more single generator symmetrical scales

These are the other single generator symmetrical scales were "P" = a
repeating subdivision of the octave =/> 1:2^(1/7).

These scales are derived from the following generalized algorithm:

X = P/((b+A*d))*(a+A*c)
X = P/((d+A*b))*(c+A*a)

Where:

"P" = any given periodicity

"A" = one of three Apical constants ('a bud which terminates a stem')
taken from the following Golden, Equal, and Silver, series:

1/1, 1/2, 2/3, 3/5, 5/8, ...

1/1.5, 1.5/3.25, 3.25/6.375, 6.375/12.8125, 12.8125/25.59375, ...

1/2, 2/5, 5/12, 12/29, 29/70, ...

"a"/"b", "c"/"d" and "c"/"d", "a"/"b" = the two adjacent fractions of
a given Ls index

"X" = the resulting generator

The following examples are given in a "Golden", "Equal", "Silver"
order; that is the first of each group has L/s = Phi; the second L/s =
2, and the third L/s = sqrt(2)+1.

These are the single generator symmetrical scales of 12 or fewer notes
where "P" = 1:2^(1/3).

6-tone symmetrical scales where "P" = 400�

[3s & 3L]

0 247 400 647 800 1047 1200
0 153 400 553 800 953 1200

0 267 400 667 800 1067 1200
0 133 400 533 800 933 1200

0 283 400 683 800 1083 1200
0 117 400 517 800 917 1200

9-tone symmetrical scales where "P" = 400�

[3s & 6L]

0 94 247 400 494 647 800 894 1047 1200
0 153 306 400 553 706 800 953 1106 1200
0 153 247 400 553 647 800 953 1047 1200

0 80 240 400 480 640 800 880 1040 1200
0 160 320 400 560 720 800 960 1120 1200
0 160 240 400 560 640 800 960 1040 1200

0 69 234 400 469 634 800 869 1034 1200
0 166 331 400 566 731 800 966 1131 1200
0 166 234 400 566 634 800 966 1034 1200

[6s & 3L]

0 179 289 400 579 689 800 979 1089 1200
0 111 221 400 511 621 800 911 1021 1200
0 111 289 400 511 689 800 911 1089 1200

0 200 300 400 600 700 800 1000 1100 1200
0 100 200 400 500 600 800 900 1000 1200
0 100 300 400 500 700 800 900 1100 1200

0 219 309 400 619 709 800 1019 1109 1200
0 91 181 400 491 581 800 891 981 1200
0 91 309 400 491 709 800 891 1109 1200

12-tone symmetrical scales where "P" = 400�

[3s & 9L]

0 68 179 289 400 468 579 689 800 868 979 1089 1200
0 111 221 332 400 511 621 732 800 911 1021 1132 1200
0 111 221 289 400 511 621 689 800 911 1021 1089 1200
0 111 179 289 400 511 579 689 800 911 979 1089 1200

0 57 171 286 400 457 571 686 800 857 971 1086 1200
0 114 229 343 400 514 629 743 800 914 1029 1143 1200
0 114 229 286 400 514 629 686 800 914 1029 1086 1200
0 114 171 286 400 514 571 686 800 914 971 1086 1200

0 49 166 283 400 449 566 683 800 849 966 1083 1200
0 117 234 351 400 517 634 751 800 917 1034 1151 1200
0 117 234 283 400 517 634 683 800 917 1034 1083 1200
0 117 166 283 400 517 566 683 800 917 966 1083 1200

[9s & 3L]

0 140 227 313 400 540 627 713 800 940 1027 1113 1200
0 87 173 260 400 487 573 660 800 887 973 1060 1200
0 87 173 313 400 487 573 713 800 887 973 1113 1200
0 87 227 313 400 487 627 713 800 887 1027 1113 1200

0 160 240 320 400 560 640 720 800 960 1040 1120 1200
0 80 160 240 400 480 560 640 800 880 960 1040 1200
0 80 160 320 400 480 560 720 800 880 960 1120 1200
0 80 240 320 400 480 640 720 800 880 1040 1120 1200

0 178 252 326 400 578 652 726 800 978 1052 1126 1200
0 74 148 222 400 474 548 622 800 874 948 1022 1200
0 74 148 326 400 474 548 726 800 874 948 1126 1200
0 74 252 326 400 474 652 726 800 874 1052 1126 1200

These are the single generator symmetrical scales of 12 or fewer notes
where "P" = 1:2^(1/4).

8-tone symmetrical scales where "P" = 300�

[4s & 4L]

0 185 300 485 600 785 900 1085 1200
0 115 300 415 600 715 900 1015 1200

0 200 300 500 600 800 900 1100 1200
0 100 300 400 600 700 900 1000 1200

0 212 300 512 600 812 900 1112 1200
0 88 300 388 600 688 900 988 1200

12-tone symmetrical scales where "P" = 300�

[4s & 8L]

0 71 185 300 371 485 600 671 785 900 971 1085 1200
0 115 229 300 415 529 600 715 829 900 1015 1129 1200
0 115 185 300 415 485 600 715 785 900 1015 1085 1200

0 60 180 300 360 480 600 660 780 900 960 1080 1200
0 120 240 300 420 540 600 720 840 900 1020 1140 1200
0 120 180 300 420 480 600 720 780 900 1020 1080 1200

0 51 176 300 351 476 600 651 776 900 951 1076 1200
0 124 249 300 424 549 600 724 849 900 1024 1149 1200
0 124 176 300 424 476 600 724 776 900 1024 1076 1200

[8s & 4L]

0 134 217 300 434 517 600 734 817 900 1034 1117 1200
0 83 166 300 383 466 600 683 766 900 983 1066 1200
0 83 217 300 383 517 600 683 817 900 983 1117 1200

0 150 225 300 450 525 600 750 825 900 1050 1125 1200
0 75 150 300 375 450 600 675 750 900 975 1050 1200
0 75 225 300 375 525 600 675 825 900 975 1125 1200

0 164 232 300 464 532 600 764 832 900 1064 1132 1200
0 68 136 300 368 436 600 668 736 900 968 1036 1200
0 68 232 300 368 532 600 668 832 900 968 1132 1200

These are the single generator symmetrical scales of 15 or fewer notes
where "P" = 1:2^(1/5).

10-tone symmetrical scales where "P" = 240�

[5s & 5L]

0 148 240 388 480 628 720 868 960 1108 1200
0 92 240 332 480 572 720 812 960 1052 1200

0 160 240 400 480 640 720 880 960 1120 1200
0 80 240 320 480 560 720 800 960 1040 1200

0 170 240 410 480 650 720 890 960 1130 1200
0 70 240 310 480 550 720 790 960 1030 1200

15-tone symmetrical scales where "P" = 240�

[5s & 10L]

0 57 148 240 297 388 480 537 628 720 777 868 960 1017 1108 1200
0 92 183 240 332 423 480 572 663 720 812 903 960 1052 1143 1200
0 92 148 240 332 388 480 572 628 720 812 868 960 1052 1108 1200

0 48 144 240 288 384 480 528 624 720 768 864 960 1008 1104 1200
0 96 192 240 336 432 480 576 672 720 816 912 960 1056 1152 1200
0 96 144 240 336 384 480 576 624 720 816 864 960 1056 1104 1200

0 41 141 240 281 381 480 521 621 720 761 861 960 1001 1101 1200
0 99 199 240 339 439 480 579 679 720 819 919 960 1059 1159 1200
0 99 141 240 339 381 480 579 621 720 819 861 960 1059 1101 1200

[10L & 5s]

0 107 174 240 347 414 480 587 654 720 827 894 960 1067 1134 1200
0 66 133 240 306 373 480 546 613 720 786 853 960 1026 1093 1200
0 66 174 240 306 414 480 546 654 720 786 894 960 1026 1134 1200

0 120 180 240 360 420 480 600 660 720 840 900 960 1080 1140 1200
0 60 120 240 300 360 480 540 600 720 780 840 960 1020 1080 1200
0 60 180 240 300 420 480 540 660 720 780 900 960 1020 1140 1200

0 131 186 240 371 426 480 611 666 720 851 906 960 1091 1146 1200
0 54 109 240 294 349 480 534 589 720 774 829 960 1014 1069 1200
0 54 186 240 294 426 480 534 666 720 774 906 960 1014 1146 1200

These are the single generator symmetrical scales of 12 or fewer notes
where "P" = 1:2^(1/6).

12-tone symmetrical scales where "P" = 200�

[6s & 6L]

0 124 200 324 400 524 600 724 800 924 1000 1124 1200
0 76 200 276 400 476 600 676 800 876 1000 1076 1200

0 133 200 333 400 533 600 733 800 933 1000 1133 1200
0 67 200 267 400 467 600 667 800 867 1000 1067 1200

0 141 200 341 400 541 600 741 800 941 1000 1141 1200
0 59 200 259 400 459 600 659 800 859 1000 1059 1200

These are the single generator symmetrical scales of 14 or fewer notes
where "P" = 1:2^(1/7).

14-tone symmetrical scales where "P" = ~171�

[7s & 7L]

0 106 171 277 343 449 514 620 686 792 857 963 1029 1135 1200
0 65 171 237 343 408 514 580 686 751 857 923 1029 1094 1200

0 114 171 286 343 457 514 629 686 800 857 971 1029 1143 1200
0 57 171 229 343 400 514 571 686 743 857 914 1029 1086 1200

0 121 171 293 343 464 514 636 686 807 857 978 1029 1150 1200
0 50 171 222 343 393 514 564 686 736 857 907 1029 1079 1200

--Dan Stearns