Scala analysis: laka-dwarf
Laka tempered (205et) dwarf(<17 27 40 48 59 63 70|)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52.683 cents 52.682930 2: 105.366 cents 105.365850 3: 204.878 cents 204.878050 4: 245.854 cents 245.853660 5: 345.366 cents 345.365850 6: 386.341 cents 386.341460 7: 474.146 cents 474.146340 8: 550.244 cents 550.243900 9: 591.220 cents 591.219510 10: 702.439 cents 702.439020 11: 743.415 cents 743.414630 12: 842.927 cents 842.926830 13: 907.317 cents 907.317070 14: 971.707 cents 971.707320 15: 1047.805 cents 1047.804880 16: 1088.780 cents 1088.780490 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 111.2195 cents 111.2195 1: 52.6829 cents 52.6829 2: 52.6829 cents 52.6829 3: 99.5122 cents 99.5122 4: 40.9756 cents 40.9756 5: 99.5122 cents 99.5122 6: 40.9756 cents 40.9756 7: 87.8049 cents 87.8049 8: 76.0976 cents 76.0976 9: 40.9756 cents 40.9756 10: 111.2195 cents 111.2195 11: 40.9756 cents 40.9756 12: 99.5122 cents 99.5122 13: 64.3902 cents 64.3902 14: 64.3902 cents 64.3902 15: 76.0976 cents 76.0976 16: 40.9756 cents 40.9756 17: 111.2195 cents 111.2195
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 40.97561 cents 1: 2 52.68293 cents 1: 2 64.39024 cents 1: 2 76.09756 cents 1: 1 87.80488 cents 1: 3 99.51220 cents 1: 2 111.21951 cents 2: 1 105.36585 cents 2: 2 117.07317 cents 2: 2 128.78049 cents 2: 5 140.48781 cents 2: 4 152.19512 cents 2: 3 163.90244 cents 3: 2 181.46341 cents 3: 2 193.17073 cents 3: 6 204.87805 cents 3: 1 216.58536 cents 3: 4 228.29268 cents 3: 1 240.00000 cents 3: 1 251.70732 cents 4: 3 245.85366 cents 4: 1 257.56097 cents 4: 3 269.26829 cents 4: 2 280.97561 cents 4: 3 292.68292 cents 4: 2 304.39024 cents 4: 3 316.09756 cents 5: 2 333.65853 cents 5: 6 345.36585 cents 5: 6 357.07317 cents 5: 2 368.78049 cents 5: 1 380.48781 cents 6: 3 386.34146 cents 6: 3 398.04878 cents 6: 1 409.75610 cents 6: 2 421.46341 cents 6: 2 433.17073 cents 6: 1 444.87805 cents 6: 5 456.58536 cents 7: 1 462.43902 cents 7: 2 474.14634 cents 7: 1 485.85366 cents 7: 11 497.56097 cents 7: 1 509.26830 cents 7: 1 520.97561 cents 8: 5 538.53658 cents 8: 2 550.24390 cents 8: 3 561.95122 cents 8: 2 573.65854 cents 8: 2 585.36586 cents 8: 2 597.07317 cents 8: 1 608.78049 cents 9: 1 591.21951 cents 9: 2 602.92683 cents 9: 2 614.63415 cents 9: 2 626.34147 cents 9: 3 638.04878 cents 9: 2 649.75609 cents 9: 5 661.46341 cents 10: 1 679.02439 cents 10: 1 690.73170 cents 10: 11 702.43902 cents 10: 1 714.14634 cents 10: 2 725.85366 cents 10: 1 737.56098 cents 11: 5 743.41463 cents 11: 1 755.12195 cents 11: 2 766.82927 cents 11: 2 778.53659 cents 11: 1 790.24390 cents 11: 3 801.95122 cents 11: 3 813.65854 cents 12: 1 819.51219 cents 12: 2 831.21951 cents 12: 6 842.92683 cents 12: 6 854.63414 cents 12: 2 866.34147 cents 13: 3 883.90244 cents 13: 2 895.60976 cents 13: 3 907.31707 cents 13: 2 919.02439 cents 13: 3 930.73171 cents 13: 1 942.43903 cents 13: 3 954.14634 cents 14: 1 948.29268 cents 14: 1 960.00000 cents 14: 4 971.70732 cents 14: 1 983.41464 cents 14: 6 995.12195 cents 14: 2 1006.82927 cents 14: 2 1018.53659 cents 15: 3 1036.09756 cents 15: 4 1047.80488 cents 15: 5 1059.51219 cents 15: 2 1071.21951 cents 15: 2 1082.92683 cents 15: 1 1094.63415 cents 16: 2 1088.78049 cents 16: 3 1100.48780 cents 16: 1 1112.19512 cents 16: 2 1123.90244 cents 16: 2 1135.60976 cents 16: 2 1147.31707 cents 16: 5 1159.02439 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.50000 = 13/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 52.7 105.4 204.9 245.9 345.4 386.3 474.1 550.2 591.2 702.4 743.4 842.9 907.3 971.7 1047.8 1088.8 1200.0 52.7 : 52.7 152.2 193.2 292.7 333.7 421.5 497.6 538.5 649.8 690.7 790.2 854.6 919.0 995.1 1036.1 1147.3 1200.0 105.4 : 99.5 140.5 240.0 281.0 368.8 444.9 485.9 597.1 638.0 737.6 802.0 866.3 942.4 983.4 1094.6 1147.3 1200.0 204.9 : 41.0 140.5 181.5 269.3 345.4 386.3 497.6 538.5 638.0 702.4 766.8 842.9 883.9 995.1 1047.8 1100.5 1200.0 245.9 : 99.5 140.5 228.3 304.4 345.4 456.6 497.6 597.1 661.5 725.9 802.0 842.9 954.1 1006.8 1059.5 1159.0 1200.0 345.4 : 41.0 128.8 204.9 245.9 357.1 398.0 497.6 562.0 626.3 702.4 743.4 854.6 907.3 960.0 1059.5 1100.5 1200.0 386.3 : 87.8 163.9 204.9 316.1 357.1 456.6 521.0 585.4 661.5 702.4 813.7 866.3 919.0 1018.5 1059.5 1159.0 1200.0 474.1 : 76.1 117.1 228.3 269.3 368.8 433.2 497.6 573.7 614.6 725.9 778.5 831.2 930.7 971.7 1071.2 1112.2 1200.0 550.2 : 41.0 152.2 193.2 292.7 357.1 421.5 497.6 538.5 649.8 702.4 755.1 854.6 895.6 995.1 1036.1 1123.9 1200.0 591.2 : 111.2 152.2 251.7 316.1 380.5 456.6 497.6 608.8 661.5 714.1 813.7 854.6 954.1 995.1 1082.9 1159.0 1200.0 702.4 : 41.0 140.5 204.9 269.3 345.4 386.3 497.6 550.2 602.9 702.4 743.4 842.9 883.9 971.7 1047.8 1088.8 1200.0 743.4 : 99.5 163.9 228.3 304.4 345.4 456.6 509.3 562.0 661.5 702.4 802.0 842.9 930.7 1006.8 1047.8 1159.0 1200.0 842.9 : 64.4 128.8 204.9 245.9 357.1 409.8 462.4 562.0 602.9 702.4 743.4 831.2 907.3 948.3 1059.5 1100.5 1200.0 907.3 : 64.4 140.5 181.5 292.7 345.4 398.0 497.6 538.5 638.0 679.0 766.8 842.9 883.9 995.1 1036.1 1135.6 1200.0 971.7 : 76.1 117.1 228.3 281.0 333.7 433.2 474.1 573.7 614.6 702.4 778.5 819.5 930.7 971.7 1071.2 1135.6 1200.0 1047.8: 41.0 152.2 204.9 257.6 357.1 398.0 497.6 538.5 626.3 702.4 743.4 854.6 895.6 995.1 1059.5 1123.9 1200.0 1088.8: 111.2 163.9 216.6 316.1 357.1 456.6 497.6 585.4 661.5 702.4 813.7 854.6 954.1 1018.5 1082.9 1159.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.9756 .. 111.2195 cents 70.24390 cents 40.97561 cents 2: 105.3659 .. 163.9024 cents 58.53659 cents -5.85366 cents 3: 181.4634 .. 251.7073 cents 70.24391 cents 17.56097 cents 4: 245.8537 .. 316.0976 cents 70.24390 cents -5.85366 cents 5: 333.6585 .. 380.4878 cents 46.82928 cents 17.56097 cents 6: 386.3415 .. 456.5854 cents 70.24390 cents 5.85365 cents 7: 462.4390 .. 520.9756 cents 58.53659 cents 5.85366 cents 8: 538.5366 .. 608.7805 cents 70.24391 cents 17.56097 cents 9: 591.2195 .. 661.4634 cents 70.24390 cents -17.56098 cents 10: 679.0244 .. 737.5610 cents 58.53659 cents 17.56098 cents 11: 743.4146 .. 813.6585 cents 70.24391 cents 5.85365 cents 12: 819.5122 .. 866.3415 cents 46.82928 cents 5.85365 cents 13: 883.9024 .. 954.1463 cents 70.24390 cents 17.56097 cents 14: 948.2927 .. 1018.5366 cents 70.24391 cents -5.85366 cents 15: 1036.0976 .. 1094.6341 cents 58.53659 cents 17.56097 cents 16: 1088.7805 .. 1159.0244 cents 70.24390 cents -5.85366 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 40.97561 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 111.21951 cents Average / Smallest step : 1.722689 Largest / Average step : 1.575610 Largest / Smallest step : 2.714286 Median interval of one step : 64.39024 cents, amount: 2 Most common interval of one step : 40.97561 cents, amount: 5 Least squares average step : 69.02070 cents, oct.: 1173.35192 cents Scale is not proper Scale is a mode of a 205-tone equal temperament with octave 2/1 degrees: 9 18 35 42 59 66 81 94 101 120 127 144 155 166 179 186 205 Least number of segments generator : 103 of 602.927 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 181 of 1059.512 cents and inv. generated superset size: 65 = 48 more = 382.353% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABCBCDECFCBGGECF Step pattern size order : BBFAFAEDAGAFCCDAG Scale is a Constant Structure, by a margin of 5.85365 cents Scale diversity : 1.580715 Lumma stability : 0.175610 Lumma impropriety factor : 0.034146 Number of different interval sizes : 104 = 6.50000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.50000 = 13/2 Median interval variety : 5.5 Lowest interval variety : 5 Smallest interval difference : 5.85365 cents Most common intervals : 497.56097 cents & inv., amount: 11 Most common triad is 0.0 497.561 702.439 cents, amount: 6 Number of recognisable fifths : 13, average 702.4390 cents Best fifths form a closed circle Formal octave complements present : 1 = 5.8824% Limited inverse transpositions with margin 70.2439 cents: 2 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
17: 1 1 1 1 1 1 1 1 0 2 1 1 1 1 1 1 1 N T3 SD: 23.0189 c. M:-40.6313 c. 19: 1 1 1 1 1 1 1 2 0 2 1 1 1 1 1 1 2 N D3 SD: 20.4788 c. M: 37.2786 c. 20: 1 1 1 1 2 0 2 1 1 2 0 2 1 1 1 1 2 N D3 S SD: 15.2455 c. M: 27.8049 c. 21: 1 1 2 0 2 1 1 2 0 2 1 2 1 1 1 1 2 N D3 SD: 13.7028 c. M:-23.6934 c. 22: 1 1 2 1 1 1 2 1 1 2 1 2 1 1 1 1 2 N D3 SD: 14.5975 c. M:-29.8004 c. 24: 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 P M ME S SD: 10.0000 c. M: 24.1463 c. 28: 1 1 3 1 2 1 2 2 1 2 1 3 1 2 1 1 3 N SD: 12.0302 c. M: 19.6516 c. 29: 1 1 3 1 2 1 2 2 1 3 1 2 2 1 2 1 3 N D3 S SD: 12.5858 c. M: 22.6072 c. 30: 1 2 2 1 3 1 2 2 1 3 1 2 2 1 2 1 3 P SD: 11.0302 c. M:-17.5610 c. 31: 1 2 2 1 3 1 2 2 1 3 1 3 1 2 2 1 3 N D3 S SD: 9.1190 c. M: 16.9945 c. 34: 2 1 3 1 3 1 3 2 1 3 1 3 2 2 2 1 3 P T3 SD: 9.9396 c. M:-19.9713 c. 35: 2 1 3 1 3 1 3 2 1 3 2 3 1 2 3 1 3 N SD: 10.2257 c. M: 16.7247 c. 37: 2 1 3 2 3 1 3 2 1 4 1 3 2 2 2 2 3 N SD: 8.6622 c. M:-13.9222 c. 41: 2 2 3 1 4 1 3 3 1 4 1 4 2 2 3 1 4 N SD: 6.6591 c. M:-11.7073 c. 46: 2 2 4 1 4 2 3 3 2 4 1 4 3 2 3 2 4 P SD: 6.3486 c. M: 12.9798 c. 48: 2 2 4 2 4 1 4 3 2 4 2 4 2 3 3 2 4 N SD: 5.9379 c. M: 11.3415 c. 53: 2 3 4 2 4 2 4 3 2 5 2 4 3 3 3 2 5 N SD: 4.2640 c. M:-7.8417 c. 63: 3 3 5 2 5 2 5 4 2 6 2 5 4 3 4 2 6 N SD: 3.8799 c. M:-8.9199 c. 65: 3 3 5 2 6 2 5 4 2 6 2 6 3 4 4 2 6 N SD: 4.1370 c. M:-6.7542 c. 77: 3 4 6 3 6 3 5 5 3 7 3 6 4 4 5 3 7 N SD: 3.7203 c. M: 6.6139 c. 87: 4 4 7 3 7 3 6 6 3 8 3 7 5 4 6 3 8 N SD: 2.7408 c. M: 6.1901 c. 90: 4 4 7 3 8 3 7 5 3 9 3 7 5 5 6 3 8 N SD: 3.6067 c. M:-5.8537 c. 93: 4 4 8 3 8 3 7 6 3 8 4 7 5 5 6 3 9 N SD: 3.3762 c. M: 5.6648 c. 94: 4 4 8 3 8 3 7 6 3 9 3 8 5 5 6 3 9 N SD: 2.2201 c. M: 3.9855 c. 111: 5 5 9 4 9 4 8 7 4 10 4 9 6 6 7 4 10 N SD: 1.8801 c. M:-3.3751 c. 140: 6 6 12 5 11 5 10 9 5 13 5 11 8 7 9 5 13 N SD: 1.9208 c. M: 3.1359 c. 142: 6 6 12 5 12 5 10 9 5 13 5 12 7 8 9 5 13 N SD: 1.7214 c. M: 3.9574 c. 152: 7 6 13 5 13 5 11 10 5 14 5 13 8 8 10 5 14 N SD: 1.4868 c. M: 2.7343 c. 181: 8 8 15 6 15 6 14 11 6 17 6 15 10 10 11 6 17 N SD: 1.3260 c. M:-3.2017 c. 184: 8 8 15 7 15 6 14 11 7 17 6 15 10 10 12 6 17 N SD: 1.5639 c. M: 2.7041 c. 195: 8 9 16 7 16 7 14 12 7 18 7 16 10 11 12 7 18 N SD: 1.4925 c. M: 3.4522 c. 205: 9 9 17 7 17 7 15 13 7 19 7 17 11 11 13 7 19 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.2420 cents 3 .. 6 match: 3 H SD: 11.0465 cents 4 .. 8 match: 4 H SD: 0.7305 cents 5 .. 10 match: 5 H SD: 10.4440 cents 6 .. 12 match: 6 H SD: 6.5460 cents 7 .. 14 match: 7 H SD: 10.0167 cents 8 .. 16 match: 8 H SD: 0.5100 cents 9 .. 18 match: 9 H SD: 7.7585 cents 10 .. 20 match: 10 H SD: 7.3111 cents 11 .. 22 match: 10 SD: 8.3854 cents 12 .. 24 match: 11 S SD: 5.8927 cents 13 .. 26 match: 11 S SD: 3.6552 cents 14 .. 28 match: 13 S SD: 6.4210 cents 15 .. 30 match: 13 SD: 5.4323 cents 16 .. 32 match: 14 S SD: 3.6344 cents 17 .. 34 match: 14 S SD: 4.7572 cents 18 .. 36 match: 15 SD: 4.9362 cents 19 .. 38 match: 15 SD: 3.6871 cents 20 .. 40 match: 15 SD: 4.4714 cents 21 .. 42 match: 13 SD: 4.9020 cents 22 .. 44 match: 15 SD: 3.6700 cents 23 .. 46 match: 14 SD: 4.0977 cents 24 .. 48 match: 17 SD: 3.3992 cents 25 .. 50 match: 15 SD: 3.3842 cents 26 .. 52 match: 17 SD: 3.3163 cents 27 .. 54 match: 16 SD: 3.3936 cents 28 .. 56 match: 16 SD: 2.8978 cents 29 .. 58 match: 16 SD: 2.8636 cents 31 .. 62 match: 17 SD: 2.6537 cents 32 .. 64 match: 17 SD: 0.8969 cents 36 .. 72 match: 16 SD: 2.4916 cents 37 .. 74 match: 17 SD: 2.3449 cents 40 .. 80 match: 17 SD: 1.9852 cents 41 .. 82 match: 17 SD: 1.9508 cents 45 .. 90 match: 17 SD: 1.8111 cents 48 .. 96 match: 17 SD: 1.5998 cents 54 .. 108 match: 17 SD: 1.4438 cents 59 .. 118 match: 17 SD: 1.4155 cents 60 .. 120 match: 17 SD: 1.3971 cents 61 .. 122 match: 17 SD: 1.3728 cents 63 .. 126 match: 17 SD: 1.3705 cents 64 .. 128 match: 17 SD: 0.6297 cents 96 .. 192 match: 17 SD: 0.6047 cents 126 .. 252 match: 17 SD: 0.5734 cents 128 .. 256 match: 17 SD: 0.5601 cents 136 .. 272 match: 17 SD: 0.5275 cents 144 .. 288 match: 17 SD: 0.5215 cents 158 .. 316 match: 17 SD: 0.4191 cents 177 .. 354 match: 17 SD: 0.4015 cents 190 .. 380 match: 17 SD: 0.3065 cents 222 .. 444 match: 17 SD: 0.2868 cents 254 .. 508 match: 17 SD: 0.2730 cents 255 .. 510 match: 17 SD: 0.2665 cents 280 .. 560 match: 17 SD: 0.2662 cents 287 .. 574 match: 17 SD: 0.2558 cents 289 .. 578 match: 17 SD: 0.2320 cents 320 .. 640 match: 17 SD: 0.2084 cents 321 .. 642 match: 17 SD: 0.1986 cents 352 .. 704 match: 17 SD: 0.1900 cents 380 .. 760 match: 17 SD: 0.1641 cents 412 .. 824 match: 17 SD: 0.1538 cents 444 .. 888 match: 17 SD: 0.1486 cents 476 .. 952 match: 17 SD: 0.1460 cents 479 .. 958 match: 17 SD: 0.1387 cents 492 .. 984 match: 17 SD: 0.1294 cents 511 .. 1022 match: 17 SD: 0.1175 cents 524 .. 1048 match: 17 SD: 0.1141 cents 556 .. 1112 match: 17 SD: 0.1107 cents 588 .. 1176 match: 17 SD: 0.1046 cents