Scala analysis: 2.3.5-7.11-9.diamond
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 63/55 235.104252 3: 11/9 347.407941 undecimal neutral third 4: 4/3 498.044999 perfect fourth 5: 10/7 617.487807 Euler's tritone 6: 3/2 701.955001 perfect fifth 7: 18/11 852.592059 undecimal neutral sixth 8: 110/63 964.895748 9: 28/15 1080.557192 grave major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 294/275 115.6614 3: 605/567 112.3037 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 15/14 119.4428 major diatonic semitone 6: 21/20 84.4672 minor semitone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone 8: 605/567 112.3037 9: 294/275 115.6614 10: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 2 605/567 112.304 cents 1: 2 294/275 115.661 cents 1: 3 15/14 119.443 cents major diatonic semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 9/8 203.910 cents major whole tone 2: 2 154/135 227.965 cents 2: 3 63/55 235.104 cents 2: 1 225/196 238.886 cents two (major diatonic semitone) 2: 2 220/189 262.941 cents 2: 1 90/77 270.080 cents 3: 3 11/9 347.408 cents undecimal neutral third 3: 4 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 2 56/45 378.602 cents septimal narrow major third 3: 1 550/441 382.384 cents 4: 1 98/75 463.069 cents 4: 4 55/42 466.851 cents 4: 1 3969/3025 470.209 cents 4: 3 4/3 498.045 cents perfect fourth 4: 1 162/121 505.184 cents 5: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 5 10/7 617.488 cents Euler's tritone 6: 1 121/81 694.816 cents two (undecimal neutral third) 6: 3 3/2 701.955 cents perfect fifth 6: 1 6050/3969 729.791 cents 6: 4 84/55 733.149 cents 6: 1 75/49 736.931 cents BP fifth 7: 1 441/275 817.616 cents 7: 2 45/28 821.398 cents septimale wide minor sixth 7: 4 44/27 845.453 cents neutral sixth 7: 3 18/11 852.592 cents undecimal neutral sixth 8: 1 77/45 929.920 cents 8: 2 189/110 937.059 cents 8: 1 392/225 961.114 cents 8: 3 110/63 964.896 cents 8: 2 135/77 972.035 cents 8: 1 16/9 996.090 cents Pythagorean minor seventh 9: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 3 28/15 1080.557 cents grave major seventh 9: 2 275/147 1084.339 cents 9: 2 1134/605 1087.696 cents 9: 1 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 119.4 235.1 347.4 498.0 617.5 702.0 852.6 964.9 1080.6 1200.0 119.4 : 115.7 228.0 378.6 498.0 582.5 733.1 845.5 961.1 1080.6 1200.0 235.1 : 112.3 262.9 382.4 466.9 617.5 729.8 845.5 964.9 1084.3 1200.0 347.4 : 150.6 270.1 354.5 505.2 617.5 733.1 852.6 972.0 1087.7 1200.0 498.0 : 119.4 203.9 354.5 466.9 582.5 702.0 821.4 937.1 1049.4 1200.0 617.5 : 84.5 235.1 347.4 463.1 582.5 702.0 817.6 929.9 1080.6 1200.0 702.0 : 150.6 262.9 378.6 498.0 617.5 733.1 845.5 996.1 1115.5 1200.0 852.6 : 112.3 228.0 347.4 466.9 582.5 694.8 845.5 964.9 1049.4 1200.0 964.9 : 115.7 235.1 354.5 470.2 582.5 733.1 852.6 937.1 1087.7 1200.0 1080.6: 119.4 238.9 354.5 466.9 617.5 736.9 821.4 972.0 1084.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 150.6371 cents 80/77, 66.1699 cents 21/20, 84.4672 cents 2: 203.9100 .. 270.0799 cents 80/77, 66.1699 cents 33/32, 53.2729 cents 3: 347.4079 .. 382.3836 cents 50/49, 34.9756 cents 847/810, 77.3281 cents 4: 463.0694 .. 505.1841 cents 6075/5929, 42.1147 cents 7203/6875, 80.6858 cents 5: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 847/810, 77.3281 cents 6: 694.8159 .. 736.9306 cents 6075/5929, 42.1147 cents 847/810, 77.3281 cents 7: 817.6164 .. 852.5921 cents 50/49, 34.9756 cents 7203/6875, 80.6858 cents 8: 929.9201 .. 996.0900 cents 80/77, 66.1699 cents 847/810, 77.3281 cents 9: 1049.3629 .. 1115.5328 cents 80/77, 66.1699 cents 33/32, 53.2729 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 12/11, 150.6371 cents Average / Smallest step : 1.420670 Largest / Average step : 1.255309 Largest / Smallest step : 1.783379 Median interval of one step : 117.55213 cents, amount: 0 Most common interval of one step : 15/14, 119.4428 cents, amount: 3 Least squares average step : 120.35208 cents, oct.: 1203.52076 cents Scale is strictly proper Step pattern alph. order: ABCDAEDCBA Step pattern size order : DCBEDAEBCD Scale is a Constant Structure, by a margin of 53.27294 cents Scale diversity : 1.331042 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.621804 Rothenberg efficiency : 0.326349 redundancy: 0.673651 Efficiency x scale size : 3.263492 Number of different interval sizes : 42 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.66667 = 14/3 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 166698/166375, 3.3578 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 5 Most common triad is 0.0 617.488 1115.533 cents, amount: 1 Number of recognisable fifths : 4, average 700.1702 cents Best major thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 90.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 3969 (O: 3969 U: 3969) Highest odd numerator or denominator: 63 Scale harmonicity : 0.011990 Average absolute harmonicity : 0.177198 Specific harmonicity : 0.072599 Fundamental : 1/6930, -12.7586 octaves, 0.0378 Hz. Guide tone : 13860, 13.7586 octaves, 3626130.335 Hz. Exponens Consonantiae : 9.604980E+07, 26.51728 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 222.0, average 22.20000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.83299, average 0.98330 Sum of Tenney's harmonic distance : 20.62167, average 2.06217 Vogel's harmonic complexity : 30.40000 Wille's k value : 5197 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 155.11788, average 2.82033 Lattice compactness (without 2's) : 130.70404, average 2.37644 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.60000 10 1 3: -2 .. 2 0.00000 12 2 5: -1 .. 1 0.10000 5 7: -1 .. 1 -0.10000 5 3 11: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 10 = 0.00000 Average absolute exponent except 2's: 26 / 10 = 2.60000 Scale is weakly epimorphic with val: <10 16 21 26 34| Scale is JI-epimorphic with val: <10 16 21 26 35| Scale is weakly epimorphic with val: <10 16 22 27 34| Scale is JI-epimorphic with val: <10 16 22 27 35| Scale is weakly epimorphic with val: <10 16 23 28 34| Scale is JI-epimorphic with val: <10 16 23 28 35| = patent Scale is weakly epimorphic with val: <10 16 24 29 34| Scale is JI-epimorphic with val: <10 16 24 29 35| Scale is weakly epimorphic with val: <10 16 25 30 34| Scale is JI-epimorphic with val: <10 16 25 30 35| Scale is weakly epimorphic with val: <10 17 21 26 33| Scale is weakly epimorphic with val: <10 17 21 26 35| Scale is weakly epimorphic with val: <10 17 21 26 38| Scale is weakly epimorphic with val: <10 17 22 27 33| Scale is weakly epimorphic with val: <10 17 22 27 35| Scale is weakly epimorphic with val: <10 17 22 27 38| Scale is weakly epimorphic with val: <10 17 23 28 33| Scale is weakly epimorphic with val: <10 17 23 28 35| Scale is weakly epimorphic with val: <10 17 23 28 38| Scale is weakly epimorphic with val: <10 17 24 29 33| Scale is weakly epimorphic with val: <10 17 24 29 35| Scale is weakly epimorphic with val: <10 17 24 29 38| Scale is weakly epimorphic with val: <10 17 25 30 33| Scale is weakly epimorphic with val: <10 17 25 30 35| Scale is weakly epimorphic with val: <10 17 25 30 38| Scale is weakly epimorphic with val: <10 18 21 26 32| Scale is weakly epimorphic with val: <10 18 21 26 35| Scale is weakly epimorphic with val: <10 18 21 26 37| Scale is weakly epimorphic with val: <10 18 22 27 32| Scale is weakly epimorphic with val: <10 18 22 27 35| Scale is weakly epimorphic with val: <10 18 22 27 37| Scale is weakly epimorphic with val: <10 18 23 28 32| Scale is weakly epimorphic with val: <10 18 23 28 35| Scale is weakly epimorphic with val: <10 18 23 28 37| Scale is weakly epimorphic with val: <10 18 24 29 32| Scale is weakly epimorphic with val: <10 18 24 29 35| Scale is weakly epimorphic with val: <10 18 24 29 37| Scale is weakly epimorphic with val: <10 18 25 30 32| Scale is weakly epimorphic with val: <10 18 25 30 35| Scale is weakly epimorphic with val: <10 18 25 30 37|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.5011 c. M:-18.0450 c. 21: 2 2 2 3 2 1 3 2 2 2 P D3 SD: 9.1123 c. M:-16.2407 c. 27: 3 2 3 3 3 2 3 3 2 3 SP M ME SD: 10.2012 c. M: 13.8905 c. 29: 3 3 2 4 3 2 4 2 3 3 SP D3 SD: 9.7055 c. M: 16.3735 c. 31: 3 3 3 4 3 2 4 3 3 3 SP D3 SD: 3.1185 c. M: 5.1808 c. 41: 4 4 4 5 4 3 5 4 4 4 SP D3 SD: 2.2524 c. M: 3.8116 c. 72: 7 7 7 9 7 5 9 7 7 7 SP D3 SD: 2.0843 c. M: 2.7761 c. 101: 10 10 9 13 10 7 13 9 10 10 SP SD: 1.7819 c. M: 2.8535 c. 111: 11 11 10 14 11 8 14 10 11 11 SP SD: 1.5001 c. M: 2.7336 c. 128: 13 12 12 16 13 9 16 12 12 13 SP SD: 1.3339 c. M:-2.4322 c. 132: 13 13 12 17 13 9 17 12 13 13 SP SD: 1.4869 c. M:-1.9550 c. 142: 14 14 13 18 14 10 18 13 14 14 SP SD: 0.9914 c. M: 1.5155 c. 159: 16 15 15 20 16 11 20 15 15 16 SP SD: 0.8988 c. M:-1.3801 c. 169: 17 16 16 21 17 12 21 16 16 17 SP SD: 0.8409 c. M: 1.2673 c. 200: 20 19 19 25 20 14 25 19 19 20 SP SD: 0.6346 c. M: 1.1043 c. 239: 24 23 22 30 24 17 30 22 23 24 SP SD: 0.8691 c. M: 1.0593 c. 241: 24 23 23 30 24 17 30 23 23 24 SP SD: 0.7048 c. M: 1.1398 c. 270: 27 26 25 34 27 19 34 25 26 27 SP SD: 0.4852 c. M: 0.7413 c. 301: 30 29 28 38 30 21 38 28 29 30 SP SD: 0.3300 c. M: 0.5641 c. 311: 31 30 29 39 31 22 39 29 30 31 SP SD: 0.2074 c. M:-0.2958 c. 342: 34 33 32 43 34 24 43 32 33 34 SP SD: 0.1136 c. M:-0.2006 c. 653: 65 63 61 82 65 46 82 61 63 65 SP SD: 0.0684 c. M: 0.1178 c. 995: 99 96 93 125 99 70 125 93 96 99 SP SD: 0.0536 c. M: 0.0716 c. 1506: 150 145 141 189 150 106 189 141 145 150 SP SD: 0.0458 c. M:-0.0791 c. 1848: 184 178 173 232 184 130 232 173 178 184 SP SD: 0.0284 c. M:-0.0447 c. 2190: 218 211 205 275 218 154 275 205 211 218 SP SD: 0.0281 c. M:-0.0464 c.
FIT/HARMONIC
1 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 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 10.5889 cents 4 x x 5 x x 6 x 7 x 8 S SD: 9.7759 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 16.1535 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 9.1155 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 14.2722 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 9.3083 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 10.8351 cents 10:11 x 12:13:14:15:16:17:19:20 SD: 11.5585 cents 11:12:13 x 15:16:17:18:19:21:22 SD: 11.6119 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 7.1388 cents 14:15:16:17:19:20:21:23:24:26:28 SD: 4.7076 cents 24:26:27:29:32:34:36:39:42:45:48 SD: 4.6485 cents 26:28:30:32:35:37:39:43:45:49:52 SD: 3.9327 cents 27:29:31:33:36:39:41:44:47:50:54 SD: 3.3479 cents 28:30:32:34:37:40:42:46:49:52:56 SD: 2.2904 cents 40:43:46:49:53:57:60:65:70:75:80 SD: 2.1277 cents 42:45:48:51:56:60:63:69:73:78:84 SD: 1.8174 cents 54:58:62:66:72:77:81:88:94:101:108 SD: 1.1637 cents 68:73:78:83:91:97:102:111:119:127:136 SD: 1.0194 cents 82:88:94:100:109:117:123:134:143:153:164 SD: 0.8211 cents 96:103:110:117:128:137:144:157:168:179:192 SD: 0.7335 cents 126:135:144:154:168:180:189:206:220:235:252 SD: 0.4466 cents 166:178:190:203:221:237:249:272:290:310:332 SD: 0.4393 cents 180:193:206:220:240:257:270:295:314:336:360 SD: 0.3809 cents 198:212:227:242:264:283:297:324:346:370:396 SD: 0.3163 cents 240:257:275:293:320:343:360:393:419:448:480 SD: 0.2670 cents 294:315:337:359:392:420:441:481:513:549:588 SD: 0.2414 cents 324:347:371:396:432:463:486:530:566:605:648 SD: 0.1609 cents 378:405:433:462:504:540:567:619:660:706:756 SD: 0.1608 cents 420:450:481:513:560:600:630:687:733:784:840 SD: 0.1569 cents 432:463:495:528:576:617:648:707:754:806:864 SD: 0.1411 cents 504:540:577:616:672:720:756:825:880:941:1008 SD: 0.1150 cents 558:598:639:682:744:797:837:913:974:1042:1116 SD: 0.1092 cents