Scala analysis: 7_6-on-3_2-untempered
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17496/16807 69.555474 septimal major diesis 2: 54/49 168.213190 Zalzal's mujannab 3: 7/6 266.870906 septimal minor third 4: 2916/2401 336.426379 two (Zalzal's mujannab) 5: 9/7 435.084095 septimal major third, BP third 6: 157464/117649 504.639569 7: 486/343 603.297285 8: 3/2 701.955001 perfect fifth 9: 26244/16807 771.510475 10: 81/49 870.168191 two (septimal major third, BP third) 11: 7/4 968.825906 harmonic seventh 12: 4374/2401 1038.381380 13: 27/14 1137.039096 septimal major seventh 14: 236196/117649 1206.594570 stearnsma +1 octave
SHOW/INTERVAL
0: 17496/16807 69.5555 septimal major diesis 1: 17496/16807 69.5555 septimal major diesis 2: 343/324 98.6577 3: 343/324 98.6577 4: 17496/16807 69.5555 septimal major diesis 5: 343/324 98.6577 6: 17496/16807 69.5555 septimal major diesis 7: 343/324 98.6577 8: 343/324 98.6577 9: 17496/16807 69.5555 septimal major diesis 10: 343/324 98.6577 11: 343/324 98.6577 12: 17496/16807 69.5555 septimal major diesis 13: 343/324 98.6577 14: 17496/16807 69.5555 septimal major diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 17496/16807 69.555 cents septimal major diesis 1: 8 343/324 98.658 cents 2: 1 139.11095 cents 2: 10 54/49 168.213 cents Zalzal's mujannab 2: 3 117649/104976 197.315 cents 3: 4 944784/823543 237.769 cents 3: 10 7/6 266.871 cents septimal minor third 4: 1 307.32414 cents 4: 8 2916/2401 336.426 cents two (Zalzal's mujannab) 4: 5 2401/1944 365.529 cents 5: 3 405.98185 cents 5: 10 9/7 435.084 cents septimal major third, BP third 5: 1 823543/629856 464.186 cents 6: 8 157464/117649 504.640 cents 6: 6 49/36 533.742 cents Arabic lute acute fourth 7: 3 574.19504 cents 7: 8 486/343 603.297 cents 7: 3 16807/11664 632.400 cents 8: 6 672.85276 cents 8: 8 3/2 701.955 cents perfect fifth 9: 1 742.40823 cents 9: 10 26244/16807 771.510 cents 9: 3 343/216 800.613 cents 10: 5 841.06595 cents 10: 8 81/49 870.168 cents two (septimal major third, BP third) 10: 1 117649/69984 899.270 cents 11: 10 1417176/823543 939.724 cents 11: 4 7/4 968.826 cents harmonic seventh 12: 3 1009.27914 cents 12: 10 4374/2401 1038.381 cents 12: 1 2401/1296 1067.484 cents two (Arabic lute acute fourth) 13: 8 1107.93685 cents 13: 6 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.53846 = 33/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 69.6 168.2 266.9 336.4 435.1 504.6 603.3 702.0 771.5 870.2 968.8 1038.4 1137.0 1206.6 69.6 : 98.7 197.3 266.9 365.5 435.1 533.7 632.4 702.0 800.6 899.3 968.8 1067.5 1137.0 1206.6 168.2 : 98.7 168.2 266.9 336.4 435.1 533.7 603.3 702.0 800.6 870.2 968.8 1038.4 1107.9 1206.6 266.9 : 69.6 168.2 237.8 336.4 435.1 504.6 603.3 702.0 771.5 870.2 939.7 1009.3 1107.9 1206.6 336.4 : 98.7 168.2 266.9 365.5 435.1 533.7 632.4 702.0 800.6 870.2 939.7 1038.4 1137.0 1206.6 435.1 : 69.6 168.2 266.9 336.4 435.1 533.7 603.3 702.0 771.5 841.1 939.7 1038.4 1107.9 1206.6 504.6 : 98.7 197.3 266.9 365.5 464.2 533.7 632.4 702.0 771.5 870.2 968.8 1038.4 1137.0 1206.6 603.3 : 98.7 168.2 266.9 365.5 435.1 533.7 603.3 672.9 771.5 870.2 939.7 1038.4 1107.9 1206.6 702.0 : 69.6 168.2 266.9 336.4 435.1 504.6 574.2 672.9 771.5 841.1 939.7 1009.3 1107.9 1206.6 771.5 : 98.7 197.3 266.9 365.5 435.1 504.6 603.3 702.0 771.5 870.2 939.7 1038.4 1137.0 1206.6 870.2 : 98.7 168.2 266.9 336.4 406.0 504.6 603.3 672.9 771.5 841.1 939.7 1038.4 1107.9 1206.6 968.8 : 69.6 168.2 237.8 307.3 406.0 504.6 574.2 672.9 742.4 841.1 939.7 1009.3 1107.9 1206.6 1038.4: 98.7 168.2 237.8 336.4 435.1 504.6 603.3 672.9 771.5 870.2 939.7 1038.4 1137.0 1206.6 1137.0: 69.6 139.1 237.8 336.4 406.0 504.6 574.2 672.9 771.5 841.1 939.7 1038.4 1107.9 1206.6 1206.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.5555 .. 98.6577 cents 5764801/5668704, 29.1022 cents 17496/16807, 69.5555 cents 2: 139.1109 .. 197.3154 cents 58.20448 cents 40.45323 cents 3: 237.7687 .. 266.8709 cents 5764801/5668704, 29.1022 cents 40.45323 cents 4: 307.3241 .. 365.5286 cents 58.20448 cents 40.45323 cents 5: 405.9819 .. 464.1863 cents 58.20448 cents 40.45323 cents 6: 504.6396 .. 533.7418 cents 5764801/5668704, 29.1022 cents 40.45323 cents 7: 574.1950 .. 632.3995 cents 58.20448 cents 40.45323 cents 8: 672.8528 .. 701.9550 cents 29.10224 cents 40.45323 cents 9: 742.4082 .. 800.6127 cents 58.20448 cents 40.45323 cents 10: 841.0659 .. 899.2704 cents 58.20448 cents 40.45323 cents 11: 939.7237 .. 968.8259 cents 5764801/5668704, 29.1022 cents 40.45323 cents 12: 1009.2791 .. 1067.4836 cents 58.20448 cents 40.45323 cents 13: 1107.9369 .. 1137.0391 cents 29.10224 cents 40.45323 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 17496/16807, 69.5555 cents, class 1 Average step (divided formal octave): 86.1853 cents Largest one step interval : 343/324, 98.6577 cents Average / Smallest step : 1.239088 Largest / Average step : 1.144716 Largest / Smallest step : 1.418403 Median interval of one step : 343/324, 98.6577 cents, amount: 8 Most common interval of one step : 343/324, 98.6577 cents, amount: 8 Least squares average step : 86.73010 cents, oct.: 1214.22136 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 1700-tone equal temperament with octave 236196/117649 degrees: 98 237 376 474 613 711 850 989 1087 1226 1365 1463 1602 1700 Least number of segments generator : 851 of 604.007 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1087 of 771.511 cents and inv. generated superset size: 857 = 843 more = 6121.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABBABBABA Step pattern size order : SLLSLSLLSLLSLS Scale is a Constant Structure, by a margin of 40.45323 cents Scale diversity : 1.299164 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.517614 Number of different interval sizes : 33 = 2.53846 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.53846 = 33/13 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 5764801/5668704, 29.1022 cents Number of recognisable fifths : 8, average 701.9550 cents Number of recognisable fourths : 8, average 504.6396 cents Scale contains two identical disjunct heptachords Formal octave complements present : 12 = 85.7143% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 7 Odd number limit : too high to compute Highest odd numerator or denominator: 117649 Scale harmonicity : 0.009404 Average absolute harmonicity : 0.050883 Specific harmonicity : 0.050228 Fundamental : 1/1411788, -20.4291 octaves, 0.0002 Hz. Guide tone : 3306744, 21.6570 octaves, 865128768.306 Hz. Exponens Consonantiae : 4.668421E+12, 42.08607 octaves Euler's gradus suavitatis : 70 Sum of Mann's harmonic distance : 359776.0, average 25698.28571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 36.03984, average 2.57427 Sum of Tenney's harmonic distance : 72.15962, average 5.15426 Vogel's harmonic complexity : 42.92857 Wille's k value : 1235314 Wilson's harmonic complexity : 82 Rectangular lattice diameter : 18 Triangular lattice diameter : 11 Lattice compactness : 578.20153, average 5.50668 Lattice compactness (without 2's) : 535.98353, average 5.10461 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.71429 20 3: -1 .. 10 4.57143 66 1 7: -6 .. 1 -2.64286 41 13 Average exponent except 2's : 27 / 14 = 1.92857 Average absolute exponent except 2's: 107 / 14 = 7.64286 Scale is JI-epimorphic with val: <13 21 37| Scale is JI-epimorphic with val: <14 22 39| = patent Scale is JI-epimorphic with val: <15 23 41|
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.5995 c. M: 20.7873 c. 22: 1 2 2 1 2 1 2 2 1 2 2 1 2 1 P D3 SD: 9.3760 c. M:-18.3878 c. 30: 2 2 3 1 3 2 2 2 2 3 2 2 2 2 P D3 SD: 11.2565 c. M: 18.2181 c. 31: 2 2 3 2 2 2 3 2 2 2 3 2 2 2 SP D3 SD: 9.8704 c. M:-19.4612 c. 34: 2 3 3 1 3 2 3 3 2 3 2 2 3 2 P T3 SD: 10.1781 c. M: 17.0337 c. 35: 2 3 3 2 3 2 3 2 2 3 3 2 3 2 SP D3 SD: 9.3204 c. M:-17.2371 c. 36: 2 3 3 2 3 2 3 3 2 3 3 2 3 2 SP D3 SD: 1.6077 c. M:-3.1531 c. 86: 5 7 7 5 7 5 7 7 5 7 7 5 7 5 SP D3 SD: 0.3795 c. M: 0.7442 c. 122: 7 10 10 7 10 7 10 10 7 10 10 7 10 7 SP D3 SD: 0.2069 c. M:-0.4058 c. 208: 12 17 17 12 17 12 17 17 12 17 17 12 17 12 SP D3 SD: 0.0355 c. M: 0.0697 c. 538: 31 44 44 31 44 31 44 44 31 44 44 31 44 31 SP D3 SD: 0.0194 c. M:-0.0381 c. 746: 43 61 61 43 61 43 61 61 43 61 61 43 61 43 SP D3 SD: 0.0041 c. M:-0.0081 c. 1700: 98 139 139 98 139 98 139 139 98 139 139 98 139 98 SP D3 SD: 0.0007 c. M: 0.0014 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 6.5946 cents 2 x x x x x x x 3 x x x x x 4 S SD: 3.2973 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 5.6603 cents 4 x x x x 5 x x 6 x x 7 x x 8 S SD: 12.3036 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 11.1684 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 3.3704 cents 7 x x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 9.0624 cents 8 x 9 x x 10:11 x 12 x 13:14 x 15:16 S SD: 11.9454 cents 9 x 10 x 11 x 12:13 x 14:15:16 x 17:18 S SD: 6.8520 cents 10 x 11 x 12:13 x 14:15:16:17 x 18:19:20 S SD: 8.0697 cents 11 x 12:13 x 14:15:16 x 17:18:19:20:21:22 S SD: 6.8785 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:23:24 S SD: 5.5021 cents 13 x 14:15:16:17 x 18 x 20:21:23:24:25:26 SD: 8.2103 cents 14 x 15:16:17:18:19:20:21:22:23 x 26:27:28 SD: 6.3584 cents 15:16:17 x 18:19:20:21 x 23:25:26:27:29:30 SD: 7.2962 cents 16:17:18:19 x x 21:23:24:25:26:28:29:31:32 SD: 6.6151 cents 17:18:19:20:21:22:23:24:26:27:28:30:31:33:34 SD: 5.2802 cents 18:19:20:21:22:23:24:26:27:28:30:32:33:35:36 SD: 4.2394 cents 20:21:22:23:24:26:27:28:30:31:33:35:36:39:40 SD: 4.1162 cents 21:22:23 x 26:27:28:30:32:33:35:37:38:41:42 SD: 4.5012 cents 22:23:24:26:27:28:29:31:33:34:36:39:40:42:44 SD: 4.3909 cents 23:24:25:27:28:30:31:33:35:36:38:40:42:44:46 SD: 3.8912 cents 24:25:26:28:29:31:32:34:36:37:40:42:44:46:48 SD: 3.2219 cents 28:29:31:33:34:36:37:40:42:44:46:49:51:54:56 SD: 2.6919 cents 29:30:32:34:35:37:39:41:44:45:48:51:53:56:58 SD: 2.5147 cents 32:33:35:37:39:41:43:45:48:50:53:56:58:62:64 SD: 2.4386 cents 38:40:42:44:46:49:51:54:57:59:63:67:69:73:76 SD: 2.3523 cents 41:43:45:48:50:53:55:58:62:64:68:72:75:79:82 SD: 1.9909 cents 46:48:51:54:56:59:62:65:69:72:76:81:84:89:92 SD: 1.8471 cents 48:50:53:56:58:62:64:68:72:75:79:84:87:93:96 SD: 1.5003 cents 60:62:66:70:73:77:80:85:90:94:99:105:109:116:120 SD: 1.3654 cents 68:71:75:79:83:87:91:96:102:106:112:119:124:131:137 SD: 1.3574 cents 70:73:77:82:85:90:94:99:105:109:116:123:128:135:141 SD: 1.1928 cents 77:80:85:90:94:99:103:109:116:120:127:135:140:149:155 SD: 1.1804 cents 78:81:86:91:95:100:104:111:117:122:129:137:142:150:157 SD: 1.1559 cents 80:83:88:93:97:103:107:113:120:125:132:140:146:154:161 SD: 0.9475 cents 95:99:105:111:115:122:127:135:143:148:157:166:173:183:191 SD: 0.9371 cents 96:100:106:112:117:123:128:136:144:150:159:168:175:185:193 SD: 0.8750 cents 98:102:108:114:119:126:131:139:147:153:162:172:179:189:197 SD: 0.6575 cents 116:121:128:135:141:149:155:164:174:181:192:203:211:224:233 SD: 0.6472 cents 126:131:139:147:153:162:169:179:189:197:208:221:230:243:253 SD: 0.6400 cents 127:132:140:148:154:163:170:180:191:198:210:222:231:245:255 SD: 0.5879 cents 139:145:153:162:169:179:186:197:209:217:230:243:253:268:279 SD: 0.5445 cents 144:150:159:168:175:185:193:204:216:225:238:252:262:278:289 SD: 0.3969 cents 168:175:185:196:204:216:225:238:252:262:278:294:306:324:337 SD: 0.2728 cents 266:277:293:310:323:342:356:377:399:415:440:466:485:513:534 SD: 0.2673 cents 276:287:304:322:335:355:369:391:414:431:456:483:503:532:554 SD: 0.2477 cents 312:325:344:364:379:401:418:442:468:487:516:546:568:602:626 SD: 0.2225 cents 336:350:370:392:408:432:450:476:504:525:555:588:612:648:675 SD: 0.2122 cents 340:354:375:397:413:437:455:482:510:531:562:595:619:656:683 SD: 0.2072 cents 360:375:397:420:437:463:482:510:540:562:595:630:656:694:723 SD: 0.1663 cents 372:387:410:434:452:478:498:527:558:581:615:651:678:717:747 SD: 0.1633 cents 392:408:432:457:476:504:525:555:588:612:648:686:714:756:787 SD: 0.1594 cents 420:437:463:490:510:540:562:595:630:656:694:735:765:810:843 SD: 0.1099 cents 588:612:648:686:714:756:787:833:882:918:972:1029:1071:1134:1180 SD: 0.0698 cents