Scala analysis: quasi-phillips
Quasi-Phillips 19 note scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.677 cents 83.676704 2: 152.139 cents 152.139461 3: 199.683 cents 199.683043 4: 268.146 cents 268.145800 5: 384.152 cents 384.152140 6: 399.366 cents 399.366086 7: 467.829 cents 467.828843 8: 500.158 cents 500.158479 9: 583.835 cents 583.835182 10: 652.298 cents 652.297940 11: 699.842 cents 699.841521 12: 768.304 cents 768.304279 13: 851.981 cents 851.980983 14: 899.525 cents 899.524564 15: 967.987 cents 967.987322 16: 1083.994 cents 1083.993661 17: 1099.208 cents 1099.207607 18: 1152.456 cents 1152.456418 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 47.5436 cents 47.5436 1: 83.6767 cents 83.6767 2: 68.4628 cents 68.4628 3: 47.5436 cents 47.5436 4: 68.4628 cents 68.4628 5: 116.0063 cents 116.0063 6: 15.2139 cents 15.2139 7: 68.4628 cents 68.4628 8: 32.3296 cents 32.3296 9: 83.6767 cents 83.6767 10: 68.4628 cents 68.4628 11: 47.5436 cents 47.5436 12: 68.4628 cents 68.4628 13: 83.6767 cents 83.6767 14: 47.5436 cents 47.5436 15: 68.4628 cents 68.4628 16: 116.0063 cents 116.0063 17: 15.2139 cents 15.2139 18: 53.2488 cents 53.2488 19: 47.5436 cents 47.5436
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 15.21395 cents 1: 1 32.32964 cents 1: 4 47.54358 cents 1: 1 53.24881 cents 1: 6 68.46276 cents 1: 3 83.67670 cents 1: 2 116.00634 cents 2: 1 68.46276 cents 2: 1 83.67670 cents 2: 2 100.79239 cents 2: 6 116.00634 cents 2: 4 131.22029 cents 2: 3 152.13946 cents 2: 2 184.46910 cents 3: 2 116.00634 cents 3: 6 184.46910 cents 3: 9 199.68304 cents 3: 2 232.01268 cents 4: 2 199.68304 cents 4: 3 232.01268 cents 4: 4 247.22662 cents 4: 3 252.93185 cents 4: 5 268.14580 cents 4: 1 300.47544 cents 4: 1 315.68938 cents 5: 2 268.14580 cents 5: 6 300.47544 cents 5: 7 315.68938 cents 5: 1 330.90333 cents 5: 1 351.82250 cents 5: 2 384.15214 cents 6: 2 315.68938 cents 6: 2 348.01902 cents 6: 2 368.93819 cents 6: 8 384.15214 cents 6: 3 399.36609 cents 6: 2 431.69572 cents 7: 2 384.15214 cents 7: 1 416.48177 cents 7: 6 431.69572 cents 7: 2 446.90967 cents 7: 4 452.61490 cents 7: 2 467.82884 cents 7: 1 484.94453 cents 7: 1 500.15848 cents 8: 1 467.82884 cents 8: 14 500.15848 cents 8: 3 515.37242 cents 8: 1 583.83518 cents 9: 2 515.37242 cents 9: 4 547.70206 cents 9: 6 568.62124 cents 9: 4 583.83518 cents 9: 1 599.04913 cents 9: 2 616.16482 cents 10: 2 583.83518 cents 10: 1 600.95087 cents 10: 4 616.16482 cents 10: 6 631.37876 cents 10: 4 652.29794 cents 10: 2 684.62758 cents 11: 1 616.16482 cents 11: 3 684.62758 cents 11: 14 699.84152 cents 11: 1 732.17116 cents 12: 1 699.84152 cents 12: 1 715.05547 cents 12: 2 732.17116 cents 12: 4 747.38510 cents 12: 2 753.09033 cents 12: 6 768.30428 cents 12: 1 783.51823 cents 12: 2 815.84786 cents 13: 2 768.30428 cents 13: 3 800.63391 cents 13: 8 815.84786 cents 13: 2 831.06181 cents 13: 2 851.98098 cents 13: 2 884.31062 cents 14: 2 815.84786 cents 14: 1 848.17750 cents 14: 1 869.09667 cents 14: 7 884.31062 cents 14: 6 899.52456 cents 14: 2 931.85420 cents 15: 1 884.31062 cents 15: 1 899.52456 cents 15: 5 931.85420 cents 15: 3 947.06815 cents 15: 4 952.77338 cents 15: 3 967.98732 cents 15: 2 1000.31696 cents 16: 2 967.98732 cents 16: 9 1000.31696 cents 16: 6 1015.53090 cents 16: 2 1083.99366 cents 17: 2 1015.53090 cents 17: 3 1047.86054 cents 17: 4 1068.77971 cents 17: 6 1083.99366 cents 17: 2 1099.20761 cents 17: 1 1116.32330 cents 17: 1 1131.53724 cents 18: 2 1083.99366 cents 18: 3 1116.32330 cents 18: 6 1131.53724 cents 18: 1 1146.75119 cents 18: 4 1152.45642 cents 18: 1 1167.67036 cents 18: 2 1184.78605 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.11111 = 55/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 83.7 152.1 199.7 268.1 384.2 399.4 467.8 500.2 583.8 652.3 699.8 768.3 852.0 899.5 968.0 1084.0 1099.2 1152.5 1200.0 83.7 : 68.5 116.0 184.5 300.5 315.7 384.2 416.5 500.2 568.6 616.2 684.6 768.3 815.8 884.3 1000.3 1015.5 1068.8 1116.3 1200.0 152.1 : 47.5 116.0 232.0 247.2 315.7 348.0 431.7 500.2 547.7 616.2 699.8 747.4 815.8 931.9 947.1 1000.3 1047.9 1131.5 1200.0 199.7 : 68.5 184.5 199.7 268.1 300.5 384.2 452.6 500.2 568.6 652.3 699.8 768.3 884.3 899.5 952.8 1000.3 1084.0 1152.5 1200.0 268.1 : 116.0 131.2 199.7 232.0 315.7 384.2 431.7 500.2 583.8 631.4 699.8 815.8 831.1 884.3 931.9 1015.5 1084.0 1131.5 1200.0 384.2 : 15.2 83.7 116.0 199.7 268.1 315.7 384.2 467.8 515.4 583.8 699.8 715.1 768.3 815.8 899.5 968.0 1015.5 1084.0 1200.0 399.4 : 68.5 100.8 184.5 252.9 300.5 368.9 452.6 500.2 568.6 684.6 699.8 753.1 800.6 884.3 952.8 1000.3 1068.8 1184.8 1200.0 467.8 : 32.3 116.0 184.5 232.0 300.5 384.2 431.7 500.2 616.2 631.4 684.6 732.2 815.8 884.3 931.9 1000.3 1116.3 1131.5 1200.0 500.2 : 83.7 152.1 199.7 268.1 351.8 399.4 467.8 583.8 599.0 652.3 699.8 783.5 852.0 899.5 968.0 1084.0 1099.2 1167.7 1200.0 583.8 : 68.5 116.0 184.5 268.1 315.7 384.2 500.2 515.4 568.6 616.2 699.8 768.3 815.8 884.3 1000.3 1015.5 1084.0 1116.3 1200.0 652.3 : 47.5 116.0 199.7 247.2 315.7 431.7 446.9 500.2 547.7 631.4 699.8 747.4 815.8 931.9 947.1 1015.5 1047.9 1131.5 1200.0 699.8 : 68.5 152.1 199.7 268.1 384.2 399.4 452.6 500.2 583.8 652.3 699.8 768.3 884.3 899.5 968.0 1000.3 1084.0 1152.5 1200.0 768.3 : 83.7 131.2 199.7 315.7 330.9 384.2 431.7 515.4 583.8 631.4 699.8 815.8 831.1 899.5 931.9 1015.5 1084.0 1131.5 1200.0 852.0 : 47.5 116.0 232.0 247.2 300.5 348.0 431.7 500.2 547.7 616.2 732.2 747.4 815.8 848.2 931.9 1000.3 1047.9 1116.3 1200.0 899.5 : 68.5 184.5 199.7 252.9 300.5 384.2 452.6 500.2 568.6 684.6 699.8 768.3 800.6 884.3 952.8 1000.3 1068.8 1152.5 1200.0 968.0 : 116.0 131.2 184.5 232.0 315.7 384.2 431.7 500.2 616.2 631.4 699.8 732.2 815.8 884.3 931.9 1000.3 1084.0 1131.5 1200.0 1084.0: 15.2 68.5 116.0 199.7 268.1 315.7 384.2 500.2 515.4 583.8 616.2 699.8 768.3 815.8 884.3 968.0 1015.5 1084.0 1200.0 1099.2: 53.2 100.8 184.5 252.9 300.5 368.9 484.9 500.2 568.6 601.0 684.6 753.1 800.6 869.1 952.8 1000.3 1068.8 1184.8 1200.0 1152.5: 47.5 131.2 199.7 247.2 315.7 431.7 446.9 515.4 547.7 631.4 699.8 747.4 815.8 899.5 947.1 1015.5 1131.5 1146.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 15.2139 .. 116.0063 cents 100.79239 cents 15.21395 cents 2: 68.4628 .. 184.4691 cents 116.00634 cents -47.54358 cents 3: 116.0063 .. 232.0127 cents 116.00634 cents -68.46276 cents 4: 199.6830 .. 315.6894 cents 116.00634 cents -32.32964 cents 5: 268.1458 .. 384.1521 cents 116.00634 cents -47.54358 cents 6: 315.6894 .. 431.6957 cents 116.00634 cents -68.46276 cents 7: 384.1521 .. 500.1585 cents 116.00634 cents -47.54358 cents 8: 467.8288 .. 583.8352 cents 116.00634 cents -32.32964 cents 9: 515.3724 .. 616.1648 cents 100.79239 cents -68.46276 cents 10: 583.8352 .. 684.6276 cents 100.79239 cents -32.32964 cents 11: 616.1648 .. 732.1712 cents 116.00634 cents -68.46276 cents 12: 699.8415 .. 815.8479 cents 116.00634 cents -32.32964 cents 13: 768.3043 .. 884.3106 cents 116.00634 cents -47.54358 cents 14: 815.8479 .. 931.8542 cents 116.00634 cents -68.46276 cents 15: 884.3106 .. 1000.3170 cents 116.00634 cents -47.54358 cents 16: 967.9873 .. 1083.9937 cents 116.00634 cents -32.32964 cents 17: 1015.5309 .. 1131.5372 cents 116.00634 cents -68.46276 cents 18: 1083.9937 .. 1184.7861 cents 100.79239 cents -47.54358 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 15.21395 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 116.00634 cents Average / Smallest step : 4.151316 Largest / Average step : 1.836767 Largest / Smallest step : 7.625000 Median interval of one step : 68.46276 cents, amount: 6 Most common interval of one step : 68.46276 cents, amount: 6 Least squares average step : 64.82250 cents, oct.: 1231.62745 cents Scale is not proper Scale is a mode of a 631-tone equal temperament with octave 2/1 degrees: 44 80 105 141 202 210 246 263 307 343 368 404 448 473 509 570 578 606 631 Least number of segments generator : 316 of 600.951 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 512 of 973.693 cents and inv. generated superset size: 115 = 96 more = 605.263% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBDEBFABCBACBDEGC Step pattern size order : FECEGAEBFECEFCEGADC Scale is not a Constant Structure Scale diversity : 1.403312 Lumma stability : 0.025357 Lumma impropriety factor : 0.714739 Number of different interval sizes : 72 = 4.00000 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.11111 = 55/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.90174 cents Most common intervals : 500.15848 cents & inv., amount: 15 Most common triad is 0.0 500.158 699.842 cents, amount: 11 Number of recognisable fifths : 16, average 700.7924 cents Number of appreciable fifths : 15, average 699.8415 cents Formal octave complements present : 3 = 15.7895% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
19: 1 1 1 1 2 0 1 1 1 1 1 1 1 1 1 2 0 1 1 N T3 SD: 17.7462 c. M: 30.9284 c. 21: 1 2 0 2 2 0 1 1 1 1 1 1 2 1 1 2 0 1 1 N SD: 15.9703 c. M: 28.2545 c. 22: 2 1 1 1 2 0 2 0 2 1 1 1 2 1 1 2 0 1 1 N T3 SD: 14.5167 c. M:-27.7482 c. 23: 2 1 1 1 2 1 1 1 1 2 0 2 1 1 2 2 0 1 1 N SD: 15.1191 c. M:-25.9629 c. 24: 2 1 1 1 3 0 1 1 2 1 1 1 2 1 1 3 0 1 1 N SD: 11.1498 c. M: 18.3043 c. 31: 2 2 1 2 3 0 2 1 2 2 1 2 2 1 2 3 0 2 1 N SD: 6.3133 c. M: 15.3366 c. 35: 2 2 2 2 3 1 2 1 2 2 1 2 3 1 2 4 0 2 1 N SD: 10.1986 c. M: 15.1053 c. 36: 3 2 1 2 4 0 2 1 3 2 1 2 3 1 2 4 0 2 1 N SD: 9.9461 c. M:-16.3233 c. 39: 3 2 1 3 3 1 2 1 3 2 2 2 3 1 2 4 1 1 2 N SD: 8.7894 c. M: 15.0677 c. 41: 3 2 2 2 4 1 2 1 3 2 2 2 3 2 2 4 1 1 2 N SD: 6.1893 c. M:-12.9875 c. 48: 3 3 2 3 4 1 3 1 3 3 2 3 3 2 3 4 1 2 2 N SD: 5.2897 c. M: 9.1521 c. 53: 4 3 2 3 5 1 3 1 4 3 2 3 4 2 3 5 1 2 2 N SD: 5.3935 c. M:-10.2264 c. 62: 4 4 2 4 6 1 3 2 4 4 2 4 4 3 3 6 1 3 2 N SD: 4.9006 c. M:-10.1529 c. 69: 5 4 2 4 7 1 4 2 5 4 2 4 5 3 4 6 1 3 3 N SD: 4.9106 c. M:-8.5716 c. 70: 5 4 3 4 6 1 4 2 5 4 3 4 5 2 4 7 1 3 3 N SD: 4.6080 c. M: 8.0960 c. 72: 5 4 3 4 7 1 4 2 5 4 3 4 5 3 4 7 1 3 3 N SD: 1.2704 c. M: 2.4564 c. 156: 11 9 6 9 15 2 9 4 11 9 6 9 11 6 9 15 2 7 6 N SD: 1.0199 c. M:-1.8652 c. 228: 16 13 9 13 22 3 13 6 16 13 9 13 16 9 13 22 3 10 9 N SD: 0.4179 c. M:-0.7924 c. 300: 21 17 12 17 29 4 17 8 21 17 12 17 21 12 17 29 4 13 12 N SD: 0.3262 c. M:-0.7924 c. 331: 23 19 13 19 32 4 19 9 23 19 13 19 23 13 19 32 4 15 13 N SD: 0.2956 c. M: 0.7182 c. 403: 28 23 16 23 39 5 23 11 28 23 16 23 28 16 23 39 5 18 16 N SD: 0.2364 c. M: 0.4483 c. 559: 39 32 22 32 54 7 32 15 39 32 22 32 39 22 32 54 7 25 22 N SD: 0.1636 c. M:-0.3164 c. 631: 44 36 25 36 61 8 36 17 44 36 25 36 44 25 36 61 8 28 25 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.0567 cents 3 .. 6 match: 3 H SD: 5.1041 cents 4 .. 8 match: 4 H SD: 0.7843 cents 5 .. 10 match: 5 H SD: 15.7291 cents 6 .. 12 match: 6 H SD: 6.3242 cents 7 .. 14 match: 7 H SD: 9.7709 cents 8 .. 16 match: 8 H SD: 4.3920 cents 9 .. 18 match: 9 H SD: 6.0182 cents 10 .. 20 match: 9 SD: 7.5266 cents 11 .. 22 match: 10 SD: 5.6943 cents 12 .. 24 match: 12 H SD: 4.8752 cents 13 .. 26 match: 13 H SD: 5.1405 cents 14 .. 28 match: 13 S SD: 7.3642 cents 15 .. 30 match: 13 SD: 5.4206 cents 16 .. 32 match: 15 S SD: 3.8003 cents 17 .. 34 match: 15 SD: 4.3743 cents 18 .. 36 match: 16 SD: 4.2008 cents 19 .. 38 match: 14 SD: 3.5396 cents 20 .. 40 match: 17 SD: 3.0595 cents 21 .. 42 match: 16 SD: 4.3504 cents 22 .. 44 match: 18 SD: 3.3279 cents 23 .. 46 match: 16 SD: 2.9238 cents 24 .. 48 match: 17 SD: 2.7765 cents 25 .. 50 match: 16 SD: 2.9792 cents 26 .. 52 match: 18 SD: 3.6506 cents 27 .. 54 match: 17 SD: 3.6408 cents 28 .. 56 match: 16 SD: 3.0736 cents 30 .. 60 match: 19 SD: 2.8234 cents 31 .. 62 match: 16 SD: 2.8844 cents 32 .. 64 match: 17 SD: 2.1917 cents 33 .. 66 match: 18 SD: 2.6105 cents 34 .. 68 match: 17 SD: 2.5681 cents 35 .. 70 match: 18 SD: 1.9797 cents 36 .. 72 match: 18 SD: 2.0730 cents 39 .. 78 match: 18 SD: 2.0502 cents 40 .. 80 match: 17 SD: 1.9065 cents 41 .. 82 match: 18 SD: 1.7110 cents 42 .. 84 match: 18 SD: 1.6011 cents 43 .. 86 match: 18 SD: 1.7493 cents 44 .. 88 match: 18 SD: 1.6519 cents 47 .. 94 match: 18 SD: 1.7615 cents 48 .. 96 match: 18 SD: 1.5217 cents 49 .. 98 match: 18 SD: 1.9931 cents 50 .. 100 match: 18 SD: 1.8301 cents 51 .. 102 match: 18 SD: 1.9302 cents 52 .. 104 match: 18 SD: 1.4511 cents 54 .. 108 match: 19 SD: 1.3271 cents 55 .. 110 match: 18 SD: 1.2906 cents 57 .. 114 match: 19 SD: 1.2237 cents 59 .. 118 match: 18 SD: 1.3294 cents 60 .. 120 match: 19 SD: 1.3273 cents 63 .. 126 match: 18 SD: 1.2514 cents 64 .. 128 match: 19 SD: 1.1561 cents 65 .. 130 match: 19 SD: 1.0019 cents 67 .. 134 match: 18 SD: 1.3061 cents 68 .. 136 match: 19 SD: 1.0892 cents 71 .. 142 match: 18 SD: 1.3720 cents 72 .. 144 match: 19 SD: 0.9582 cents 75 .. 150 match: 18 SD: 1.0243 cents 77 .. 154 match: 19 SD: 0.7970 cents 79 .. 158 match: 18 SD: 1.0523 cents 80 .. 160 match: 19 SD: 0.9104 cents 84 .. 168 match: 19 SD: 0.8148 cents 88 .. 176 match: 19 SD: 0.7980 cents 96 .. 192 match: 19 SD: 0.6948 cents 100 .. 200 match: 19 SD: 0.6296 cents 107 .. 214 match: 19 SD: 0.5366 cents 120 .. 240 match: 19 SD: 0.5081 cents 132 .. 264 match: 19 SD: 0.4764 cents 161 .. 322 match: 19 SD: 0.3951 cents 162 .. 324 match: 19 SD: 0.3813 cents 184 .. 368 match: 19 SD: 0.3813 cents 185 .. 370 match: 19 SD: 0.3414 cents 197 .. 394 match: 19 SD: 0.2600 cents 239 .. 478 match: 19 SD: 0.2285 cents 286 .. 572 match: 19 SD: 0.2254 cents 317 .. 634 match: 19 SD: 0.2043 cents 319 .. 638 match: 19 SD: 0.1975 cents 335 .. 670 match: 19 SD: 0.1873 cents 346 .. 692 match: 19 SD: 0.1815 cents 370 .. 740 match: 19 SD: 0.1604 cents 406 .. 812 match: 19 SD: 0.1527 cents 423 .. 846 match: 19 SD: 0.1505 cents 424 .. 848 match: 19 SD: 0.1298 cents 442 .. 884 match: 19 SD: 0.1261 cents 524 .. 1048 match: 19 SD: 0.1252 cents 531 .. 1062 match: 19 SD: 0.1192 cents 555 .. 1110 match: 19 SD: 0.1164 cents 566 .. 1132 match: 19 SD: 0.1119 cents