FW: [tuning] Re: Cursory appraisal of concordance (H.E.)

-----Original Message-----
From: Paul H. Erlich
Sent: Tuesday, September 26, 2000 1:27 AM
To: 'Joseph Pehrson'
Cc: ' Monz'
Subject: RE: [tuning] Re: Cursory appraisal of concordance (H.E.)

Joseph:

You switched the descriptions for the two new chords,

0 272 772 974
0 202 702 974

on your site . . .

Here's a ranking of the tetrads according to what I anticipate the solution
to tetradic harmonic entropy for simple JI chords would be like, the
geometric mean of the numbers used in the otonal representation of the
chord, and ignoring roughness (the Sethares factor) as well as diadic and
triadic harmonic entropy:

We have to exclude

from this ranking, since the approximation only works for simple JI chords.

bass tenor alto soprano otonal_rep g.m.

0 388 702 970 4:5:6:7 5.3836
0 318 816 1020 5:6:8:9 6.8173
0 498 702 886 6:8:9:10 8.1072
0 202 702 974 8:9:12:14 10.4872
0 204 702 1088 8:9:12:15 10.6697
0 386 702 1088 8:10:12:15 10.9545
0 184 498 886 9:10:12:15 11.2818
0 316 702 1018 10:12:15:18 13.4164
0 498 886 1384 9:12:15:20 13.4164
0 502 1002 1390 9:12:16:20 13.6346
0 268 702 970 12:14:18:21 15.8745
0 388 702 886 12:15:18:20 15.9549
0 388 886 1274 12:15:20:25 17.3205
0 498 888 1282 12:16:20:25 17.6022
0 318 818 1320 15:18:24:32 21.3394
0 500 816 1316 15:20:24:32 21.9089
0 388 776 1090 16:20:25:30 22.1336
0 186 576 888 18:20:25:30 22.7951
0 498 702 1086 24:32:36:45 33.3979
0 386 884 1088 24:30:40:45 33.7405
0 312 702 888 30:36:45:50 39.4822
0 184 388 886 36:40:45:50 42.4264
0 384 588 1086 32:40:45:60 43.1165
0 272 772 974 36:42:56:63 48.0585
0 388 888 1390 36:45:60:80 52.8067
0 204 702 1020 40:45:60:72 52.8067
0 314 702 1090 40:48:60:75 54.2161
0 502 1002 1320 45:60:80:96 67.4810
0 394 784 1282 48:60:75:100 68.1732
0 268 582 970 60:70:84:105 78.0152
0 302 502 1004 not JI
0 502 702 1004 not JI
0 492 980 1472 not JI
0 500 886 1320 not JI
0 434 820 1320 not JI
0 442 884 1326 not JI

The 9:11:13:15 chord Monz just posted would get an 11.7874 according to this
method, putting it above 10:12:15:18 (tha major seventh chord). I don't
think so!