Scala analysis: smalldimos19
Small diesic 19-note MOS, 31/120 version
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40.000 cents 40.000000 2: 80.000 cents 80.000000 3: 230.000 cents 230.000000 4: 270.000 cents 270.000000 5: 310.000 cents 310.000000 6: 350.000 cents 350.000000 7: 390.000 cents 390.000000 8: 540.000 cents 540.000000 9: 580.000 cents 580.000000 10: 620.000 cents 620.000000 11: 660.000 cents 660.000000 12: 810.000 cents 810.000000 13: 850.000 cents 850.000000 14: 890.000 cents 890.000000 15: 930.000 cents 930.000000 16: 970.000 cents 970.000000 17: 1120.000 cents 1120.000000 18: 1160.000 cents 1160.000000 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40.0000 cents 40.0000 1: 40.0000 cents 40.0000 2: 40.0000 cents 40.0000 3: 150.0000 cents 150.0000 4: 40.0000 cents 40.0000 5: 40.0000 cents 40.0000 6: 40.0000 cents 40.0000 7: 40.0000 cents 40.0000 8: 150.0000 cents 150.0000 9: 40.0000 cents 40.0000 10: 40.0000 cents 40.0000 11: 40.0000 cents 40.0000 12: 150.0000 cents 150.0000 13: 40.0000 cents 40.0000 14: 40.0000 cents 40.0000 15: 40.0000 cents 40.0000 16: 40.0000 cents 40.0000 17: 150.0000 cents 150.0000 18: 40.0000 cents 40.0000 19: 40.0000 cents 40.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 15 40.00000 cents 1: 4 150.00000 cents 2: 11 80.00000 cents 2: 8 190.00000 cents 3: 7 120.00000 cents 3: 12 230.00000 cents 4: 3 160.00000 cents 4: 16 270.00000 cents 5: 18 310.00000 cents 5: 1 420.00000 cents 6: 14 350.00000 cents 6: 5 460.00000 cents 7: 10 390.00000 cents 7: 9 500.00000 cents 8: 6 430.00000 cents 8: 13 540.00000 cents 9: 2 470.00000 cents 9: 17 580.00000 cents 10: 17 620.00000 cents 10: 2 730.00000 cents 11: 13 660.00000 cents 11: 6 770.00000 cents 12: 9 700.00000 cents 12: 10 810.00000 cents 13: 5 740.00000 cents 13: 14 850.00000 cents 14: 1 780.00000 cents 14: 18 890.00000 cents 15: 16 930.00000 cents 15: 3 1040.00000 cents 16: 12 970.00000 cents 16: 7 1080.00000 cents 17: 8 1010.00000 cents 17: 11 1120.00000 cents 18: 4 1050.00000 cents 18: 15 1160.00000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
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 : 40.0 80.0 230.0 270.0 310.0 350.0 390.0 540.0 580.0 620.0 660.0 810.0 850.0 890.0 930.0 970.0 1120.0 1160.0 1200.0 40.0 : 40.0 190.0 230.0 270.0 310.0 350.0 500.0 540.0 580.0 620.0 770.0 810.0 850.0 890.0 930.0 1080.0 1120.0 1160.0 1200.0 80.0 : 150.0 190.0 230.0 270.0 310.0 460.0 500.0 540.0 580.0 730.0 770.0 810.0 850.0 890.0 1040.0 1080.0 1120.0 1160.0 1200.0 230.0 : 40.0 80.0 120.0 160.0 310.0 350.0 390.0 430.0 580.0 620.0 660.0 700.0 740.0 890.0 930.0 970.0 1010.0 1050.0 1200.0 270.0 : 40.0 80.0 120.0 270.0 310.0 350.0 390.0 540.0 580.0 620.0 660.0 700.0 850.0 890.0 930.0 970.0 1010.0 1160.0 1200.0 310.0 : 40.0 80.0 230.0 270.0 310.0 350.0 500.0 540.0 580.0 620.0 660.0 810.0 850.0 890.0 930.0 970.0 1120.0 1160.0 1200.0 350.0 : 40.0 190.0 230.0 270.0 310.0 460.0 500.0 540.0 580.0 620.0 770.0 810.0 850.0 890.0 930.0 1080.0 1120.0 1160.0 1200.0 390.0 : 150.0 190.0 230.0 270.0 420.0 460.0 500.0 540.0 580.0 730.0 770.0 810.0 850.0 890.0 1040.0 1080.0 1120.0 1160.0 1200.0 540.0 : 40.0 80.0 120.0 270.0 310.0 350.0 390.0 430.0 580.0 620.0 660.0 700.0 740.0 890.0 930.0 970.0 1010.0 1050.0 1200.0 580.0 : 40.0 80.0 230.0 270.0 310.0 350.0 390.0 540.0 580.0 620.0 660.0 700.0 850.0 890.0 930.0 970.0 1010.0 1160.0 1200.0 620.0 : 40.0 190.0 230.0 270.0 310.0 350.0 500.0 540.0 580.0 620.0 660.0 810.0 850.0 890.0 930.0 970.0 1120.0 1160.0 1200.0 660.0 : 150.0 190.0 230.0 270.0 310.0 460.0 500.0 540.0 580.0 620.0 770.0 810.0 850.0 890.0 930.0 1080.0 1120.0 1160.0 1200.0 810.0 : 40.0 80.0 120.0 160.0 310.0 350.0 390.0 430.0 470.0 620.0 660.0 700.0 740.0 780.0 930.0 970.0 1010.0 1050.0 1200.0 850.0 : 40.0 80.0 120.0 270.0 310.0 350.0 390.0 430.0 580.0 620.0 660.0 700.0 740.0 890.0 930.0 970.0 1010.0 1160.0 1200.0 890.0 : 40.0 80.0 230.0 270.0 310.0 350.0 390.0 540.0 580.0 620.0 660.0 700.0 850.0 890.0 930.0 970.0 1120.0 1160.0 1200.0 930.0 : 40.0 190.0 230.0 270.0 310.0 350.0 500.0 540.0 580.0 620.0 660.0 810.0 850.0 890.0 930.0 1080.0 1120.0 1160.0 1200.0 970.0 : 150.0 190.0 230.0 270.0 310.0 460.0 500.0 540.0 580.0 620.0 770.0 810.0 850.0 890.0 1040.0 1080.0 1120.0 1160.0 1200.0 1120.0: 40.0 80.0 120.0 160.0 310.0 350.0 390.0 430.0 470.0 620.0 660.0 700.0 740.0 890.0 930.0 970.0 1010.0 1050.0 1200.0 1160.0: 40.0 80.0 120.0 270.0 310.0 350.0 390.0 430.0 580.0 620.0 660.0 700.0 850.0 890.0 930.0 970.0 1010.0 1160.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.0000 .. 150.0000 cents 110.00000 cents 40.00000 cents 2: 80.0000 .. 190.0000 cents 110.00000 cents -70.00000 cents 3: 120.0000 .. 230.0000 cents 110.00000 cents -70.00000 cents 4: 160.0000 .. 270.0000 cents 110.00000 cents -70.00000 cents 5: 310.0000 .. 420.0000 cents 110.00000 cents 40.00000 cents 6: 350.0000 .. 460.0000 cents 110.00000 cents -70.00000 cents 7: 390.0000 .. 500.0000 cents 110.00000 cents -70.00000 cents 8: 430.0000 .. 540.0000 cents 110.00000 cents -70.00000 cents 9: 470.0000 .. 580.0000 cents 110.00000 cents -70.00000 cents 10: 620.0000 .. 730.0000 cents 110.00000 cents 40.00000 cents 11: 660.0000 .. 770.0000 cents 110.00000 cents -70.00000 cents 12: 700.0000 .. 810.0000 cents 110.00000 cents -70.00000 cents 13: 740.0000 .. 850.0000 cents 110.00000 cents -70.00000 cents 14: 780.0000 .. 890.0000 cents 110.00000 cents -70.00000 cents 15: 930.0000 .. 1040.0000 cents 110.00000 cents 40.00000 cents 16: 970.0000 .. 1080.0000 cents 110.00000 cents -70.00000 cents 17: 1010.0000 .. 1120.0000 cents 110.00000 cents -70.00000 cents 18: 1050.0000 .. 1160.0000 cents 110.00000 cents -70.00000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 40.00000 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 150.00000 cents Average / Smallest step : 1.578947 Largest / Average step : 2.375000 Largest / Smallest step : 3.750000 Median interval of one step : 40.00000 cents, amount: 15 Most common interval of one step : 40.00000 cents, amount: 15 Least squares average step : 63.46964 cents, oct.: 1205.92308 cents Scale is not proper Scale has Myhill's property chromas: 110.00000 cents and 70.00000 cents, ratio: 1.571429 generators: 5 of 310.00000 cents and 14 of 890.00000 cents ET pair of linear temperament : 27&31 Scale is distributional even Scale is a mode of a 120-tone equal temperament with octave 2/1 degrees: 4 8 23 27 31 35 39 54 58 62 66 81 85 89 93 97 112 116 120 generators: 31 and 89 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 120-tone equal temperament Step pattern alph. order: AABAAAABAAABAAAABAA Step pattern size order : SSLSSSSLSSSLSSSSLSS Interval vector is [ 0 0 0 15 0 0 0 11 0 0 0 7 0 0 4 3 0 0 8 0 0 0 12 0 0 0 16 0 0 0 18 0 0 0 14 0 0 0 10 0 0 1 6 0 0 5 2 0 0 9 0 0 0 13 0 0 0 17 0 0 ] Scale is a Constant Structure, by a margin of 10.00000 cents Scale diversity : 1.190909 Lumma stability : 0.166667 Lumma impropriety factor : 0.566667 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 10.00000 cents Most common intervals : 310.00000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 390.000 890.000 cents Most common triad is 0.0 310.000 890.000 cents, amount: 17 Number of recognisable fifths : 9, average 700.0000 cents Scale contains two identical disjunct "tetrachords" of 9 notes Formal octave complements present : 19 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
19: 1 0 3 0 1 1 0 3 0 1 0 3 0 1 1 0 3 0 1 N I SD: 19.3833 c. M: 28.9474 c. 21: 1 0 3 1 0 1 1 2 1 1 1 2 1 1 0 1 3 0 1 N I SD: 16.3540 c. M: 25.7143 c. 22: 1 0 3 1 1 0 1 3 1 0 1 3 1 0 1 1 3 0 1 N I SD: 15.6211 c. M:-25.4545 c. 23: 1 1 2 1 1 1 0 3 1 1 1 3 0 1 1 1 2 1 1 N I SD: 16.2344 c. M:-24.7826 c. 24: 1 1 3 0 1 1 1 3 1 0 1 3 1 1 1 0 3 1 1 N I SD: 14.5095 c. M:-20.0000 c. 25: 1 1 3 1 0 1 1 3 1 1 1 3 1 1 0 1 3 1 1 N I SD: 13.0586 c. M: 22.0000 c. 27: 1 1 3 1 1 1 1 3 1 1 1 3 1 1 1 1 3 1 1 N M DE I SD: 6.0858 c. M:-10.0000 c. 31: 1 1 4 1 1 1 1 4 1 1 1 4 1 1 1 1 4 1 1 N M DE I SD: 1.7668 c. M: 2.9032 c. 89: 3 3 11 3 3 3 3 11 3 3 3 11 3 3 3 3 11 3 3 N M DE I SD: 0.6154 c. M:-1.0112 c. 120: 4 4 15 4 4 4 4 15 4 4 4 15 4 4 4 4 15 4 4 N M DE I 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: 20.9775 cents 3 .. 6 match: 3 H SD: 14.1109 cents 4 .. 8 match: 4 H SD: 10.5332 cents 5 .. 10 match: 5 H SD: 9.6273 cents 6 .. 12 match: 6 H SD: 15.4125 cents 7 .. 14 match: 7 H SD: 10.2414 cents 8 .. 16 match: 8 H SD: 7.5835 cents 9 .. 18 match: 9 H SD: 9.5664 cents 10 .. 20 match: 10 H SD: 11.2391 cents 11 .. 22 match: 9 SD: 8.9732 cents 12 .. 24 match: 11 SD: 7.8967 cents 13 .. 26 match: 10 SD: 6.5136 cents 14 .. 28 match: 13 SD: 6.8652 cents 15 .. 30 match: 12 SD: 5.3175 cents 16 .. 32 match: 11 SD: 4.2990 cents 17 .. 34 match: 14 SD: 4.5216 cents 18 .. 36 match: 13 SD: 4.4215 cents 19 .. 38 match: 14 S SD: 3.3116 cents 20 .. 40 match: 14 SD: 2.7074 cents 21 .. 42 match: 14 SD: 2.7175 cents 22 .. 44 match: 16 SD: 3.0700 cents 23 .. 46 match: 16 SD: 3.1173 cents 24 .. 48 match: 16 SD: 2.7653 cents 25 .. 50 match: 16 SD: 2.4915 cents 26 .. 52 match: 15 SD: 3.7470 cents 27 .. 54 match: 17 SD: 2.6861 cents 28 .. 56 match: 17 SD: 2.3147 cents 29 .. 58 match: 16 SD: 3.4345 cents 30 .. 60 match: 18 SD: 2.2712 cents 31 .. 62 match: 18 SD: 2.6914 cents 32 .. 64 match: 18 SD: 2.6568 cents 33 .. 66 match: 18 SD: 2.7593 cents 35 .. 70 match: 19 SD: 1.6936 cents 40 .. 80 match: 19 SD: 1.6507 cents 41 .. 82 match: 19 SD: 1.4967 cents 49 .. 98 match: 19 SD: 1.4885 cents 52 .. 104 match: 19 SD: 1.4757 cents 55 .. 110 match: 19 SD: 1.3917 cents 58 .. 116 match: 19 SD: 1.2948 cents 63 .. 126 match: 19 SD: 1.1609 cents 71 .. 142 match: 19 SD: 1.0179 cents 76 .. 152 match: 19 SD: 0.8713 cents 82 .. 164 match: 19 SD: 0.8273 cents 84 .. 168 match: 19 SD: 0.8158 cents 88 .. 176 match: 19 SD: 0.7973 cents 90 .. 180 match: 19 SD: 0.7391 cents 106 .. 212 match: 19 SD: 0.6993 cents 107 .. 214 match: 19 SD: 0.6287 cents 112 .. 224 match: 19 SD: 0.5809 cents 125 .. 250 match: 19 SD: 0.5472 cents 126 .. 252 match: 19 SD: 0.5280 cents 128 .. 256 match: 19 SD: 0.5123 cents 131 .. 262 match: 19 SD: 0.4988 cents 134 .. 268 match: 19 SD: 0.4762 cents 153 .. 306 match: 19 SD: 0.4211 cents 169 .. 338 match: 19 SD: 0.3957 cents 170 .. 340 match: 19 SD: 0.3736 cents 174 .. 348 match: 19 SD: 0.3541 cents 183 .. 366 match: 19 SD: 0.3371 cents 211 .. 422 match: 19 SD: 0.3133 cents 213 .. 426 match: 19 SD: 0.2606 cents 254 .. 508 match: 19 SD: 0.2179 cents 290 .. 580 match: 19 SD: 0.2149 cents 295 .. 590 match: 19 SD: 0.2148 cents 297 .. 594 match: 19 SD: 0.2129 cents 332 .. 664 match: 19 SD: 0.2049 cents 336 .. 672 match: 19 SD: 0.1939 cents 344 .. 688 match: 19 SD: 0.1815 cents 357 .. 714 match: 19 SD: 0.1784 cents 379 .. 758 match: 19 SD: 0.1585 cents 423 .. 846 match: 19 SD: 0.1476 cents 443 .. 886 match: 19 SD: 0.1433 cents 464 .. 928 match: 19 SD: 0.1218 cents 522 .. 1044 match: 19 SD: 0.1189 cents 550 .. 1100 match: 19 SD: 0.0983 cents