: 1. Huygens meantone 2. Pajara 3. Magic 4. Semisixths 5. Dominant Seventh 6. Tripletone 7. Negri 8. Hemifourths 9. Kleismic/Hanson 10. Superpythagorean 11. Injera 12. Miracle 13. Biporky 14. Orwell 15. Diminished 16. Schismic 17. Augmented 18. 1/12 oct. period, 25 cent generator (we discussed this years ago) 19. Flattone 20. Blackwood 21. Supermajor seconds 22. Nonkleismic 23. Porcupine Here is the data for first three wedgie entries and implied badness, for the implied top 32: 1 4 10 0.68784 2 -4 -4 0.78033 5 1 12 0.78742 7 9 13 0.78759 1 4 -2 0.82001 3 0 -6 0.83995 4 -3 2 0.86556 2 8 1 0.87254 6 5 3 0.87815 1 9 -2 0.88068 2 8 8 0.89638 6 -7 -2 0.90191 6 10 10 0.9041 7 -3 8 0.91204 4 4 4 0.91347 1 -8 -14 0.91872 3 0 6 0.93351 0 0 12 0.93521 1 4 -9 0.93554 0 5 0 0.9488 3 12 -1 0.9593 10 9 7 0.95971 3 5 -6 0.97257 9 5 -3 1.0207 8 6 6 1.0259 6 -2 -2 1.0335 6 5 22 1.0337 3 12 11 1.0342 2 -9 -4 1.0395 11 13 17 1.0435 6 10 3 1.0498 4 2 2 1.0499
Message: 9879 - Contents - Hide Contents Date: Sun, 08 Feb 2004 21:39:35 Subject: Re: Jamesbond in 14-et From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: >>> Did you see the horagram I posted? >> You posted a lot of horagrams. So far I've not seen what you can do > with them you can't do with a little algebra,"A little algebra" to you is "a little forbidding" for most musicians.> but maybe this horagram > will make me see the point of it all. Which one is it?jamesbond.bmp, zipped inside Yahoo groups: /tuning_files/files/Erlich/seven... * [with cont.]
Message: 9880 - Contents - Hide Contents Date: Sun, 08 Feb 2004 21:44:38 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:>> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> >> wrote:>>> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> >> wrote: >>> >>>>> I>>>>> think using log(err) and log(complexity) makes far more sense. >>>>>>>> I don't think they make more sense practically. >>>>>> I think they probably will make more sense both practically and >>> theoretically, >>>> As I see it, no way. >> You've taken me seriously enough to at least looked at it, or are you > just blowing the issue off?What, you didn't believe me when I said "countless hours"?>> Example: when you look at the graph with log >> (err) as one of the axes, the indication is that JI is infinitely far >> away. This is ridiculous. >> No it isn't. JI has *zero error*!Yes, that's very different from "minus infinity error"!>> The JI line should be right there, with >> some temperaments many times more distant from it than others. >> Otherwise, you're operating in the realm of hopelessly impractical >> abstraction. >> It's what we've been doing, in effect, for the last few years, so this > argument makes no sense at all to me.The only criterion for making sense is agreeing with habit? Why don't you actually take me seriously enough to at least look at it, instead of blowing the issue off?>>> but you've been ignoring this issue. Are you going to >>> think about it, at least? >>>> Countless hours already spent thinking about it, and discussing it >> here. >> The only one who seems to have thought about it is me.Then you must not be reading our posts.>I've been > trying to get you to at least think about it, so far with no >success.What would count as "thinking about it" to you? Agreeing with you?> Do you care about convincing the rest of us that what you are doing > makes a particle of sense, or is it going to be a committee of two?Not only have we tried to be completely explicit and impartial in our logic, but you may note that Herman's guidelines had a very big influence on us. How big is the committee that thinks log-flat has any practical relevance?
Message: 9881 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:42:43 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma>> >'m sorry it came across that way. But the fact is we had already >> thought about it and found it too extreme, not possible to match up >> with the historical data (vague though that is). Sorry we didn't >> spell that out. >>It would be nice if some attempt was made to bring the rest of us on >board. I don't know what Carl or Graham think, but I have not been >convinced.My latest position is that I can live with log-flat badness with appropriate cutoffs. The problem with anything more tricky is that we have no data. Not vague historical data, actually no data. By putting all this energy into the list of temperaments, we're loosing touch with reality. Rather than worry about what is and isn't on the list, I'd like to figure out why Paul's creepy complexity gives the numbers it does. But as long as Dave and Paul were having fun I didn't want to say anything. They have a way of coming up with neat stuff, though so far their conversation has been impenetrable to me. -Carl
Message: 9882 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:22:05 Subject: Re: Jamesbond in 14-et From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> "A little algebra" to you is "a little forbidding" for most musicians.My aging eyes have more trouble with these things than yours do also, I suspect.
Message: 9883 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:48:19 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma>At one stage Carl gave some good arguments why the cutoff might be >as far from loglog as > >err^2 + k * comp^2 < xYes, I think I did say that, in multiplicitive form.>And I went along with this until I saw the ET plots.Ok, can you recommend a plot to look at, and what you saw that changed your mind? None of the plots I've seen have been labeled nor made any sense to me.>Perhaps this >still makes sense as a badness measure for ranking temperaments, but >not as a cutoff for what to include in an article. But I'm not even >sure if that's a coherent suggestion. Which suggestion? -Carl
Message: 9884 - Contents - Hide Contents Date: Sun, 08 Feb 2004 16:17:38 Subject: Re: Some warped egresses From: Herman Miller Gene Ward Smith wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote: >>> I think I've found a couple of good JI approximations for retuning >> _Egress_. The first one is a nice symmetrical looking one with lots of >> consonances, which looks like it'd work nicely with any of the >> pelog-type approximations, and would also work as 14 consecutive steps >> of meantone, Fb-B. >> >> 404 Not Found * [with cont.] Search for http://www.io.com/~hmiller/midi/egress/egress-jimajor.mid in Wayback Machine >> >> 0 0 0 0 0 ! Bb 5/4 -2 0 1 0 >> 1 -2 1 -1 1 ! B > >> This looks as if it should be 2 * 3^(-2) * 5 * 7^(-1) * 11 = 110/63, > but instead it's |-2 1 -2 1> = 21/20.The first column of MIDICONV tuning files is just the note number.
Message: 9885 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:38:34 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> What, you didn't believe me when I said "countless hours"?I'll believe it when I see the log-log plots I've been trying to get you to do, with no success.>> The only one who seems to have thought about it is me. >> Then you must not be reading our posts.Which ones addressed this issue?>> I've been >> trying to get you to at least think about it, so far with no >> success. >> What would count as "thinking about it" to you? Agreeing with you?Some evidence you've actually considered it would be nice. A plot would be grand. Some attempt to theoretically justify what you two are doing would be appreciated.
Message: 9886 - Contents - Hide Contents Date: Sun, 08 Feb 2004 23:56:24 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma>>> >t one stage Carl gave some good arguments why the cutoff might be >>> as far from loglog as >>> >>> err^2 + k * comp^2 < x >>>> Yes, I think I did say that, in multiplicitive form. >>>>> And I went along with this until I saw the ET plots. >>>> Ok, can you recommend a plot to look at, and what you saw that >> changed your mind? None of the plots I've seen have been labeled >> nor made any sense to me. >>Those Paul gave in > >Yahoo groups: /tuning-math/message/9202 * [with cont.] > >Particularly the 5-limit one, which I assume most people have the >greatest feel for. > >Complexity is horizontal, error is vertical, Aha. >labels are the notes per octave of the ET.How can error be in notes?>>> Perhaps this >>> still makes sense as a badness measure for ranking temperaments, but >>> not as a cutoff for what to include in an article. But I'm not even >>> sure if that's a coherent suggestion. >> >> Which suggestion? >>That something might make a good badness measure for ranking temps but >not be good for determining a cutoff. I'd like to retract that now. Ok. -Carl
Message: 9887 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:39:56 Subject: Re: Some warped egresses From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote:> The first column of MIDICONV tuning files is just the note number.Why not tell us that?
Message: 9888 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:46:38 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote: >>> What, you didn't believe me when I said "countless hours"? >> I'll believe it when I see the log-log plots I've been trying to get > you to do, with no success.I've posted quite a few log-log plots, thanks very much. Seeing them is what made me realize that they assume JI is infinitely far away, and how absurd that is.>>> The only one who seems to have thought about it is me. >>>> Then you must not be reading our posts. >> Which ones addressed this issue?All the ones about 5-limit linear temperaments and about ETs in various limits.>>> I've been >>> trying to get you to at least think about it, so far with no >>> success. >>>> What would count as "thinking about it" to you? Agreeing with you? >> Some evidence you've actually considered it would be nice. A plot > would be grand.OK, what would you like me to plot that I haven't already plotted? I've looked at every single plot I've posted in both log-log and linear axes, just out of curiosity, but none of them change the fact that considering JI to be infinitely far away is like agreeing with Zeno that you can never traverse a room. Any measure of the "pain" of error will not predict this infinite distance, if it has any connection with the real world.> Some attempt to theoretically justify what you two are > doing would be appreciated.Dave and I just recently shared some new theoretical insights, I thought. Carl sort of got hooked in too, on the "rectangular badness" issue. Why don't you take some time and re-read what you glossed over -- I've glossed over reading things before, but I think I've been pretty comprehensive since last month.
Message: 9889 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:53:10 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Paul Erlich --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:> A plot > would be grand.Here's the log-log version of the most recent plot: groups.yahoo.com/group/tuning_files/files/Erlich/7lin23loglog.gif
Message: 9890 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:54:36 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> I've posted quite a few log-log plots, thanks very much.For instance? Don't assume I can see how you label the axes easily, because I can't. Seeing them> is what made me realize that they assume JI is infinitely far away, > and how absurd that is. >>>>> The only one who seems to have thought about it is me. >>>>>> Then you must not be reading our posts. >>>> Which ones addressed this issue? >> All the ones about 5-limit linear temperaments and about ETs in > various limits.For instance? Can you show me specifically?>> Some attempt to theoretically justify what you two are >> doing would be appreciated. >> Dave and I just recently shared some new theoretical insights, I > thought.What insights? I've seen you say things which didn't register to me as making sense, but I could be missing something. What, exactly, are you up to? Carl sort of got hooked in too, on the "rectangular badness"> issue. Why don't you take some time and re-read what you glossed > over -- I've glossed over reading things before, but I think I've > been pretty comprehensive since last month.Can you say what, in particular, I should read, which has the theory in it?
Message: 9891 - Contents - Hide Contents Date: Sun, 08 Feb 2004 22:58:22 Subject: A post with pending questions From: Paul Erlich 9052
Message: 9892 - Contents - Hide Contents Date: Sun, 08 Feb 2004 23:22:00 Subject: Loglog From: Gene Ward Smith I checked the files I saved of the graphs being posted, and found no loglog examples. I then went over to tuning-files, and found one example, uploaded today. I can't tell by looking at it what the logs are logs of, however. Clarifying this would be nice. It would also be nice if, having created all these loglog images, they were made available to the rest of us.
Message: 9893 - Contents - Hide Contents Date: Sun, 08 Feb 2004 23:31:28 Subject: Re: A post with pending questions From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:> 9052I thought this was supposed to be a guessing game to which you knew the answer. If you meant to ask a real question I wish you would have made that clearer. Are you asking to find a hypothetical norm here?
Message: 9894 - Contents - Hide Contents Date: Mon, 09 Feb 2004 01:01:30 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:> --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> > wrote: >>> Some evidence you've actually considered it would be nice. A plot >> would be grand. Some attempt to theoretically justify what you two are >> doing would be appreciated. >> I'm not sure what "it" is that you think we haven't considered.The "it" is using log(complexity) and log(error) in drawing moats, and trying to make the moats involve straight lines if possible. Paul thinks JI is a temperament too and should be on the chart somewhere, which I think is an absurd thing to worry about. What's your view?> And by "theoretically justify" do you mean justify purely from > mathematical considerations?I mean that combining error and complexity, and not their logs, seems a little like adding the distance to the moon in inches to the gross national product in dollars--where's the justification that we are talking about something comparable?> I understand you're still in favour of log-flat cutoffs which can be > written in the form > log(err) + k * log(complexity) < xThose seem to me to make more sense logically.> Paul and I have been considering those of the form > > err^p + k * comp^p < x > > which can be made to look a lot like the previous one when 0<p<0.5.Which is what I thought. Why then the fanatical opposition to even thinking about it?> And we find that what works best is a value of p that's slightly less > than one, i.e. the cutoff functions that we construct based on our > knowledge of which ETs have been popular historically, are somewhere > between log and linear, but much closer to linear.This is based on actually looking at loglog charts?> But rather than trying to come up with precise values for p and the > scaling constants for cutoffs, we are looking for what we call > "moats". These are places where moderate changes in these constants > will make no difference to which temperaments are included.I'd like to put this moat business on a theoretical basis which makes sense to me, and a good way to start would be shifting to loglog. I really don't see why that idea is so horrible. Of course if we must use curved lines the difference between the approaches is less important, but first can we show it is somehow better to use curved lines?
Message: 9896 - Contents - Hide Contents Date: Mon, 09 Feb 2004 01:09:10 Subject: 23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears) From: Dave Keenan I wrote:> This looks reasonable to me as a cutoff, although maybe still too > many, ...After more careful examination, I find this moat to be ideal. I can't find one closer to the origin without leaving out temperaments I really wouldn't want to leave out. Well done.
Message: 9898 - Contents - Hide Contents Date: Mon, 09 Feb 2004 23:14:07 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma>> >or musicians, I'd make the list 5 for each limit; 10 tops. For >> people reading a theory paper, 20 would be interesting. >>Ridiculous. I've *composed* in about that many temperaments.You're not a professional musician, are you? -Carl
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