Scala analysis: xen15-gilson-generalized-pythagorean-3-2-41
Generalized Pythagorean Scale, 3/2 stacked 41=24+17 times
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 531441/524288 23.460010 Pythagorean comma, ditonic comma 2: 46.920 cents 46.920021 3: 70.380 cents 70.380031 4: 2187/2048 113.685006 apotome 5: 1162261467/1073741824 137.145016 Pythagorean-19 comma 6: 160.605 cents 160.605027 7: 9/8 203.910002 major whole tone 8: 4782969/4194304 227.370012 Pythagorean double augmented prime 9: 250.830 cents 250.830023 10: 274.290 cents 274.290033 11: 19683/16384 317.595008 Pythagorean augmented second 12: 341.055 cents 341.055018 13: 364.515 cents 364.515029 14: 81/64 407.820003 Pythagorean major third 15: 43046721/33554432 431.280014 Pythagorean double augmented second 16: 454.740 cents 454.740024 17: 478.200 cents 478.200035 18: 177147/131072 521.505010 Pythagorean augmented third 19: 544.965 cents 544.965020 20: 568.425 cents 568.425030 21: 729/512 611.730005 Pythagorean tritone 22: 387420489/268435456 635.190016 Pythagorean double augmented third 23: 658.650 cents 658.650026 24: 3/2 701.955001 perfect fifth 25: 1594323/1048576 725.415011 Pythagorean double augmented fourth 26: 748.875 cents 748.875022 27: 772.335 cents 772.335032 28: 6561/4096 815.640007 Pythagorean augmented fifth 29: 839.100 cents 839.100017 30: 862.560 cents 862.560028 31: 27/16 905.865003 Pythagorean major sixth 32: 14348907/8388608 929.325013 Pythagorean double augmented fifth 33: 952.785 cents 952.785023 34: 976.245 cents 976.245034 35: 59049/32768 1019.550009 Pythagorean augmented sixth 36: 1043.010 cents 1043.010019 37: 1066.470 cents 1066.470029 38: 243/128 1109.775004 Pythagorean major seventh 39: 129140163/67108864 1133.235015 40: 1156.695 cents 1156.695025 41: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 43.3050 cents 43.3050 1: 531441/524288 23.4600 Pythagorean comma, ditonic comma 2: 23.4600 cents 23.4600 3: 23.4600 cents 23.4600 4: 43.3050 cents 43.3050 5: 531441/524288 23.4600 Pythagorean comma, ditonic comma 6: 23.4600 cents 23.4600 7: 43.3050 cents 43.3050 8: 531441/524288 23.4600 Pythagorean comma, ditonic comma 9: 23.4600 cents 23.4600 10: 23.4600 cents 23.4600 11: 43.3050 cents 43.3050 12: 23.4600 cents 23.4600 13: 23.4600 cents 23.4600 14: 43.3050 cents 43.3050 15: 531441/524288 23.4600 Pythagorean comma, ditonic comma 16: 23.4600 cents 23.4600 17: 23.4600 cents 23.4600 18: 43.3050 cents 43.3050 19: 23.4600 cents 23.4600 20: 23.4600 cents 23.4600 21: 43.3050 cents 43.3050 22: 531441/524288 23.4600 Pythagorean comma, ditonic comma 23: 23.4600 cents 23.4600 24: 43.3050 cents 43.3050 25: 531441/524288 23.4600 Pythagorean comma, ditonic comma 26: 23.4600 cents 23.4600 27: 23.4600 cents 23.4600 28: 43.3050 cents 43.3050 29: 23.4600 cents 23.4600 30: 23.4600 cents 23.4600 31: 43.3050 cents 43.3050 32: 531441/524288 23.4600 Pythagorean comma, ditonic comma 33: 23.4600 cents 23.4600 34: 23.4600 cents 23.4600 35: 43.3050 cents 43.3050 36: 23.4600 cents 23.4600 37: 23.4600 cents 23.4600 38: 43.3050 cents 43.3050 39: 531441/524288 23.4600 Pythagorean comma, ditonic comma 40: 23.4600 cents 23.4600 41: 43.3050 cents 43.3050
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 29 531441/524288 23.460 cents Pythagorean comma, ditonic comma 1: 12 43.30498 cents 2: 17 46.92002 cents 2: 24 66.76499 cents 3: 5 70.38003 cents 3: 36 256/243 90.225 cents limma, Pythagorean minor second 4: 34 2187/2048 113.685 cents apotome 4: 7 133.52997 cents 5: 22 1162261467/10737418 137.145 cents Pythagorean-19 comma 5: 19 156.98998 cents 6: 10 160.60503 cents 6: 31 65536/59049 180.450 cents Pythagorean diminished third 7: 39 9/8 203.910 cents major whole tone 7: 2 223.75497 cents 8: 27 4782969/4194304 227.370 cents Pythagorean double augmented prime 8: 14 247.21498 cents 9: 15 250.83002 cents 9: 26 270.67499 cents 10: 3 274.29003 cents 10: 38 32/27 294.135 cents Pythagorean minor third 11: 32 19683/16384 317.595 cents Pythagorean augmented second 11: 9 337.43997 cents 12: 20 341.05502 cents 12: 21 360.89998 cents 13: 8 364.51503 cents 13: 33 8192/6561 384.360 cents Pythagorean diminished fourth 14: 37 81/64 407.820 cents Pythagorean major third 14: 4 427.66497 cents 15: 25 43046721/33554432 431.280 cents Pythagorean double augmented second 15: 16 451.12498 cents 16: 13 454.74002 cents 16: 28 474.58499 cents 17: 1 478.20003 cents 17: 40 4/3 498.045 cents perfect fourth 18: 30 177147/131072 521.505 cents Pythagorean augmented third 18: 11 541.34997 cents 19: 18 544.96502 cents 19: 23 564.80998 cents 20: 6 568.42503 cents 20: 35 1024/729 588.270 cents Pythagorean diminished fifth 21: 35 729/512 611.730 cents Pythagorean tritone 21: 6 631.57497 cents 22: 23 387420489/268435456 635.190 cents Pythagorean double augmented third 22: 18 655.03498 cents 23: 11 658.65003 cents 23: 30 262144/177147 678.495 cents Pythagorean diminished sixth 24: 40 3/2 701.955 cents perfect fifth 24: 1 721.79997 cents 25: 28 1594323/1048576 725.415 cents Pythagorean double augmented fourth 25: 13 745.25998 cents 26: 16 748.87502 cents 26: 25 768.71999 cents 27: 4 772.33503 cents 27: 37 128/81 792.180 cents Pythagorean minor sixth 28: 33 6561/4096 815.640 cents Pythagorean augmented fifth 28: 8 835.48497 cents 29: 21 839.10002 cents 29: 20 858.94498 cents 30: 9 862.56003 cents 30: 32 32768/19683 882.405 cents Pythagorean diminished seventh 31: 38 27/16 905.865 cents Pythagorean major sixth 31: 3 925.70997 cents 32: 26 14348907/8388608 929.325 cents Pythagorean double augmented fifth 32: 15 949.16998 cents 33: 14 952.78502 cents 33: 27 972.62999 cents 34: 2 976.24503 cents 34: 39 16/9 996.090 cents Pythagorean minor seventh 35: 31 59049/32768 1019.550 cents Pythagorean augmented sixth 35: 10 1039.39497 cents 36: 19 1043.01002 cents 36: 22 1062.85498 cents 37: 7 1066.47003 cents 37: 34 4096/2187 1086.315 cents Pythagorean diminished octave 38: 36 243/128 1109.775 cents Pythagorean major seventh 38: 5 1129.61997 cents 39: 24 129140163/67108864 1133.235 cents 39: 17 1153.07998 cents 40: 12 1156.69502 cents 40: 29 1048576/531441 1176.540 cents Pythagorean diminished ninth 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 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 0.0 : 23.5 46.9 70.4 113.7 137.1 160.6 203.9 227.4 250.8 274.3 317.6 341.1 364.5 407.8 431.3 454.7 478.2 521.5 545.0 568.4 611.7 635.2 658.7 702.0 725.4 748.9 772.3 815.6 839.1 862.6 905.9 929.3 952.8 976.2 1019.6 1043.0 1066.5 1109.8 1133.2 1156.7 1200.0 23.5 : 23.5 46.9 90.2 113.7 137.1 180.4 203.9 227.4 250.8 294.1 317.6 341.1 384.4 407.8 431.3 454.7 498.0 521.5 545.0 588.3 611.7 635.2 678.5 702.0 725.4 748.9 792.2 815.6 839.1 882.4 905.9 929.3 952.8 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1176.5 1200.0 46.9 : 23.5 66.8 90.2 113.7 157.0 180.4 203.9 227.4 270.7 294.1 317.6 360.9 384.4 407.8 431.3 474.6 498.0 521.5 564.8 588.3 611.7 655.0 678.5 702.0 725.4 768.7 792.2 815.6 858.9 882.4 905.9 929.3 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 70.4 : 43.3 66.8 90.2 133.5 157.0 180.4 203.9 247.2 270.7 294.1 337.4 360.9 384.4 407.8 451.1 474.6 498.0 541.3 564.8 588.3 631.6 655.0 678.5 702.0 745.3 768.7 792.2 835.5 858.9 882.4 905.9 949.2 972.6 996.1 1039.4 1062.9 1086.3 1129.6 1153.1 1176.5 1200.0 113.7 : 23.5 46.9 90.2 113.7 137.1 160.6 203.9 227.4 250.8 294.1 317.6 341.1 364.5 407.8 431.3 454.7 498.0 521.5 545.0 588.3 611.7 635.2 658.7 702.0 725.4 748.9 792.2 815.6 839.1 862.6 905.9 929.3 952.8 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1156.7 1200.0 137.1 : 23.5 66.8 90.2 113.7 137.1 180.4 203.9 227.4 270.7 294.1 317.6 341.1 384.4 407.8 431.3 474.6 498.0 521.5 564.8 588.3 611.7 635.2 678.5 702.0 725.4 768.7 792.2 815.6 839.1 882.4 905.9 929.3 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1133.2 1176.5 1200.0 160.6 : 43.3 66.8 90.2 113.7 157.0 180.4 203.9 247.2 270.7 294.1 317.6 360.9 384.4 407.8 451.1 474.6 498.0 541.3 564.8 588.3 611.7 655.0 678.5 702.0 745.3 768.7 792.2 815.6 858.9 882.4 905.9 949.2 972.6 996.1 1039.4 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 203.9 : 23.5 46.9 70.4 113.7 137.1 160.6 203.9 227.4 250.8 274.3 317.6 341.1 364.5 407.8 431.3 454.7 498.0 521.5 545.0 568.4 611.7 635.2 658.7 702.0 725.4 748.9 772.3 815.6 839.1 862.6 905.9 929.3 952.8 996.1 1019.6 1043.0 1066.5 1109.8 1133.2 1156.7 1200.0 227.4 : 23.5 46.9 90.2 113.7 137.1 180.4 203.9 227.4 250.8 294.1 317.6 341.1 384.4 407.8 431.3 474.6 498.0 521.5 545.0 588.3 611.7 635.2 678.5 702.0 725.4 748.9 792.2 815.6 839.1 882.4 905.9 929.3 972.6 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1176.5 1200.0 250.8 : 23.5 66.8 90.2 113.7 157.0 180.4 203.9 227.4 270.7 294.1 317.6 360.9 384.4 407.8 451.1 474.6 498.0 521.5 564.8 588.3 611.7 655.0 678.5 702.0 725.4 768.7 792.2 815.6 858.9 882.4 905.9 949.2 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 274.3 : 43.3 66.8 90.2 133.5 157.0 180.4 203.9 247.2 270.7 294.1 337.4 360.9 384.4 427.7 451.1 474.6 498.0 541.3 564.8 588.3 631.6 655.0 678.5 702.0 745.3 768.7 792.2 835.5 858.9 882.4 925.7 949.2 972.6 996.1 1039.4 1062.9 1086.3 1129.6 1153.1 1176.5 1200.0 317.6 : 23.5 46.9 90.2 113.7 137.1 160.6 203.9 227.4 250.8 294.1 317.6 341.1 384.4 407.8 431.3 454.7 498.0 521.5 545.0 588.3 611.7 635.2 658.7 702.0 725.4 748.9 792.2 815.6 839.1 882.4 905.9 929.3 952.8 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1156.7 1200.0 341.1 : 23.5 66.8 90.2 113.7 137.1 180.4 203.9 227.4 270.7 294.1 317.6 360.9 384.4 407.8 431.3 474.6 498.0 521.5 564.8 588.3 611.7 635.2 678.5 702.0 725.4 768.7 792.2 815.6 858.9 882.4 905.9 929.3 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1133.2 1176.5 1200.0 364.5 : 43.3 66.8 90.2 113.7 157.0 180.4 203.9 247.2 270.7 294.1 337.4 360.9 384.4 407.8 451.1 474.6 498.0 541.3 564.8 588.3 611.7 655.0 678.5 702.0 745.3 768.7 792.2 835.5 858.9 882.4 905.9 949.2 972.6 996.1 1039.4 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 407.8 : 23.5 46.9 70.4 113.7 137.1 160.6 203.9 227.4 250.8 294.1 317.6 341.1 364.5 407.8 431.3 454.7 498.0 521.5 545.0 568.4 611.7 635.2 658.7 702.0 725.4 748.9 792.2 815.6 839.1 862.6 905.9 929.3 952.8 996.1 1019.6 1043.0 1066.5 1109.8 1133.2 1156.7 1200.0 431.3 : 23.5 46.9 90.2 113.7 137.1 180.4 203.9 227.4 270.7 294.1 317.6 341.1 384.4 407.8 431.3 474.6 498.0 521.5 545.0 588.3 611.7 635.2 678.5 702.0 725.4 768.7 792.2 815.6 839.1 882.4 905.9 929.3 972.6 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1176.5 1200.0 454.7 : 23.5 66.8 90.2 113.7 157.0 180.4 203.9 247.2 270.7 294.1 317.6 360.9 384.4 407.8 451.1 474.6 498.0 521.5 564.8 588.3 611.7 655.0 678.5 702.0 745.3 768.7 792.2 815.6 858.9 882.4 905.9 949.2 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 478.2 : 43.3 66.8 90.2 133.5 157.0 180.4 223.8 247.2 270.7 294.1 337.4 360.9 384.4 427.7 451.1 474.6 498.0 541.3 564.8 588.3 631.6 655.0 678.5 721.8 745.3 768.7 792.2 835.5 858.9 882.4 925.7 949.2 972.6 996.1 1039.4 1062.9 1086.3 1129.6 1153.1 1176.5 1200.0 521.5 : 23.5 46.9 90.2 113.7 137.1 180.4 203.9 227.4 250.8 294.1 317.6 341.1 384.4 407.8 431.3 454.7 498.0 521.5 545.0 588.3 611.7 635.2 678.5 702.0 725.4 748.9 792.2 815.6 839.1 882.4 905.9 929.3 952.8 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1156.7 1200.0 545.0 : 23.5 66.8 90.2 113.7 157.0 180.4 203.9 227.4 270.7 294.1 317.6 360.9 384.4 407.8 431.3 474.6 498.0 521.5 564.8 588.3 611.7 655.0 678.5 702.0 725.4 768.7 792.2 815.6 858.9 882.4 905.9 929.3 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1133.2 1176.5 1200.0 568.4 : 43.3 66.8 90.2 133.5 157.0 180.4 203.9 247.2 270.7 294.1 337.4 360.9 384.4 407.8 451.1 474.6 498.0 541.3 564.8 588.3 631.6 655.0 678.5 702.0 745.3 768.7 792.2 835.5 858.9 882.4 905.9 949.2 972.6 996.1 1039.4 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 611.7 : 23.5 46.9 90.2 113.7 137.1 160.6 203.9 227.4 250.8 294.1 317.6 341.1 364.5 407.8 431.3 454.7 498.0 521.5 545.0 588.3 611.7 635.2 658.7 702.0 725.4 748.9 792.2 815.6 839.1 862.6 905.9 929.3 952.8 996.1 1019.6 1043.0 1066.5 1109.8 1133.2 1156.7 1200.0 635.2 : 23.5 66.8 90.2 113.7 137.1 180.4 203.9 227.4 270.7 294.1 317.6 341.1 384.4 407.8 431.3 474.6 498.0 521.5 564.8 588.3 611.7 635.2 678.5 702.0 725.4 768.7 792.2 815.6 839.1 882.4 905.9 929.3 972.6 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1176.5 1200.0 658.7 : 43.3 66.8 90.2 113.7 157.0 180.4 203.9 247.2 270.7 294.1 317.6 360.9 384.4 407.8 451.1 474.6 498.0 541.3 564.8 588.3 611.7 655.0 678.5 702.0 745.3 768.7 792.2 815.6 858.9 882.4 905.9 949.2 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 702.0 : 23.5 46.9 70.4 113.7 137.1 160.6 203.9 227.4 250.8 274.3 317.6 341.1 364.5 407.8 431.3 454.7 498.0 521.5 545.0 568.4 611.7 635.2 658.7 702.0 725.4 748.9 772.3 815.6 839.1 862.6 905.9 929.3 952.8 976.2 1019.6 1043.0 1066.5 1109.8 1133.2 1156.7 1200.0 725.4 : 23.5 46.9 90.2 113.7 137.1 180.4 203.9 227.4 250.8 294.1 317.6 341.1 384.4 407.8 431.3 474.6 498.0 521.5 545.0 588.3 611.7 635.2 678.5 702.0 725.4 748.9 792.2 815.6 839.1 882.4 905.9 929.3 952.8 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1176.5 1200.0 748.9 : 23.5 66.8 90.2 113.7 157.0 180.4 203.9 227.4 270.7 294.1 317.6 360.9 384.4 407.8 451.1 474.6 498.0 521.5 564.8 588.3 611.7 655.0 678.5 702.0 725.4 768.7 792.2 815.6 858.9 882.4 905.9 929.3 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 772.3 : 43.3 66.8 90.2 133.5 157.0 180.4 203.9 247.2 270.7 294.1 337.4 360.9 384.4 427.7 451.1 474.6 498.0 541.3 564.8 588.3 631.6 655.0 678.5 702.0 745.3 768.7 792.2 835.5 858.9 882.4 905.9 949.2 972.6 996.1 1039.4 1062.9 1086.3 1129.6 1153.1 1176.5 1200.0 815.6 : 23.5 46.9 90.2 113.7 137.1 160.6 203.9 227.4 250.8 294.1 317.6 341.1 384.4 407.8 431.3 454.7 498.0 521.5 545.0 588.3 611.7 635.2 658.7 702.0 725.4 748.9 792.2 815.6 839.1 862.6 905.9 929.3 952.8 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1156.7 1200.0 839.1 : 23.5 66.8 90.2 113.7 137.1 180.4 203.9 227.4 270.7 294.1 317.6 360.9 384.4 407.8 431.3 474.6 498.0 521.5 564.8 588.3 611.7 635.2 678.5 702.0 725.4 768.7 792.2 815.6 839.1 882.4 905.9 929.3 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1133.2 1176.5 1200.0 862.6 : 43.3 66.8 90.2 113.7 157.0 180.4 203.9 247.2 270.7 294.1 337.4 360.9 384.4 407.8 451.1 474.6 498.0 541.3 564.8 588.3 611.7 655.0 678.5 702.0 745.3 768.7 792.2 815.6 858.9 882.4 905.9 949.2 972.6 996.1 1039.4 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 905.9 : 23.5 46.9 70.4 113.7 137.1 160.6 203.9 227.4 250.8 294.1 317.6 341.1 364.5 407.8 431.3 454.7 498.0 521.5 545.0 568.4 611.7 635.2 658.7 702.0 725.4 748.9 772.3 815.6 839.1 862.6 905.9 929.3 952.8 996.1 1019.6 1043.0 1066.5 1109.8 1133.2 1156.7 1200.0 929.3 : 23.5 46.9 90.2 113.7 137.1 180.4 203.9 227.4 270.7 294.1 317.6 341.1 384.4 407.8 431.3 474.6 498.0 521.5 545.0 588.3 611.7 635.2 678.5 702.0 725.4 748.9 792.2 815.6 839.1 882.4 905.9 929.3 972.6 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1176.5 1200.0 952.8 : 23.5 66.8 90.2 113.7 157.0 180.4 203.9 247.2 270.7 294.1 317.6 360.9 384.4 407.8 451.1 474.6 498.0 521.5 564.8 588.3 611.7 655.0 678.5 702.0 725.4 768.7 792.2 815.6 858.9 882.4 905.9 949.2 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 976.2 : 43.3 66.8 90.2 133.5 157.0 180.4 223.8 247.2 270.7 294.1 337.4 360.9 384.4 427.7 451.1 474.6 498.0 541.3 564.8 588.3 631.6 655.0 678.5 702.0 745.3 768.7 792.2 835.5 858.9 882.4 925.7 949.2 972.6 996.1 1039.4 1062.9 1086.3 1129.6 1153.1 1176.5 1200.0 1019.6: 23.5 46.9 90.2 113.7 137.1 180.4 203.9 227.4 250.8 294.1 317.6 341.1 384.4 407.8 431.3 454.7 498.0 521.5 545.0 588.3 611.7 635.2 658.7 702.0 725.4 748.9 792.2 815.6 839.1 882.4 905.9 929.3 952.8 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1156.7 1200.0 1043.0: 23.5 66.8 90.2 113.7 157.0 180.4 203.9 227.4 270.7 294.1 317.6 360.9 384.4 407.8 431.3 474.6 498.0 521.5 564.8 588.3 611.7 635.2 678.5 702.0 725.4 768.7 792.2 815.6 858.9 882.4 905.9 929.3 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1133.2 1176.5 1200.0 1066.5: 43.3 66.8 90.2 133.5 157.0 180.4 203.9 247.2 270.7 294.1 337.4 360.9 384.4 407.8 451.1 474.6 498.0 541.3 564.8 588.3 611.7 655.0 678.5 702.0 745.3 768.7 792.2 835.5 858.9 882.4 905.9 949.2 972.6 996.1 1039.4 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 1109.8: 23.5 46.9 90.2 113.7 137.1 160.6 203.9 227.4 250.8 294.1 317.6 341.1 364.5 407.8 431.3 454.7 498.0 521.5 545.0 568.4 611.7 635.2 658.7 702.0 725.4 748.9 792.2 815.6 839.1 862.6 905.9 929.3 952.8 996.1 1019.6 1043.0 1066.5 1109.8 1133.2 1156.7 1200.0 1133.2: 23.5 66.8 90.2 113.7 137.1 180.4 203.9 227.4 270.7 294.1 317.6 341.1 384.4 407.8 431.3 474.6 498.0 521.5 545.0 588.3 611.7 635.2 678.5 702.0 725.4 768.7 792.2 815.6 839.1 882.4 905.9 929.3 972.6 996.1 1019.6 1043.0 1086.3 1109.8 1133.2 1176.5 1200.0 1156.7: 43.3 66.8 90.2 113.7 157.0 180.4 203.9 247.2 270.7 294.1 317.6 360.9 384.4 407.8 451.1 474.6 498.0 521.5 564.8 588.3 611.7 655.0 678.5 702.0 745.3 768.7 792.2 815.6 858.9 882.4 905.9 949.2 972.6 996.1 1019.6 1062.9 1086.3 1109.8 1153.1 1176.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 23.4600 .. 43.3050 cents 19.84496 cents 531441/524288, 23.4600 cents 2: 46.9200 .. 66.7650 cents 19.84496 cents 3.61505 cents 3: 70.3800 .. 90.2250 cents 19.84496 cents 3.61505 cents 4: 113.6850 .. 133.5300 cents 19.84496 cents 531441/524288, 23.4600 cents 5: 137.1450 .. 156.9900 cents 19.84496 cents 3.61505 cents 6: 160.6050 .. 180.4500 cents 19.84496 cents 3.61505 cents 7: 203.9100 .. 223.7550 cents 19.84496 cents 531441/524288, 23.4600 cents 8: 227.3700 .. 247.2150 cents 19.84496 cents 3.61505 cents 9: 250.8300 .. 270.6750 cents 19.84496 cents 3.61505 cents 10: 274.2900 .. 294.1350 cents 19.84496 cents 3.61505 cents 11: 317.5950 .. 337.4400 cents 19.84496 cents 531441/524288, 23.4600 cents 12: 341.0550 .. 360.9000 cents 19.84496 cents 3.61505 cents 13: 364.5150 .. 384.3600 cents 19.84496 cents 3.61505 cents 14: 407.8200 .. 427.6650 cents 19.84496 cents 531441/524288, 23.4600 cents 15: 431.2800 .. 451.1250 cents 19.84496 cents 3.61505 cents 16: 454.7400 .. 474.5850 cents 19.84496 cents 3.61505 cents 17: 478.2000 .. 498.0450 cents 19.84496 cents 3.61505 cents 18: 521.5050 .. 541.3500 cents 19.84496 cents 531441/524288, 23.4600 cents 19: 544.9650 .. 564.8100 cents 19.84496 cents 3.61505 cents 20: 568.4250 .. 588.2700 cents 19.84496 cents 3.61505 cents 21: 611.7300 .. 631.5750 cents 19.84496 cents 531441/524288, 23.4600 cents 22: 635.1900 .. 655.0350 cents 19.84496 cents 3.61505 cents 23: 658.6500 .. 678.4950 cents 19.84496 cents 3.61505 cents 24: 701.9550 .. 721.8000 cents 19.84496 cents 531441/524288, 23.4600 cents 25: 725.4150 .. 745.2600 cents 19.84496 cents 3.61505 cents 26: 748.8750 .. 768.7200 cents 19.84496 cents 3.61505 cents 27: 772.3350 .. 792.1800 cents 19.84496 cents 3.61505 cents 28: 815.6400 .. 835.4850 cents 19.84496 cents 531441/524288, 23.4600 cents 29: 839.1000 .. 858.9450 cents 19.84496 cents 3.61505 cents 30: 862.5600 .. 882.4050 cents 19.84496 cents 3.61505 cents 31: 905.8650 .. 925.7100 cents 19.84496 cents 531441/524288, 23.4600 cents 32: 929.3250 .. 949.1700 cents 19.84496 cents 3.61505 cents 33: 952.7850 .. 972.6300 cents 19.84496 cents 3.61505 cents 34: 976.2450 .. 996.0900 cents 19.84496 cents 3.61505 cents 35: 1019.5500 .. 1039.3950 cents 19.84496 cents 531441/524288, 23.4600 cents 36: 1043.0100 .. 1062.8550 cents 19.84496 cents 3.61505 cents 37: 1066.4700 .. 1086.3150 cents 19.84496 cents 3.61505 cents 38: 1109.7750 .. 1129.6200 cents 19.84496 cents 531441/524288, 23.4600 cents 39: 1133.2350 .. 1153.0800 cents 19.84496 cents 3.61505 cents 40: 1156.6950 .. 1176.5400 cents 19.84496 cents 3.61505 cents
SHOW DATA
Number of notes : 41 -- Interval properties -- Smallest interval : 23.46001 cents, class 1 Average step (divided formal octave): 29.2683 cents Largest one step interval : 43.30498 cents Average / Smallest step : 1.247582 Largest / Average step : 1.479587 Largest / Smallest step : 1.845906 Median interval of one step : 531441/524288, 23.4600 cents, amount: 29 Most common interval of one step : 531441/524288, 23.4600 cents, amount: 29 Least squares average step : 28.92423 cents, oct.: 1185.89334 cents Scale is strictly proper Scale has Myhill's property chromas: 19.84496 cents and 3.61505 cents, ratio: 5.489547 generators: 498.04500 cents and 24 of 701.95500 cents ET pair of linear temperament : 12&41 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 13 26 39 63 76 89 113 126 139 152 176 189 202 226 239 252 265 289 302 315 339 352 365 389 402 415 428 452 465 478 502 515 528 541 565 578 591 615 628 641 665 generators: 276 and 389 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAABAAABAABAAABAABAABAAABAABAAABAABAAB Step pattern size order : SSSLSSLSSSLSSLSSSLSSLSSLSSSLSSLSSSLSSLSSL Scale is a Constant Structure, by a margin of 3.61505 cents Ratio Whole / Half tone : 2.260017 Scale diversity : 1.110811 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.338501 Rothenberg efficiency : 0.682927 redundancy: 0.317073 Efficiency x scale size : 28.000000 Number of different interval sizes : 80 = 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 : 3.61505 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 40 Scale is a chain of 20 triads 0.0 498.045 996.090 cents Most common triad is 0.0 498.045 701.955 cents, amount: 39 Number of recognisable fifths : 40, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 81 Formal octave complements present : 1 = 2.4390% Scale is n-1 differentially coherent in interval classes 16 and 17 combined Scale is n-1 differentially coherent in interval class 17 Scale is n-1 differentially coherent in interval classes 23 and 24 combined Scale is n-1 differentially coherent in interval class 24 Limited inverse transpositions : 17 Inversional symmetry on degrees : 29 Inversional symmetry on intervals : 8-9 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
41: 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 N T3 SD: 19.8894 c. M: 28.7843 c. 42: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 2 0 1 2 1 0 1 2 1 0 2 1 1 1 N D3 SD: 8.3217 c. M:-15.3343 c. 43: 1 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 2 1 0 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 2 1 0 2 N D3 SD: 7.8779 c. M:-13.3409 c. 44: 1 1 1 1 1 1 1 1 1 1 2 1 0 2 1 1 1 1 1 1 1 1 1 2 1 0 1 2 1 1 1 1 1 1 1 1 1 2 1 0 2 N D3 SD: 7.8759 c. M:-13.4904 c. 45: 1 1 1 1 1 1 2 1 0 1 2 1 1 1 1 1 1 2 0 1 2 1 1 1 1 1 1 2 0 1 2 1 1 1 1 1 1 2 0 1 2 N D3 SD: 7.5658 c. M: 13.2350 c. 47: 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 2 P M ME S SD: 7.2517 c. M: 12.5933 c. 48: 1 1 1 2 0 1 2 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 0 2 1 1 1 2 1 1 1 1 1 2 N D3 SD: 7.0137 c. M: 12.5600 c. 49: 1 1 1 2 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 2 N D3 S SD: 6.9845 c. M:-11.5959 c. 52: 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 N D3 SD: 6.6193 c. M:-11.3469 c. 53: 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 P M ME S SD: 1.5850 c. M: 2.7283 c. 200: 4 4 4 7 4 4 7 4 4 4 7 4 4 7 4 4 4 7 4 4 7 4 4 7 4 4 4 7 4 4 7 4 4 4 7 4 4 7 4 4 7 SP M DE S SD: 1.0457 c. M:-1.8000 c. 253: 5 5 5 9 5 5 9 5 5 5 9 5 5 9 5 5 5 9 5 5 9 5 5 9 5 5 5 9 5 5 9 5 5 5 9 5 5 9 5 5 9 SP M DE S SD: 0.4946 c. M:-0.8513 c. 306: 6 6 6 11 6 6 11 6 6 6 11 6 6 11 6 6 6 11 6 6 11 6 6 11 6 6 6 11 6 6 11 6 6 6 11 6 6 11 6 6 11 SP M DE S SD: 0.1344 c. M:-0.2313 c. 359: 7 7 7 13 7 7 13 7 7 7 13 7 7 13 7 7 7 13 7 7 13 7 7 13 7 7 7 13 7 7 13 7 7 7 13 7 7 13 7 7 13 SP M DE S SD: 0.1194 c. M: 0.2056 c. 665: 13 13 13 24 13 13 24 13 13 13 24 13 13 24 13 13 13 24 13 13 24 13 13 24 13 13 13 24 13 13 24 13 13 13 24 13 13 24 13 13 24 SP M DE S SD: 0.0026 c. M: 0.0045 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: 9.7544 cents 4 .. 8 match: 4 H SD: 5.6875 cents 5 .. 10 match: 5 H SD: 2.8976 cents 6 .. 12 match: 6 H SD: 5.1417 cents 7 .. 14 match: 7 H SD: 2.0559 cents 8 .. 16 match: 8 H SD: 3.9970 cents 9 .. 18 match: 9 H SD: 4.8258 cents 10 .. 20 match: 10 H SD: 1.8593 cents 11 .. 22 match: 11 H SD: 2.7317 cents 12 .. 24 match: 12 H SD: 3.7255 cents 13 .. 26 match: 13 H SD: 1.7310 cents 14 .. 28 match: 14 H SD: 1.7324 cents 15 .. 30 match: 15 H SD: 2.6231 cents 16 .. 32 match: 16 H SD: 2.6820 cents 17 .. 34 match: 17 H SD: 2.2469 cents 18 .. 36 match: 18 H SD: 2.8864 cents 19 .. 38 match: 19 H SD: 2.0588 cents 20 .. 40 match: 20 H SD: 1.8221 cents 21 .. 42 match: 21 H SD: 2.0934 cents 22 .. 44 match: 22 H SD: 2.0034 cents 23 .. 46 match: 23 H SD: 1.7667 cents 24 .. 48 match: 22 SD: 2.0312 cents 25 .. 50 match: 25 H SD: 1.6174 cents 26 .. 52 match: 26 H SD: 1.5494 cents 27 .. 54 match: 24 SD: 2.1701 cents 28 .. 56 match: 28 H SD: 1.5756 cents 29 .. 58 match: 28 S SD: 1.6100 cents 30 .. 60 match: 29 SD: 1.5338 cents 31 .. 62 match: 26 SD: 1.4952 cents 32 .. 64 match: 27 SD: 1.4978 cents 33 .. 66 match: 29 SD: 1.7075 cents 34 .. 68 match: 32 SD: 1.3901 cents 35 .. 70 match: 33 SD: 1.4182 cents 36 .. 72 match: 29 SD: 1.4749 cents 37 .. 74 match: 33 SD: 1.5229 cents 38 .. 76 match: 35 SD: 1.4054 cents 39 .. 78 match: 33 SD: 1.3130 cents 40 .. 80 match: 34 SD: 1.2107 cents 41 .. 82 match: 35 SD: 1.0995 cents 42 .. 84 match: 35 SD: 1.1382 cents 43 .. 86 match: 36 SD: 1.2683 cents 44 .. 88 match: 35 SD: 1.3247 cents 45 .. 90 match: 35 SD: 1.0843 cents 46 .. 92 match: 38 SD: 1.0020 cents 47 .. 94 match: 37 SD: 1.2790 cents 48 .. 96 match: 37 SD: 1.0350 cents 49 .. 98 match: 37 SD: 1.1695 cents 50 .. 100 match: 39 SD: 0.9803 cents 51 .. 102 match: 39 SD: 1.1138 cents 52 .. 104 match: 38 SD: 0.9946 cents 53 .. 106 match: 37 SD: 1.1658 cents 54 .. 108 match: 38 SD: 0.9611 cents 55 .. 110 match: 37 SD: 1.1559 cents 56 .. 112 match: 39 SD: 0.8988 cents 57 .. 114 match: 40 SD: 0.9535 cents 58 .. 116 match: 40 SD: 1.0661 cents 59 .. 118 match: 40 SD: 0.8514 cents 60 .. 120 match: 39 SD: 0.8294 cents 61 .. 122 match: 40 SD: 0.9774 cents 63 .. 126 match: 41 SD: 0.8010 cents 64 .. 128 match: 41 SD: 0.7883 cents 70 .. 140 match: 41 SD: 0.6639 cents 82 .. 164 match: 41 SD: 0.6450 cents 86 .. 172 match: 41 SD: 0.6419 cents 90 .. 180 match: 41 SD: 0.6089 cents 94 .. 188 match: 41 SD: 0.5784 cents 98 .. 196 match: 41 SD: 0.5647 cents 100 .. 200 match: 41 SD: 0.5372 cents 106 .. 212 match: 41 SD: 0.4796 cents 116 .. 232 match: 41 SD: 0.4390 cents 120 .. 240 match: 41 SD: 0.4104 cents 128 .. 256 match: 41 SD: 0.4014 cents 135 .. 270 match: 41 SD: 0.3782 cents 142 .. 284 match: 41 SD: 0.3498 cents 144 .. 288 match: 41 SD: 0.3014 cents 173 .. 346 match: 41 SD: 0.2864 cents 192 .. 384 match: 41 SD: 0.2590 cents 208 .. 416 match: 41 SD: 0.2318 cents 219 .. 438 match: 41 SD: 0.2312 cents 222 .. 444 match: 41 SD: 0.2298 cents 226 .. 452 match: 41 SD: 0.2238 cents 244 .. 488 match: 41 SD: 0.2051 cents 248 .. 496 match: 41 SD: 0.2002 cents 263 .. 526 match: 41 SD: 0.2001 cents 264 .. 528 match: 41 SD: 0.1951 cents 279 .. 558 match: 41 SD: 0.1791 cents 286 .. 572 match: 41 SD: 0.1790 cents 289 .. 578 match: 41 SD: 0.1780 cents 290 .. 580 match: 41 SD: 0.1524 cents 327 .. 654 match: 41 SD: 0.1507 cents 342 .. 684 match: 41 SD: 0.1441 cents 358 .. 716 match: 41 SD: 0.1434 cents 359 .. 718 match: 41 SD: 0.1414 cents 362 .. 724 match: 41 SD: 0.1404 cents 367 .. 734 match: 41 SD: 0.1383 cents 368 .. 736 match: 41 SD: 0.1338 cents 384 .. 768 match: 41 SD: 0.1165 cents 432 .. 864 match: 41 SD: 0.1038 cents 486 .. 972 match: 41 SD: 0.0989 cents 505 .. 1010 match: 41 SD: 0.0948 cents 512 .. 1024 match: 41 SD: 0.0778 cents