Scala analysis: monzo_pyth-quartertone
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46.920 cents 46.920020 2: 90.225 cents 90.225000 3: 156.990 cents 156.989980 4: 203.910 cents 203.910000 5: 250.830 cents 250.830020 6: 294.135 cents 294.135000 7: 341.055 cents 341.055020 8: 407.820 cents 407.820000 9: 451.125 cents 451.124980 10: 498.045 cents 498.045000 11: 544.965 cents 544.965020 12: 611.730 cents 611.730010 13: 655.035 cents 655.034980 14: 701.955 cents 701.955000 15: 748.875 cents 748.875020 16: 792.180 cents 792.180000 17: 858.945 cents 858.944980 18: 905.865 cents 905.865000 19: 949.170 cents 949.169980 20: 996.090 cents 996.090000 21: 1043.010 cents 1043.010020 22: 1109.775 cents 1109.775000 23: 1153.080 cents 1153.079980 24: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 46.9200 cents 46.9200 1: 46.9200 cents 46.9200 2: 43.3050 cents 43.3050 3: 66.7650 cents 66.7650 4: 46.9200 cents 46.9200 5: 46.9200 cents 46.9200 6: 43.3050 cents 43.3050 7: 46.9200 cents 46.9200 8: 66.7650 cents 66.7650 9: 43.3050 cents 43.3050 10: 46.9200 cents 46.9200 11: 46.9200 cents 46.9200 12: 66.7650 cents 66.7650 13: 43.3050 cents 43.3050 14: 46.9200 cents 46.9200 15: 46.9200 cents 46.9200 16: 43.3050 cents 43.3050 17: 66.7650 cents 66.7650 18: 46.9200 cents 46.9200 19: 43.3050 cents 43.3050 20: 46.9200 cents 46.9200 21: 46.9200 cents 46.9200 22: 66.7650 cents 66.7650 23: 43.3050 cents 43.3050 24: 46.9200 cents 46.9200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 43.30498 cents 1: 12 46.92002 cents 1: 5 66.76498 cents 2: 9 90.22500 cents 2: 5 93.84004 cents 2: 5 110.06996 cents 2: 5 113.68500 cents 3: 9 137.14502 cents 3: 12 156.98998 cents 3: 3 160.60502 cents 4: 2 180.44999 cents 4: 2 184.06504 cents 4: 2 200.29496 cents 4: 18 203.91000 cents 5: 11 247.21498 cents 5: 12 250.83002 cents 5: 1 270.67499 cents 6: 15 294.13500 cents 6: 3 297.75004 cents 6: 3 313.97996 cents 6: 3 317.59500 cents 7: 1 337.43997 cents 7: 12 341.05502 cents 7: 11 360.89998 cents 8: 4 384.36000 cents 8: 4 387.97504 cents 8: 4 404.20496 cents 8: 12 407.82000 cents 9: 3 431.28001 cents 9: 12 451.12498 cents 9: 9 454.74002 cents 10: 21 498.04500 cents 10: 1 501.66004 cents 10: 1 517.88996 cents 10: 1 521.50501 cents 11: 5 541.34998 cents 11: 12 544.96502 cents 11: 7 564.80999 cents 12: 6 588.27000 cents 12: 6 591.88504 cents 12: 6 608.11496 cents 12: 6 611.73001 cents 13: 7 635.19002 cents 13: 12 655.03498 cents 13: 5 658.65002 cents 14: 1 678.49499 cents 14: 1 682.11004 cents 14: 1 698.33996 cents 14: 21 701.95500 cents 15: 9 745.25998 cents 15: 12 748.87502 cents 15: 3 768.71998 cents 16: 12 792.18000 cents 16: 4 795.79504 cents 16: 4 812.02496 cents 16: 4 815.64000 cents 17: 11 839.10002 cents 17: 12 858.94498 cents 17: 1 862.56003 cents 18: 3 882.40500 cents 18: 3 886.02004 cents 18: 3 902.24996 cents 18: 15 905.86500 cents 19: 1 929.32501 cents 19: 12 949.16998 cents 19: 11 952.78502 cents 20: 18 996.09000 cents 20: 2 999.70504 cents 20: 2 1015.93496 cents 20: 2 1019.55000 cents 21: 3 1039.39498 cents 21: 12 1043.01002 cents 21: 9 1062.85498 cents 22: 5 1086.31500 cents 22: 5 1089.93004 cents 22: 5 1106.15996 cents 22: 9 1109.77500 cents 23: 5 1133.23502 cents 23: 12 1153.07998 cents 23: 7 1156.69502 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.47826 = 80/23
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0.0 : 46.9 90.2 157.0 203.9 250.8 294.1 341.1 407.8 451.1 498.0 545.0 611.7 655.0 702.0 748.9 792.2 858.9 905.9 949.2 996.1 1043.0 1109.8 1153.1 1200.0 46.9 : 43.3 110.1 157.0 203.9 247.2 294.1 360.9 404.2 451.1 498.0 564.8 608.1 655.0 702.0 745.3 812.0 858.9 902.2 949.2 996.1 1062.9 1106.2 1153.1 1200.0 90.2 : 66.8 113.7 160.6 203.9 250.8 317.6 360.9 407.8 454.7 521.5 564.8 611.7 658.7 702.0 768.7 815.6 858.9 905.9 952.8 1019.5 1062.9 1109.8 1156.7 1200.0 157.0 : 46.9 93.8 137.1 184.1 250.8 294.1 341.1 388.0 454.7 498.0 545.0 591.9 635.2 702.0 748.9 792.2 839.1 886.0 952.8 996.1 1043.0 1089.9 1133.2 1200.0 203.9 : 46.9 90.2 137.1 203.9 247.2 294.1 341.1 407.8 451.1 498.0 545.0 588.3 655.0 702.0 745.3 792.2 839.1 905.9 949.2 996.1 1043.0 1086.3 1153.1 1200.0 250.8 : 43.3 90.2 157.0 200.3 247.2 294.1 360.9 404.2 451.1 498.0 541.3 608.1 655.0 698.3 745.3 792.2 858.9 902.2 949.2 996.1 1039.4 1106.2 1153.1 1200.0 294.1 : 46.9 113.7 157.0 203.9 250.8 317.6 360.9 407.8 454.7 498.0 564.8 611.7 655.0 702.0 748.9 815.6 858.9 905.9 952.8 996.1 1062.9 1109.8 1156.7 1200.0 341.1 : 66.8 110.1 157.0 203.9 270.7 314.0 360.9 407.8 451.1 517.9 564.8 608.1 655.0 702.0 768.7 812.0 858.9 905.9 949.2 1015.9 1062.9 1109.8 1153.1 1200.0 407.8 : 43.3 90.2 137.1 203.9 247.2 294.1 341.1 384.4 451.1 498.0 541.3 588.3 635.2 702.0 745.3 792.2 839.1 882.4 949.2 996.1 1043.0 1086.3 1133.2 1200.0 451.1 : 46.9 93.8 160.6 203.9 250.8 297.8 341.1 407.8 454.7 498.0 545.0 591.9 658.7 702.0 748.9 795.8 839.1 905.9 952.8 999.7 1043.0 1089.9 1156.7 1200.0 498.0 : 46.9 113.7 157.0 203.9 250.8 294.1 360.9 407.8 451.1 498.0 545.0 611.7 655.0 702.0 748.9 792.2 858.9 905.9 952.8 996.1 1043.0 1109.8 1153.1 1200.0 545.0 : 66.8 110.1 157.0 203.9 247.2 314.0 360.9 404.2 451.1 498.0 564.8 608.1 655.0 702.0 745.3 812.0 858.9 905.9 949.2 996.1 1062.9 1106.2 1153.1 1200.0 611.7 : 43.3 90.2 137.1 180.4 247.2 294.1 337.4 384.4 431.3 498.0 541.3 588.3 635.2 678.5 745.3 792.2 839.1 882.4 929.3 996.1 1039.4 1086.3 1133.2 1200.0 655.0 : 46.9 93.8 137.1 203.9 250.8 294.1 341.1 388.0 454.7 498.0 545.0 591.9 635.2 702.0 748.9 795.8 839.1 886.0 952.8 996.1 1043.0 1089.9 1156.7 1200.0 702.0 : 46.9 90.2 157.0 203.9 247.2 294.1 341.1 407.8 451.1 498.0 545.0 588.3 655.0 702.0 748.9 792.2 839.1 905.9 949.2 996.1 1043.0 1109.8 1153.1 1200.0 748.9 : 43.3 110.1 157.0 200.3 247.2 294.1 360.9 404.2 451.1 498.0 541.3 608.1 655.0 702.0 745.3 792.2 858.9 902.2 949.2 996.1 1062.9 1106.2 1153.1 1200.0 792.2 : 66.8 113.7 157.0 203.9 250.8 317.6 360.9 407.8 454.7 498.0 564.8 611.7 658.7 702.0 748.9 815.6 858.9 905.9 952.8 1019.6 1062.9 1109.8 1156.7 1200.0 858.9 : 46.9 90.2 137.1 184.1 250.8 294.1 341.1 388.0 431.3 498.0 545.0 591.9 635.2 682.1 748.9 792.2 839.1 886.0 952.8 996.1 1043.0 1089.9 1133.2 1200.0 905.9 : 43.3 90.2 137.1 203.9 247.2 294.1 341.1 384.4 451.1 498.0 545.0 588.3 635.2 702.0 745.3 792.2 839.1 905.9 949.2 996.1 1043.0 1086.3 1153.1 1200.0 949.2 : 46.9 93.8 160.6 203.9 250.8 297.8 341.1 407.8 454.7 501.7 545.0 591.9 658.7 702.0 748.9 795.8 862.6 905.9 952.8 999.7 1043.0 1109.8 1156.7 1200.0 996.1 : 46.9 113.7 157.0 203.9 250.8 294.1 360.9 407.8 454.7 498.0 545.0 611.7 655.0 702.0 748.9 815.6 858.9 905.9 952.8 996.1 1062.9 1109.8 1153.1 1200.0 1043.0: 66.8 110.1 157.0 203.9 247.2 314.0 360.9 407.8 451.1 498.0 564.8 608.1 655.0 702.0 768.7 812.0 858.9 905.9 949.2 1015.9 1062.9 1106.2 1153.1 1200.0 1109.8: 43.3 90.2 137.1 180.5 247.2 294.1 341.1 384.4 431.3 498.0 541.3 588.3 635.2 702.0 745.3 792.2 839.1 882.4 949.2 996.1 1039.4 1086.3 1133.2 1200.0 1153.1: 46.9 93.8 137.1 203.9 250.8 297.8 341.1 388.0 454.7 498.0 545.0 591.9 658.7 702.0 748.9 795.8 839.1 905.9 952.8 996.1 1043.0 1089.9 1156.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.3050 .. 66.7650 cents 23.46000 cents 43.30498 cents 2: 90.2250 .. 113.6850 cents 23.46000 cents 23.46002 cents 3: 137.1450 .. 160.6050 cents 23.46000 cents 23.46002 cents 4: 180.4500 .. 203.9100 cents 23.46001 cents 19.84497 cents 5: 247.2150 .. 270.6750 cents 23.46001 cents 43.30498 cents 6: 294.1350 .. 317.5950 cents 23.46000 cents 23.46001 cents 7: 337.4400 .. 360.9000 cents 23.46001 cents 19.84497 cents 8: 384.3600 .. 407.8200 cents 23.46000 cents 23.46002 cents 9: 431.2800 .. 454.7400 cents 23.46001 cents 23.46001 cents 10: 498.0450 .. 521.5050 cents 23.46001 cents 43.30498 cents 11: 541.3500 .. 564.8100 cents 23.46001 cents 19.84497 cents 12: 588.2700 .. 611.7300 cents 23.46001 cents 23.46001 cents 13: 635.1900 .. 658.6500 cents 23.46000 cents 23.46001 cents 14: 678.4950 .. 701.9550 cents 23.46001 cents 19.84497 cents 15: 745.2600 .. 768.7200 cents 23.46000 cents 43.30498 cents 16: 792.1800 .. 815.6400 cents 23.46000 cents 23.46002 cents 17: 839.1000 .. 862.5600 cents 23.46001 cents 23.46002 cents 18: 882.4050 .. 905.8650 cents 23.46000 cents 19.84497 cents 19: 929.3250 .. 952.7850 cents 23.46001 cents 23.46001 cents 20: 996.0900 .. 1019.5500 cents 23.46000 cents 43.30498 cents 21: 1039.3950 .. 1062.8550 cents 23.46000 cents 19.84498 cents 22: 1086.3150 .. 1109.7750 cents 23.46000 cents 23.46002 cents 23: 1133.2350 .. 1156.6950 cents 23.46000 cents 23.46002 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 43.30497 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 66.76498 cents Average / Smallest step : 1.154602 Largest / Average step : 1.335300 Largest / Smallest step : 1.541739 Median interval of one step : 46.92002 cents, amount: 12 Most common interval of one step : 46.92002 cents, amount: 12 Least squares average step : 50.06376 cents, oct.: 1201.53027 cents Scale is strictly proper Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 26 50 87 113 139 163 189 226 250 276 302 339 363 389 415 439 476 502 526 552 578 615 639 665 Least number of segments generator : 334 of 602.707 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 389 of 701.955 cents and inv. generated superset size: 53 = 29 more = 220.833% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCAABACBAACBAABCABAACBA Step pattern size order : MSLMMSMLSMMLSMMSLMSMMLSM Scale is a Constant Structure, by a margin of 19.84497 cents Scale diversity : 1.236604 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.550350 Number of different interval sizes : 80 = 3.47826 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.47826 = 80/23 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 3.61504 cents Most common intervals : 498.04500 cents & inv., amount: 21 Most common triad is 0.0 498.045 701.955 cents, amount: 18 Number of recognisable fifths : 22, average 701.7907 cents Formal octave complements present : 23 = 95.8333% Limited inverse transpositions with margin 23.4600 cents: 19 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
24: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.0874 c. M: 11.7300 c. 29: 1 1 2 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 P M ME SD: 6.0483 c. M:-10.0205 c. 53: 2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2 2 2 3 2 2 SP M ME SD: 1.1488 c. M: 1.7734 c. 176: 7 6 10 7 7 6 7 10 6 7 7 10 6 7 7 6 10 7 6 7 7 10 6 7 SP SD: 0.9857 c. M:-1.9064 c. 200: 8 7 11 8 8 7 8 11 7 8 8 11 7 8 8 7 11 8 7 8 8 11 7 8 SP SD: 0.7579 c. M:-1.1700 c. 229: 9 8 13 9 9 8 9 13 8 9 9 13 8 9 9 8 13 9 8 9 9 13 8 9 SP SD: 0.6337 c. M:-1.3704 c. 253: 10 9 14 10 10 9 10 14 9 10 10 14 9 10 10 9 14 10 9 10 10 14 9 10 SP SD: 0.3585 c. M: 0.5534 c. 306: 12 11 17 12 12 11 12 17 11 12 12 17 11 12 12 11 17 12 11 12 12 17 11 12 SP SD: 0.0974 c. M:-0.1504 c. 359: 14 13 20 14 14 13 14 20 13 14 14 20 13 14 14 13 20 14 13 14 14 20 13 14 SP SD: 0.0866 c. M:-0.1336 c. 665: 26 24 37 26 26 24 26 37 24 26 26 37 24 26 26 24 37 26 24 26 26 37 24 26 SP SD: 0.0019 c. M: 0.0030 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0000 cents 3 .. 6 match: 3 H SD: 7.1688 cents 4 .. 8 match: 4 H SD: 7.2839 cents 5 .. 10 match: 5 H SD: 9.4684 cents 6 .. 12 match: 6 H SD: 4.5953 cents 7 .. 14 match: 7 H SD: 6.1465 cents 8 .. 16 match: 8 H SD: 5.1402 cents 9 .. 18 match: 9 H SD: 4.4971 cents 10 .. 20 match: 10 H SD: 4.9802 cents 11 .. 22 match: 11 H SD: 2.0186 cents 12 .. 24 match: 12 H SD: 4.0049 cents 13 .. 26 match: 13 H SD: 4.4840 cents 14 .. 28 match: 14 H SD: 4.1102 cents 15 .. 30 match: 15 H SD: 4.4603 cents 16 .. 32 match: 16 H SD: 3.5393 cents 17 .. 34 match: 17 H SD: 3.1626 cents 18 .. 36 match: 17 S SD: 3.1421 cents 19 .. 38 match: 19 H SD: 2.3676 cents 20 .. 40 match: 20 H SD: 3.4270 cents 21 .. 42 match: 20 S SD: 3.3890 cents 22 .. 44 match: 21 S SD: 2.1896 cents 23 .. 46 match: 21 S SD: 2.9733 cents 24 .. 48 match: 22 SD: 2.7273 cents 25 .. 50 match: 20 SD: 3.6336 cents 26 .. 52 match: 23 SD: 2.6026 cents 27 .. 54 match: 22 SD: 2.7228 cents 28 .. 56 match: 23 SD: 2.7621 cents 29 .. 58 match: 23 SD: 2.8603 cents 30 .. 60 match: 24 SD: 2.3133 cents 31 .. 62 match: 24 SD: 2.1226 cents 33 .. 66 match: 24 SD: 1.5598 cents 40 .. 80 match: 24 SD: 1.5593 cents 41 .. 82 match: 24 SD: 1.4947 cents 50 .. 100 match: 24 SD: 1.3627 cents 54 .. 108 match: 24 SD: 1.2266 cents 57 .. 114 match: 24 SD: 1.2250 cents 59 .. 118 match: 24 SD: 1.1919 cents 63 .. 126 match: 24 SD: 1.1024 cents 64 .. 128 match: 24 SD: 0.9308 cents 70 .. 140 match: 24 SD: 0.8536 cents 76 .. 152 match: 24 SD: 0.8313 cents 78 .. 156 match: 24 SD: 0.7760 cents 95 .. 190 match: 24 SD: 0.7533 cents 96 .. 192 match: 24 SD: 0.6773 cents 97 .. 194 match: 24 SD: 0.6710 cents 98 .. 196 match: 24 SD: 0.6574 cents 108 .. 216 match: 24 SD: 0.6232 cents 109 .. 218 match: 24 SD: 0.5899 cents 114 .. 228 match: 24 SD: 0.4959 cents 128 .. 256 match: 24 SD: 0.4864 cents 135 .. 270 match: 24 SD: 0.4394 cents 146 .. 292 match: 24 SD: 0.4029 cents 148 .. 296 match: 24 SD: 0.3897 cents 167 .. 334 match: 24 SD: 0.3797 cents 168 .. 336 match: 24 SD: 0.3619 cents 184 .. 368 match: 24 SD: 0.3377 cents 189 .. 378 match: 24 SD: 0.3196 cents 207 .. 414 match: 24 SD: 0.3014 cents 222 .. 444 match: 24 SD: 0.2519 cents 248 .. 496 match: 24 SD: 0.2390 cents 276 .. 552 match: 24 SD: 0.2328 cents 282 .. 564 match: 24 SD: 0.2199 cents 294 .. 588 match: 24 SD: 0.2105 cents 297 .. 594 match: 24 SD: 0.2069 cents 302 .. 604 match: 24 SD: 0.2063 cents 316 .. 632 match: 24 SD: 0.2037 cents 319 .. 638 match: 24 SD: 0.2004 cents 335 .. 670 match: 24 SD: 0.1688 cents 390 .. 780 match: 24 SD: 0.1583 cents 392 .. 784 match: 24 SD: 0.1547 cents 400 .. 800 match: 24 SD: 0.1503 cents 410 .. 820 match: 24 SD: 0.1350 cents 432 .. 864 match: 24 SD: 0.1251 cents 464 .. 928 match: 24 SD: 0.1204 cents 474 .. 948 match: 24 SD: 0.1179 cents 486 .. 972 match: 24 SD: 0.1075 cents 576 .. 1152 match: 24 SD: 0.1052 cents 578 .. 1156 match: 24 SD: 0.0966 cents