> 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