Scala analysis: ennon28
Nonoctave Ennealimmal, [3, 5/3] just tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 245/216 218.100524 4: 7/6 266.870906 septimal minor third 5: 49/40 351.338099 larger approximation to neutral third 6: 63/50 400.108480 quasi-equal major third 7: 250/189 484.250233 8: 49/36 533.741811 Arabic lute acute fourth 9: 10/7 617.487807 Euler's tritone 10: 72/49 666.258189 Arabic lute grave fifth 11: 54/35 750.725382 septimal semi-augmented fifth 12: 100/63 799.891520 quasi-equal minor sixth 13: 5/3 884.358713 major sixth, BP sixth 14: 7/4 968.825906 harmonic seventh 15: 9/5 1017.596288 just minor seventh, BP seventh 16: 189/100 1102.063481 17: 35/18 1151.229619 septimal semi-diminished octave 18: 49/24 1235.696812 slendro diesis, septimal 1/6-tone +1 octave 19: 21/10 1284.467193 minor semitone +1 octave 20: 108/49 1368.213190 Zalzal's mujannab +1 octave 21: 245/108 1418.100524 22: 50/21 1501.846520 BP second, quasi-equal minor third +1 octave 23: 49/20 1551.338099 larger approximation to neutral third +1 octave 24: 18/7 1635.084095 septimal major 10th 25: 500/189 1684.250233 26: 25/9 1768.717426 classic augmented eleventh, BP twelfth 27: 20/7 1817.487807 Euler's tritone +1 octave 28: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 21/20 84.4672 minor semitone 1: 21/20 84.4672 minor semitone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 6125/5832 84.8629 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 21/20 84.4672 minor semitone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 12500/11907 84.1418 8: 1029/1000 49.4916 keega 9: 360/343 83.7460 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 21/20 84.4672 minor semitone 12: 250/243 49.1661 maximal diesis, Porcupine comma 13: 21/20 84.4672 minor semitone 14: 21/20 84.4672 minor semitone 15: 36/35 48.7704 septimal diesis, 1/4-tone 16: 21/20 84.4672 minor semitone 17: 250/243 49.1661 maximal diesis, Porcupine comma 18: 21/20 84.4672 minor semitone 19: 36/35 48.7704 septimal diesis, 1/4-tone 20: 360/343 83.7460 21: 12005/11664 49.8873 22: 360/343 83.7460 23: 1029/1000 49.4916 keega 24: 360/343 83.7460 25: 250/243 49.1661 maximal diesis, Porcupine comma 26: 21/20 84.4672 minor semitone 27: 36/35 48.7704 septimal diesis, 1/4-tone 28: 21/20 84.4672 minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 36/35 48.770 cents septimal diesis, 1/4-tone 1: 3 250/243 49.166 cents maximal diesis, Porcupine comma 1: 2 1029/1000 49.492 cents keega 1: 1 12005/11664 49.887 cents 1: 4 360/343 83.746 cents 1: 1 12500/11907 84.142 cents 1: 9 21/20 84.467 cents minor semitone 1: 1 6125/5832 84.863 cents 2: 2 2592/2401 132.516 cents 2: 2 10000/9261 132.912 cents 2: 12 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 10 175/162 133.633 cents 2: 2 441/400 168.934 cents two (minor semitone) 3: 2 972/875 182.008 cents 3: 8 10/9 182.404 cents minor whole tone 3: 1 2401/2160 183.125 cents 3: 3 1944/1715 216.984 cents 3: 4 500/441 217.379 cents 3: 5 567/500 217.705 cents 3: 5 245/216 218.101 cents 4: 8 400/343 266.150 cents 4: 2 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 4: 14 7/6 266.871 cents septimal minor third 4: 2 11907/10000 302.172 cents 4: 2 343/288 302.568 cents 5: 1 2880/2401 314.920 cents 5: 6 6/5 315.641 cents minor third 5: 2 875/729 316.037 cents 5: 8 60/49 350.617 cents smaller approximation to neutral third 5: 1 15309/12500 350.942 cents 5: 1 6250/5103 351.013 cents 5: 9 49/40 351.338 cents larger approximation to neutral third 6: 6 432/343 399.387 cents 6: 4 5000/3969 399.783 cents 6: 8 63/50 400.108 cents quasi-equal major third 6: 4 1225/972 400.504 cents 6: 2 9/7 435.084 cents septimal major third, BP third 6: 4 1029/800 435.805 cents 7: 1 15552/12005 448.158 cents 7: 2 4000/3087 448.553 cents 7: 4 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 7: 6 324/245 483.854 cents 7: 5 250/189 484.250 cents 7: 7 1323/1000 484.576 cents 7: 3 1715/1296 484.971 cents 8: 1 11664/8575 532.625 cents 8: 9 200/147 533.021 cents 8: 3 1701/1250 533.346 cents 8: 7 49/36 533.742 cents Arabic lute acute fourth 8: 3 243/175 568.322 cents 8: 3 25/18 568.717 cents classic augmented fourth 8: 1 27783/20000 569.043 cents 8: 1 2401/1728 569.439 cents 9: 3 480/343 581.791 cents 9: 1 50000/35721 582.187 cents 9: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 9: 1 8748/6125 617.092 cents 9: 13 10/7 617.488 cents Euler's tritone 9: 2 35721/25000 617.813 cents 9: 7 343/240 618.209 cents 10: 7 72/49 666.258 cents Arabic lute grave fifth 10: 3 2500/1701 666.654 cents 10: 7 147/100 666.979 cents 10: 1 8575/5832 667.375 cents 10: 10 3/2 701.955 cents perfect fifth 11: 3 2000/1323 715.424 cents 11: 14 54/35 750.725 cents septimal semi-augmented fifth 11: 5 125/81 751.121 cents 11: 4 3087/2000 751.447 cents 11: 2 12005/7776 751.842 cents 12: 3 1944/1225 799.496 cents 12: 7 100/63 799.892 cents quasi-equal minor sixth 12: 2 3969/2500 800.217 cents two (quasi-equal major third) 12: 4 343/216 800.613 cents 12: 1 3888/2401 834.471 cents 12: 1 5000/3087 834.867 cents 12: 6 81/50 835.193 cents acute minor sixth 12: 4 175/108 835.588 cents 13: 1 80/49 848.662 cents smaller approximation to neutral sixth 13: 6 1458/875 883.963 cents 13: 19 5/3 884.359 cents major sixth, BP sixth 13: 2 2401/1440 885.080 cents 14: 9 12/7 933.129 cents septimal major sixth 14: 1 1250/729 933.525 cents 14: 4 343/200 933.850 cents 14: 4 600/343 968.105 cents 14: 1 2187/1250 968.430 cents 14: 9 7/4 968.826 cents harmonic seventh 15: 2 4320/2401 1016.875 cents 15: 19 9/5 1017.596 cents just minor seventh, BP seventh 15: 6 875/486 1017.992 cents 15: 1 147/80 1053.293 cents 16: 4 324/175 1066.367 cents 16: 6 50/27 1066.762 cents grave major seventh 16: 1 9261/5000 1067.088 cents 16: 1 2401/1296 1067.484 cents two (Arabic lute acute fourth) 16: 4 648/343 1101.342 cents 16: 2 2500/1323 1101.738 cents 16: 7 189/100 1102.063 cents 16: 3 1225/648 1102.459 cents 17: 2 23328/12005 1150.113 cents 17: 4 2000/1029 1150.508 cents 17: 5 243/125 1150.834 cents octave - maximal diesis 17: 14 35/18 1151.230 cents septimal semi-diminished octave 17: 3 3969/2000 1186.531 cents 18: 10 2/1 1200.000 cents octave 18: 1 17496/8575 1234.580 cents 18: 7 100/49 1234.976 cents Erlich's decatonic comma, tritonic diesis +1 octave 18: 3 5103/2500 1235.301 cents 18: 7 49/24 1235.697 cents slendro diesis, septimal 1/6-tone +1 octave 19: 7 720/343 1283.746 cents 19: 2 25000/11907 1284.142 cents 19: 13 21/10 1284.467 cents minor semitone +1 octave 19: 1 6125/2916 1284.863 cents 19: 1 15/7 1319.443 cents septimal minor ninth, BP ninth 19: 1 107163/50000 1319.768 cents 19: 3 343/160 1320.164 cents 20: 1 5184/2401 1332.516 cents 20: 1 20000/9261 1332.912 cents 20: 3 54/25 1333.238 cents large limma, BP small semitone, Zarlino semitone +1 octave 20: 3 175/81 1333.633 cents 20: 7 108/49 1368.213 cents Zalzal's mujannab +1 octave 20: 3 1250/567 1368.609 cents BP great semitone, major BP chroma +1 octave 20: 9 441/200 1368.934 cents two (minor semitone) 20: 1 8575/3888 1369.330 cents 21: 3 3888/1715 1416.984 cents 21: 7 1000/441 1417.379 cents 21: 5 567/250 1417.705 cents 21: 6 245/108 1418.101 cents 21: 4 81/35 1452.680 cents Al-Hwarizmi's lute middle finger +1 octave 21: 2 9261/4000 1453.402 cents 21: 1 12005/5184 1453.797 cents 22: 4 800/343 1466.150 cents 22: 2 7/3 1466.871 cents minimal tenth, BP tenth 22: 4 2916/1225 1501.451 cents 22: 8 50/21 1501.847 cents BP second, quasi-equal minor third +1 octave 22: 4 11907/5000 1502.172 cents 22: 6 343/144 1502.568 cents 23: 9 120/49 1550.617 cents smaller approximation to neutral third +1 octave 23: 1 15309/6250 1550.942 cents 23: 1 12500/5103 1551.013 cents 23: 8 49/20 1551.338 cents larger approximation to neutral third +1 octave 23: 2 2187/875 1585.918 cents 23: 6 5/2 1586.314 cents major 10th 23: 1 2401/960 1587.035 cents 24: 2 864/343 1599.387 cents 24: 2 10000/3969 1599.783 cents 24: 14 18/7 1635.084 cents septimal major 10th 24: 2 625/243 1635.480 cents 24: 8 1029/400 1635.805 cents 25: 5 648/245 1683.854 cents 25: 5 500/189 1684.250 cents 25: 4 1323/500 1684.576 cents 25: 3 1715/648 1684.971 cents 25: 1 6480/2401 1718.830 cents 25: 8 27/10 1719.551 cents acute fourth +1 octave 25: 2 875/324 1719.947 cents 26: 2 400/147 1733.021 cents 26: 10 486/175 1768.322 cents 26: 12 25/9 1768.717 cents classic augmented eleventh, BP twelfth 26: 2 27783/10000 1769.043 cents 26: 2 2401/864 1769.439 cents 27: 1 17496/6125 1817.092 cents 27: 9 20/7 1817.488 cents Euler's tritone +1 octave 27: 1 35721/12500 1817.813 cents 27: 4 343/120 1818.209 cents 27: 1 34992/12005 1852.068 cents 27: 2 1000/343 1852.463 cents 27: 3 729/250 1852.789 cents 27: 7 35/12 1853.185 cents septimal semi-diminished fifth +1 octave Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.29630 = 170/27
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 0.0 : 84.5 133.2 218.1 266.9 351.3 400.1 484.3 533.7 617.5 666.3 750.7 799.9 884.4 968.8 1017.6 1102.1 1151.2 1235.7 1284.5 1368.2 1418.1 1501.8 1551.3 1635.1 1684.3 1768.7 1817.5 1902.0 84.5 : 48.8 133.6 182.4 266.9 315.6 399.8 449.3 533.0 581.8 666.3 715.4 799.9 884.4 933.1 1017.6 1066.8 1151.2 1200.0 1283.7 1333.6 1417.4 1466.9 1550.6 1599.8 1684.3 1733.0 1817.5 1902.0 133.2 : 84.9 133.6 218.1 266.9 351.0 400.5 484.3 533.0 617.5 666.7 751.1 835.6 884.4 968.8 1018.0 1102.5 1151.2 1235.0 1284.9 1368.6 1418.1 1501.8 1551.0 1635.5 1684.3 1768.7 1853.2 1902.0 218.1 : 48.8 133.2 182.0 266.1 315.6 399.4 448.2 532.6 581.8 666.3 750.7 799.5 884.0 933.1 1017.6 1066.4 1150.1 1200.0 1283.7 1333.2 1417.0 1466.1 1550.6 1599.4 1683.9 1768.3 1817.1 1902.0 266.9 : 84.5 133.2 217.4 266.9 350.6 399.4 483.9 533.0 617.5 702.0 750.7 835.2 884.4 968.8 1017.6 1101.3 1151.2 1235.0 1284.5 1368.2 1417.4 1501.8 1550.6 1635.1 1719.6 1768.3 1853.2 1902.0 351.3 : 48.8 132.9 182.4 266.1 314.9 399.4 448.6 533.0 617.5 666.3 750.7 799.9 884.4 933.1 1016.9 1066.8 1150.5 1200.0 1283.7 1332.9 1417.4 1466.1 1550.6 1635.1 1683.9 1768.7 1817.5 1902.0 400.1 : 84.1 133.6 217.4 266.1 350.6 399.8 484.3 568.7 617.5 702.0 751.1 835.6 884.4 968.1 1018.0 1101.7 1151.2 1235.0 1284.1 1368.6 1417.4 1501.8 1586.3 1635.1 1719.9 1768.7 1853.2 1902.0 484.3 : 49.5 133.2 182.0 266.5 315.6 400.1 484.6 533.3 617.8 667.0 751.4 800.2 884.0 933.9 1017.6 1067.1 1150.8 1200.0 1284.5 1333.2 1417.7 1502.2 1550.9 1635.8 1684.6 1769.0 1817.8 1902.0 533.7 : 83.7 132.5 217.0 266.1 350.6 435.1 483.9 568.3 617.5 702.0 750.7 834.5 884.4 968.1 1017.6 1101.3 1150.5 1235.0 1283.7 1368.2 1452.7 1501.5 1586.3 1635.1 1719.6 1768.3 1852.5 1902.0 617.5 : 48.8 133.2 182.4 266.9 351.3 400.1 484.6 533.7 618.2 667.0 750.7 800.6 884.4 933.9 1017.6 1066.8 1151.2 1200.0 1284.5 1368.9 1417.7 1502.6 1551.3 1635.8 1684.6 1768.7 1818.2 1902.0 666.3 : 84.5 133.6 218.1 302.6 351.3 435.8 485.0 569.4 618.2 702.0 751.8 835.6 885.1 968.8 1018.0 1102.5 1151.2 1235.7 1320.2 1368.9 1453.8 1502.6 1587.0 1635.8 1719.9 1769.4 1853.2 1902.0 750.7 : 49.2 133.6 218.1 266.9 351.3 400.5 485.0 533.7 617.5 667.4 751.1 800.6 884.4 933.5 1018.0 1066.8 1151.2 1235.7 1284.5 1369.3 1418.1 1502.6 1551.3 1635.5 1685.0 1768.7 1817.5 1902.0 799.9 : 84.5 168.9 217.7 302.2 351.3 435.8 484.6 568.3 618.2 702.0 751.4 835.2 884.4 968.8 1017.6 1102.1 1186.5 1235.3 1320.2 1368.9 1453.4 1502.2 1586.3 1635.8 1719.6 1768.3 1852.8 1902.0 884.4 : 84.5 133.2 217.7 266.9 351.3 400.1 483.9 533.7 617.5 667.0 750.7 799.9 884.4 933.1 1017.6 1102.1 1150.8 1235.7 1284.5 1368.9 1417.7 1501.8 1551.3 1635.1 1683.9 1768.3 1817.5 1902.0 968.8 : 48.8 133.2 182.4 266.9 315.6 399.4 449.3 533.0 582.5 666.3 715.4 799.9 848.7 933.1 1017.6 1066.4 1151.2 1200.0 1284.5 1333.2 1417.4 1466.9 1550.6 1599.4 1683.9 1733.0 1817.5 1902.0 1017.6: 84.5 133.6 218.1 266.9 350.6 400.5 484.3 533.7 617.5 666.7 751.1 799.9 884.4 968.8 1017.6 1102.5 1151.2 1235.7 1284.5 1368.6 1418.1 1501.8 1550.6 1635.1 1684.3 1768.7 1853.2 1902.0 1102.1: 49.2 133.6 182.4 266.1 316.0 399.8 449.3 533.0 582.2 666.7 715.4 799.9 884.4 933.1 1018.0 1066.8 1151.2 1200.0 1284.1 1333.6 1417.4 1466.1 1550.6 1599.8 1684.3 1768.7 1817.5 1902.0 1151.2: 84.5 133.2 217.0 266.9 350.6 400.1 483.9 533.0 617.5 666.3 750.7 835.2 884.0 968.8 1017.6 1102.1 1150.8 1235.0 1284.5 1368.2 1417.0 1501.5 1550.6 1635.1 1719.6 1768.3 1852.8 1902.0 1235.7: 48.8 132.5 182.4 266.1 315.6 399.4 448.6 533.0 581.8 666.3 750.7 799.5 884.4 933.1 1017.6 1066.4 1150.5 1200.0 1283.7 1332.5 1417.0 1466.1 1550.6 1635.1 1683.9 1768.3 1817.5 1902.0 1284.5: 83.7 133.6 217.4 266.9 350.6 399.8 484.3 533.0 617.5 702.0 750.7 835.6 884.4 968.8 1017.6 1101.7 1151.2 1235.0 1283.7 1368.2 1417.4 1501.8 1586.3 1635.1 1719.6 1768.7 1853.2 1902.0 1368.2: 49.9 133.6 183.1 266.9 316.0 400.5 449.3 533.7 618.2 667.0 751.8 800.6 885.1 933.9 1018.0 1067.5 1151.2 1200.0 1284.5 1333.6 1418.1 1502.6 1551.3 1635.8 1685.0 1769.4 1818.2 1902.0 1418.1: 83.7 133.2 217.0 266.1 350.6 399.4 483.9 568.3 617.1 702.0 750.7 835.2 884.0 968.1 1017.6 1101.3 1150.1 1234.6 1283.7 1368.2 1452.7 1501.5 1585.9 1635.1 1719.6 1768.3 1852.1 1902.0 1501.8: 49.5 133.2 182.4 266.9 315.6 400.1 484.6 533.3 618.2 667.0 751.4 800.2 884.4 933.9 1017.6 1066.4 1150.8 1200.0 1284.5 1368.9 1417.7 1502.2 1551.3 1635.8 1684.6 1768.3 1818.2 1902.0 1551.3: 83.7 132.9 217.4 266.1 350.6 435.1 483.9 568.7 617.5 702.0 750.7 834.9 884.4 968.1 1016.9 1101.3 1150.5 1235.0 1319.4 1368.2 1452.7 1501.8 1586.3 1635.1 1718.8 1768.7 1852.5 1902.0 1635.1: 49.2 133.6 182.4 266.9 351.3 400.1 485.0 533.7 618.2 667.0 751.1 800.6 884.4 933.1 1017.6 1066.8 1151.2 1235.7 1284.5 1368.9 1418.1 1502.6 1551.3 1635.1 1685.0 1768.7 1818.2 1902.0 1684.3: 84.5 133.2 217.7 302.2 350.9 435.8 484.6 569.0 617.8 702.0 751.4 835.2 884.0 968.4 1017.6 1102.1 1186.5 1235.3 1319.8 1368.9 1453.4 1502.2 1585.9 1635.8 1719.6 1769.0 1852.8 1902.0 1768.7: 48.8 133.2 217.7 266.5 351.3 400.1 484.6 533.3 617.5 667.0 750.7 799.5 884.0 933.1 1017.6 1102.1 1150.8 1235.3 1284.5 1368.9 1417.7 1501.5 1551.3 1635.1 1684.6 1768.3 1817.5 1902.0 1817.5: 84.5 168.9 217.7 302.6 351.3 435.8 484.6 568.7 618.2 702.0 750.7 835.2 884.4 968.8 1053.3 1102.1 1186.5 1235.7 1320.2 1368.9 1452.7 1502.6 1586.3 1635.8 1719.6 1768.7 1853.2 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 84.8629 cents 214375/209952, 36.0926 cents 36/35, 48.7704 cents 2: 132.5164 .. 168.9344 cents 117649/115200, 36.4180 cents 15116544/14706125, 47.6534 cents 3: 182.0080 .. 218.1005 cents 214375/209952, 36.0926 cents 1728/1715, 13.0736 cents 4: 266.1497 .. 302.5677 cents 117649/115200, 36.4180 cents 17280/16807, 48.0492 cents 5: 314.9201 .. 351.3381 cents 117649/115200, 36.4180 cents 829440/823543, 12.3524 cents 6: 399.3873 .. 435.8053 cents 117649/115200, 36.4180 cents 17280/16807, 48.0492 cents 7: 448.1577 .. 484.9714 cents 20588575/20155392, 36.8138 cents 829440/823543, 12.3524 cents 8: 532.6249 .. 569.4386 cents 20588575/20155392, 36.8138 cents 15116544/14706125, 47.6534 cents 9: 581.7910 .. 618.2090 cents 117649/115200, 36.4180 cents 829440/823543, 12.3524 cents 10: 666.2582 .. 701.9550 cents 49/48, 35.6968 cents 17280/16807, 48.0492 cents 11: 715.4243 .. 751.8423 cents 117649/115200, 36.4180 cents 4000/3969, 13.4693 cents 12: 799.4958 .. 835.5883 cents 214375/209952, 36.0926 cents 15116544/14706125, 47.6534 cents 13: 848.6619 .. 885.0799 cents 117649/115200, 36.4180 cents 1728/1715, 13.0736 cents 14: 933.1291 .. 968.8259 cents 49/48, 35.6968 cents 17280/16807, 48.0492 cents 15: 1016.8751 .. 1053.2931 cents 117649/115200, 36.4180 cents 17280/16807, 48.0492 cents 16: 1066.3667 .. 1102.4592 cents 214375/209952, 36.0926 cents 1728/1715, 13.0736 cents 17: 1150.1127 .. 1186.5307 cents 117649/115200, 36.4180 cents 15116544/14706125, 47.6534 cents 18: 1200.0000 .. 1235.6968 cents 49/48, 35.6968 cents 4000/3969, 13.4693 cents 19: 1283.7460 .. 1320.1640 cents 117649/115200, 36.4180 cents 17280/16807, 48.0492 cents 20: 1332.5164 .. 1369.3301 cents 20588575/20155392, 36.8138 cents 829440/823543, 12.3524 cents 21: 1416.9836 .. 1453.7973 cents 20588575/20155392, 36.8138 cents 15116544/14706125, 47.6534 cents 22: 1466.1497 .. 1502.5677 cents 117649/115200, 36.4180 cents 829440/823543, 12.3524 cents 23: 1550.6169 .. 1587.0349 cents 117649/115200, 36.4180 cents 17280/16807, 48.0492 cents 24: 1599.3873 .. 1635.8053 cents 117649/115200, 36.4180 cents 829440/823543, 12.3524 cents 25: 1683.8545 .. 1719.9470 cents 214375/209952, 36.0926 cents 17280/16807, 48.0492 cents 26: 1733.0206 .. 1769.4386 cents 117649/115200, 36.4180 cents 1728/1715, 13.0736 cents 27: 1817.0921 .. 1853.1846 cents 214375/209952, 36.0926 cents 15116544/14706125, 47.6534 cents
SHOW DATA
Number of notes : 28 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 67.9270 cents Largest one step interval : 6125/5832, 84.8629 cents Average / Smallest step : 1.392791 Largest / Average step : 1.249326 Largest / Smallest step : 1.740051 Median interval of one step : 360/343, 83.7460 cents, amount: 4 Most common interval of one step : 21/20, 84.4672 cents, amount: 9 Least squares average step : 67.88560 cents, oct.: 1900.79683 cents Scale is strictly proper Step pattern alph. order: ABCBABDEFBAGAABAGABFHFEFGABA Step pattern size order : GAHAGAFCEAGBGGAGBGAEDECEBGAG Scale is a Constant Structure, by a margin of 12.35237 cents Scale diversity : 0.281147 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.484345 Number of different interval sizes : 170 = 6.29630 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 6.29630 = 170/27 Median interval variety : 6 Lowest interval variety : 4 Smallest interval difference : 78125000/78121827, 0.0703 cents Most common intervals : 5/3, 884.3587 cents & inv., amount: 19 Most common triad is 0.0 884.359 1017.596 cents, amount: 12 Number of recognisable fifths : 13, average 705.0633 cents Number of appreciable fifths : 10, average 701.9550 cents Number of recognisable fourths : 21, average 484.3487 cents Number of appreciable fourths : 0 Scale contains a complete diamond : 9 49 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 21 = 75.0000% 2/1 octave complements present : 4 = 14.2857% Limited inverse transpositions with margin 36.4180 cents: 13 -- Rational properties -- Prime limit : 7 Odd number limit : 107163 (O: 107163 U: 35721) Highest odd numerator or denominator: 245 Scale harmonicity : 0.010511 Average absolute harmonicity : 0.057988 Specific harmonicity : 0.062733 Fundamental : 1/264600, -18.0135 octaves, 0.0010 Hz. Guide tone : 1323000, 20.3354 octaves, 346130622.893 Hz. Exponens Consonantiae : 3.500658E+11, 38.34884 octaves Euler's gradus suavitatis : 63 Sum of Mann's harmonic distance : 1795.5, average 64.12500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 41.77236, average 1.49187 Sum of Tenney's harmonic distance : 81.93407, average 2.92622 Vogel's harmonic complexity : 38.39286 Wille's k value : 270112 Wilson's harmonic complexity : 71 Rectangular lattice diameter : 15 Triangular lattice diameter : 8 Lattice compactness : 1697.08200, average 4.18000 Lattice compactness (without 2's) : 1415.51164, average 3.48648 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.32143 41 3: -3 .. 3 -0.03571 47 1 5: -2 .. 3 0.21429 30 4 7: -2 .. 2 0.25000 31 23 Average exponent except 2's : 12 / 28 = 0.42857 Average absolute exponent except 2's: 108 / 28 = 3.85714 Scale is JI-epimorphic with val: <18 28 41 50| = patent
FIT/MODE
28: 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 SP B ME I SD: 10.2368 c. M: 17.8484 c. 43: 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 P M ME SD: 2.5631 c. M:-4.2673 c. 71: 3 2 3 2 3 2 3 2 3 2 3 2 3 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 SP M ME SD: 2.5033 c. M: 4.4544 c. 114: 5 3 5 3 5 3 5 3 5 3 5 3 5 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 SP M DE SD: 0.6397 c. M: 1.2109 c. 157: 7 4 7 4 7 4 7 4 7 4 7 4 7 7 4 7 4 7 4 7 4 7 4 7 4 7 4 7 SP M DE SD: 0.3681 c. M: 0.7200 c. 271: 12 7 12 7 12 7 12 7 12 7 12 7 12 12 7 12 7 12 7 12 7 12 7 12 7 12 7 12 SP M DE SD: 0.2653 c. M: 0.5337 c. 428: 19 11 19 11 19 11 19 11 19 11 19 11 19 19 11 19 11 19 11 19 11 19 11 19 11 19 11 19 SP M DE SD: 0.2527 c. M: 0.5219 c. 699: 31 18 31 18 31 18 31 18 31 18 31 18 31 31 18 31 18 31 18 31 18 31 18 31 18 31 18 31 SP M DE SD: 0.2494 c. M: 0.4774 c. 970: 43 25 43 25 43 25 43 25 43 25 43 25 43 43 25 43 25 43 25 43 25 43 25 43 25 43 25 43 SP M DE SD: 0.2513 c. M: 0.4578 c. 1127: 50 29 50 29 50 29 50 29 50 29 50 29 50 50 29 50 29 50 29 50 29 50 29 50 29 50 29 50 SP M DE SD: 0.2494 c. M: 0.4943 c. 1439: 64 37 64 37 64 37 63 38 63 37 64 37 64 64 37 64 37 64 37 63 38 63 38 63 37 64 37 64 SP SD: 0.2293 c. M: 0.5007 c. 1482: 66 38 66 38 66 38 65 39 65 38 66 38 66 66 38 66 38 66 38 65 39 65 39 65 38 66 38 66 SP SD: 0.2273 c. M: 0.4682 c. 1553: 69 40 69 40 69 40 68 41 68 40 69 40 69 69 40 69 40 69 40 68 41 68 41 68 40 69 40 69 SP SD: 0.2104 c. M: 0.4948 c. 1596: 71 41 71 41 71 41 70 42 70 41 71 41 71 71 41 71 41 71 41 70 42 70 42 70 41 71 41 71 SP SD: 0.1954 c. M: 0.4196 c. 1651: 73 43 73 43 73 42 73 43 73 42 74 42 74 73 42 74 42 74 42 73 43 73 43 72 43 73 43 73 SP SD: 0.3340 c. M: 0.4095 c. 1654: 73 43 74 42 74 42 73 43 73 42 74 43 73 74 42 73 43 74 42 73 43 73 43 73 43 73 43 73 SP SD: 0.3015 c. M:-0.5502 c. 1660: 74 42 74 43 74 42 74 43 73 43 73 43 74 74 42 74 43 74 42 73 44 73 43 73 43 74 42 74 SP SD: 0.2907 c. M:-0.5739 c. 1667: 74 43 74 43 74 43 73 44 73 43 74 43 74 74 43 74 43 74 43 73 44 73 44 73 43 74 43 74 SP SD: 0.2037 c. M: 0.4896 c. 1689: 75 43 76 43 75 43 75 44 74 44 75 43 75 75 44 75 43 75 44 74 44 75 44 74 44 75 43 75 SP SD: 0.3090 c. M:-0.4049 c. 1690: 75 43 76 43 75 43 75 44 75 43 75 44 75 75 43 75 44 75 43 75 44 74 44 75 44 75 43 75 SP SD: 0.2998 c. M: 0.5854 c. 1693: 75 44 75 44 75 43 75 44 75 43 75 44 75 75 44 75 44 75 43 75 44 75 44 74 44 75 44 75 SP SD: 0.2772 c. M: 0.5037 c. 1710: 76 44 76 44 76 44 75 45 75 44 76 44 76 76 44 76 44 76 44 75 45 75 45 75 44 76 44 76 SP SD: 0.1771 c. M: 0.4196 c. 1727: 77 44 77 44 77 44 77 45 76 44 77 44 77 77 44 77 44 77 44 76 46 76 45 76 44 77 44 77 SP SD: 0.2923 c. M:-0.4017 c. 1731: 77 44 78 44 77 44 77 45 76 44 77 45 77 77 44 77 45 77 44 76 46 76 45 76 45 77 44 77 SP SD: 0.2453 c. M:-0.5529 c. 1753: 78 45 78 45 78 45 77 46 77 45 78 45 78 78 45 78 45 78 45 77 46 77 46 77 45 78 45 78 SP SD: 0.1733 c. M: 0.3745 c. 1824: 81 47 81 47 81 47 80 48 80 47 81 47 81 81 47 81 47 81 47 80 48 80 48 80 47 81 47 81 SP SD: 0.1705 c. M: 0.4196 c. 1867: 83 48 83 48 83 48 82 49 82 48 83 48 83 83 48 83 48 83 48 82 49 82 49 82 48 83 48 83 SP SD: 0.1546 c. M: 0.3570 c. 1959: 87 50 88 50 87 50 87 51 86 50 87 51 87 87 50 87 51 87 50 86 52 86 51 86 51 87 50 87 SP SD: 0.1828 c. M:-0.3560 c. 1981: 88 51 88 51 88 51 87 52 87 51 88 51 88 88 51 88 51 88 51 87 52 87 52 87 51 88 51 88 SP SD: 0.1471 c. M: 0.3606 c. 1998: 89 51 89 51 89 51 89 52 88 51 89 51 89 89 51 89 51 89 51 88 53 88 52 88 51 89 51 89 SP SD: 0.2468 c. M: 0.3469 c. 2002: 89 51 90 51 89 51 89 52 88 51 89 52 89 89 51 89 52 89 51 88 53 88 52 88 52 89 51 89 SP SD: 0.1830 c. M:-0.4058 c. 2024: 90 52 90 52 90 52 89 53 89 52 90 52 90 90 52 90 52 90 52 89 53 89 53 89 52 90 52 90 SP SD: 0.1411 c. M: 0.3059 c. 2138: 95 55 95 55 95 55 94 56 94 55 95 55 95 95 55 95 55 95 55 94 56 94 56 94 55 95 55 95 SP SD: 0.1320 c. M: 0.3103 c. 2230: 99 57 100 57 99 57 99 58 98 57 99 58 99 99 57 99 58 99 57 98 59 98 58 98 58 99 57 99 SP SD: 0.1393 c. M:-0.2632 c. 2252: 100 58 100 58 100 58 99 59 99 58 100 58 100 100 58 100 58 100 58 99 59 99 59 99 58 100 58 100 SP SD: 0.1320 c. M: 0.3159 c. 2295: 102 59 102 59 102 59 101 60 101 59 102 59 102 102 59 102 59 102 59 101 60 101 60 101 59 102 59 102 SP SD: 0.1241 c. M: 0.2669 c. 2344: 104 60 105 60 104 60 104 61 103 60 104 61 104 104 60 104 61 104 60 103 62 103 61 103 61 104 60 104 SP SD: 0.1305 c. M:-0.2516 c. 2387: 106 61 107 61 106 61 106 62 105 61 106 62 106 106 61 106 62 106 61 105 63 105 62 105 62 106 61 106 SP SD: 0.1196 c. M:-0.2219 c. 2501: 111 64 112 64 111 64 111 65 110 64 111 65 111 111 64 111 65 111 64 110 66 110 65 110 65 111 64 111 SP SD: 0.1096 c. M:-0.2081 c.
FIT/HARMONIC
1 .. 3 match: 2 H SD: 17.8484 cents 2 .. 6 match: 4 H SD: 15.3538 cents 3 .. 9 match: 6 H SD: 8.9414 cents 4 .. 12 match: 8 H SD: 8.3537 cents 5 .. 15 match: 10 H SD: 6.8695 cents 6 .. 18 match: 12 H SD: 7.2040 cents 7 .. 21 match: 14 H SD: 6.5447 cents 8 .. 24 match: 16 H SD: 5.4323 cents 9 .. 27 match: 18 H SD: 4.2961 cents 10 .. 30 match: 19 S SD: 5.6735 cents 11 .. 33 match: 20 SD: 3.9651 cents 12 .. 36 match: 20 SD: 3.9080 cents 13 .. 39 match: 20 SD: 3.8798 cents 14 .. 42 match: 22 SD: 3.7237 cents 15 .. 45 match: 25 SD: 3.2727 cents 16 .. 48 match: 25 SD: 3.2938 cents 17 .. 51 match: 26 SD: 3.2181 cents 18 .. 54 match: 25 SD: 3.1257 cents 19 .. 57 match: 27 SD: 2.4359 cents 20 .. 60 match: 25 SD: 2.8129 cents 21 .. 63 match: 27 SD: 2.6921 cents 22 .. 66 match: 28 SD: 2.3539 cents 23 .. 69 match: 28 SD: 2.3387 cents 24 .. 72 match: 28 SD: 2.0741 cents 28 .. 84 match: 28 SD: 1.9996 cents 30 .. 90 match: 27 SD: 1.7331 cents 31 .. 93 match: 27 SD: 1.6747 cents 35 .. 105 match: 28 SD: 1.5313 cents 36 .. 108 match: 28 SD: 1.3804 cents 37 .. 111 match: 28 SD: 1.3461 cents 39 .. 117 match: 28 SD: 1.3452 cents 44 .. 132 match: 28 SD: 1.2426 cents 49 .. 147 match: 28 SD: 1.0789 cents 53 .. 159 match: 28 SD: 0.8589 cents 61 .. 183 match: 28 SD: 0.8061 cents 66 .. 198 match: 28 SD: 0.7734 cents 72 .. 216 match: 28 SD: 0.6969 cents 77 .. 231 match: 28 SD: 0.6299 cents 84 .. 252 match: 28 SD: 0.6046 cents 89 .. 267 match: 28 SD: 0.5181 cents 96 .. 288 match: 28 SD: 0.5064 cents 102 .. 306 match: 28 SD: 0.4958 cents 111 .. 333 match: 28 SD: 0.4836 cents 112 .. 336 match: 28 SD: 0.4740 cents 119 .. 357 match: 28 SD: 0.4194 cents 124 .. 372 match: 28 SD: 0.3859 cents 138 .. 414 match: 28 SD: 0.3554 cents 155 .. 465 match: 28 SD: 0.3497 cents 160 .. 480 match: 28 SD: 0.3474 cents 161 .. 483 match: 28 SD: 0.3054 cents 164 .. 492 match: 28 SD: 0.2880 cents 177 .. 531 match: 28 SD: 0.2813 cents 186 .. 558 match: 28 SD: 0.2610 cents 199 .. 597 match: 28 SD: 0.2424 cents 200 .. 600 match: 28 SD: 0.2417 cents 215 .. 645 match: 28 SD: 0.2350 cents 216 .. 648 match: 28 SD: 0.2239 cents 235 .. 705 match: 28 SD: 0.2218 cents 236 .. 708 match: 28 SD: 0.2087 cents 238 .. 714 match: 28 SD: 0.2043 cents 239 .. 717 match: 28 SD: 0.1914 cents 276 .. 828 match: 28 SD: 0.1679 cents 300 .. 900 match: 28 SD: 0.1658 cents 313 .. 939 match: 28 SD: 0.1595 cents 320 .. 960 match: 28 SD: 0.1517 cents 335 .. 1005 match: 28 SD: 0.1505 cents 341 .. 1023 match: 28 SD: 0.1392 cents 360 .. 1080 match: 28 SD: 0.1334 cents 378 .. 1134 match: 28 SD: 0.1323 cents 396 .. 1188 match: 28 SD: 0.1159 cents 427 .. 1281 match: 28 SD: 0.1155 cents 439 .. 1317 match: 28 SD: 0.1112 cents 462 .. 1386 match: 28 SD: 0.0790 cents 499 .. 1497 match: 28 SD: 0.0733 cents