Scala analysis: raintree
Raintree scale
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: 9/8 203.910002 major whole tone 3: 1215/1024 296.088718 wide augmented second 4: 512/405 405.866283 narrow diminished fourth 5: 4/3 498.044999 perfect fourth 6: 64/45 609.776284 2nd tritone 7: 3/2 701.955001 perfect fifth 8: 405/256 794.133717 wide augmented fifth 9: 2048/1215 903.911282 narrow diminished seventh 10: 16/9 996.089998 Pythagorean minor seventh 11: 256/135 1107.821284 octave - major chroma 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 135/128 92.1787 major chroma, major limma 2: 16/15 111.7313 minor diatonic semitone 3: 135/128 92.1787 major chroma, major limma 4: 524288/492075 109.7776 5: 135/128 92.1787 major chroma, major limma 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 8: 135/128 92.1787 major chroma, major limma 9: 524288/492075 109.7776 10: 135/128 92.1787 major chroma, major limma 11: 16/15 111.7313 minor diatonic semitone 12: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 135/128 92.179 cents major chroma, major limma 1: 2 524288/492075 109.778 cents 1: 3 16/15 111.731 cents minor diatonic semitone 2: 2 18225/16384 184.357 cents two (major chroma, major limma) 2: 4 4096/3645 201.956 cents narrow diminished third 2: 6 9/8 203.910 cents major whole tone 3: 3 32/27 294.135 cents Pythagorean minor third 3: 6 1215/1024 296.089 cents wide augmented second 3: 3 65536/54675 313.688 cents 4: 1 5/4 386.314 cents major third 4: 3 164025/131072 388.267 cents 4: 7 512/405 405.866 cents narrow diminished fourth 4: 1 81/64 407.820 cents Pythagorean major third 5: 9 4/3 498.045 cents perfect fourth 5: 2 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 5: 1 8192/6075 517.598 cents 6: 5 45/32 590.224 cents diatonic tritone 6: 1 1476225/1048576 592.177 cents two (wide augmented second) 6: 1 2097152/1476225 607.823 cents 6: 5 64/45 609.776 cents 2nd tritone 7: 1 6075/4096 682.402 cents 7: 2 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 7: 9 3/2 701.955 cents perfect fifth 8: 1 128/81 792.180 cents Pythagorean minor sixth 8: 7 405/256 794.134 cents wide augmented fifth 8: 3 262144/164025 811.733 cents two (narrow diminished fourth) 8: 1 8/5 813.686 cents minor sixth 9: 3 54675/32768 886.312 cents 9: 6 2048/1215 903.911 cents narrow diminished seventh 9: 3 27/16 905.865 cents Pythagorean major sixth 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 4 3645/2048 998.044 cents wide augmented sixth 10: 2 32768/18225 1015.643 cents 11: 3 15/8 1088.269 cents classic major seventh 11: 2 492075/262144 1090.222 cents 11: 7 256/135 1107.821 cents octave - major chroma Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 203.9 296.1 405.9 498.0 609.8 702.0 794.1 903.9 996.1 1107.8 1200.0 92.2 : 111.7 203.9 313.7 405.9 517.6 609.8 702.0 811.7 903.9 1015.6 1107.8 1200.0 203.9 : 92.2 202.0 294.1 405.9 498.0 590.2 700.0 792.2 903.9 996.1 1088.3 1200.0 296.1 : 109.8 202.0 313.7 405.9 498.0 607.8 700.0 811.7 903.9 996.1 1107.8 1200.0 405.9 : 92.2 203.9 296.1 388.3 498.0 590.2 702.0 794.1 886.3 998.0 1090.2 1200.0 498.0 : 111.7 203.9 296.1 405.9 498.0 609.8 702.0 794.1 905.9 998.0 1107.8 1200.0 609.8 : 92.2 184.4 294.1 386.3 498.0 590.2 682.4 794.1 886.3 996.1 1088.3 1200.0 702.0 : 92.2 202.0 294.1 405.9 498.0 590.2 702.0 794.1 903.9 996.1 1107.8 1200.0 794.1 : 109.8 202.0 313.7 405.9 498.0 609.8 702.0 811.7 903.9 1015.6 1107.8 1200.0 903.9 : 92.2 203.9 296.1 388.3 500.0 592.2 702.0 794.1 905.9 998.0 1090.2 1200.0 996.1 : 111.7 203.9 296.1 407.8 500.0 609.8 702.0 813.7 905.9 998.0 1107.8 1200.0 1107.8: 92.2 184.4 296.1 388.3 498.0 590.2 702.0 794.1 886.3 996.1 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 111.7313 cents 2048/2025, 19.5526 cents 135/128, 92.1787 cents 2: 184.3574 .. 203.9100 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 3: 294.1350 .. 313.6876 cents 2048/2025, 19.5526 cents 256/243, 90.2250 cents 4: 386.3137 .. 407.8200 cents 81/80, 21.5063 cents 273375/262144, 72.6261 cents 5: 498.0450 .. 517.5976 cents 2048/2025, 19.5526 cents 256/243, 90.2250 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 7: 682.4024 .. 701.9550 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 8: 792.1800 .. 813.6863 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 9: 886.3124 .. 905.8650 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 10: 996.0900 .. 1015.6426 cents 2048/2025, 19.5526 cents 256/243, 90.2250 cents 11: 1088.2687 .. 1107.8213 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.084849 Largest / Average step : 1.117313 Largest / Smallest step : 1.212116 Median interval of one step : 135/128, 92.1787 cents, amount: 7 Most common interval of one step : 135/128, 92.1787 cents, amount: 7 Least squares average step : 100.16847 cents, oct.: 1202.02160 cents Scale is strictly proper Step pattern alph. order: ABACABAACABA Step pattern size order : SLSMSLSSMSLS Scale is a Constant Structure, by a margin of 72.62615 cents Scale diversity : 1.140678 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.817512 Rothenberg efficiency : 0.416997 redundancy: 0.583003 Efficiency x scale size : 5.003968 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 11, average 701.5998 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 9 1215 Formal octave complements present : 11 = 91.6667% Limited inverse transpositions with margin 19.5526 cents: 7 -- Rational properties -- Prime limit : 5 Odd number limit : 1476225 (O: 1476225 U: 1476225) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.016538 Average absolute harmonicity : 0.167195 Specific harmonicity : 0.093625 Fundamental : 1/1244160, -20.2467 octaves, 0.0002 Hz. Guide tone : 2488320, 21.2467 octaves, 651008126.650 Hz. Exponens Consonantiae : 3.095868E+12, 41.49348 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 3950.0, average 329.16667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 20.16067, average 1.68006 Sum of Tenney's harmonic distance : 41.23277, average 3.43606 Vogel's harmonic complexity : 30.08333 Wille's k value : 738112 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 12 Triangular lattice diameter : 12 Lattice compactness : 688.41941, average 8.82589 Lattice compactness (without 2's) : 296.74321, average 3.80440 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 11 1.00000 70 1 3: -5 .. 5 -0.16667 32 4 5: -1 .. 1 -0.08333 7 7 Average exponent except 2's :-3 / 12 =-0.25000 Average absolute exponent except 2's: 39 / 12 = 3.25000 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.4434 c. M: 9.7763 c. Twelve-tone Chromatic (1/11-comma) 41: 3 4 3 4 3 4 3 3 4 3 4 3 SP M ME SD: 3.1313 c. M:-4.8579 c. 53: 4 5 4 5 4 5 4 4 5 4 5 4 SP M ME SD: 1.2716 c. M:-1.7491 c. 65: 5 6 5 6 5 6 5 5 6 5 6 5 SP M ME SD: 0.5182 c. M:-0.8331 c. 340: 26 32 26 31 26 32 26 26 31 26 32 26 SP SD: 0.4897 c. M:-0.8120 c. 352: 27 33 27 32 27 33 27 27 32 27 33 27 SP SD: 0.3895 c. M:-0.6355 c. 364: 28 34 28 33 28 34 28 28 33 28 34 28 SP SD: 0.3728 c. M:-0.6146 c. 405: 31 38 31 37 31 38 31 31 37 31 38 31 SP SD: 0.3384 c. M:-0.5941 c. 417: 32 39 32 38 32 39 32 32 38 32 39 32 SP SD: 0.2483 c. M:-0.4065 c. 429: 33 40 33 39 33 40 33 33 39 33 40 33 SP SD: 0.2466 c. M:-0.4148 c. 470: 36 44 36 43 36 44 36 36 43 36 44 36 SP SD: 0.2341 c. M:-0.4365 c. 482: 37 45 37 44 37 45 37 37 44 37 45 37 SP SD: 0.1453 c. M:-0.2394 c. 547: 42 51 42 50 42 51 42 42 50 42 51 42 SP SD: 0.0674 c. M:-0.1119 c. 612: 47 57 47 56 47 57 47 47 56 47 57 47 SP SD: 0.0152 c. M:-0.0276 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 6.5175 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.3876 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.8780 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.6380 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.9788 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.0765 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.9338 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.5058 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 10.5476 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3663 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 10.2016 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.8942 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.9517 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.7325 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.3700 cents 26:27:29:31:33:35:37:39:41:44:46:49:52 SD: 3.3310 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.8240 cents 33:35:37:39:42:44:47:50:52:56:59:63:66 SD: 2.6799 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 1.6708 cents 48:51:54:57:61:64:68:72:76:81:85:91:96 SD: 1.5485 cents 54:57:61:64:68:72:77:81:85:91:96:102:108 SD: 1.3040 cents 71:75:80:84:90:95:101:107:112:120:126:135:142 SD: 1.2968 cents 72:76:81:85:91:96:102:108:114:121:128:137:144 SD: 1.1430 cents 76:80:86:90:96:101:108:114:120:128:135:144:152 SD: 1.1144 cents 80:84:90:95:101:107:114:120:127:135:142:152:160 SD: 1.0728 cents 86:91:97:102:109:115:122:129:136:145:153:163:172 SD: 0.9123 cents 90:95:101:107:114:120:128:135:142:152:160:171:180 SD: 0.7826 cents 112:118:126:133:142:149:159:168:177:189:199:212:224 SD: 0.7133 cents 114:120:128:135:144:152:162:171:180:192:203:216:228 SD: 0.6554 cents 128:135:144:152:162:171:182:192:203:216:228:243:256 SD: 0.6164 cents 144:152:162:171:182:192:205:216:228:243:256:273:288 SD: 0.3018 cents 216:228:243:256:273:288:307:324:342:364:384:410:432 SD: 0.2930 cents 242:255:272:287:306:323:344:363:383:408:430:459:484 SD: 0.2814 cents 258:272:290:306:326:344:367:387:408:435:459:489:516 SD: 0.2216 cents 306:323:344:363:387:408:435:459:484:516:544:580:612 SD: 0.2060 cents 360:380:405:427:455:480:512:540:570:607:640:683:720 SD: 0.1970 cents 386:407:434:458:488:515:549:579:611:651:686:732:772 SD: 0.1791 cents 402:424:452:477:508:536:572:603:636:678:715:762:804 SD: 0.1713 cents 424:447:477:503:536:565:603:636:671:715:754:804:848 SD: 0.1395 cents 552:582:621:655:698:736:785:828:873:930:981:1047:1104 SD: 0.1186 cents