single generator scales with symmetry at the half-octave

These are the single generator symmetrical scales of 12 or less notes
where "P" = 600�. They are given in a Golden, Equal, Silver, "Apical"
order; that is the first of each group has L/s = Phi; the second L/s =
2, and the third L/s = sqrt(2).

4-tone symmetrical scales where "P" = 600�

[2s & 2L]

0 371 600 971 1200
0 229 600 829 1200

0 400 600 1000 1200
0 200 600 800 1200

0 424 600 1024 1200
0 176 600 776 1200

6-tone symmetrical scales where "P" = 600�

[2s & 4L]

0 142 371 600 742 971 1200
0 229 458 600 829 1058 1200
0 229 371 600 829 971 1200

0 120 360 600 720 960 1200
0 240 480 600 840 1080 1200
0 240 360 600 840 960 1200

0 103 351 600 703 951 1200
0 249 497 600 849 1097 1200
0 249 351 600 849 951 1200

[4s & 2L]

0 268 434 600 868 1034 1200
0 166 332 600 766 932 1200
0 166 434 600 766 1034 1200

0 300 450 600 900 1050 1200
0 150 300 600 750 900 1200
0 150 450 600 750 1050 1200

0 328 464 600 928 1064 1200
0 136 272 600 736 872 1200
0 136 464 600 736 1064 1200

8-tone symmetrical scales where "P" = 600�

[2s & 6L]

0 102 268 434 600 702 868 1034 1200
0 166 332 498 600 766 932 1098 1200
0 166 332 434 600 766 932 1034 1200
0 166 268 434 600 766 868 1034 1200

0 86 257 429 600 686 857 1029 1200
0 171 343 514 600 771 943 1114 1200
0 171 343 429 600 771 943 1029 1200
0 171 257 429 600 771 857 1029 1200

0 73 249 424 600 673 849 1024 1200
0 176 351 527 600 776 951 1127 1200
0 176 351 424 600 776 951 1024 1200
0 176 249 424 600 776 849 1024 1200

[6s & 2L]

0 210 340 470 600 810 940 1070 1200
0 130 260 390 600 730 860 990 1200
0 130 260 470 600 730 860 1070 1200
0 130 340 470 600 730 940 1070 1200

0 240 360 480 600 840 960 1080 1200
0 120 240 360 600 720 840 960 1200
0 120 240 480 600 720 840 1080 1200
0 120 360 480 600 720 960 1080 1200

0 268 378 489 600 868 978 1089 1200
0 111 222 332 600 711 822 932 1200
0 111 222 489 600 711 822 1089 1200
0 111 378 489 600 711 978 1089 1200

10-tone symmetrical scales where "P" = 600�

[2s & 8L]

0 173 280 386 493 600 773 880 986 1093 1200
0 107 214 320 427 600 707 814 920 1027 1200
0 107 214 320 493 600 707 814 920 1093 1200
0 107 214 386 493 600 707 814 986 1093 1200
0 107 280 386 493 600 707 880 986 1093 1200

0 164 273 382 491 600 764 873 982 1091 1200
0 109 218 327 436 600 709 818 927 1036 1200
0 109 218 327 491 600 709 818 927 1091 1200
0 109 218 382 491 600 709 818 982 1091 1200
0 109 273 382 491 600 709 873 982 1091 1200

0 157 268 378 489 600 757 868 978 1089 1200
0 111 222 332 443 600 711 822 932 1043 1200
0 111 222 332 489 600 711 822 932 1089 1200
0 111 222 378 489 600 711 822 978 1089 1200
0 111 268 378 489 600 711 868 978 1089 1200

[4s & 6L]

0 142 283 371 512 600 742 883 971 1112 1200
0 142 229 371 458 600 742 829 971 1058 1200
0 88 229 317 458 600 688 829 917 1058 1200
0 142 229 371 512 600 742 829 971 1112 1200
0 88 229 371 458 600 688 829 971 1058 1200

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

0 157 313 378 535 600 757 913 978 1135 1200
0 157 222 378 443 600 757 822 978 1043 1200
0 65 222 287 443 600 665 822 887 1043 1200
0 157 222 378 535 600 757 822 978 1135 1200
0 65 222 378 443 600 665 822 978 1043 1200

[6s & 4L]

0 96 192 348 444 600 696 792 948 1044 1200
0 96 252 348 504 600 696 852 948 1104 1200
0 156 252 408 504 600 756 852 1008 1104 1200
0 96 252 348 444 600 696 852 948 1044 1200
0 156 252 348 504 600 756 852 948 1104 1200

0 86 171 343 429 600 686 771 943 1029 1200
0 86 257 343 514 600 686 857 943 1114 1200
0 171 257 429 514 600 771 857 1029 1114 1200
0 86 257 343 429 600 686 857 943 1029 1200
0 171 257 343 514 600 771 857 943 1114 1200

0 77 153 338 415 600 677 753 938 1015 1200
0 77 262 338 523 600 677 862 938 1123 1200
0 185 262 447 523 600 785 862 1047 1123 1200
0 77 262 338 415 600 677 862 938 1015 1200
0 185 262 338 523 600 785 862 938 1123 1200

[8s & 2L]

0 173 280 386 493 600 773 880 986 1093 1200
0 107 214 320 427 600 707 814 920 1027 1200
0 107 214 320 493 600 707 814 920 1093 1200
0 107 214 386 493 600 707 814 986 1093 1200
0 107 280 386 493 600 707 880 986 1093 1200

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

0 226 319 413 506 600 826 919 1013 1106 1200
0 94 187 281 374 600 694 787 881 974 1200
0 94 187 281 506 600 694 787 881 1106 1200
0 94 187 413 506 600 694 787 1013 1106 1200
0 94 319 413 506 600 694 919 1013 1106 1200

12-tone symmetrical scales where "P" = 600�

[2s & 10L]

0 66 173 280 386 493 600 666 773 880 986 1093 1200
0 107 214 320 427 534 600 707 814 920 1027 1134 1200
0 107 214 320 427 493 600 707 814 920 1027 1093 1200
0 107 214 320 386 493 600 707 814 920 986 1093 1200
0 107 214 280 386 493 600 707 814 880 986 1093 1200
0 107 173 280 386 493 600 707 773 880 986 1093 1200

0 55 164 273 382 491 600 655 764 873 982 1091 1200
0 109 218 327 436 545 600 709 818 927 1036 1145 1200
0 109 218 327 436 491 600 709 818 927 1036 1091 1200
0 109 218 327 382 491 600 709 818 927 982 1091 1200
0 109 218 273 382 491 600 709 818 873 982 1091 1200
0 109 164 273 382 491 600 709 764 873 982 1091 1200

0 46 157 268 378 489 600 646 757 868 978 1089 1200
0 111 222 332 443 554 600 711 822 932 1043 1154 1200
0 111 222 332 443 489 600 711 822 932 1043 1089 1200
0 111 222 332 378 489 600 711 822 932 978 1089 1200
0 111 222 268 378 489 600 711 822 868 978 1089 1200
0 111 157 268 378 489 600 711 757 868 978 1089 1200

[10s & 2L]

0 147 237 328 419 509 600 747 837 928 1019 1109 1200
0 91 181 272 363 453 600 691 781 872 963 1053 1200
0 91 181 272 363 509 600 691 781 872 963 1109 1200
0 91 181 272 419 509 600 691 781 872 1019 1109 1200
0 91 181 328 419 509 600 691 781 928 1019 1109 1200
0 91 237 328 419 509 600 691 837 928 1019 1109 1200

0 171 257 343 429 514 600 771 857 943 1029 1114 1200
0 86 171 257 343 429 600 686 771 857 943 1029 1200
0 86 171 257 343 514 600 686 771 857 943 1114 1200
0 86 171 257 429 514 600 686 771 857 1029 1114 1200
0 86 171 343 429 514 600 686 771 943 1029 1114 1200
0 86 257 343 429 514 600 686 857 943 1029 1114 1200

0 195 276 357 438 519 600 795 876 957 1038 1119 1200
0 81 162 243 324 405 600 681 762 843 924 1005 1200
0 81 162 243 324 519 600 681 762 843 924 1119 1200
0 81 162 243 438 519 600 681 762 843 1038 1119 1200
0 81 162 357 438 519 600 681 762 957 1038 1119 1200
0 81 276 357 438 519 600 681 876 957 1038 1119 1200

-- Dan Stearns

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
> These are the single generator symmetrical scales of 12 or less
notes
> where "P" = 600¢. They are given in a Golden, Equal,
Silver, "Apical"
> order; that is the first of each group has L/s = Phi; the second
L/s =
> 2, and the third L/s = sqrt(2).

Many of the third of each set seems to have L/s = sqrt(2)+1, rather
than L/s = sqrt(2). Right? Or am I misunderstanding what you mean by
L/s here?

Paul Erlich wrote,

> Many of the third of each set seems to have L/s = sqrt(2)+1, rather
than L/s = sqrt(2). Right? Or am I misunderstanding what you mean by
L/s here?

No, your right. It should have read "They are given in a Golden,
Equal, Silver, "Apical" 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." Sorry.

--Dan Stearns