Scala analysis: smalldiglum19
Small diesic "glumma" variant of 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: 120.000 cents 120.000000 4: 160.000 cents 160.000000 5: 310.000 cents 310.000000 6: 350.000 cents 350.000000 7: 390.000 cents 390.000000 8: 430.000 cents 430.000000 9: 470.000 cents 470.000000 10: 620.000 cents 620.000000 11: 660.000 cents 660.000000 12: 700.000 cents 700.000000 13: 740.000 cents 740.000000 14: 890.000 cents 890.000000 15: 930.000 cents 930.000000 16: 970.000 cents 970.000000 17: 1010.000 cents 1010.000000 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: 40.0000 cents 40.0000 4: 40.0000 cents 40.0000 5: 150.0000 cents 150.0000 6: 40.0000 cents 40.0000 7: 40.0000 cents 40.0000 8: 40.0000 cents 40.0000 9: 40.0000 cents 40.0000 10: 150.0000 cents 150.0000 11: 40.0000 cents 40.0000 12: 40.0000 cents 40.0000 13: 40.0000 cents 40.0000 14: 150.0000 cents 150.0000 15: 40.0000 cents 40.0000 16: 40.0000 cents 40.0000 17: 40.0000 cents 40.0000 18: 150.0000 cents 150.0000 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: 1 200.00000 cents 5: 16 310.00000 cents 5: 2 420.00000 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: 3 470.00000 cents 9: 15 580.00000 cents 9: 1 690.00000 cents 10: 1 510.00000 cents 10: 15 620.00000 cents 10: 3 730.00000 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: 2 780.00000 cents 14: 16 890.00000 cents 14: 1 1000.00000 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: 3 Average number of different intervals per interval class: 2.22222 = 20/9
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 : 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 1160.0 1200.0 40.0 : 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 1120.0 1160.0 1200.0 80.0 : 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 1080.0 1120.0 1160.0 1200.0 120.0 : 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 1040.0 1080.0 1120.0 1160.0 1200.0 160.0 : 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 1000.0 1040.0 1080.0 1120.0 1160.0 1200.0 310.0 : 40.0 80.0 120.0 160.0 310.0 350.0 390.0 430.0 580.0 620.0 660.0 700.0 850.0 890.0 930.0 970.0 1010.0 1050.0 1200.0 350.0 : 40.0 80.0 120.0 270.0 310.0 350.0 390.0 540.0 580.0 620.0 660.0 810.0 850.0 890.0 930.0 970.0 1010.0 1160.0 1200.0 390.0 : 40.0 80.0 230.0 270.0 310.0 350.0 500.0 540.0 580.0 620.0 770.0 810.0 850.0 890.0 930.0 970.0 1120.0 1160.0 1200.0 430.0 : 40.0 190.0 230.0 270.0 310.0 460.0 500.0 540.0 580.0 730.0 770.0 810.0 850.0 890.0 930.0 1080.0 1120.0 1160.0 1200.0 470.0 : 150.0 190.0 230.0 270.0 420.0 460.0 500.0 540.0 690.0 730.0 770.0 810.0 850.0 890.0 1040.0 1080.0 1120.0 1160.0 1200.0 620.0 : 40.0 80.0 120.0 270.0 310.0 350.0 390.0 540.0 580.0 620.0 660.0 700.0 740.0 890.0 930.0 970.0 1010.0 1050.0 1200.0 660.0 : 40.0 80.0 230.0 270.0 310.0 350.0 500.0 540.0 580.0 620.0 660.0 700.0 850.0 890.0 930.0 970.0 1010.0 1160.0 1200.0 700.0 : 40.0 190.0 230.0 270.0 310.0 460.0 500.0 540.0 580.0 620.0 660.0 810.0 850.0 890.0 930.0 970.0 1120.0 1160.0 1200.0 740.0 : 150.0 190.0 230.0 270.0 420.0 460.0 500.0 540.0 580.0 620.0 770.0 810.0 850.0 890.0 930.0 1080.0 1120.0 1160.0 1200.0 890.0 : 40.0 80.0 120.0 270.0 310.0 350.0 390.0 430.0 470.0 620.0 660.0 700.0 740.0 780.0 930.0 970.0 1010.0 1050.0 1200.0 930.0 : 40.0 80.0 230.0 270.0 310.0 350.0 390.0 430.0 580.0 620.0 660.0 700.0 740.0 890.0 930.0 970.0 1010.0 1160.0 1200.0 970.0 : 40.0 190.0 230.0 270.0 310.0 350.0 390.0 540.0 580.0 620.0 660.0 700.0 850.0 890.0 930.0 970.0 1120.0 1160.0 1200.0 1010.0: 150.0 190.0 230.0 270.0 310.0 350.0 500.0 540.0 580.0 620.0 660.0 810.0 850.0 890.0 930.0 1080.0 1120.0 1160.0 1200.0 1160.0: 40.0 80.0 120.0 160.0 200.0 350.0 390.0 430.0 470.0 510.0 660.0 700.0 740.0 780.0 930.0 970.0 1010.0 1050.0 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: 200.0000 .. 420.0000 cents 220.00000 cents -70.00000 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 .. 690.0000 cents 220.00000 cents -70.00000 cents 10: 510.0000 .. 730.0000 cents 220.00000 cents -180.00000 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 .. 1000.0000 cents 220.00000 cents -70.00000 cents 15: 930.0000 .. 1040.0000 cents 110.00000 cents -70.00000 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 : 60.53036 cents, oct.: 1150.07692 cents Scale is not proper Scale is 3-distributional even Scale is a mode of a 120-tone equal temperament with octave 2/1 degrees: 4 8 12 16 31 35 39 43 47 62 66 70 74 89 93 97 101 116 120 Least number of segments generator : 77 of 770.000 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 89 of 890.000 cents and inv. generated superset size: 22 = 3 more = 115.789% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 120-tone equal temperament Step pattern alph. order: AAAABAAAABAAABAAABA Step pattern size order : SSSSLSSSSLSSSLSSSLS Interval vector is [ 0 0 0 15 0 0 0 11 0 0 0 7 0 0 4 3 0 0 8 1 0 0 12 0 0 0 16 0 0 0 16 0 0 0 14 0 0 0 10 0 0 2 6 0 0 5 3 0 0 9 1 0 0 13 0 0 0 15 0 0 ] Scale is a Constant Structure, by a margin of 10.00000 cents Scale diversity : 1.210321 Lumma stability : 0.066667 Lumma impropriety factor : 0.733333 Number of different interval sizes : 40 = 2.22222 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.22222 = 20/9 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 10.00000 cents Number of recognisable fifths : 10, average 699.0000 cents Formal octave complements present : 5 = 26.3158% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
19: 1 0 1 1 2 1 0 1 0 3 0 1 1 2 1 0 1 2 1 N SD: 18.2389 c. M:-29.4737 c. 20: 1 0 1 1 2 1 0 1 1 2 1 1 0 3 0 1 1 2 1 N SD: 16.7017 c. M: 30.0000 c. 21: 1 0 1 1 2 1 1 1 0 3 1 0 1 3 0 1 1 2 1 N SD: 16.2981 c. M:-27.1429 c. 23: 1 1 0 1 3 1 0 1 1 3 1 0 1 3 1 1 0 3 1 N SD: 14.4934 c. M: 24.7826 c. 24: 1 0 1 1 3 1 1 0 1 3 1 1 1 3 0 1 1 3 1 N SD: 16.5434 c. M: 30.0000 c. 25: 1 0 1 1 3 1 1 1 1 3 0 1 1 3 1 1 1 3 1 N SD: 18.3590 c. M: 36.0000 c. 26: 1 0 1 1 3 1 1 1 1 3 1 1 1 3 1 1 1 3 1 N SD: 17.6058 c. M: 33.8462 c. 27: 1 1 1 1 3 1 1 1 1 3 1 1 1 3 1 1 1 3 1 N D3 SD: 10.1227 c. M:-18.8889 c. 31: 1 1 1 1 4 1 1 1 1 4 1 1 1 4 1 1 1 4 1 N D3 SD: 2.9388 c. M: 5.4839 c. 89: 3 3 3 3 11 3 3 3 3 11 3 3 3 11 3 3 3 11 3 N D3 SD: 1.0236 c. M:-1.9101 c. 120: 4 4 4 4 15 4 4 4 4 15 4 4 4 15 4 4 4 15 4 N D3 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: 9.5356 cents 4 .. 8 match: 4 H SD: 1.0837 cents 5 .. 10 match: 5 H SD: 16.6428 cents 6 .. 12 match: 6 H SD: 10.8420 cents 7 .. 14 match: 7 H SD: 14.7913 cents 8 .. 16 match: 7 S SD: 13.6364 cents 9 .. 18 match: 8 S SD: 6.1459 cents 10 .. 20 match: 8 SD: 5.4514 cents 11 .. 22 match: 9 S SD: 6.3600 cents 12 .. 24 match: 11 S SD: 7.0506 cents 13 .. 26 match: 9 SD: 4.5739 cents 14 .. 28 match: 10 SD: 4.1683 cents 15 .. 30 match: 12 SD: 4.8772 cents 16 .. 32 match: 13 SD: 5.0569 cents 17 .. 34 match: 13 S SD: 5.0971 cents 18 .. 36 match: 13 SD: 4.0985 cents 19 .. 38 match: 13 SD: 3.0656 cents 20 .. 40 match: 14 SD: 2.9517 cents 21 .. 42 match: 15 SD: 3.0090 cents 22 .. 44 match: 15 SD: 3.3336 cents 23 .. 46 match: 14 SD: 3.1862 cents 24 .. 48 match: 15 SD: 2.5024 cents 25 .. 50 match: 15 SD: 2.8231 cents 26 .. 52 match: 17 SD: 3.2313 cents 27 .. 54 match: 16 SD: 3.3703 cents 28 .. 56 match: 18 SD: 2.3987 cents 29 .. 58 match: 17 SD: 3.2780 cents 30 .. 60 match: 17 SD: 2.4888 cents 31 .. 62 match: 18 SD: 2.5960 cents 32 .. 64 match: 18 SD: 2.0384 cents 33 .. 66 match: 18 SD: 2.9714 cents 34 .. 68 match: 18 SD: 2.7684 cents 35 .. 70 match: 18 SD: 2.2467 cents 36 .. 72 match: 18 SD: 2.1704 cents 39 .. 78 match: 19 SD: 1.6152 cents 45 .. 90 match: 19 SD: 1.5361 cents 52 .. 104 match: 19 SD: 1.4532 cents 58 .. 116 match: 19 SD: 1.3199 cents 60 .. 120 match: 19 SD: 1.2901 cents 67 .. 134 match: 19 SD: 1.1024 cents 71 .. 142 match: 19 SD: 1.0072 cents 80 .. 160 match: 19 SD: 0.9215 cents 81 .. 162 match: 19 SD: 0.8926 cents 82 .. 164 match: 19 SD: 0.7798 cents 86 .. 172 match: 19 SD: 0.6568 cents 112 .. 224 match: 19 SD: 0.6253 cents 122 .. 244 match: 19 SD: 0.6189 cents 124 .. 248 match: 19 SD: 0.5572 cents 125 .. 250 match: 19 SD: 0.4957 cents 153 .. 306 match: 19 SD: 0.4495 cents 167 .. 334 match: 19 SD: 0.4024 cents 170 .. 340 match: 19 SD: 0.3867 cents 174 .. 348 match: 19 SD: 0.3642 cents 205 .. 410 match: 19 SD: 0.3199 cents 209 .. 418 match: 19 SD: 0.3023 cents 249 .. 498 match: 19 SD: 0.2551 cents 269 .. 538 match: 19 SD: 0.2482 cents 291 .. 582 match: 19 SD: 0.2453 cents 295 .. 590 match: 19 SD: 0.2413 cents 302 .. 604 match: 19 SD: 0.2319 cents 321 .. 642 match: 19 SD: 0.2198 cents 336 .. 672 match: 19 SD: 0.2114 cents 343 .. 686 match: 19 SD: 0.2112 cents 351 .. 702 match: 19 SD: 0.2087 cents 353 .. 706 match: 19 SD: 0.2012 cents 362 .. 724 match: 19 SD: 0.1991 cents 375 .. 750 match: 19 SD: 0.1933 cents 379 .. 758 match: 19 SD: 0.1701 cents 420 .. 840 match: 19 SD: 0.1681 cents 423 .. 846 match: 19 SD: 0.1451 cents 443 .. 886 match: 19 SD: 0.1409 cents 504 .. 1008 match: 19 SD: 0.1213 cents 506 .. 1012 match: 19 SD: 0.1154 cents 567 .. 1134 match: 19 SD: 0.1127 cents 571 .. 1142 match: 19 SD: 0.1115 cents