This time, major seventh chord wins, followed by five minor seven th chords!

There was no justification for assuming that the 6 diadic entropy values
should simply be summed for each tetrad. Another approach would be to
exponentiate them before summing. For simple ratios, this would be like
summing the n*d complexities of the 6 diads (an approach Pierre Lamonthe
used in a private e-mail). The resulting ranking of those 125 tetrads is, I
feel, more palatable:

bass is always 0

rank tenor alto soprano name
1. 386 702 1088 5-lim maj7
2. 316 702 1018 5-lim min7
3-4. 388 702 886 5-lim min7 1st inv
3-4. 184 498 886 5-lim min7 3rd inv
5. 498 886 1384 5-lim min7 2nd inv (open voicing)
6. 268 702 970 7-lim min7
7-8. 184 388 886 5-lim min 1st inv add4
7-8. 498 702 886 5-lim maj 2nd inv add2
9-10. 204 702 1088 5-lim maj 2nd inv / 4
9-10. 386 884 1088 5-lim min 1st inv add9
11-12. 302 502 1004 ~12-tET 7sus4 2nd inv
11-12. 502 702 1004 ~12-tET 7sus4
13. 202 500 702 ~12-tET7sus4 1st inv
14-15. 204 388 702 5-lim maj add2
14-15. 314 498 702 5-lim min add4
16. 492 980 1472 ~22-tET 7sus4 2nd inv (open voicing)
17-18. 186 576 888 5-lim dom7 3rd inv
17-18. 312 702 888 5-lim hlf-dim7 1st inv
19-20. 502 1002 1390 5-lim maj 2nd inv / 2
19-20. 388 888 1390 5-lim min 1st inv add11
21-22. 384 588 1086 5-lim maj7 #11 no5
21-22. 498 702 1086 5-lim maj7 sus4
23-24. 318 816 1020 5-lim maj 1st inv add9
23-24. 204 702 1020 5-lim min 2nd inv / 4
25-26. 268 582 970 7-lim hlf-dim7
25-26. 388 702 970 7-lim dom7

I'l tell you again that ranks of mirror-image tetrads always tied. Other
than that, you're on your own for the rest of this list:

388 886 1274
272 772 974
202 702 974
204 432 702
270 498 702
388 776 1090
314 702 1090
316 630 1018
388 702 1018
264 650 966
316 702 966
388 578 886
308 498 886
272 702 886
184 614 886
314 498 812
182 448 884
436 702 884
196 582 1080
498 884 1080
316 584 1018
434 702 1018
188 500 1000
500 812 1000
272 702 1088
386 816 1088
500 816 1316
498 888 1282
394 784 1282
318 818 1320
502 1002 1320
500 886 1320
434 820 1320
382 646 1084
438 702 1084
262 702 1026
324 764 1026
266 436 702
260 702 1142
440 882 1142
314 584 812
228 498 812
386 582 968
310 578 888
268 582 1080
498 812 1080
188 498 812
314 624 812
266 578 886
308 620 886
190 500 778
278 588 778
192 582 970
388 778 970
312 810 1122
310 586 1084
498 774 1084
196 388 584
442 884 1326
498 810 1120
310 622 1120
316 814 966
152 650 966
238 622 884
262 646 884
196 390 780
390 584 780
386 652 968
316 582 968
390 626 1016
238 628 1020
392 782 1020
208 592 800
200 586 812
226 612 812
432 818 1020
202 588 1020
386 584 816
232 430 816
266 448 884
436 618 884
388 584 1018
434 630 1018
320 636 956
196 388 814
426 618 814
232 432 620
188 388 620
442 882 1064
182 622 1064
434 586 1020
312 580 1124
544 812 1124
192 636 964
328 772 964
442 828 1270
198 430 628
154 326 774
448 620 774

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13187

>
> bass is always 0
>
> rank tenor alto soprano name
> 1. 386 702 1088 5-lim maj7
> 2. 316 702 1018 5-lim min7
> 3-4. 388 702 886 5-lim min7 1st inv
> 3-4. 184 498 886 5-lim min7 3rd inv
> 5. 498 886 1384 5-lim min7 2nd inv (open
voicing)
> 6. 268 702 970 7-lim min7
> 7-8. 184 388 886 5-lim min 1st inv add4
> 7-8. 498 702 886 5-lim maj 2nd inv add2
> 9-10. 204 702 1088 5-lim maj 2nd inv / 4
> 9-10. 386 884 1088 5-lim min 1st inv add9
> 11-12. 302 502 1004 ~12-tET 7sus4 2nd inv
> 11-12. 502 702 1004 ~12-tET 7sus4
> 13. 202 500 702 ~12-tET7sus4 1st inv
> 14-15. 204 388 702 5-lim maj add2
> 14-15. 314 498 702 5-lim min add4
> 16. 492 980 1472 ~22-tET 7sus4 2nd inv (open
voicing)
> 17-18. 186 576 888 5-lim dom7 3rd inv
> 17-18. 312 702 888 5-lim hlf-dim7 1st inv
> 19-20. 502 1002 1390 5-lim maj 2nd inv / 2
> 19-20. 388 888 1390 5-lim min 1st inv add11
> 21-22. 384 588 1086 5-lim maj7 #11 no5
> 21-22. 498 702 1086 5-lim maj7 sus4
> 23-24. 318 816 1020 5-lim maj 1st inv add9
> 23-24. 204 702 1020 5-lim min 2nd inv / 4
> 25-26. 268 582 970 7-lim hlf-dim7
> 25-26. 388 702 970 7-lim dom7
>
> I'l tell you again that ranks of mirror-image tetrads always tied.

So, is this it for the top 26?? I guess I can go ahead and assign
numbers on the Tuning Lab site, correct??
______________ ____ __ __
Joseph Pehrson

Joseph wrote,

>So, is this it for the top 26?? I guess I can go ahead and assign
>numbers on the Tuning Lab site, correct??

Well, there are some chords in this set of 26 that are not in your set of
36, and vice versa . . .