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126 7-limit linears   Message List  
Reply | Forward Message #9317 of 17519 |
23 "pro-moated" 7-limit linear temps, L_1 complex.(was: Re: 126 7-limit linears)

> 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:

http://groups.yahoo.com/group/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




Sun Feb 8, 2004 9:36 pm

paulerlich
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Message #9317 of 17519 |
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... riiight . . . ... Of course not -- it has infinite complexity according to any of the charts, since it exceeds the dimension being considered. ... seems ...
Paul Erlich
paulerlich
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Feb 9, 2004
11:34 pm

... 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 ...
Paul Erlich
paulerlich
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Feb 8, 2004
9:37 pm

... I prefer to put the scaling constants inside the exponentiation like this (err/15.8)^(2/3) + (complexity/28.6)^(2/3) < 1. Then you can see at a glance what...
Dave Keenan
dkeenanuqnetau
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Feb 9, 2004
12:58 am

... 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...
Dave Keenan
dkeenanuqnetau
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Feb 9, 2004
1:09 am

... can't ... Thanks Dave!...
Paul Erlich
paulerlich
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Feb 9, 2004
11:36 pm

... that an ... like this ... chart ... ago) ... The badness measure is only "implied" by the above; as you know, I don't favor using actual badness measures....
Paul Erlich
paulerlich
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Feb 9, 2004
11:31 pm

Hi Gene, Would you be so kind as to produce a file like the one below, but instead of culling to 126 lines, leave all 32201 in there? That would be great. If...
Paul Erlich
paulerlich
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Apr 4, 2004
11:22 pm

... would ... I could either upload something or email it. Which is better? ... Not unless I write code to fully automate the process first. Are we getting...
Gene Ward Smith
genewardsmith
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Apr 5, 2004
12:45 am

... a ... should ... Uploading keeps things public. If that doesn't work, e-mail. ... for ... John Chalmers just reneged on his much earlier reneging of having...
Paul Erlich
paulerlich
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Apr 5, 2004
1:23 am

... A little has been organized on my web site. I'm wondering again about what and where to publish, after having seen what's gotten published lately. There's...
Gene Ward Smith
genewardsmith
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Apr 5, 2004
2:41 am

... about ... So do I -- particularly the projects that mean most to me. This is why I have composed so little. You've done me better -- many, many better --...
Paul Erlich
paulerlich
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Apr 5, 2004
10:44 pm

... Thanks, Paul. I only have one website: www.xenharmony.org...
Gene Ward Smith
genewardsmith
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Apr 5, 2004
11:46 pm

... going to ... forever? ... again about ... published ... up ... Yes, please write the book. I'll bet if you set aside a couple of weeks to concentrate on a...
gooseplex
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Apr 7, 2004
1:08 am

... I presume you want TOP error, but what complexity do you want? Should I use logflat badness? This will take some amount of time to compute, so I want to...
Gene Ward Smith
genewardsmith
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Apr 6, 2004
8:22 am

... The same complexity you used there, when you culled to 126 (just click "up thread" repeatedly if you forgot). It was the L1 kind. ... No badness figure...
Paul Erlich
paulerlich
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Apr 7, 2004
9:30 am

Hi Gene, I hope you're making progress on un-culling the list. Would it be rude of me to request a similar list for 11- limit 'linears'? Dave told me I should...
Paul Erlich
paulerlich
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Apr 10, 2004
10:08 pm

... I think I'll finish by today. ... and ... I think getting a big list of 11-limits would be nice. I hope I don't need to get 32000....
Gene Ward Smith
genewardsmith
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Apr 11, 2004
7:55 pm

... Awesome! ... don't ... As long as we're sure we're getting a complete list up to some fairly modest error and complexity bounds, I'm happy. I hope to ...
Paul Erlich
paulerlich
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Apr 11, 2004
9:27 pm
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