Scala analysis: hi19_72
inverted smithgw_hahn19 in 72-et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50.000 cents 50.000000 2: 116.667 cents 116.666667 3: 183.333 cents 183.333333 4: 233.333 cents 233.333333 5: 316.667 cents 316.666667 6: 383.333 cents 383.333333 7: 433.333 cents 433.333333 8: 500.000 cents 500.000000 9: 583.333 cents 583.333333 10: 616.667 cents 616.666667 11: 700.000 cents 700.000000 12: 766.667 cents 766.666667 13: 816.667 cents 816.666667 14: 883.333 cents 883.333333 15: 933.333 cents 933.333333 16: 1000.000 cents 1000.000000 17: 1083.333 cents 1083.333333 18: 1116.667 cents 1116.666667 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 83.3333 cents 83.3333 1: 50.0000 cents 50.0000 2: 66.6667 cents 66.6667 3: 66.6667 cents 66.6667 4: 50.0000 cents 50.0000 5: 83.3333 cents 83.3333 6: 66.6667 cents 66.6667 7: 50.0000 cents 50.0000 8: 66.6667 cents 66.6667 9: 83.3333 cents 83.3333 10: 33.3333 cents 33.3333 11: 83.3333 cents 83.3333 12: 66.6667 cents 66.6667 13: 50.0000 cents 50.0000 14: 66.6667 cents 66.6667 15: 50.0000 cents 50.0000 16: 66.6667 cents 66.6667 17: 83.3333 cents 83.3333 18: 33.3333 cents 33.3333 19: 83.3333 cents 83.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 33.33333 cents 1: 5 50.00000 cents 1: 7 66.66667 cents 1: 5 83.33333 cents 2: 12 116.66667 cents 2: 3 133.33333 cents 2: 4 150.00000 cents 3: 2 166.66667 cents 3: 8 183.33333 cents 3: 9 200.00000 cents 4: 7 233.33333 cents 4: 2 250.00000 cents 4: 10 266.66667 cents 5: 5 300.00000 cents 5: 11 316.66667 cents 5: 2 333.33333 cents 5: 1 350.00000 cents 6: 3 350.00000 cents 6: 1 366.66667 cents 6: 13 383.33333 cents 6: 2 400.00000 cents 7: 2 416.66667 cents 7: 9 433.33333 cents 7: 4 450.00000 cents 7: 4 466.66667 cents 8: 1 483.33333 cents 8: 13 500.00000 cents 8: 3 516.66667 cents 8: 2 533.33333 cents 9: 1 533.33333 cents 9: 5 550.00000 cents 9: 4 566.66667 cents 9: 9 583.33333 cents 10: 9 616.66667 cents 10: 4 633.33333 cents 10: 5 650.00000 cents 10: 1 666.66667 cents 11: 2 666.66667 cents 11: 3 683.33333 cents 11: 13 700.00000 cents 11: 1 716.66667 cents 12: 4 733.33333 cents 12: 4 750.00000 cents 12: 9 766.66667 cents 12: 2 783.33333 cents 13: 2 800.00000 cents 13: 13 816.66667 cents 13: 1 833.33333 cents 13: 3 850.00000 cents 14: 1 850.00000 cents 14: 2 866.66667 cents 14: 11 883.33333 cents 14: 5 900.00000 cents 15: 10 933.33333 cents 15: 2 950.00000 cents 15: 7 966.66667 cents 16: 9 1000.00000 cents 16: 8 1016.66667 cents 16: 2 1033.33333 cents 17: 4 1050.00000 cents 17: 3 1066.66667 cents 17: 12 1083.33333 cents 18: 5 1116.66667 cents 18: 7 1133.33333 cents 18: 5 1150.00000 cents 18: 2 1166.66667 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.66667 = 11/3
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 : 50.0 116.7 183.3 233.3 316.7 383.3 433.3 500.0 583.3 616.7 700.0 766.7 816.7 883.3 933.3 1000.0 1083.3 1116.7 1200.0 50.0 : 66.7 133.3 183.3 266.7 333.3 383.3 450.0 533.3 566.7 650.0 716.7 766.7 833.3 883.3 950.0 1033.3 1066.7 1150.0 1200.0 116.7 : 66.7 116.7 200.0 266.7 316.7 383.3 466.7 500.0 583.3 650.0 700.0 766.7 816.7 883.3 966.7 1000.0 1083.3 1133.3 1200.0 183.3 : 50.0 133.3 200.0 250.0 316.7 400.0 433.3 516.7 583.3 633.3 700.0 750.0 816.7 900.0 933.3 1016.7 1066.7 1133.3 1200.0 233.3 : 83.3 150.0 200.0 266.7 350.0 383.3 466.7 533.3 583.3 650.0 700.0 766.7 850.0 883.3 966.7 1016.7 1083.3 1150.0 1200.0 316.7 : 66.7 116.7 183.3 266.7 300.0 383.3 450.0 500.0 566.7 616.7 683.3 766.7 800.0 883.3 933.3 1000.0 1066.7 1116.7 1200.0 383.3 : 50.0 116.7 200.0 233.3 316.7 383.3 433.3 500.0 550.0 616.7 700.0 733.3 816.7 866.7 933.3 1000.0 1050.0 1133.3 1200.0 433.3 : 66.7 150.0 183.3 266.7 333.3 383.3 450.0 500.0 566.7 650.0 683.3 766.7 816.7 883.3 950.0 1000.0 1083.3 1150.0 1200.0 500.0 : 83.3 116.7 200.0 266.7 316.7 383.3 433.3 500.0 583.3 616.7 700.0 750.0 816.7 883.3 933.3 1016.7 1083.3 1133.3 1200.0 583.3 : 33.3 116.7 183.3 233.3 300.0 350.0 416.7 500.0 533.3 616.7 666.7 733.3 800.0 850.0 933.3 1000.0 1050.0 1116.7 1200.0 616.7 : 83.3 150.0 200.0 266.7 316.7 383.3 466.7 500.0 583.3 633.3 700.0 766.7 816.7 900.0 966.7 1016.7 1083.3 1166.7 1200.0 700.0 : 66.7 116.7 183.3 233.3 300.0 383.3 416.7 500.0 550.0 616.7 683.3 733.3 816.7 883.3 933.3 1000.0 1083.3 1116.7 1200.0 766.7 : 50.0 116.7 166.7 233.3 316.7 350.0 433.3 483.3 550.0 616.7 666.7 750.0 816.7 866.7 933.3 1016.7 1050.0 1133.3 1200.0 816.7 : 66.7 116.7 183.3 266.7 300.0 383.3 433.3 500.0 566.7 616.7 700.0 766.7 816.7 883.3 966.7 1000.0 1083.3 1150.0 1200.0 883.3 : 50.0 116.7 200.0 233.3 316.7 366.7 433.3 500.0 550.0 633.3 700.0 750.0 816.7 900.0 933.3 1016.7 1083.3 1133.3 1200.0 933.3 : 66.7 150.0 183.3 266.7 316.7 383.3 450.0 500.0 583.3 650.0 700.0 766.7 850.0 883.3 966.7 1033.3 1083.3 1150.0 1200.0 1000.0: 83.3 116.7 200.0 250.0 316.7 383.3 433.3 516.7 583.3 633.3 700.0 783.3 816.7 900.0 966.7 1016.7 1083.3 1133.3 1200.0 1083.3: 33.3 116.7 166.7 233.3 300.0 350.0 433.3 500.0 550.0 616.7 700.0 733.3 816.7 883.3 933.3 1000.0 1050.0 1116.7 1200.0 1116.7: 83.3 133.3 200.0 266.7 316.7 400.0 466.7 516.7 583.3 666.7 700.0 783.3 850.0 900.0 966.7 1016.7 1083.3 1166.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 83.3333 cents 50.00000 cents 33.33333 cents 2: 116.6667 .. 150.0000 cents 33.33333 cents 33.33333 cents 3: 166.6667 .. 200.0000 cents 33.33333 cents 16.66667 cents 4: 233.3333 .. 266.6667 cents 33.33333 cents 33.33333 cents 5: 300.0000 .. 350.0000 cents 50.00000 cents 33.33333 cents 6: 350.0000 .. 400.0000 cents 50.00000 cents 1/1, 0.0000 cents 7: 416.6667 .. 466.6667 cents 50.00000 cents 16.66667 cents 8: 483.3333 .. 533.3333 cents 50.00000 cents 16.66667 cents 9: 533.3333 .. 583.3333 cents 50.00000 cents 0.00000 cents 10: 616.6667 .. 666.6667 cents 50.00000 cents 33.33333 cents 11: 666.6667 .. 716.6667 cents 50.00000 cents 0.00000 cents 12: 733.3333 .. 783.3333 cents 50.00000 cents 16.66667 cents 13: 800.0000 .. 850.0000 cents 50.00000 cents 16.66667 cents 14: 850.0000 .. 900.0000 cents 50.00000 cents 1/1, 0.0000 cents 15: 933.3333 .. 966.6667 cents 33.33333 cents 33.33333 cents 16: 1000.0000 .. 1033.3333 cents 33.33333 cents 33.33333 cents 17: 1050.0000 .. 1083.3333 cents 33.33333 cents 16.66667 cents 18: 1116.6667 .. 1166.6667 cents 50.00000 cents 33.33333 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 83.33333 cents Average / Smallest step : 1.894737 Largest / Average step : 1.319444 Largest / Smallest step : 2.500000 Median interval of one step : 66.66667 cents, amount: 7 Most common interval of one step : 66.66667 cents, amount: 7 Least squares average step : 62.87449 cents, oct.: 1194.61538 cents Scale is proper Scale is a mode of a 72-tone equal temperament with octave 1200.000 cents degrees: 3 7 11 14 19 23 26 30 35 37 42 46 49 53 56 60 65 67 72 Least number of segments generator : 49 of 816.667 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 53 of 883.333 cents and inv. generated superset size: 41 = 22 more = 215.789% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBACBABCDCBABABCDC Step pattern size order : BCCBDCBCDADCBCBCDAD Interval vector is [ 0 2 5 7 5 0 12 3 4 2 8 9 0 7 2 10 0 5 11 2 4 1 13 2 2 9 4 4 1 13 3 3 5 4 9 0 ] Scale is not a Constant Structure Scale diversity : 1.376671 Rothenberg stability : 0.959064 = 164/171 Lumma stability : 0.333333 Number of different interval sizes : 62 = 3.44444 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 16.66667 cents Number of recognisable fifths : 14, average 701.1905 cents Number of appreciable fifths : 13, average 700.0000 cents Best minor thirds form a closed circle Formal octave complements present : 13 = 68.4211% -- Rational properties --
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.7075 c. M:-20.1754 c. 24: 1 1 2 1 1 2 1 1 2 0 2 1 1 2 1 1 2 0 2 N D3 S SD: 14.3066 c. M:-16.6667 c. 26: 1 2 1 1 2 1 1 2 2 0 2 2 1 1 1 2 1 1 2 N D3 SD: 12.9648 c. M:-21.7949 c. 27: 1 2 1 1 2 2 1 1 2 1 2 1 1 2 1 1 2 1 2 N D3 SD: 11.3283 c. M: 22.2222 c. 31: 1 2 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 P D3 S SD: 5.6347 c. M: 11.2903 c. 41: 2 2 2 2 3 2 2 2 3 1 3 2 2 2 2 2 3 1 3 P D3 SD: 4.2604 c. M:-8.5366 c. 53: 2 3 3 2 4 3 2 3 4 1 4 3 2 3 2 3 4 1 4 N SD: 3.8385 c. M: 7.2327 c. 72: 3 4 4 3 5 4 3 4 5 2 5 4 3 4 3 4 5 2 5 P 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: 0.7359 cents 4 .. 8 match: 4 H SD: 7.8443 cents 5 .. 10 match: 5 H SD: 3.5790 cents 6 .. 12 match: 6 H SD: 7.9712 cents 7 .. 14 match: 7 H SD: 2.8363 cents 8 .. 16 match: 8 H SD: 6.8768 cents 9 .. 18 match: 9 H SD: 4.4599 cents 10 .. 20 match: 10 H SD: 3.6630 cents 11 .. 22 match: 11 H SD: 7.5932 cents 12 .. 24 match: 12 H SD: 5.5737 cents 13 .. 26 match: 13 H SD: 5.9084 cents 14 .. 28 match: 14 H SD: 3.6474 cents 15 .. 30 match: 15 H SD: 4.3493 cents 16 .. 32 match: 15 SD: 5.0641 cents 17 .. 34 match: 15 S SD: 5.1566 cents 18 .. 36 match: 16 S SD: 3.8056 cents 19 .. 38 match: 14 SD: 5.0827 cents 20 .. 40 match: 18 S SD: 3.6080 cents 21 .. 42 match: 18 SD: 3.6658 cents 22 .. 44 match: 17 SD: 4.2636 cents 23 .. 46 match: 18 SD: 3.9799 cents 24 .. 48 match: 17 SD: 3.0801 cents 25 .. 50 match: 19 SD: 3.0448 cents 27 .. 54 match: 19 SD: 2.8316 cents 28 .. 56 match: 19 SD: 2.1813 cents 29 .. 58 match: 18 SD: 2.6066 cents 30 .. 60 match: 19 SD: 2.4548 cents 32 .. 64 match: 19 SD: 2.2813 cents 35 .. 70 match: 19 SD: 2.0818 cents 36 .. 72 match: 19 SD: 2.0048 cents 40 .. 80 match: 19 SD: 1.8714 cents 42 .. 84 match: 19 SD: 1.6421 cents 45 .. 90 match: 19 SD: 1.4366 cents 54 .. 108 match: 19 SD: 1.3876 cents 56 .. 112 match: 19 SD: 1.1555 cents 60 .. 120 match: 19 SD: 1.0332 cents 63 .. 126 match: 19 SD: 1.0189 cents 70 .. 140 match: 19 SD: 0.8244 cents 96 .. 192 match: 19 SD: 0.7925 cents 98 .. 196 match: 19 SD: 0.6083 cents 105 .. 210 match: 19 SD: 0.5674 cents 126 .. 252 match: 19 SD: 0.5549 cents 129 .. 258 match: 19 SD: 0.5270 cents 138 .. 276 match: 19 SD: 0.5020 cents 140 .. 280 match: 19 SD: 0.4528 cents 144 .. 288 match: 19 SD: 0.4527 cents 159 .. 318 match: 19 SD: 0.4451 cents 161 .. 322 match: 19 SD: 0.3911 cents 173 .. 346 match: 19 SD: 0.3744 cents 189 .. 378 match: 19 SD: 0.3669 cents 199 .. 398 match: 19 SD: 0.3632 cents 201 .. 402 match: 19 SD: 0.3414 cents 203 .. 406 match: 19 SD: 0.3329 cents 214 .. 428 match: 19 SD: 0.2988 cents 215 .. 430 match: 19 SD: 0.2476 cents 269 .. 538 match: 19 SD: 0.2215 cents 299 .. 598 match: 19 SD: 0.1972 cents 339 .. 678 match: 19 SD: 0.1946 cents 347 .. 694 match: 19 SD: 0.1900 cents 374 .. 748 match: 19 SD: 0.1744 cents 375 .. 750 match: 19 SD: 0.1707 cents 400 .. 800 match: 19 SD: 0.1700 cents 404 .. 808 match: 19 SD: 0.1481 cents 444 .. 888 match: 19 SD: 0.1473 cents 472 .. 944 match: 19 SD: 0.1292 cents 484 .. 968 match: 19 SD: 0.1257 cents 514 .. 1028 match: 19 SD: 0.1228 cents 544 .. 1088 match: 19 SD: 0.1122 cents 574 .. 1148 match: 19 SD: 0.0919 cents