Scala analysis: phillips19
Pauline Phillips, 19 note organ manual scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 84.000 cents 84.000000 2: 155.000 cents 155.000000 3: 200.000 cents 200.000000 4: 268.000 cents 268.000000 5: 384.000 cents 384.000000 6: 400.000 cents 400.000000 7: 468.000 cents 468.000000 8: 500.000 cents 500.000000 9: 584.000 cents 584.000000 10: 668.000 cents 668.000000 11: 700.000 cents 700.000000 12: 768.000 cents 768.000000 13: 855.000 cents 855.000000 14: 900.000 cents 900.000000 15: 968.000 cents 968.000000 16: 1084.000 cents 1084.000000 17: 1100.000 cents 1100.000000 18: 1168.000 cents 1168.000000 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32.0000 cents 32.0000 1: 84.0000 cents 84.0000 2: 71.0000 cents 71.0000 3: 45.0000 cents 45.0000 4: 68.0000 cents 68.0000 5: 116.0000 cents 116.0000 6: 16.0000 cents 16.0000 7: 68.0000 cents 68.0000 8: 32.0000 cents 32.0000 9: 84.0000 cents 84.0000 10: 84.0000 cents 84.0000 11: 32.0000 cents 32.0000 12: 68.0000 cents 68.0000 13: 87.0000 cents 87.0000 14: 45.0000 cents 45.0000 15: 68.0000 cents 68.0000 16: 116.0000 cents 116.0000 17: 16.0000 cents 16.0000 18: 68.0000 cents 68.0000 19: 32.0000 cents 32.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16.00000 cents 1: 3 32.00000 cents 1: 2 45.00000 cents 1: 5 68.00000 cents 1: 1 71.00000 cents 1: 3 84.00000 cents 1: 1 87.00000 cents 1: 2 116.00000 cents 2: 2 84.00000 cents 2: 3 100.00000 cents 2: 2 113.00000 cents 2: 4 116.00000 cents 2: 3 132.00000 cents 2: 2 155.00000 cents 2: 1 168.00000 cents 2: 2 184.00000 cents 3: 2 116.00000 cents 3: 4 184.00000 cents 3: 2 187.00000 cents 3: 9 200.00000 cents 3: 2 229.00000 cents 4: 2 200.00000 cents 4: 5 232.00000 cents 4: 2 245.00000 cents 4: 1 255.00000 cents 4: 6 268.00000 cents 4: 1 271.00000 cents 4: 1 300.00000 cents 4: 1 316.00000 cents 5: 1 271.00000 cents 5: 1 284.00000 cents 5: 7 300.00000 cents 5: 2 313.00000 cents 5: 4 316.00000 cents 5: 1 332.00000 cents 5: 1 355.00000 cents 5: 2 384.00000 cents 6: 2 316.00000 cents 6: 2 345.00000 cents 6: 2 368.00000 cents 6: 4 384.00000 cents 6: 2 387.00000 cents 6: 5 400.00000 cents 6: 2 416.00000 cents 7: 2 384.00000 cents 7: 1 416.00000 cents 7: 2 429.00000 cents 7: 6 432.00000 cents 7: 2 455.00000 cents 7: 4 468.00000 cents 7: 1 484.00000 cents 7: 1 500.00000 cents 8: 1 471.00000 cents 8: 14 500.00000 cents 8: 1 513.00000 cents 8: 2 516.00000 cents 8: 1 584.00000 cents 9: 2 516.00000 cents 9: 2 532.00000 cents 9: 2 545.00000 cents 9: 4 568.00000 cents 9: 4 584.00000 cents 9: 2 587.00000 cents 9: 1 600.00000 cents 9: 2 616.00000 cents 10: 2 584.00000 cents 10: 1 600.00000 cents 10: 2 613.00000 cents 10: 4 616.00000 cents 10: 4 632.00000 cents 10: 2 655.00000 cents 10: 2 668.00000 cents 10: 2 684.00000 cents 11: 1 616.00000 cents 11: 2 684.00000 cents 11: 1 687.00000 cents 11: 14 700.00000 cents 11: 1 729.00000 cents 12: 1 700.00000 cents 12: 1 716.00000 cents 12: 4 732.00000 cents 12: 2 745.00000 cents 12: 6 768.00000 cents 12: 2 771.00000 cents 12: 1 784.00000 cents 12: 2 816.00000 cents 13: 2 784.00000 cents 13: 5 800.00000 cents 13: 2 813.00000 cents 13: 4 816.00000 cents 13: 2 832.00000 cents 13: 2 855.00000 cents 13: 2 884.00000 cents 14: 2 816.00000 cents 14: 1 845.00000 cents 14: 1 868.00000 cents 14: 4 884.00000 cents 14: 2 887.00000 cents 14: 7 900.00000 cents 14: 1 916.00000 cents 14: 1 929.00000 cents 15: 1 884.00000 cents 15: 1 900.00000 cents 15: 1 929.00000 cents 15: 6 932.00000 cents 15: 1 945.00000 cents 15: 2 955.00000 cents 15: 5 968.00000 cents 15: 2 1000.00000 cents 16: 2 971.00000 cents 16: 9 1000.00000 cents 16: 2 1013.00000 cents 16: 4 1016.00000 cents 16: 2 1084.00000 cents 17: 2 1016.00000 cents 17: 1 1032.00000 cents 17: 2 1045.00000 cents 17: 3 1068.00000 cents 17: 4 1084.00000 cents 17: 2 1087.00000 cents 17: 3 1100.00000 cents 17: 2 1116.00000 cents 18: 2 1084.00000 cents 18: 1 1113.00000 cents 18: 3 1116.00000 cents 18: 1 1129.00000 cents 18: 5 1132.00000 cents 18: 2 1155.00000 cents 18: 3 1168.00000 cents 18: 2 1184.00000 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.22222 = 65/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 84.0 155.0 200.0 268.0 384.0 400.0 468.0 500.0 584.0 668.0 700.0 768.0 855.0 900.0 968.0 1084.0 1100.0 1168.0 1200.0 84.0 : 71.0 116.0 184.0 300.0 316.0 384.0 416.0 500.0 584.0 616.0 684.0 771.0 816.0 884.0 1000.0 1016.0 1084.0 1116.0 1200.0 155.0 : 45.0 113.0 229.0 245.0 313.0 345.0 429.0 513.0 545.0 613.0 700.0 745.0 813.0 929.0 945.0 1013.0 1045.0 1129.0 1200.0 200.0 : 68.0 184.0 200.0 268.0 300.0 384.0 468.0 500.0 568.0 655.0 700.0 768.0 884.0 900.0 968.0 1000.0 1084.0 1155.0 1200.0 268.0 : 116.0 132.0 200.0 232.0 316.0 400.0 432.0 500.0 587.0 632.0 700.0 816.0 832.0 900.0 932.0 1016.0 1087.0 1132.0 1200.0 384.0 : 16.0 84.0 116.0 200.0 284.0 316.0 384.0 471.0 516.0 584.0 700.0 716.0 784.0 816.0 900.0 971.0 1016.0 1084.0 1200.0 400.0 : 68.0 100.0 184.0 268.0 300.0 368.0 455.0 500.0 568.0 684.0 700.0 768.0 800.0 884.0 955.0 1000.0 1068.0 1184.0 1200.0 468.0 : 32.0 116.0 200.0 232.0 300.0 387.0 432.0 500.0 616.0 632.0 700.0 732.0 816.0 887.0 932.0 1000.0 1116.0 1132.0 1200.0 500.0 : 84.0 168.0 200.0 268.0 355.0 400.0 468.0 584.0 600.0 668.0 700.0 784.0 855.0 900.0 968.0 1084.0 1100.0 1168.0 1200.0 584.0 : 84.0 116.0 184.0 271.0 316.0 384.0 500.0 516.0 584.0 616.0 700.0 771.0 816.0 884.0 1000.0 1016.0 1084.0 1116.0 1200.0 668.0 : 32.0 100.0 187.0 232.0 300.0 416.0 432.0 500.0 532.0 616.0 687.0 732.0 800.0 916.0 932.0 1000.0 1032.0 1116.0 1200.0 700.0 : 68.0 155.0 200.0 268.0 384.0 400.0 468.0 500.0 584.0 655.0 700.0 768.0 884.0 900.0 968.0 1000.0 1084.0 1168.0 1200.0 768.0 : 87.0 132.0 200.0 316.0 332.0 400.0 432.0 516.0 587.0 632.0 700.0 816.0 832.0 900.0 932.0 1016.0 1100.0 1132.0 1200.0 855.0 : 45.0 113.0 229.0 245.0 313.0 345.0 429.0 500.0 545.0 613.0 729.0 745.0 813.0 845.0 929.0 1013.0 1045.0 1113.0 1200.0 900.0 : 68.0 184.0 200.0 268.0 300.0 384.0 455.0 500.0 568.0 684.0 700.0 768.0 800.0 884.0 968.0 1000.0 1068.0 1155.0 1200.0 968.0 : 116.0 132.0 200.0 232.0 316.0 387.0 432.0 500.0 616.0 632.0 700.0 732.0 816.0 900.0 932.0 1000.0 1087.0 1132.0 1200.0 1084.0: 16.0 84.0 116.0 200.0 271.0 316.0 384.0 500.0 516.0 584.0 616.0 700.0 784.0 816.0 884.0 971.0 1016.0 1084.0 1200.0 1100.0: 68.0 100.0 184.0 255.0 300.0 368.0 484.0 500.0 568.0 600.0 684.0 768.0 800.0 868.0 955.0 1000.0 1068.0 1184.0 1200.0 1168.0: 32.0 116.0 187.0 232.0 300.0 416.0 432.0 500.0 532.0 616.0 700.0 732.0 800.0 887.0 932.0 1000.0 1116.0 1132.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.0000 .. 116.0000 cents 100.00000 cents 16.00000 cents 2: 84.0000 .. 184.0000 cents 100.00000 cents -32.00000 cents 3: 116.0000 .. 229.0000 cents 113.00000 cents -68.00000 cents 4: 200.0000 .. 316.0000 cents 116.00000 cents -29.00000 cents 5: 271.0000 .. 384.0000 cents 113.00000 cents -45.00000 cents 6: 316.0000 .. 416.0000 cents 100.00000 cents -68.00000 cents 7: 384.0000 .. 500.0000 cents 116.00000 cents -32.00000 cents 8: 471.0000 .. 584.0000 cents 113.00000 cents -29.00000 cents 9: 516.0000 .. 616.0000 cents 100.00000 cents -68.00000 cents 10: 584.0000 .. 684.0000 cents 100.00000 cents -32.00000 cents 11: 616.0000 .. 729.0000 cents 113.00000 cents -68.00000 cents 12: 700.0000 .. 816.0000 cents 116.00000 cents -29.00000 cents 13: 784.0000 .. 884.0000 cents 100.00000 cents -32.00000 cents 14: 816.0000 .. 929.0000 cents 113.00000 cents -68.00000 cents 15: 884.0000 .. 1000.0000 cents 116.00000 cents -45.00000 cents 16: 971.0000 .. 1084.0000 cents 113.00000 cents -29.00000 cents 17: 1016.0000 .. 1116.0000 cents 100.00000 cents -68.00000 cents 18: 1084.0000 .. 1184.0000 cents 100.00000 cents -32.00000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 16.00000 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 116.00000 cents Average / Smallest step : 3.947368 Largest / Average step : 1.836667 Largest / Smallest step : 7.250000 Median interval of one step : 68.00000 cents, amount: 5 Most common interval of one step : 68.00000 cents, amount: 5 Least squares average step : 65.02713 cents, oct.: 1235.51538 cents Scale is not proper Scale is a mode of a 1200-tone equal temperament with octave 2/1 degrees: 84 155 200 268 384 400 468 500 584 668 700 768 855 900 968 1084 1100 1168 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 667 of 667.000 cents and inv. generated superset size: 601 = 582 more = 3163.158% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFDGAAGDHCDEFDG Step pattern size order : FECDHADBFFBDGCDHADB Scale is not a Constant Structure Scale diversity : 1.477394 Lumma stability : 0.026667 Lumma impropriety factor : 0.645000 Number of different interval sizes : 97 = 5.38889 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 7.22222 = 65/9 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 3.00000 cents Most common intervals : 500.00000 cents & inv., amount: 15 Most common triad is 0.0 500.000 700.000 cents, amount: 11 Number of recognisable fifths : 17, average 700.1765 cents Number of appreciable fifths : 15, average 700.0000 cents Formal octave complements present : 3 = 15.7895% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
19: 1 1 1 1 2 0 1 1 1 1 1 1 1 1 1 2 0 1 1 N T3 SD: 20.6057 c. M: 36.4211 c. 20: 1 2 0 1 2 1 1 0 2 1 1 1 1 1 1 2 0 1 1 N D3 SD: 18.1485 c. M: 28.0000 c. 21: 1 2 1 1 2 0 1 1 1 2 0 1 2 1 1 2 0 1 1 N SD: 16.3304 c. M:-28.5714 c. 22: 2 1 1 1 2 0 2 0 2 1 1 1 2 1 1 2 0 2 0 N D3 SD: 16.1277 c. M:-32.0000 c. 23: 2 1 1 1 2 1 1 1 1 2 0 2 1 1 2 2 0 1 1 N SD: 14.9557 c. M:-23.3043 c. 24: 2 1 1 1 3 0 1 1 2 1 1 1 2 1 1 3 0 1 1 N SD: 12.6033 c. M: 18.0000 c. 25: 2 1 1 2 2 0 2 0 2 2 1 1 2 1 1 3 0 1 1 N SD: 12.5026 c. M:-20.0000 c. 28: 2 2 1 1 3 0 2 1 2 2 0 2 2 1 2 2 1 1 1 N SD: 11.7017 c. M:-17.7143 c. 29: 2 2 1 1 3 1 1 1 2 2 1 2 2 1 1 3 1 1 1 N SD: 11.3986 c. M: 19.7241 c. 31: 2 2 1 2 3 0 2 1 2 2 1 2 2 1 2 3 0 2 1 N SD: 6.7336 c. M: 16.1290 c. 36: 3 2 1 2 4 0 2 1 3 2 1 2 3 1 2 4 0 2 1 N SD: 8.2936 c. M:-16.0000 c. 39: 3 2 2 2 3 1 2 1 3 3 1 2 3 1 2 4 1 2 1 N SD: 8.1416 c. M:-15.3846 c. 41: 3 2 2 2 4 1 2 1 3 3 1 2 3 2 2 4 1 2 1 N SD: 5.5530 c. M:-12.1951 c. 48: 3 3 2 3 4 1 3 1 3 4 1 3 3 2 3 4 1 3 1 N SD: 5.9294 c. M: 9.0000 c. 52: 4 3 2 3 5 0 3 2 3 4 1 3 4 2 3 5 1 3 1 N SD: 6.3834 c. M:-8.9231 c. 53: 4 3 2 3 5 1 3 1 4 4 1 3 4 2 3 5 1 3 1 N SD: 5.7679 c. M:-11.2453 c. 59: 4 4 2 3 6 1 3 2 4 4 1 4 4 2 4 5 1 3 2 N SD: 5.4477 c. M: 8.6780 c. 60: 4 4 2 3 6 1 3 2 4 4 2 3 5 2 3 6 1 3 2 N SD: 5.1196 c. M: 8.0000 c. 62: 4 4 2 4 6 1 3 2 4 4 2 4 4 2 4 6 1 3 2 N SD: 5.0622 c. M: 9.9355 c. 63: 4 4 3 3 6 1 4 1 5 4 2 3 5 2 4 6 1 3 2 N SD: 4.9456 c. M:-9.5238 c. 69: 5 4 2 4 7 1 4 2 5 4 2 4 5 3 4 6 1 4 2 N SD: 4.6628 c. M: 8.6957 c. 70: 5 4 3 4 6 1 4 2 5 5 2 4 5 2 4 7 1 4 2 N SD: 4.4892 c. M: 8.5714 c. 72: 5 4 3 4 7 1 4 2 5 5 2 4 5 3 4 7 1 4 2 N SD: 1.8129 c. M: 5.0000 c. 84: 6 5 3 5 8 1 5 2 6 6 2 5 6 3 5 8 1 5 2 N SD: 2.1941 c. M:-3.4286 c. 115: 8 7 4 7 11 1 7 3 8 8 3 7 8 4 7 11 1 7 3 N SD: 2.1588 c. M: 4.3478 c. 125: 9 7 5 7 12 2 7 3 9 9 3 7 9 5 7 12 2 7 3 N SD: 2.0815 c. M:-4.0000 c. 144: 10 9 5 8 14 2 8 4 10 10 4 8 11 5 8 14 2 8 4 N SD: 1.3508 c. M:-3.3333 c. 156: 11 9 6 9 15 2 9 4 11 11 4 9 11 6 9 15 2 9 4 N SD: 0.8356 c. M:-1.2308 c. 216: 15 13 8 12 21 3 12 6 15 15 6 12 16 8 12 21 3 12 6 N SD: 0.8291 c. M: 1.3333 c. 228: 16 13 9 13 22 3 13 6 16 16 6 13 16 9 13 22 3 13 6 N SD: 0.8098 c. M: 2.3684 c. 288: 20 17 11 16 28 4 16 8 20 20 8 16 21 11 16 28 4 16 8 N SD: 0.8533 c. M: 1.3333 c. 300: 21 18 11 17 29 4 17 8 21 21 8 17 22 11 17 29 4 17 8 N SD: 0.3244 c. M:-1.0000 c. 372: 26 22 14 21 36 5 21 10 26 26 10 21 27 14 21 36 5 21 10 N SD: 0.1651 c. M: 0.2581 c. 672: 47 40 25 38 65 9 38 18 47 47 18 38 49 25 38 65 9 38 18 N SD: 0.1447 c. M:-0.3571 c. 828: 58 49 31 47 80 11 47 22 58 58 22 47 60 31 47 80 11 47 22 N SD: 0.0742 c. M:-0.1159 c. 1200: 84 71 45 68 116 16 68 32 84 84 32 68 87 45 68 116 16 68 32 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: 0.9775 cents 3 .. 6 match: 3 H SD: 5.2543 cents 4 .. 8 match: 4 H SD: 0.7849 cents 5 .. 10 match: 5 H SD: 16.0481 cents 6 .. 12 match: 6 H SD: 6.3537 cents 7 .. 14 match: 7 H SD: 9.7264 cents 8 .. 16 match: 8 H SD: 4.5431 cents 9 .. 18 match: 9 H SD: 6.7418 cents 10 .. 20 match: 9 SD: 7.6543 cents 11 .. 22 match: 10 SD: 5.9836 cents 12 .. 24 match: 12 H SD: 4.9598 cents 13 .. 26 match: 13 H SD: 5.6717 cents 14 .. 28 match: 13 S SD: 7.6879 cents 15 .. 30 match: 13 SD: 5.6702 cents 16 .. 32 match: 14 S SD: 4.0545 cents 17 .. 34 match: 15 S SD: 4.3979 cents 18 .. 36 match: 16 SD: 4.7107 cents 19 .. 38 match: 14 SD: 3.3534 cents 20 .. 40 match: 17 SD: 3.3153 cents 21 .. 42 match: 16 SD: 4.2159 cents 22 .. 44 match: 18 SD: 3.4648 cents 23 .. 46 match: 16 SD: 2.5264 cents 24 .. 48 match: 17 SD: 2.9516 cents 25 .. 50 match: 16 SD: 2.9400 cents 26 .. 52 match: 18 SD: 3.6311 cents 27 .. 54 match: 15 SD: 3.2799 cents 28 .. 56 match: 16 SD: 2.8390 cents 29 .. 58 match: 18 SD: 3.1907 cents 30 .. 60 match: 19 SD: 2.6962 cents 31 .. 62 match: 16 SD: 2.8329 cents 32 .. 64 match: 17 SD: 2.0655 cents 33 .. 66 match: 17 SD: 2.7615 cents 34 .. 68 match: 17 SD: 2.3959 cents 35 .. 70 match: 18 SD: 2.3010 cents 36 .. 72 match: 18 SD: 1.9856 cents 39 .. 78 match: 18 SD: 2.0922 cents 40 .. 80 match: 18 SD: 1.8897 cents 41 .. 82 match: 18 SD: 1.7922 cents 42 .. 84 match: 18 SD: 1.5921 cents 43 .. 86 match: 18 SD: 1.8233 cents 44 .. 88 match: 18 SD: 1.7246 cents 47 .. 94 match: 18 SD: 1.6454 cents 48 .. 96 match: 18 SD: 1.6011 cents 50 .. 100 match: 18 SD: 1.8483 cents 51 .. 102 match: 18 SD: 1.8376 cents 52 .. 104 match: 19 SD: 1.6067 cents 53 .. 106 match: 19 SD: 1.4976 cents 54 .. 108 match: 19 SD: 1.3937 cents 55 .. 110 match: 18 SD: 1.3128 cents 57 .. 114 match: 19 SD: 1.2998 cents 59 .. 118 match: 18 SD: 1.3692 cents 60 .. 120 match: 19 SD: 1.2142 cents 63 .. 126 match: 18 SD: 1.2571 cents 64 .. 128 match: 19 SD: 1.0372 cents 67 .. 134 match: 18 SD: 1.3575 cents 68 .. 136 match: 19 SD: 1.2176 cents 71 .. 142 match: 18 SD: 1.3500 cents 72 .. 144 match: 19 SD: 0.8829 cents 75 .. 150 match: 18 SD: 1.0005 cents 77 .. 154 match: 19 SD: 0.8659 cents 84 .. 168 match: 19 SD: 0.7154 cents 97 .. 194 match: 19 SD: 0.6790 cents 100 .. 200 match: 19 SD: 0.6183 cents 107 .. 214 match: 19 SD: 0.5967 cents 116 .. 232 match: 19 SD: 0.5664 cents 125 .. 250 match: 19 SD: 0.5570 cents 132 .. 264 match: 19 SD: 0.5147 cents 138 .. 276 match: 19 SD: 0.3959 cents 161 .. 322 match: 19 SD: 0.3137 cents 204 .. 408 match: 19 SD: 0.3038 cents 222 .. 444 match: 19 SD: 0.2914 cents 238 .. 476 match: 19 SD: 0.2754 cents 245 .. 490 match: 19 SD: 0.2569 cents 277 .. 554 match: 19 SD: 0.2241 cents 287 .. 574 match: 19 SD: 0.2139 cents 299 .. 598 match: 19 SD: 0.1825 cents 374 .. 748 match: 19 SD: 0.1806 cents 376 .. 752 match: 19 SD: 0.1746 cents 383 .. 766 match: 19 SD: 0.1592 cents 399 .. 798 match: 19 SD: 0.1578 cents 418 .. 836 match: 19 SD: 0.1438 cents 442 .. 884 match: 19 SD: 0.1425 cents 484 .. 968 match: 19 SD: 0.1223 cents 523 .. 1046 match: 19 SD: 0.1178 cents 580 .. 1160 match: 19 SD: 0.1093 cents