Scala analysis: 7-and-12
7-note and 12-note equal temperament, coinciding on Bb
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 100.000 cents 100.000000 2: 142.857 cents 142.857140 3: 200.000 cents 200.000000 4: 300.000 cents 300.000000 5: 314.286 cents 314.285710 6: 400.000 cents 400.000000 7: 485.714 cents 485.714290 8: 500.000 cents 500.000000 9: 600.000 cents 600.000000 10: 657.143 cents 657.142860 11: 700.000 cents 700.000000 12: 800.000 cents 800.000000 13: 828.571 cents 828.571430 14: 900.000 cents 900.000000 15: 1000.000 cents 1000.000000 16: 1100.000 cents 1100.000000 17: 1171.429 cents 1171.428750 18: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28.5712 cents 28.5712 1: 100.0000 cents 100.0000 2: 42.8571 cents 42.8571 3: 57.1429 cents 57.1429 4: 100.0000 cents 100.0000 5: 14.2857 cents 14.2857 6: 85.7143 cents 85.7143 7: 85.7143 cents 85.7143 8: 14.2857 cents 14.2857 9: 100.0000 cents 100.0000 10: 57.1429 cents 57.1429 11: 42.8571 cents 42.8571 12: 100.0000 cents 100.0000 13: 28.5714 cents 28.5714 14: 71.4286 cents 71.4286 15: 100.0000 cents 100.0000 16: 100.0000 cents 100.0000 17: 71.4287 cents 71.4287 18: 28.5712 cents 28.5712
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 14.28571 cents 1: 1 28.57125 cents 1: 1 28.57143 cents 1: 2 42.85714 cents 1: 2 57.14286 cents 1: 1 71.42857 cents 1: 1 71.42875 cents 1: 2 85.71429 cents 1: 6 100.00000 cents 2: 6 100.00000 cents 2: 2 114.28571 cents 2: 1 128.57125 cents 2: 1 128.57143 cents 2: 2 142.85714 cents 2: 2 157.14286 cents 2: 3 171.42858 cents 2: 1 200.00000 cents 3: 1 171.42839 cents 3: 3 171.42857 cents 3: 2 185.71429 cents 3: 10 200.00000 cents 3: 1 271.42857 cents 3: 1 271.42875 cents 4: 1 200.00000 cents 4: 2 214.28571 cents 4: 1 228.57125 cents 4: 1 228.57143 cents 4: 2 242.85714 cents 4: 2 257.14286 cents 4: 2 285.71429 cents 4: 6 300.00000 cents 4: 1 342.85732 cents 5: 6 300.00000 cents 5: 2 314.28571 cents 5: 1 328.57125 cents 5: 1 328.57143 cents 5: 4 342.85715 cents 5: 1 371.42857 cents 5: 1 371.42875 cents 5: 2 400.00000 cents 6: 1 342.85696 cents 6: 1 342.85714 cents 6: 2 357.14286 cents 6: 2 385.71429 cents 6: 8 400.00000 cents 6: 2 442.85714 cents 6: 1 471.42857 cents 6: 1 471.42875 cents 7: 2 400.00000 cents 7: 2 414.28571 cents 7: 1 428.57125 cents 7: 1 428.57143 cents 7: 2 457.14286 cents 7: 2 485.71429 cents 7: 6 500.00000 cents 7: 1 514.28571 cents 7: 1 514.28589 cents 8: 6 500.00000 cents 8: 1 514.28554 cents 8: 4 514.28572 cents 8: 2 542.85714 cents 8: 1 571.42857 cents 8: 1 571.42875 cents 8: 3 600.00000 cents 9: 1 528.57125 cents 9: 1 528.57143 cents 9: 2 557.14286 cents 9: 2 585.71429 cents 9: 6 600.00000 cents 9: 2 614.28571 cents 9: 2 642.85714 cents 9: 1 671.42857 cents 9: 1 671.42875 cents 10: 3 600.00000 cents 10: 1 628.57125 cents 10: 1 628.57143 cents 10: 2 657.14286 cents 10: 5 685.71429 cents 10: 6 700.00000 cents 11: 1 685.71411 cents 11: 1 685.71429 cents 11: 6 700.00000 cents 11: 2 714.28571 cents 11: 2 742.85714 cents 11: 1 771.42857 cents 11: 1 771.42875 cents 11: 2 785.71429 cents 11: 2 800.00000 cents 12: 1 728.57125 cents 12: 1 728.57143 cents 12: 2 757.14286 cents 12: 8 800.00000 cents 12: 2 814.28571 cents 12: 2 842.85714 cents 12: 1 857.14286 cents 12: 1 857.14304 cents 13: 2 800.00000 cents 13: 1 828.57125 cents 13: 1 828.57143 cents 13: 4 857.14286 cents 13: 1 871.42857 cents 13: 1 871.42875 cents 13: 2 885.71429 cents 13: 6 900.00000 cents 14: 1 857.14268 cents 14: 6 900.00000 cents 14: 2 914.28571 cents 14: 2 942.85714 cents 14: 2 957.14286 cents 14: 1 971.42857 cents 14: 1 971.42875 cents 14: 2 985.71429 cents 14: 1 1000.00000 cents 15: 1 928.57125 cents 15: 1 928.57143 cents 15: 10 1000.00000 cents 15: 2 1014.28571 cents 15: 3 1028.57143 cents 15: 1 1028.57161 cents 16: 1 1000.00000 cents 16: 3 1028.57142 cents 16: 2 1042.85714 cents 16: 2 1057.14286 cents 16: 1 1071.42857 cents 16: 1 1071.42875 cents 16: 2 1085.71429 cents 16: 6 1100.00000 cents 17: 6 1100.00000 cents 17: 2 1114.28571 cents 17: 1 1128.57125 cents 17: 1 1128.57143 cents 17: 2 1142.85714 cents 17: 2 1157.14286 cents 17: 1 1171.42857 cents 17: 1 1171.42875 cents 17: 2 1185.71429 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.0 : 100.0 142.9 200.0 300.0 314.3 400.0 485.7 500.0 600.0 657.1 700.0 800.0 828.6 900.0 1000.0 1100.0 1171.4 1200.0 100.0 : 42.9 100.0 200.0 214.3 300.0 385.7 400.0 500.0 557.1 600.0 700.0 728.6 800.0 900.0 1000.0 1071.4 1100.0 1200.0 142.9 : 57.1 157.1 171.4 257.1 342.9 357.1 457.1 514.3 557.1 657.1 685.7 757.1 857.1 957.1 1028.6 1057.1 1157.1 1200.0 200.0 : 100.0 114.3 200.0 285.7 300.0 400.0 457.1 500.0 600.0 628.6 700.0 800.0 900.0 971.4 1000.0 1100.0 1142.9 1200.0 300.0 : 14.3 100.0 185.7 200.0 300.0 357.1 400.0 500.0 528.6 600.0 700.0 800.0 871.4 900.0 1000.0 1042.9 1100.0 1200.0 314.3 : 85.7 171.4 185.7 285.7 342.9 385.7 485.7 514.3 585.7 685.7 785.7 857.1 885.7 985.7 1028.6 1085.7 1185.7 1200.0 400.0 : 85.7 100.0 200.0 257.1 300.0 400.0 428.6 500.0 600.0 700.0 771.4 800.0 900.0 942.9 1000.0 1100.0 1114.3 1200.0 485.7 : 14.3 114.3 171.4 214.3 314.3 342.9 414.3 514.3 614.3 685.7 714.3 814.3 857.1 914.3 1014.3 1028.6 1114.3 1200.0 500.0 : 100.0 157.1 200.0 300.0 328.6 400.0 500.0 600.0 671.4 700.0 800.0 842.9 900.0 1000.0 1014.3 1100.0 1185.7 1200.0 600.0 : 57.1 100.0 200.0 228.6 300.0 400.0 500.0 571.4 600.0 700.0 742.9 800.0 900.0 914.3 1000.0 1085.7 1100.0 1200.0 657.1 : 42.9 142.9 171.4 242.9 342.9 442.9 514.3 542.9 642.9 685.7 742.9 842.9 857.1 942.9 1028.6 1042.9 1142.9 1200.0 700.0 : 100.0 128.6 200.0 300.0 400.0 471.4 500.0 600.0 642.9 700.0 800.0 814.3 900.0 985.7 1000.0 1100.0 1157.1 1200.0 800.0 : 28.6 100.0 200.0 300.0 371.4 400.0 500.0 542.9 600.0 700.0 714.3 800.0 885.7 900.0 1000.0 1057.1 1100.0 1200.0 828.6 : 71.4 171.4 271.4 342.9 371.4 471.4 514.3 571.4 671.4 685.7 771.4 857.1 871.4 971.4 1028.6 1071.4 1171.4 1200.0 900.0 : 100.0 200.0 271.4 300.0 400.0 442.9 500.0 600.0 614.3 700.0 785.7 800.0 900.0 957.1 1000.0 1100.0 1128.6 1200.0 1000.0: 100.0 171.4 200.0 300.0 342.9 400.0 500.0 514.3 600.0 685.7 700.0 800.0 857.1 900.0 1000.0 1028.6 1100.0 1200.0 1100.0: 71.4 100.0 200.0 242.9 300.0 400.0 414.3 500.0 585.7 600.0 700.0 757.1 800.0 900.0 928.6 1000.0 1100.0 1200.0 1171.4: 28.6 128.6 171.4 228.6 328.6 342.9 428.6 514.3 528.6 628.6 685.7 728.6 828.6 857.1 928.6 1028.6 1128.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.2857 .. 100.0000 cents 85.71429 cents 14.28571 cents 2: 100.0000 .. 200.0000 cents 100.00000 cents 1/1, 0.0000 cents 3: 171.4284 .. 271.4287 cents 100.00036 cents -28.57161 cents 4: 200.0000 .. 342.8573 cents 142.85732 cents -71.42875 cents 5: 300.0000 .. 400.0000 cents 100.00000 cents -42.85732 cents 6: 342.8570 .. 471.4288 cents 128.57179 cents -57.14304 cents 7: 400.0000 .. 514.2859 cents 114.28589 cents -71.42875 cents 8: 500.0000 .. 600.0000 cents 100.00000 cents -14.28589 cents 9: 528.5712 .. 671.4288 cents 142.85750 cents -71.42875 cents 10: 600.0000 .. 700.0000 cents 100.00000 cents -71.42875 cents 11: 685.7141 .. 800.0000 cents 114.28589 cents -14.28589 cents 12: 728.5713 .. 857.1430 cents 128.57179 cents -71.42875 cents 13: 800.0000 .. 900.0000 cents 100.00000 cents -57.14304 cents 14: 857.1427 .. 1000.0000 cents 142.85732 cents -42.85732 cents 15: 928.5713 .. 1028.5716 cents 100.00036 cents -71.42875 cents 16: 1000.0000 .. 1100.0000 cents 100.00000 cents -28.57161 cents 17: 1100.0000 .. 1185.7143 cents 85.71429 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 18 -- Interval properties -- Smallest interval : 14.28571 cents, class 1 Average step (divided formal octave): 66.6667 cents Largest one step interval : 100.00000 cents Average / Smallest step : 4.666668 Largest / Average step : 1.500000 Largest / Smallest step : 7.000002 Median interval of one step : 71.42866 cents, amount: 0 Most common interval of one step : 100.00000 cents, amount: 6 Least squares average step : 66.53119 cents, oct.: 1197.56150 cents Scale is not proper Scale is a mode of a 84-tone equal temperament with octave 2/1 degrees: 7 10 14 21 22 28 34 35 42 46 49 56 58 63 70 77 82 84 Least number of segments generator : 43 of 614.286 cents and inv. number of contiguous generator circle segments: 4 Shortest superset generator : 43 of 614.286 cents and inv. generated superset size: 78 = 60 more = 433.333% Number of contiguous 1-step segments: 2 Step pattern alph. order: ABCADEEDACBAFGAAHI Step pattern size order : GCDGAFFAGDCGBEGGEB Interval vector is [ 2 1 2 2 1 2 12 2 1 2 2 6 2 12 2 1 2 2 1 2 12 2 1 3 2 1 2 12 2 1 2 2 1 2 12 1 1 2 2 1 2 6 ] Scale is not a Constant Structure Scale diversity : 1.532961 Lumma stability : 0.023810 Lumma impropriety factor : 0.595240 Number of different interval sizes : 114 = 6.70588 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 8.05882 = 137/17 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.00018 cents Most common triad is 0.0 100.000 200.000 cents, amount: 12 Number of recognisable fifths : 20, average 697.1429 cents Number of appreciable fifths : 14, average 702.0408 cents Formal octave complements present : 12 = 66.6667% Limited inverse transpositions : 12 Inversional symmetry on degrees : 6 15 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
18: 1 0 1 2 0 1 2 0 1 1 1 1 1 1 1 2 1 1 N T3 SD: 48.7950 c. M: 76.1905 c. 19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 P M ME SD: 25.9456 c. M: 47.3684 c. 20: 1 1 1 2 0 1 2 0 2 1 0 2 1 1 1 2 1 1 N SD: 23.4352 c. M: 40.0000 c. 22: 2 1 1 2 0 1 2 0 2 1 1 2 0 2 1 2 1 1 N SD: 15.9117 c. M:-27.2727 c. 24: 2 1 1 2 0 2 2 0 2 1 1 2 1 1 2 2 1 1 N T3 S SD: 8.9087 c. M: 21.4288 c. 33: 3 1 1 3 1 2 2 1 2 2 1 3 1 2 2 3 2 1 N SD: 10.4346 c. M: 18.1818 c. 34: 3 1 2 3 0 2 3 0 3 2 1 3 0 3 2 3 2 1 N SD: 10.2958 c. M:-17.6471 c. 35: 3 1 2 2 1 2 3 0 3 2 1 3 1 2 3 3 2 1 N SD: 11.9333 c. M: 25.7143 c. 36: 3 1 2 3 0 3 3 0 3 2 1 3 1 2 3 3 2 1 N S SD: 5.9391 c. M: 14.2857 c. 45: 4 1 2 4 1 3 3 1 3 3 1 4 1 3 3 4 3 1 N SD: 7.6520 c. M: 13.3333 c. 46: 4 1 3 4 0 3 4 0 4 2 2 4 1 3 3 4 3 1 N SD: 7.6099 c. M:-13.0435 c. 48: 4 2 2 4 1 3 3 1 4 2 2 4 1 3 4 4 3 1 N S SD: 4.4543 c. M: 10.7143 c. 57: 5 2 3 4 1 4 4 1 5 2 2 5 1 4 5 4 4 1 N SD: 6.0411 c. M:-10.5263 c. 58: 5 2 3 5 0 4 4 1 5 3 2 5 1 4 4 5 4 1 N SD: 6.0354 c. M:-10.3448 c. 60: 5 2 3 5 1 4 4 1 5 3 2 5 1 4 5 5 4 1 N S SD: 3.5635 c. M: 8.5714 c. 72: 6 3 3 6 1 5 5 1 6 3 3 6 2 4 6 6 4 2 N S SD: 2.9696 c. M: 7.1429 c. 84: 7 3 4 7 1 6 6 1 7 4 3 7 2 5 7 7 5 2 N S SD: 0.0000 c. M: 0.0002 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.9775 cents 3 .. 6 match: 3 H SD: 5.2543 cents 4 .. 8 match: 4 H SD: 8.5256 cents 5 .. 10 match: 5 H SD: 5.6731 cents 6 .. 12 match: 6 H SD: 10.2558 cents 7 .. 14 match: 7 H SD: 9.8077 cents 8 .. 16 match: 8 H SD: 7.7346 cents 9 .. 18 match: 9 H SD: 6.4058 cents 10 .. 20 match: 10 H SD: 5.2575 cents 11 .. 22 match: 11 H SD: 8.3242 cents 12 .. 24 match: 11 SD: 5.1816 cents 13 .. 26 match: 11 SD: 7.7286 cents 14 .. 28 match: 13 S SD: 6.6007 cents 15 .. 30 match: 12 SD: 3.6964 cents 16 .. 32 match: 14 SD: 4.4580 cents 17 .. 34 match: 13 SD: 4.6662 cents 18 .. 36 match: 15 SD: 4.8184 cents 19 .. 38 match: 14 SD: 3.4780 cents 20 .. 40 match: 15 S SD: 4.2166 cents 21 .. 42 match: 15 SD: 4.4524 cents 22 .. 44 match: 16 SD: 3.3152 cents 23 .. 46 match: 16 SD: 4.2350 cents 24 .. 48 match: 16 SD: 2.7879 cents 25 .. 50 match: 14 SD: 4.0815 cents 26 .. 52 match: 16 SD: 2.6046 cents 27 .. 54 match: 15 SD: 3.1133 cents 28 .. 56 match: 16 SD: 3.1820 cents 29 .. 58 match: 17 SD: 3.4193 cents 30 .. 60 match: 15 SD: 3.0680 cents 31 .. 62 match: 16 SD: 2.2571 cents 32 .. 64 match: 17 SD: 2.0995 cents 33 .. 66 match: 17 SD: 2.5591 cents 34 .. 68 match: 17 SD: 1.7677 cents 35 .. 70 match: 16 SD: 2.2774 cents 36 .. 72 match: 16 SD: 1.9808 cents 37 .. 74 match: 16 SD: 2.2057 cents 38 .. 76 match: 18 SD: 2.2035 cents 39 .. 78 match: 17 SD: 2.1684 cents 40 .. 80 match: 16 SD: 2.5927 cents 41 .. 82 match: 17 SD: 2.0990 cents 42 .. 84 match: 16 SD: 2.1593 cents 43 .. 86 match: 17 SD: 2.1247 cents 44 .. 88 match: 18 SD: 1.9392 cents 45 .. 90 match: 16 SD: 2.0955 cents 46 .. 92 match: 16 SD: 1.4192 cents 47 .. 94 match: 17 SD: 1.6636 cents 48 .. 96 match: 17 SD: 1.6968 cents 49 .. 98 match: 17 SD: 1.6134 cents 50 .. 100 match: 18 SD: 1.3902 cents 51 .. 102 match: 16 SD: 1.5418 cents 52 .. 104 match: 16 SD: 1.8850 cents 53 .. 106 match: 18 SD: 1.7741 cents 54 .. 108 match: 18 SD: 1.4227 cents 55 .. 110 match: 17 SD: 1.5639 cents 56 .. 112 match: 17 SD: 1.2523 cents 57 .. 114 match: 17 SD: 1.5242 cents 58 .. 116 match: 17 SD: 1.3979 cents 60 .. 120 match: 18 SD: 1.3475 cents 61 .. 122 match: 16 SD: 1.4993 cents 62 .. 124 match: 17 SD: 1.3718 cents 63 .. 126 match: 18 SD: 1.3233 cents 64 .. 128 match: 17 SD: 1.4389 cents 65 .. 130 match: 18 SD: 0.9664 cents 67 .. 134 match: 16 SD: 1.2789 cents 68 .. 136 match: 18 SD: 1.0866 cents 70 .. 140 match: 17 SD: 0.9610 cents 72 .. 144 match: 17 SD: 0.9841 cents 73 .. 146 match: 17 SD: 1.1210 cents 76 .. 152 match: 17 SD: 1.4124 cents 77 .. 154 match: 17 SD: 1.2776 cents 78 .. 156 match: 18 SD: 1.0968 cents 79 .. 158 match: 17 SD: 1.2387 cents 80 .. 160 match: 18 SD: 0.7326 cents 82 .. 164 match: 16 SD: 0.8139 cents 85 .. 170 match: 17 SD: 0.9357 cents 88 .. 176 match: 17 SD: 1.0729 cents 89 .. 178 match: 18 SD: 0.8043 cents 90 .. 180 match: 18 SD: 0.7985 cents 95 .. 190 match: 18 SD: 0.7898 cents 96 .. 192 match: 18 SD: 0.6849 cents 104 .. 208 match: 18 SD: 0.6089 cents 116 .. 232 match: 18 SD: 0.5001 cents 150 .. 300 match: 18 SD: 0.4532 cents 164 .. 328 match: 18 SD: 0.4260 cents 170 .. 340 match: 18 SD: 0.4258 cents 173 .. 346 match: 18 SD: 0.4148 cents 185 .. 370 match: 18 SD: 0.3594 cents 186 .. 372 match: 18 SD: 0.3204 cents 220 .. 440 match: 18 SD: 0.3021 cents 247 .. 494 match: 18 SD: 0.2827 cents 253 .. 506 match: 18 SD: 0.2785 cents 254 .. 508 match: 18 SD: 0.2759 cents 266 .. 532 match: 18 SD: 0.2663 cents 269 .. 538 match: 18 SD: 0.2272 cents 301 .. 602 match: 18 SD: 0.2004 cents 349 .. 698 match: 18 SD: 0.1984 cents 358 .. 716 match: 18 SD: 0.1864 cents 370 .. 740 match: 18 SD: 0.1838 cents 386 .. 772 match: 18 SD: 0.1610 cents 407 .. 814 match: 18 SD: 0.1531 cents 427 .. 854 match: 18 SD: 0.1456 cents 466 .. 932 match: 18 SD: 0.1169 cents 522 .. 1044 match: 18 SD: 0.1102 cents 572 .. 1144 match: 18 SD: 0.1018 cents