two unanswered questions answered

Using the generalized L-out-of-M-out-of-N method that I posted Sunday,
here's some 5-tone three-term index examples where a*T = c; that is
the product of the smallest stepsize and the Tribonacci constant
equals the largest stepsize.

This method, while still in need of some "finishing", could be seen as
a counterpoint to the generalized two-term (stepsize) scales after
Kornerup, where an internally consistent standard that is tethered to
neither JI nor ET exists for any arbitrary three-term (stepsize) scale
as well... and "trivalence", while a special and frequent condition
here, is not a synonymous one.

1, 1, 3, 5, 9, 17, ...

0 230 504 777 926 1200
0 274 548 696 970 1200
0 274 423 696 926 1200
0 149 423 652 926 1200
0 274 504 777 1051 1200

1, 3, 1, 5, 9, 15, ...

0 248 496 791 1039 1200
0 248 543 791 952 1200
0 295 543 704 952 1200
0 248 409 657 905 1200
0 161 409 657 952 1200

3, 1, 1, 5, 7, 13, ...

0 290 478 666 1012 1200
0 188 376 722 910 1200
0 188 534 722 1012 1200
0 346 534 824 1012 1200
0 188 478 666 854 1200

1, 2, 2, 5, 9, 16, ...

0 239 523 761 916 1200
0 284 523 677 961 1200
0 239 393 677 916 1200
0 155 439 677 961 1200
0 284 523 807 1045 1200

2, 1, 2, 5, 8, 15, ...

0 256 562 728 1034 1200
0 306 472 777 944 1200
0 166 472 638 894 1200
0 306 472 728 1034 1200
0 166 423 728 894 1200

2, 2, 1, 5, 8, 14, ...

0 267 441 708 1027 1200
0 173 441 759 933 1200
0 267 586 759 1027 1200
0 319 492 759 933 1200
0 173 441 614 881 1200

--Dan Stearns