Scala analysis: graham
Graham's 5-limit transversal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 3125/2916 119.838564 quasi-equal 10-tone semitone 2: 125/108 253.076139 semi-augmented whole tone 3: 5/4 386.313714 major third 4: 625/486 435.479851 5: 25/18 568.717426 classic augmented fourth 6: 3/2 701.955001 perfect fifth 7: 81/50 835.192576 acute minor sixth 8: 5/3 884.358713 major sixth, BP sixth 9: 9/5 1017.596288 just minor seventh, BP seventh 10: 243/125 1150.833863 octave - maximal diesis 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 250/243 49.1661 maximal diesis, Porcupine comma 1: 3125/2916 119.8386 quasi-equal 10-tone semitone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 250/243 49.1661 maximal diesis, Porcupine comma 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 250/243 49.1661 maximal diesis, Porcupine comma 9: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 10: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 11: 250/243 49.1661 maximal diesis, Porcupine comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 250/243 49.166 cents maximal diesis, Porcupine comma 1: 1 3125/2916 119.839 cents quasi-equal 10-tone semitone 1: 7 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 390625/354294 169.005 cents 2: 5 10/9 182.404 cents minor whole tone 2: 1 125/108 253.076 cents semi-augmented whole tone 2: 4 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 2 15625/13122 302.242 cents 3: 7 6/5 315.641 cents minor third 3: 1 5/4 386.314 cents major third 3: 1 19683/15625 399.713 cents 4: 1 100/81 364.807 cents grave major third 4: 4 625/486 435.480 cents 4: 6 162/125 448.879 cents 5: 2 78125/59049 484.646 cents 5: 2 4/3 498.045 cents perfect fourth 5: 3 25/18 568.717 cents classic augmented fourth 5: 4 4374/3125 582.116 cents 6: 4 3125/2187 617.884 cents 6: 3 36/25 631.283 cents classic diminished fifth 6: 2 3/2 701.955 cents perfect fifth 6: 2 118098/78125 715.354 cents 7: 6 125/81 751.121 cents 7: 4 972/625 764.520 cents 7: 1 81/50 835.193 cents acute minor sixth 8: 1 31250/19683 800.287 cents 8: 1 8/5 813.686 cents minor sixth 8: 7 5/3 884.359 cents major sixth, BP sixth 8: 2 26244/15625 897.758 cents 9: 4 1250/729 933.525 cents 9: 1 216/125 946.924 cents semi-augmented sixth 9: 5 9/5 1017.596 cents just minor seventh, BP seventh 9: 1 708588/390625 1030.995 cents 10: 7 50/27 1066.762 cents grave major seventh 10: 1 5832/3125 1080.161 cents 10: 3 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.60000 = 18/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 119.8 253.1 386.3 435.5 568.7 702.0 835.2 884.4 1017.6 1150.8 1200.0 119.8 : 133.2 266.5 315.6 448.9 582.1 715.4 764.5 897.8 1031.0 1080.2 1200.0 253.1 : 133.2 182.4 315.6 448.9 582.1 631.3 764.5 897.8 946.9 1066.8 1200.0 386.3 : 49.2 182.4 315.6 448.9 498.0 631.3 764.5 813.7 933.5 1066.8 1200.0 435.5 : 133.2 266.5 399.7 448.9 582.1 715.4 764.5 884.4 1017.6 1150.8 1200.0 568.7 : 133.2 266.5 315.6 448.9 582.1 631.3 751.1 884.4 1017.6 1066.8 1200.0 702.0 : 133.2 182.4 315.6 448.9 498.0 617.9 751.1 884.4 933.5 1066.8 1200.0 835.2 : 49.2 182.4 315.6 364.8 484.6 617.9 751.1 800.3 933.5 1066.8 1200.0 884.4 : 133.2 266.5 315.6 435.5 568.7 702.0 751.1 884.4 1017.6 1150.8 1200.0 1017.6: 133.2 182.4 302.2 435.5 568.7 617.9 751.1 884.4 1017.6 1066.8 1200.0 1150.8: 49.2 169.0 302.2 435.5 484.6 617.9 751.1 884.4 933.5 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 133.2376 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents 2: 169.0047 .. 266.4751 cents 258280326/244140625, 97.4704 cents 9765625/9565938, 35.7671 cents 3: 302.2423 .. 399.7127 cents 258280326/244140625, 97.4704 cents 9765625/9565938, 35.7671 cents 4: 364.8074 .. 448.8789 cents 6561/6250, 84.0714 cents 1562500/1594323,-34.9053 cents 5: 484.6460 .. 582.1164 cents 258280326/244140625, 97.4704 cents 9765625/9565938, 35.7671 cents 6: 617.8836 .. 715.3540 cents 258280326/244140625, 97.4704 cents 9765625/9565938, 35.7671 cents 7: 751.1211 .. 835.1926 cents 6561/6250, 84.0714 cents 9765625/9565938, 35.7671 cents 8: 800.2873 .. 897.7577 cents 258280326/244140625, 97.4704 cents 1562500/1594323,-34.9053 cents 9: 933.5249 .. 1030.9953 cents 258280326/244140625, 97.4704 cents 9765625/9565938, 35.7671 cents 10: 1066.7624 .. 1150.8339 cents 6561/6250, 84.0714 cents 9765625/9565938, 35.7671 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 250/243, 49.1661 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 27/25, 133.2376 cents Average / Smallest step : 2.218822 Largest / Average step : 1.221344 Largest / Smallest step : 2.709946 Median interval of one step : 27/25, 133.2376 cents, amount: 7 Most common interval of one step : 27/25, 133.2376 cents, amount: 7 Least squares average step : 113.37963 cents, oct.: 1247.17590 cents Scale is not proper Step pattern alph. order: ABBCBBBCBBC Step pattern size order : MLLSLLLSLLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.362033 Lumma stability : 0.290585 Lumma impropriety factor : 0.058176 Rothenberg efficiency : 0.384848 redundancy: 0.615152 Efficiency x scale size : 4.233333 Number of different interval sizes : 36 = 3.60000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.60000 = 18/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 78732/78125, 13.3990 cents Number of recognisable fifths : 4, average 708.6545 cents Number of appreciable fifths : 2, average 701.9550 cents Formal octave complements present : 1 = 9.0909% Limited inverse transpositions with margin 84.0714 cents: 7 -- Rational properties -- Prime limit : 5 Odd number limit : 390625 (O: 390625 U: 390625) Highest odd numerator or denominator: 3125 Scale harmonicity : 0.011971 Average absolute harmonicity : 0.162769 Specific harmonicity : 0.074588 Fundamental : 1/364500, -18.4756 octaves, 0.0007 Hz. Guide tone : 1518750, 20.5345 octaves, 397343827.301 Hz. Exponens Consonantiae : 5.535844E+11, 39.01001 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 3983.0, average 362.09091 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.90898, average 1.53718 Sum of Tenney's harmonic distance : 32.52519, average 2.95684 Vogel's harmonic complexity : 37.36364 Wille's k value : 227812 Wilson's harmonic complexity : 73 Rectangular lattice diameter : 19 Triangular lattice diameter : 11 Lattice compactness : 335.16257, average 5.07822 Lattice compactness (without 2's) : 316.75711, average 4.79935 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.81818 11 1 3: -6 .. 5 -0.45455 29 1 5: -3 .. 5 0.90909 22 9 Average exponent except 2's : 5 / 11 = 0.45455 Average absolute exponent except 2's: 51 / 11 = 4.63636 Scale is weakly epimorphic with val: <11 15 24| Scale is JI-epimorphic with val: <11 17 25| Scale is weakly epimorphic with val: <11 19 26|
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 40.1533 c. M: 71.5562 c. 12: 1 2 1 0 2 1 1 1 1 2 0 N D3 S SD: 28.9735 c. M:-49.1661 c. 13: 1 2 1 1 1 2 1 1 1 1 1 N D3 S SD: 25.6482 c. M: 43.1416 c. 15: 1 2 2 0 2 2 1 1 2 1 1 N D3 SD: 23.9621 c. M: 39.8386 c. 17: 2 2 1 1 2 2 2 1 1 2 1 N D3 SD: 21.6803 c. M: 33.3725 c. 19: 2 2 2 1 2 2 2 1 2 2 1 P M ME S SD: 7.6171 c. M: 14.1399 c. Sensi-11 27: 3 3 3 1 3 3 3 1 3 3 1 N M DE S SD: 9.2943 c. M:-13.6863 c. Sensi-11 33: 3 4 4 1 4 3 4 1 4 4 1 N SD: 9.0469 c. M:-13.6863 c. 34: 3 4 4 1 4 4 4 1 4 4 1 N SD: 8.4287 c. M: 13.9562 c. 41: 4 5 4 2 4 5 5 1 5 4 2 N SD: 7.8563 c. M:-13.5879 c. 42: 4 5 5 1 5 5 4 2 5 4 2 N SD: 7.8136 c. M:-13.6863 c. 45: 4 5 5 2 5 5 5 2 5 5 2 N SD: 8.8841 c. M: 13.1719 c. 46: 5 5 5 2 5 5 5 2 5 5 2 N M DE S SD: 5.3140 c. M:-10.5962 c. Sensi-11 52: 5 6 6 2 6 5 6 2 6 6 2 N SD: 5.3468 c. M: 9.6473 c. 53: 5 6 6 2 6 6 6 2 6 6 2 N SD: 3.3337 c. M: 6.6310 c. 68: 7 7 8 3 7 8 7 3 8 7 3 N SD: 4.3105 c. M: 6.0173 c. 72: 7 8 8 3 8 8 8 3 8 8 3 N SD: 2.0695 c. M: 3.1719 c. 99: 10 11 11 4 11 11 11 4 11 11 4 N SD: 1.0362 c. M:-1.5651 c. 152: 15 17 17 6 17 17 17 6 17 17 6 N SD: 1.0134 c. M:-1.7977 c. 171: 17 19 19 7 19 19 19 7 19 19 7 N SD: 0.2909 c. M: 0.5403 c. 270: 27 30 30 11 30 30 30 11 30 30 11 N SD: 0.2281 c. M:-0.3630 c. 441: 44 49 49 18 49 49 49 18 49 49 18 N SD: 0.1017 c. M:-0.1865 c. 730: 73 81 81 30 81 81 81 30 81 81 30 N SD: 0.0936 c. M:-0.1614 c. 901: 90 100 100 37 100 100 100 37 100 100 37 N SD: 0.0634 c. M: 0.1204 c. 1072: 107 119 119 44 119 119 119 44 119 119 44 N SD: 0.0770 c. M: 0.1197 c. 1171: 117 130 130 48 130 130 130 48 130 130 48 N SD: 0.0291 c. M:-0.0590 c. 1342: 134 149 149 55 149 149 149 55 149 149 55 N SD: 0.0159 c. M: 0.0246 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x 4 x x x 5 x x 6 S SD: 20.8550 cents 4 x x 5 x x 6 x x 7 x 8 S SD: 12.1926 cents 5 x 6 x x 7 x 8 x 9 x 10 S SD: 13.5162 cents 6 x 7 x 8 x 9 x 10:11 x 12 S SD: 11.9185 cents 7 x 8 x 9:10 x 11:12:13 x 14 S SD: 14.9432 cents 8 x 9:10 x 11:12:13 x 14 x 16 S SD: 10.2291 cents 9:10 x 11:12 x 14 x 15:16 x 18 S SD: 16.7631 cents 10:11:12 x 13:14:15:16:17:18:19:20 S SD: 9.8511 cents 11:12:13 x 14:15:17:18 x 20:21:22 SD: 9.8426 cents 12:13:14:15 x 17:18:19:20:22:23:24 SD: 6.9983 cents 13:14:15:16:17:18:20:21:22:23:25:26 SD: 6.7866 cents 14:15:16 x 18:19:21:23 x 25:27:28 SD: 6.1377 cents 15:16:17:19 x 21:23:24:25:27:29:30 SD: 6.4087 cents 16:17:19:20:21:22:24:26:27:29:31:32 SD: 6.0393 cents 17:18:20:21:22:24:26 x 28:31:33:34 SD: 6.8087 cents 18:19:21 x 23:25:27:29:30:32:35:36 SD: 3.9441 cents 19:20:22:24 x 26:29:31:32:34:37:38 SD: 5.8758 cents 20:21:23:25:26:28:30:32:33:36:39:40 SD: 4.7322 cents 22:24:25 x 28:31:33:36:37:40:43:44 SD: 6.2003 cents 23:25:27:29:30:32:35:37:38:41:45:46 SD: 5.3310 cents 24:26:28:30:31:33:36:39:40:43:47:48 SD: 3.0916 cents 26:28:30 x 33:36:39:42:43:47:51:52 SD: 3.3834 cents 28:30:32:35:36:39:42:45:47:50:54:56 SD: 3.1846 cents 31:33:36:39:40:43:47:50:52:56:60:62 SD: 2.8042 cents 32:34:37:40:41:44:48:52:53:58:62:64 SD: 2.7149 cents 36:39:42:45:46:50:54:58:60:65:70:72 SD: 2.5457 cents 39:42:45:49:50:54:59:63:65:70:76:78 SD: 2.0708 cents 44:47:51:55:57:61:66:71:73:79:86:88 SD: 1.8724 cents 52:56:60:65:67:72:78:84:87:94:101:104 SD: 1.4791 cents 56:60:65:70:72:78:84:91:93:101:109:112 SD: 1.0460 cents 84:90:97:105:108:117:126:136:140:151:163:168 SD: 0.6837 cents 108:116:125:135:139:150:162:175:180:194:210:216 SD: 0.4975 cents 140:150:162:175:180:194:210:227:233:252:272:280 SD: 0.4605 cents 164:176:190:205:211:228:246:266:273:295:319:328 SD: 0.4391 cents 192:206:222:240:247:267:288:311:320:346:373:384 SD: 0.3798 cents 196:210:227:245:252:272:294:318:327:353:381:392 SD: 0.3464 cents 224:240:259:280:288:311:336:363:373:403:435:448 SD: 0.2938 cents 252:270:292:315:324:350:378:408:420:454:490:504 SD: 0.2530 cents 280:300:324:350:360:389:420:454:467:504:544:560 SD: 0.2153 cents 324:347:375:405:417:450:486:525:540:583:630:648 SD: 0.1775 cents 336:360:389:420:432:467:504:544:560:605:653:672 SD: 0.1746 cents 360:386:417:450:463:500:540:583:600:648:700:720 SD: 0.1634 cents 432:463:500:540:556:600:648:700:720:778:840:864 SD: 0.1586 cents 444:476:514:555:571:617:666:719:740:799:863:888 SD: 0.1332 cents 476:510:551:595:612:661:714:771:793:857:925:952 SD: 0.1161 cents 560:600:648:700:720:778:840:907:933:1008:1089:1120 SD: 0.1139 cents 584:626:676:730:751:811:876:946:973:1051:1135:1168 SD: 0.0880 cents