Scala analysis: evangelina
Erv Wilson's everyday go-to scale (Kraig Grady, T66325).
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 13/12 138.572661 tridecimal 2/3-tone 3: 10/9 182.403712 minor whole tone 4: 9/8 203.910002 major whole tone 5: 7/6 266.870906 septimal minor third 6: 11/9 347.407941 undecimal neutral third 7: 5/4 386.313714 major third 8: 81/64 407.820003 Pythagorean major third 9: 4/3 498.044999 perfect fourth 10: 11/8 551.317942 undecimal semi-augmented fourth 11: 45/32 590.223716 diatonic tritone 12: 17/12 603.000409 2nd septendecimal tritone 13: 3/2 701.955001 perfect fifth 14: 405/256 794.133717 wide augmented fifth 15: 13/8 840.527662 tridecimal neutral sixth 16: 5/3 884.358713 major sixth, BP sixth 17: 27/16 905.865003 Pythagorean major sixth 18: 7/4 968.825906 harmonic seventh 19: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 20: 15/8 1088.268715 classic major seventh 21: 243/128 1109.775004 Pythagorean major seventh 22: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 135/128 92.1787 major chroma, major limma 2: 416/405 46.3939 3: 40/39 43.8311 tridecimal minor diesis 4: 81/80 21.5063 syntonic comma, Didymus comma 5: 28/27 62.9609 Archytas' 1/3-tone 6: 22/21 80.5370 undecimal minor semitone 7: 45/44 38.9058 1/5-tone 8: 81/80 21.5063 syntonic comma, Didymus comma 9: 256/243 90.2250 limma, Pythagorean minor second 10: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 11: 45/44 38.9058 1/5-tone 12: 136/135 12.7767 13: 18/17 98.9546 Arabic lute index finger 14: 135/128 92.1787 major chroma, major limma 15: 416/405 46.3939 16: 40/39 43.8311 tridecimal minor diesis 17: 81/80 21.5063 syntonic comma, Didymus comma 18: 28/27 62.9609 Archytas' 1/3-tone 19: 22/21 80.5370 undecimal minor semitone 20: 45/44 38.9058 1/5-tone 21: 81/80 21.5063 syntonic comma, Didymus comma 22: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 136/135 12.777 cents 1: 4 81/80 21.506 cents syntonic comma, Didymus comma 1: 3 45/44 38.906 cents 1/5-tone 1: 2 40/39 43.831 cents tridecimal minor diesis 1: 2 416/405 46.394 cents 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 2 135/128 92.179 cents major chroma, major limma 1: 1 18/17 98.955 cents Arabic lute index finger 2: 1 34/33 51.682 cents 2: 2 729/704 60.412 cents undecimal major diesis 2: 2 27/26 65.337 cents tridecimal comma 2: 2 21/20 84.467 cents minor semitone 2: 2 256/243 90.225 cents limma, Pythagorean minor second 2: 1 135/128 92.179 cents major chroma, major limma 2: 3 16/15 111.731 cents minor diatonic semitone 2: 2 15/14 119.443 cents major diatonic semitone 2: 2 13/12 138.573 cents tridecimal 2/3-tone 2: 3 88/81 143.498 cents 2nd undecimal neutral second 2: 1 10/9 182.404 cents minor whole tone 2: 1 1215/1088 191.133 cents 3: 1 17/16 104.955 cents 17th harmonic 3: 2 16/15 111.731 cents minor diatonic semitone 3: 2 14/13 128.298 cents 2/3-tone 3: 2 243/224 140.949 cents Archytas' 2/3-tone 3: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 3 11/10 165.004 cents Ptolemy's second, 4/5-tone 3: 5 10/9 182.404 cents minor whole tone 3: 2 9/8 203.910 cents major whole tone 3: 1 832/729 228.798 cents 3: 1 39/34 237.527 cents 4: 2 448/405 174.692 cents 4: 1 272/243 195.180 cents Persian whole tone 4: 9 9/8 203.910 cents major whole tone 4: 2 44/39 208.835 cents 4: 2 8/7 231.174 cents septimal whole tone 4: 2 405/352 242.816 cents 4: 2 52/45 250.304 cents 4: 1 2560/2187 272.629 cents grave minor third 4: 1 20/17 281.358 cents septendecimal augmented second 5: 1 17/15 216.687 cents septendecimal whole tone 5: 2 729/640 225.416 cents acute major second 5: 1 405/352 242.816 cents 5: 2 15/13 247.741 cents tridecimal 5/4-tone 5: 2 1408/1215 255.229 cents 5: 2 7/6 266.871 cents septimal minor third 5: 1 33/28 284.447 cents undecimal minor third 5: 2 13/11 289.210 cents tridecimal minor third 5: 6 32/27 294.135 cents Pythagorean minor third 5: 1 1215/1024 296.089 cents wide augmented second 5: 1 81/68 302.865 cents Persian wosta 5: 1 135/112 323.353 cents septimal wide minor third 6: 1 51/44 255.592 cents 6: 2 243/208 269.247 cents 6: 2 32/27 294.135 cents Pythagorean minor third 6: 5 6/5 315.641 cents minor third 6: 1 135/112 323.353 cents septimal wide minor third 6: 2 40/33 333.041 cents 6: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 6: 3 11/9 347.408 cents undecimal neutral third 6: 1 896/729 357.096 cents 6: 1 21/17 365.825 cents submajor third 6: 1 26/21 369.747 cents 6: 2 5/4 386.314 cents major third 7: 2 6/5 315.641 cents minor third 7: 1 17/14 336.130 cents supraminor third 7: 3 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 7: 2 16/13 359.472 cents tridecimal neutral third 7: 1 99/80 368.914 cents 7: 2 56/45 378.602 cents septimal narrow major third 7: 4 5/4 386.314 cents major third 7: 2 81/64 407.820 cents Pythagorean major third 7: 1 80/63 413.578 cents wide major third 7: 2 104/81 432.708 cents 7: 1 2816/2187 437.633 cents 7: 1 22/17 446.363 cents 8: 1 34/27 399.090 cents septendecimal major third 8: 2 512/405 405.866 cents narrow diminished fourth 8: 4 81/64 407.820 cents Pythagorean major third 8: 1 33/26 412.745 cents tridecimal major third 8: 2 14/11 417.508 cents undecimal diminished fourth or major third 8: 2 9/7 435.084 cents septimal major third, BP third 8: 1 3645/2816 446.726 cents 8: 1 135/104 451.651 cents 8: 2 13/10 454.214 cents tridecimal semi-diminished fourth 8: 2 176/135 459.139 cents 8: 3 320/243 476.539 cents grave fourth 8: 1 45/34 485.268 cents 9: 1 51/40 420.597 cents septendecimal diminished fourth 9: 1 135/104 451.651 cents 9: 1 176/135 459.139 cents 9: 1 21/16 470.781 cents narrow fourth 9: 1 117/88 493.120 cents tridecimal gentle fourth 9: 15 4/3 498.045 cents perfect fourth 9: 1 729/544 506.775 cents 9: 1 1215/896 527.263 cents 10: 1 17/13 464.428 cents 10: 1 4/3 498.045 cents perfect fourth 10: 5 27/20 519.551 cents acute fourth 10: 3 15/11 536.951 cents undecimal augmented fourth 10: 1 160/117 541.876 cents 10: 1 1664/1215 544.439 cents 10: 2 11/8 551.318 cents undecimal semi-augmented fourth 10: 2 112/81 561.006 cents 10: 1 39/28 573.657 cents 10: 1 88/63 578.582 cents 10: 1 1024/729 588.270 cents Pythagorean diminished fifth 10: 2 45/32 590.224 cents diatonic tritone 10: 1 24/17 597.000 cents 1st septendecimal tritone 11: 1 544/405 510.822 cents 11: 3 243/176 558.457 cents 11: 2 18/13 563.382 cents tridecimal augmented fourth 11: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 11: 1 1024/729 588.270 cents Pythagorean diminished fifth 11: 2 45/32 590.224 cents diatonic tritone 11: 2 64/45 609.776 cents 2nd tritone 11: 1 729/512 611.730 cents Pythagorean tritone 11: 2 10/7 617.488 cents Euler's tritone 11: 2 13/9 636.618 cents tridecimal diminished fifth 11: 3 352/243 641.543 cents 11: 1 405/272 689.178 cents 12: 1 17/12 603.000 cents 2nd septendecimal tritone 12: 2 64/45 609.776 cents 2nd tritone 12: 1 729/512 611.730 cents Pythagorean tritone 12: 1 63/44 621.418 cents 12: 1 56/39 626.343 cents 12: 2 81/56 638.994 cents 12: 2 16/11 648.682 cents undecimal semi-diminished fifth 12: 1 1215/832 655.561 cents 12: 1 117/80 658.124 cents 12: 3 22/15 663.049 cents undecimal diminished fifth 12: 5 40/27 680.449 cents grave fifth 12: 1 3/2 701.955 cents perfect fifth 12: 1 26/17 735.572 cents 13: 1 1792/1215 672.737 cents 13: 1 1088/729 693.225 cents 13: 15 3/2 701.955 cents perfect fifth 13: 1 176/117 706.880 cents 13: 1 32/21 729.219 cents wide fifth 13: 1 135/88 740.861 cents 13: 1 208/135 748.349 cents 13: 1 80/51 779.403 cents 14: 1 68/45 714.732 cents 14: 3 243/160 723.461 cents acute fifth 14: 2 135/88 740.861 cents 14: 2 20/13 745.786 cents tridecimal semi-augmented fifth 14: 1 208/135 748.349 cents 14: 1 5632/3645 753.274 cents 14: 2 14/9 764.916 cents septimal minor sixth 14: 2 11/7 782.492 cents undecimal augmented fifth 14: 1 52/33 787.255 cents tridecimal minor sixth 14: 4 128/81 792.180 cents Pythagorean minor sixth 14: 2 405/256 794.134 cents wide augmented fifth 14: 1 27/17 800.910 cents septendecimal minor sixth 15: 1 17/11 753.637 cents 15: 1 2187/1408 762.367 cents 15: 2 81/52 767.292 cents 15: 1 63/40 786.422 cents narrow minor sixth 15: 2 128/81 792.180 cents Pythagorean minor sixth 15: 4 8/5 813.686 cents minor sixth 15: 2 45/28 821.398 cents septimale wide minor sixth 15: 1 160/99 831.086 cents 15: 2 13/8 840.528 cents tridecimal neutral sixth 15: 3 44/27 845.453 cents neutral sixth 15: 1 28/17 863.870 cents submajor sixth 15: 2 5/3 884.359 cents major sixth, BP sixth 16: 2 8/5 813.686 cents minor sixth 16: 1 21/13 830.253 cents 16: 1 34/21 834.175 cents supraminor sixth 16: 1 729/448 842.904 cents 16: 3 18/11 852.592 cents undecimal neutral sixth 16: 1 64/39 857.517 cents 39th subharmonic 16: 2 33/20 866.959 cents 16: 1 224/135 876.647 cents narrow septimal major sixth 16: 5 5/3 884.359 cents major sixth, BP sixth 16: 2 27/16 905.865 cents Pythagorean major sixth 16: 2 416/243 930.753 cents 16: 1 88/51 944.408 cents 17: 1 224/135 876.647 cents narrow septimal major sixth 17: 1 136/81 897.135 cents 17: 1 2048/1215 903.911 cents narrow diminished seventh 17: 6 27/16 905.865 cents Pythagorean major sixth 17: 2 22/13 910.790 cents tridecimal major sixth 17: 1 56/33 915.553 cents 17: 2 12/7 933.129 cents septimal major sixth 17: 2 1215/704 944.771 cents 17: 2 26/15 952.259 cents tridecimal semi-augmented sixth 17: 1 704/405 957.184 cents 17: 2 1280/729 974.584 cents grave minor seventh 17: 1 30/17 983.313 cents septendecimal minor seventh 18: 1 17/10 918.642 cents septendecimal diminished seventh 18: 1 2187/1280 927.371 cents acute major sixth 18: 2 45/26 949.696 cents 18: 2 704/405 957.184 cents 18: 2 7/4 968.826 cents harmonic seventh 18: 2 39/22 991.165 cents 18: 9 16/9 996.090 cents Pythagorean minor seventh 18: 1 243/136 1004.820 cents 18: 2 405/224 1025.308 cents 19: 1 68/39 962.473 cents 19: 1 729/416 971.202 cents 19: 2 16/9 996.090 cents Pythagorean minor seventh 19: 5 9/5 1017.596 cents just minor seventh, BP seventh 19: 3 20/11 1034.996 cents large minor seventh 19: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 19: 2 448/243 1059.051 cents 19: 2 13/7 1071.702 cents 16/3-tone 19: 2 15/8 1088.269 cents classic major seventh 19: 1 32/17 1095.045 cents 17th subharmonic 20: 1 2176/1215 1008.867 cents 20: 1 9/5 1017.596 cents just minor seventh, BP seventh 20: 3 81/44 1056.502 cents 2nd undecimal neutral seventh 20: 2 24/13 1061.427 cents tridecimal neutral seventh 20: 2 28/15 1080.557 cents grave major seventh 20: 3 15/8 1088.269 cents classic major seventh 20: 1 256/135 1107.821 cents octave - major chroma 20: 2 243/128 1109.775 cents Pythagorean major seventh 20: 2 40/21 1115.533 cents acute major seventh 20: 2 52/27 1134.663 cents 20: 2 1408/729 1139.588 cents 20: 1 33/17 1148.318 cents 21: 1 17/9 1101.045 cents septendecimal major seventh 21: 2 256/135 1107.821 cents octave - major chroma 21: 2 243/128 1109.775 cents Pythagorean major seventh 21: 2 21/11 1119.463 cents undecimal major seventh 21: 2 27/14 1137.039 cents septimal major seventh 21: 1 64/33 1146.727 cents 33rd subharmonic 21: 2 405/208 1153.606 cents 21: 2 39/20 1156.169 cents 21: 3 88/45 1161.094 cents 21: 4 160/81 1178.494 cents octave - syntonic comma 21: 1 135/68 1187.223 cents Highest number of different intervals for one interval class: 13 Average number of different intervals per interval class: 11.14286 = 78/7
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 0.0 : 92.2 138.6 182.4 203.9 266.9 347.4 386.3 407.8 498.0 551.3 590.2 603.0 702.0 794.1 840.5 884.4 905.9 968.8 1049.4 1088.3 1109.8 1200.0 92.2 : 46.4 90.2 111.7 174.7 255.2 294.1 315.6 405.9 459.1 498.0 510.8 609.8 702.0 748.3 792.2 813.7 876.6 957.2 996.1 1017.6 1107.8 1200.0 138.6 : 43.8 65.3 128.3 208.8 247.7 269.2 359.5 412.7 451.7 464.4 563.4 655.6 702.0 745.8 767.3 830.3 910.8 949.7 971.2 1061.4 1153.6 1200.0 182.4 : 21.5 84.5 165.0 203.9 225.4 315.6 368.9 407.8 420.6 519.6 611.7 658.1 702.0 723.5 786.4 867.0 905.9 927.4 1017.6 1109.8 1156.2 1200.0 203.9 : 63.0 143.5 182.4 203.9 294.1 347.4 386.3 399.1 498.0 590.2 636.6 680.4 702.0 764.9 845.5 884.4 905.9 996.1 1088.3 1134.7 1178.5 1200.0 266.9 : 80.5 119.4 140.9 231.2 284.4 323.4 336.1 435.1 527.3 573.7 617.5 639.0 702.0 782.5 821.4 842.9 933.1 1025.3 1071.7 1115.5 1137.0 1200.0 347.4 : 38.9 60.4 150.6 203.9 242.8 255.6 354.5 446.7 493.1 537.0 558.5 621.4 702.0 740.9 762.4 852.6 944.8 991.2 1035.0 1056.5 1119.5 1200.0 386.3 : 21.5 111.7 165.0 203.9 216.7 315.6 407.8 454.2 498.0 519.6 582.5 663.0 702.0 723.5 813.7 905.9 952.3 996.1 1017.6 1080.6 1161.1 1200.0 407.8 : 90.2 143.5 182.4 195.2 294.1 386.3 432.7 476.5 498.0 561.0 641.5 680.4 702.0 792.2 884.4 930.8 974.6 996.1 1059.1 1139.6 1178.5 1200.0 498.0 : 53.3 92.2 105.0 203.9 296.1 342.5 386.3 407.8 470.8 551.3 590.2 611.7 702.0 794.1 840.5 884.4 905.9 968.8 1049.4 1088.3 1109.8 1200.0 551.3 : 38.9 51.7 150.6 242.8 289.2 333.0 354.5 417.5 498.0 537.0 558.5 648.7 740.9 787.3 831.1 852.6 915.6 996.1 1035.0 1056.5 1146.7 1200.0 590.2 : 12.8 111.7 203.9 250.3 294.1 315.6 378.6 459.1 498.0 519.6 609.8 702.0 748.3 792.2 813.7 876.6 957.2 996.1 1017.6 1107.8 1161.1 1200.0 603.0 : 99.0 191.1 237.5 281.4 302.9 365.8 446.4 485.3 506.8 597.0 689.2 735.6 779.4 800.9 863.9 944.4 983.3 1004.8 1095.0 1148.3 1187.2 1200.0 702.0 : 92.2 138.6 182.4 203.9 266.9 347.4 386.3 407.8 498.0 590.2 636.6 680.4 702.0 764.9 845.5 884.4 905.9 996.1 1049.4 1088.3 1101.0 1200.0 794.1 : 46.4 90.2 111.7 174.7 255.2 294.1 315.6 405.9 498.0 544.4 588.3 609.8 672.7 753.3 792.2 813.7 903.9 957.2 996.1 1008.9 1107.8 1200.0 840.5 : 43.8 65.3 128.3 208.8 247.7 269.2 359.5 451.7 498.0 541.9 563.4 626.3 706.9 745.8 767.3 857.5 910.8 949.7 962.5 1061.4 1153.6 1200.0 884.4 : 21.5 84.5 165.0 203.9 225.4 315.6 407.8 454.2 498.0 519.6 582.5 663.0 702.0 723.5 813.7 867.0 905.9 918.6 1017.6 1109.8 1156.2 1200.0 905.9 : 63.0 143.5 182.4 203.9 294.1 386.3 432.7 476.5 498.0 561.0 641.5 680.4 702.0 792.2 845.5 884.4 897.1 996.1 1088.3 1134.7 1178.5 1200.0 968.8 : 80.5 119.4 140.9 231.2 323.4 369.7 413.6 435.1 498.0 578.6 617.5 639.0 729.2 782.5 821.4 834.2 933.1 1025.3 1071.7 1115.5 1137.0 1200.0 1049.4: 38.9 60.4 150.6 242.8 289.2 333.0 354.5 417.5 498.0 537.0 558.5 648.7 702.0 740.9 753.6 852.6 944.8 991.2 1035.0 1056.5 1119.5 1200.0 1088.3: 21.5 111.7 203.9 250.3 294.1 315.6 378.6 459.1 498.0 519.6 609.8 663.0 702.0 714.7 813.7 905.9 952.3 996.1 1017.6 1080.6 1161.1 1200.0 1109.8: 90.2 182.4 228.8 272.6 294.1 357.1 437.6 476.5 498.0 588.3 641.5 680.4 693.2 792.2 884.4 930.8 974.6 996.1 1059.1 1139.6 1178.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 12.7767 .. 98.9546 cents 1215/1156, 86.1779 cents 136/135, 12.7767 cents 2: 51.6825 .. 191.1333 cents 40095/36992, 139.4508 cents 289/297,-47.2721 cents 3: 104.9554 .. 237.5273 cents 312/289, 132.5718 cents 1156/1215,-86.1779 cents 4: 174.6922 .. 281.3583 cents 2025/1904, 106.6661 cents 15232/15795,-62.8351 cents 5: 216.6867 .. 323.3528 cents 2025/1904, 106.6661 cents 289/300,-64.6716 cents 6: 255.5925 .. 386.3137 cents 55/51, 130.7212 cents 476/495,-67.7603 cents 7: 315.6413 .. 446.3625 cents 55/51, 130.7212 cents 24/25,-70.6724 cents 8: 399.0904 .. 485.2683 cents 1215/1156, 86.1779 cents 289/297,-47.2721 cents 9: 420.5967 .. 527.2628 cents 2025/1904, 106.6661 cents 289/300,-64.6716 cents 10: 464.4277 .. 596.9996 cents 312/289, 132.5718 cents 15232/15795,-62.8351 cents 11: 510.8217 .. 689.1783 cents 164025/147968, 178.3566 cents 1156/1215,-86.1779 cents 12: 603.0004 .. 735.5723 cents 312/289, 132.5718 cents 1156/1215,-86.1779 cents 13: 672.7372 .. 779.4033 cents 2025/1904, 106.6661 cents 15232/15795,-62.8351 cents 14: 714.7317 .. 800.9096 cents 1215/1156, 86.1779 cents 289/300,-64.6716 cents 15: 753.6375 .. 884.3587 cents 55/51, 130.7212 cents 289/297,-47.2721 cents 16: 813.6863 .. 944.4075 cents 55/51, 130.7212 cents 24/25,-70.6724 cents 17: 876.6472 .. 983.3133 cents 2025/1904, 106.6661 cents 476/495,-67.7603 cents 18: 918.6417 .. 1025.3078 cents 2025/1904, 106.6661 cents 289/300,-64.6716 cents 19: 962.4727 .. 1095.0446 cents 312/289, 132.5718 cents 15232/15795,-62.8351 cents 20: 1008.8667 .. 1148.3175 cents 40095/36992, 139.4508 cents 1156/1215,-86.1779 cents 21: 1101.0454 .. 1187.2233 cents 1215/1156, 86.1779 cents 289/297,-47.2721 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 136/135, 12.7767 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 18/17, 98.9546 cents Average / Smallest step : 4.269137 Largest / Average step : 1.814168 Largest / Smallest step : 7.744930 Median interval of one step : 416/405, 46.3939 cents, amount: 2 Most common interval of one step : 81/80, 21.5063 cents, amount: 4 Least squares average step : 54.30562 cents, oct.: 1194.72372 cents Scale is not proper Step pattern alph. order: ABCDEFGDHIGJKABCDEFGDH Step pattern size order : JEDBGHCBIFCAKJEDBGHCBI Scale is not a Constant Structure Scale diversity : 1.627070 Lumma stability : 0.021294 Lumma impropriety factor : 0.877566 Number of different interval sizes : 202 = 9.61905 / class Number of one step interval sizes : 11 Highest interval variety : 13 Mean interval variety : 11.14286 = 78/7 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 61965/61952, 0.3632 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 16 Most common triad is 0.0 498.045 701.955 cents, amount: 11 Number of recognisable fifths : 20, average 701.7648 cents Number of appreciable fifths : 19, average 701.0823 cents Scale contains two identical disjunct "tetrachords" of 10 notes Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 13.6364% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 6 and 7 combined Scale is n-1 differentially coherent in interval classes 9 and 10 combined -- Rational properties -- Prime limit : 17 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 405 Scale harmonicity : 0.008635 Average absolute harmonicity : 0.124137 Specific harmonicity : 0.086043 Fundamental : 1/2304, -11.1699 octaves, 0.1136 Hz. Guide tone : 82702620, 26.3014 octaves, 21637119709.374 Hz. Exponens Consonantiae : 1.905468E+11, 37.47135 octaves Euler's gradus suavitatis : 73 Sum of Mann's harmonic distance : 903.0, average 41.04545 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 25.82592, average 1.17391 Sum of Tenney's harmonic distance : 49.13066, average 2.23321 Vogel's harmonic complexity : 19.18182 Wille's k value : 1822 Wilson's harmonic complexity : 74 Rectangular lattice diameter : 12 Triangular lattice diameter : 7 Lattice compactness : 1073.03354, average 4.24124 Lattice compactness (without 2's) : 667.75430, average 2.63935 Number of different primes : 7 Prime exponents' range, average, count, tones@limit: 2: -8 .. 2 -2.54545 64 1 3: -2 .. 5 0.68182 35 6 5: 0 .. 1 0.31818 7 7 7: 0 .. 1 0.09091 2 2 11: 0 .. 1 0.13636 3 3 13: 0 .. 1 0.09091 2 2 17: 0 .. 1 0.04545 1 1 Average exponent except 2's : 30 / 22 = 1.36364 Average absolute exponent except 2's: 50 / 22 = 2.27273 Scale is weakly epimorphic with val: <22 35 50 60 77 84 91| Scale is weakly epimorphic with val: <22 35 50 62 77 82 91| Scale is weakly epimorphic with val: <22 35 51 62 76 80 91|
FIT/MODE
22: 1 1 1 1 1 1 1 0 2 1 1 0 2 1 1 1 0 2 1 1 0 2 N T3 SD: 18.5640 c. M: 37.6333 c. 24: 2 1 1 0 1 2 1 0 2 1 1 0 2 2 1 1 0 1 2 1 0 2 N SD: 9.9124 c. M: 18.8259 c. 31: 2 2 1 0 2 2 1 1 2 1 1 1 2 3 1 1 0 2 2 1 1 2 N SD: 10.6840 c. M:-18.7695 c. 32: 2 2 1 0 2 2 1 1 2 2 1 0 3 2 1 2 0 2 2 1 1 2 N SD: 10.1695 c. M: 17.1787 c. 34: 3 1 1 1 2 2 1 1 2 2 1 0 3 3 1 1 1 2 2 1 1 2 N SD: 10.6799 c. M:-19.6368 c. 36: 3 1 1 1 2 2 2 0 3 2 1 0 3 3 1 2 0 2 2 2 0 3 N SD: 9.5489 c. M: 16.0296 c. 37: 3 1 2 0 2 3 1 1 2 2 1 1 3 2 2 1 1 2 2 2 0 3 N SD: 9.3143 c. M: 15.7553 c. 38: 3 1 2 0 2 3 1 1 3 1 2 0 3 3 2 1 1 2 2 1 1 3 N SD: 8.9259 c. M: 14.5845 c. 41: 3 2 1 1 2 3 1 1 3 2 1 1 3 3 2 1 1 2 3 1 1 3 N SD: 5.0445 c. M:-11.6337 c. 53: 4 2 2 1 3 3 2 1 4 2 2 1 4 4 2 2 1 3 3 2 1 4 N SD: 3.8793 c. M:-8.3203 c. 67: 5 3 2 1 4 4 3 1 5 3 2 1 5 5 3 2 2 3 5 2 1 5 N SD: 4.8134 c. M:-7.7161 c. 68: 5 3 2 2 3 5 2 1 5 3 2 1 6 5 3 2 1 4 4 3 1 5 N SD: 4.6284 c. M: 8.1865 c. 77: 6 3 3 1 4 5 3 1 6 3 3 1 6 6 3 3 1 4 5 3 1 6 N SD: 3.0490 c. M: 5.8634 c. 94: 7 4 3 2 5 6 3 2 7 4 3 1 8 7 4 3 2 5 6 3 2 7 N SD: 2.2571 c. M: 3.6803 c. 118: 9 5 4 2 6 8 4 2 9 5 4 1 10 9 5 4 2 6 8 4 2 9 N SD: 1.7360 c. M:-3.8002 c. 130: 10 5 5 2 7 9 4 2 10 6 4 1 11 10 5 5 2 7 9 4 2 10 N SD: 1.6173 c. M:-3.3613 c. 159: 12 6 6 3 8 11 5 3 12 7 5 2 13 12 6 6 3 8 11 5 3 12 N SD: 1.4604 c. M: 2.7918 c. 171: 13 7 6 3 9 12 5 3 13 8 5 2 14 13 7 6 3 9 12 5 3 13 N SD: 1.4100 c. M:-3.4693 c. 183: 14 7 7 3 10 12 6 3 14 8 6 2 15 14 7 7 3 10 12 6 3 14 N SD: 0.9060 c. M:-1.9816 c. 224: 17 9 8 4 12 15 7 4 17 10 7 3 18 17 9 8 4 12 15 7 4 17 N SD: 0.8479 c. M:-2.3567 c. 248: 19 10 9 4 13 17 8 4 19 11 8 3 20 19 10 9 4 13 17 8 4 19 N SD: 1.0178 c. M:-1.8383 c. 265: 20 11 9 5 14 18 8 5 20 12 8 3 22 20 11 9 5 14 18 8 5 20 N SD: 1.1069 c. M:-1.8047 c. 270: 21 10 10 5 14 18 9 5 20 12 9 3 22 21 10 10 5 14 18 9 5 20 N SD: 0.7552 c. M:-1.4440 c. 301: 23 12 11 5 16 20 10 5 23 13 10 3 25 23 12 11 5 16 20 10 5 23 N SD: 0.7434 c. M: 1.4694 c. 311: 24 12 11 6 16 21 10 6 23 14 10 3 26 24 12 11 6 16 21 10 6 23 N SD: 0.6728 c. M:-1.4790 c. 342: 26 13 13 6 18 23 11 6 26 15 11 4 28 26 13 13 6 18 23 11 6 26 N SD: 0.7668 c. M: 1.9312 c. 364: 28 14 13 7 19 24 12 7 27 16 12 4 30 28 14 13 7 19 24 12 7 27 N SD: 0.6514 c. M: 1.2541 c. 388: 30 15 14 7 20 26 13 7 29 17 13 4 32 30 15 14 7 20 26 13 7 29 N SD: 0.5567 c. M: 1.0162 c. 400: 31 15 15 7 21 27 13 7 30 18 13 4 33 31 15 15 7 21 27 13 7 30 N SD: 0.5129 c. M:-0.8663 c. 441: 34 17 16 8 23 30 14 8 33 20 14 5 36 34 17 16 8 23 30 14 8 33 N SD: 0.4787 c. M:-1.0812 c. 494: 38 19 18 9 26 33 16 9 37 22 16 5 41 38 19 18 9 26 33 16 9 37 N SD: 0.2167 c. M: 0.5713 c. 718: 55 28 26 13 38 48 23 13 54 32 23 8 59 55 28 26 13 38 48 23 13 54 N SD: 0.2435 c. M:-0.5386 c. 742: 57 29 27 13 39 50 24 13 56 33 24 8 61 57 29 27 13 39 50 24 13 56 N SD: 0.2358 c. M:-0.5109 c. 882: 68 34 32 16 46 59 29 16 66 39 29 9 73 68 34 32 16 46 59 29 16 66 N SD: 0.2634 c. M: 0.4692 c. 901: 69 35 33 16 47 61 29 16 68 40 29 10 74 69 35 33 16 47 61 29 16 68 N SD: 0.2435 c. M: 0.5684 c. 935: 72 36 34 17 49 63 30 17 70 42 30 10 77 72 36 34 17 49 63 30 17 70 N SD: 0.2449 c. M:-0.5537 c. 954: 73 37 35 17 50 64 31 17 72 42 31 10 79 73 37 35 17 50 64 31 17 72 N SD: 0.2599 c. M: 0.4847 c. 988: 76 38 36 18 52 66 32 18 74 44 32 11 81 76 38 36 18 52 66 32 18 74 N SD: 0.2257 c. M:-0.6433 c. 1012: 78 39 37 18 53 68 33 18 76 45 33 11 83 78 39 37 18 53 68 33 18 76 N SD: 0.2055 c. M:-0.5569 c. 1019: 78 40 37 18 54 68 33 18 77 45 33 11 84 78 40 37 18 54 68 33 18 77 N SD: 0.2566 c. M: 0.4521 c. 1029: 79 40 37 19 54 69 33 19 77 46 33 11 85 79 40 37 19 54 69 33 19 77 N SD: 0.2465 c. M: 0.4795 c. 1053: 81 41 38 19 55 71 34 19 79 47 34 11 87 81 41 38 19 55 71 34 19 79 N SD: 0.1946 c. M:-0.4980 c. 1065: 82 41 39 19 56 71 35 19 80 47 35 11 88 82 41 39 19 56 71 35 19 80 N SD: 0.1811 c. M: 0.3657 c. 1106: 85 43 40 20 58 74 36 20 83 49 36 12 91 85 43 40 20 58 74 36 20 83 N SD: 0.1475 c. M:-0.3403 c. 1236: 95 48 45 22 65 83 40 22 93 55 40 13 102 95 48 45 22 65 83 40 22 93 N SD: 0.1156 c. M:-0.2623 c. 1395: 107 54 51 25 73 94 45 25 105 62 45 15 115 107 54 51 25 73 94 45 25 105 N SD: 0.1034 c. M: 0.2238 c. 1807: 139 70 66 32 95 121 59 32 136 80 59 19 149 139 70 66 32 95 121 59 32 136 N SD: 0.1278 c. M:-0.2209 c. 1848: 142 71 68 33 97 124 60 33 139 82 60 20 152 142 71 68 33 97 124 60 33 139 N SD: 0.0996 c. M: 0.2679 c. 1889: 145 73 69 34 99 127 61 34 142 84 61 20 156 145 73 69 34 99 127 61 34 142 N SD: 0.0678 c. M: 0.1418 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: 0.0000 cents 4 .. 8 match: 4 H SD: 0.0000 cents 5 .. 10 match: 5 H SD: 9.9197 cents 6 .. 12 match: 6 H SD: 0.0000 cents 7 .. 14 match: 7 H SD: 7.6263 cents 8 .. 16 match: 8 H SD: 0.0000 cents 9 .. 18 match: 9 H SD: 5.8829 cents 10 .. 20 match: 10 H SD: 6.9636 cents 11 .. 22 match: 11 H SD: 6.8210 cents 12 .. 24 match: 12 H SD: 1.3838 cents 13 .. 26 match: 12 S SD: 5.8604 cents 14 .. 28 match: 14 H SD: 5.6151 cents 15 .. 30 match: 12 SD: 5.1236 cents 16 .. 32 match: 15 S SD: 3.8519 cents 17 .. 34 match: 15 S SD: 4.7833 cents 18 .. 36 match: 16 S SD: 3.7514 cents 19 .. 38 match: 16 SD: 3.0658 cents 20 .. 40 match: 15 SD: 4.0053 cents 21 .. 42 match: 17 SD: 4.2043 cents 22 .. 44 match: 18 SD: 3.1019 cents 23 .. 46 match: 19 SD: 3.2257 cents 24 .. 48 match: 19 S SD: 2.0927 cents 25 .. 50 match: 17 SD: 3.4566 cents 26 .. 52 match: 18 SD: 2.9444 cents 27 .. 54 match: 18 SD: 3.1795 cents 28 .. 56 match: 17 SD: 3.2434 cents 29 .. 58 match: 20 SD: 2.7612 cents 30 .. 60 match: 20 SD: 2.5169 cents 31 .. 62 match: 18 SD: 2.5634 cents 32 .. 64 match: 20 SD: 2.0998 cents 33 .. 66 match: 21 SD: 2.4566 cents 34 .. 68 match: 18 SD: 2.3205 cents 35 .. 70 match: 19 SD: 1.9783 cents 36 .. 72 match: 20 SD: 1.8545 cents 37 .. 74 match: 20 SD: 1.8674 cents 38 .. 76 match: 21 SD: 1.8895 cents 39 .. 78 match: 20 SD: 2.0646 cents 40 .. 80 match: 22 SD: 1.7683 cents 41 .. 82 match: 20 SD: 1.7603 cents 42 .. 84 match: 20 SD: 1.8617 cents 43 .. 86 match: 20 SD: 2.0184 cents 44 .. 88 match: 21 SD: 2.0586 cents 45 .. 90 match: 22 SD: 1.7288 cents 46 .. 92 match: 20 SD: 1.7256 cents 47 .. 94 match: 21 SD: 1.7360 cents 48 .. 96 match: 21 SD: 0.9937 cents 49 .. 98 match: 21 SD: 1.5462 cents 50 .. 100 match: 20 SD: 1.4340 cents 51 .. 102 match: 20 SD: 1.6518 cents 52 .. 104 match: 22 SD: 1.6259 cents 53 .. 106 match: 21 SD: 1.3847 cents 54 .. 108 match: 21 SD: 1.3331 cents 55 .. 110 match: 22 SD: 1.3229 cents 56 .. 112 match: 21 SD: 1.2402 cents 58 .. 116 match: 20 SD: 1.3278 cents 59 .. 118 match: 21 SD: 1.2457 cents 60 .. 120 match: 22 SD: 1.1941 cents 61 .. 122 match: 21 SD: 1.2865 cents 62 .. 124 match: 21 SD: 1.2425 cents 63 .. 126 match: 21 SD: 1.3098 cents 64 .. 128 match: 22 SD: 1.0489 cents 68 .. 136 match: 21 SD: 1.3257 cents 69 .. 138 match: 22 SD: 1.1590 cents 70 .. 140 match: 22 SD: 1.1529 cents 71 .. 142 match: 22 SD: 0.9173 cents 72 .. 144 match: 22 SD: 0.4412 cents 73 .. 146 match: 21 SD: 1.0143 cents 79 .. 158 match: 22 SD: 0.9453 cents 80 .. 160 match: 21 SD: 0.8351 cents 85 .. 170 match: 21 SD: 1.0378 cents 86 .. 172 match: 22 SD: 0.8725 cents 88 .. 176 match: 22 SD: 0.7987 cents 89 .. 178 match: 22 SD: 0.7804 cents 91 .. 182 match: 22 SD: 0.7564 cents 96 .. 192 match: 22 SD: 0.5182 cents 120 .. 240 match: 22 SD: 0.4564 cents 144 .. 288 match: 22 SD: 0.2634 cents 216 .. 432 match: 22 SD: 0.1898 cents 288 .. 576 match: 22 SD: 0.1460 cents 360 .. 720 match: 22 SD: 0.1443 cents 384 .. 768 match: 22 SD: 0.1053 cents 504 .. 1008 match: 22 SD: 0.0934 cents 576 .. 1152 match: 22 SD: 0.0771 cents