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Message: 9878 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. Blackwood Following 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/7lin23.gif * 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 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/sevenlimit.zip *
Message: 9880 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 Date: Sun, 08 Feb 2004 22:42:43 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma >> I'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: 9883 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 < 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. >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: 9886 Date: Sun, 08 Feb 2004 23:56:24 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 < 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 * > >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: 9888 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 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: 9891 Date: Sun, 08 Feb 2004 22:58:22 Subject: A post with pending questions From: Paul Erlich 9052
Message: 9896 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 Date: Mon, 09 Feb 2004 23:14:07 Subject: Re: 23 "pro-moated" 7-limit linear temps From: Carl Lumma >> For 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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