Scala analysis: parizek_7lqmtd2
7-limit Quasi-meantone no. 2 (1/1 is D)
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: 28/25 196.198479 middle second 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 75/56 505.756522 marvelous fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 112/75 694.243478 marvelous fifth 8: 8/5 813.686286 minor sixth 9: 375/224 892.070236 10: 224/125 1009.884765 11: 28/15 1080.557192 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 392/375 76.7557 3: 15/14 119.4428 major diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 15/14 119.4428 major diatonic semitone 6: 392/375 76.7557 7: 16/15 111.7313 minor diatonic semitone 8: 15/14 119.4428 major diatonic semitone 9: 1875/1792 78.3839 10: 50176/46875 117.8145 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 392/375 76.756 cents 1: 1 1875/1792 78.384 cents 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 50176/46875 117.815 cents 1: 5 15/14 119.443 cents major diatonic semitone 2: 2 6272/5625 188.487 cents 2: 3 125/112 190.115 cents classic augmented semitone 2: 4 28/25 196.198 cents middle second 2: 1 28125/25088 197.827 cents 2: 1 8/7 231.174 cents septimal whole tone 2: 1 225/196 238.886 cents two (major diatonic semitone) 3: 3 7/6 266.871 cents septimal minor third 3: 3 448/375 307.930 cents 3: 3 1875/1568 309.558 cents 3: 3 6/5 315.641 cents minor third 4: 1 56/45 378.602 cents septimal narrow major third 4: 7 5/4 386.314 cents major third 4: 3 32/25 427.373 cents classic diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 5: 1 98/75 463.069 cents 5: 3 4/3 498.045 cents perfect fourth 5: 2 12544/9375 504.128 cents 5: 6 75/56 505.757 cents marvelous fourth 6: 2 1568/1125 574.801 cents 6: 2 625/448 576.429 cents 6: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 10/7 617.488 cents Euler's tritone 6: 2 896/625 623.571 cents 6: 2 1125/784 625.199 cents 7: 6 112/75 694.243 cents marvelous fifth 7: 2 9375/6272 695.872 cents 7: 3 3/2 701.955 cents perfect fifth 7: 1 75/49 736.931 cents BP fifth 8: 1 14/9 764.916 cents septimal minor sixth 8: 3 25/16 772.627 cents classic augmented fifth 8: 7 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 3 3136/1875 890.442 cents 9: 3 375/224 892.070 cents 9: 3 12/7 933.129 cents septimal major sixth 10: 1 392/225 961.114 cents 10: 1 7/4 968.826 cents harmonic seventh 10: 1 50176/28125 1002.173 cents 10: 4 25/14 1003.802 cents middle minor seventh 10: 3 224/125 1009.885 cents 10: 2 5625/3136 1011.513 cents two (marvelous fourth) 11: 5 28/15 1080.557 cents grave major seventh 11: 1 46875/25088 1082.185 cents 11: 1 15/8 1088.269 cents classic major seventh 11: 1 3584/1875 1121.616 cents 11: 2 375/196 1123.244 cents 11: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.90909 = 54/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 119.4 196.2 315.6 386.3 505.8 582.5 694.2 813.7 892.1 1009.9 1080.6 1200.0 119.4 : 76.8 196.2 266.9 386.3 463.1 574.8 694.2 772.6 890.4 961.1 1080.6 1200.0 196.2 : 119.4 190.1 309.6 386.3 498.0 617.5 695.9 813.7 884.4 1003.8 1123.2 1200.0 315.6 : 70.7 190.1 266.9 378.6 498.0 576.4 694.2 764.9 884.4 1003.8 1080.6 1200.0 386.3 : 119.4 196.2 307.9 427.4 505.8 623.6 694.2 813.7 933.1 1009.9 1129.3 1200.0 505.8 : 76.8 188.5 307.9 386.3 504.1 574.8 694.2 813.7 890.4 1009.9 1080.6 1200.0 582.5 : 111.7 231.2 309.6 427.4 498.0 617.5 736.9 813.7 933.1 1003.8 1123.2 1200.0 694.2 : 119.4 197.8 315.6 386.3 505.8 625.2 702.0 821.4 892.1 1011.5 1088.3 1200.0 813.7 : 78.4 196.2 266.9 386.3 505.8 582.5 702.0 772.6 892.1 968.8 1080.6 1200.0 892.1 : 117.8 188.5 307.9 427.4 504.1 623.6 694.2 813.7 890.4 1002.2 1121.6 1200.0 1009.9: 70.7 190.1 309.6 386.3 505.8 576.4 695.9 772.6 884.4 1003.8 1082.2 1200.0 1080.6: 119.4 238.9 315.6 435.1 505.8 625.2 702.0 813.7 933.1 1011.5 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 119.4428 cents 36/35, 48.7704 cents 25/24, 70.6724 cents 2: 188.4870 .. 238.8856 cents 1265625/1229312, 50.3987 cents 87808/84375, 69.0441 cents 3: 266.8709 .. 315.6413 cents 36/35, 48.7704 cents 686/675, 27.9853 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 28/27, 62.9609 cents 5: 463.0694 .. 505.7565 cents 5625/5488, 42.6871 cents 686/675, 27.9853 cents 6: 574.8007 .. 625.1993 cents 1265625/1229312, 50.3987 cents 87808/84375, 69.0441 cents 7: 694.2435 .. 736.9306 cents 5625/5488, 42.6871 cents 87808/84375, 69.0441 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 686/675, 27.9853 cents 9: 884.3587 .. 933.1291 cents 36/35, 48.7704 cents 28/27, 62.9609 cents 10: 961.1144 .. 1011.5130 cents 1265625/1229312, 50.3987 cents 686/675, 27.9853 cents 11: 1080.5572 .. 1129.3276 cents 36/35, 48.7704 cents 87808/84375, 69.0441 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 1.414979 Largest / Average step : 1.194428 Largest / Smallest step : 1.690091 Median interval of one step : 114.77291 cents, amount: 0 Most common interval of one step : 15/14, 119.4428 cents, amount: 5 Least squares average step : 99.70874 cents, oct.: 1196.50482 cents Scale is strictly proper Step pattern alph. order: ABACABDAEFCA Step pattern size order : FBFAFBDFCEAF Scale is a Constant Structure, by a margin of 27.98529 cents Scale diversity : 1.308019 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.546154 Rothenberg efficiency : 0.305315 redundancy: 0.694685 Efficiency x scale size : 3.663781 Number of different interval sizes : 54 = 4.90909 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.90909 = 54/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 703125/702464, 1.6283 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 7 Most common triad is 0.0 386.314 813.686 cents, amount: 3 Number of recognisable fifths : 11, average 696.6427 cents Best fifths form a closed circle Scale contains a complete diamond : 7 15 75 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 7 = 58.3333% Limited inverse transpositions with margin 48.7704 cents: 7 -- Rational properties -- Prime limit : 7 Odd number limit : 46875 (O: 46875 U: 46875) Highest odd numerator or denominator: 375 Scale harmonicity : 0.013458 Average absolute harmonicity : 0.137069 Specific harmonicity : 0.079782 Fundamental : 1/84000, -16.3581 octaves, 0.0031 Hz. Guide tone : 84000, 16.3581 octaves, 21976547.485 Hz. Exponens Consonantiae : 7.056000E+09, 32.71620 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 719.5, average 59.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.11319, average 1.25943 Sum of Tenney's harmonic distance : 30.93484, average 2.57790 Vogel's harmonic complexity : 30.58333 Wille's k value : 70312 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 10 Triangular lattice diameter : 7 Lattice compactness : 330.11874, average 4.23229 Lattice compactness (without 2's) : 193.86057, average 2.48539 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 5 0.58333 29 1 3: -1 .. 1 0.16667 6 5: -3 .. 3 -0.33333 18 3 7: -1 .. 1 0.16667 8 8 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 32 / 12 = 2.66667 Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 21 25 32| Scale is weakly epimorphic with val: <12 21 26 34| Scale is weakly epimorphic with val: <12 21 31 32|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.6572 c. M: 19.4428 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 6.5159 c. M: 14.0911 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 2.8419 c. M: 5.9639 c. Genus diatonico-chromaticum 81: 8 5 8 5 8 5 8 8 5 8 5 8 SP M DE SD: 2.6596 c. M: 4.7344 c. 87: 9 5 9 5 9 5 8 9 6 8 5 9 SP SD: 3.3865 c. M:-4.6951 c. 90: 9 6 9 5 9 6 8 9 6 9 5 9 SP SD: 2.3580 c. M:-4.3587 c. 109: 11 7 11 6 11 7 10 11 7 11 6 11 SP SD: 1.7121 c. M:-3.6248 c. 118: 12 7 12 7 12 7 11 12 8 11 7 12 SP SD: 2.2935 c. M: 3.1051 c. 121: 12 8 12 7 12 8 11 12 8 12 7 12 SP SD: 1.2338 c. M:-2.6118 c. 140: 14 9 14 8 14 9 13 14 9 14 8 14 SP SD: 0.7855 c. M:-1.5438 c. 159: 16 10 16 9 16 10 15 16 10 16 9 16 SP SD: 1.1347 c. M: 1.5042 c. 171: 17 11 17 10 17 11 16 17 11 17 10 17 SP SD: 0.4086 c. M: 0.8422 c. 323: 32 21 32 19 32 21 30 32 21 32 19 32 SP SD: 0.4851 c. M:-0.7695 c. 373: 37 24 37 22 37 24 35 37 24 37 22 37 SP SD: 0.4517 c. M: 0.9174 c. 410: 41 26 41 24 41 26 38 41 27 40 24 41 SP SD: 0.4003 c. M:-0.6127 c. 422: 42 27 42 25 42 27 39 42 28 41 25 42 SP SD: 0.3758 c. M:-0.8208 c. 441: 44 28 44 26 44 28 41 44 29 43 26 44 SP SD: 0.2726 c. M:-0.4468 c. 472: 47 30 47 28 47 30 44 47 31 46 28 47 SP SD: 0.2802 c. M: 0.5627 c. 562: 56 36 56 33 56 36 52 56 37 55 33 56 SP SD: 0.2641 c. M:-0.4565 c. 581: 58 37 58 34 58 37 54 58 38 57 34 58 SP SD: 0.2208 c. M:-0.3656 c. 593: 59 38 59 35 59 38 55 59 39 58 35 59 SP SD: 0.1692 c. M:-0.3412 c. 612: 61 39 61 36 61 39 57 61 40 60 36 61 SP SD: 0.1099 c. M:-0.1650 c. 764: 76 49 76 45 76 49 71 76 50 75 45 76 SP SD: 0.0904 c. M:-0.2103 c. 783: 78 50 78 46 78 50 73 78 51 77 46 78 SP SD: 0.0844 c. M: 0.1367 c. 1376: 137 88 137 81 137 88 128 137 90 135 81 137 SP SD: 0.0432 c. M:-0.0809 c. 1407: 140 90 140 83 140 90 131 140 92 138 83 140 SP SD: 0.0419 c. M: 0.0767 c. 1547: 154 99 154 91 154 99 144 154 101 152 91 154 SP SD: 0.0351 c. M:-0.0700 c. 1578: 157 101 157 93 157 101 147 157 103 155 93 157 SP SD: 0.0372 c. M: 0.0550 c. 2159: 215 138 215 127 215 138 201 215 141 212 127 215 SP SD: 0.0350 c. M:-0.0604 c. 2190: 218 140 218 129 218 140 204 218 143 215 129 218 SP SD: 0.0207 c. M: 0.0464 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: 3.8558 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.6352 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.4442 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 1.5423 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.9023 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.4232 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.4559 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.4506 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3441 cents 11:12 x 13:14:15 x 16:18 x 20:21:22 S SD: 10.7448 cents 12:13 x 14:15:16:17:18:19:20 x 22:24 S SD: 6.8150 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.3313 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.4456 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 3.8699 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.2865 cents 25:27:28:30:31:33:35:37:40:42:45:47:50 SD: 3.2314 cents 30:32:34:36:38:40:42:45:48:50:54:56:60 SD: 2.9379 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.8312 cents 35:38:39:42:44:47:49:52:56:59:63:65:70 SD: 2.7414 cents 39:42:44:47:49:52:55:58:62:65:70:73:78 SD: 2.4366 cents 40:43:45:48:50:54:56:60:64:67:72:75:80 SD: 1.7916 cents 52:56:58:62:65:70:73:78:83:87:93:97:104 SD: 1.7590 cents 53:57:59:64:66:71:74:79:85:89:95:99:106 SD: 1.6515 cents 55:59:62:66:69:74:77:82:88:92:99:103:110 SD: 1.5222 cents 59:63:66:71:74:79:83:88:94:99:106:110:118 SD: 1.3585 cents 65:70:73:78:81:87:91:97:104:109:116:121:130 SD: 1.2198 cents 67:72:75:80:84:90:94:100:107:112:120:125:134 SD: 1.1438 cents 80:86:90:96:100:107:112:119:128:134:143:149:160 SD: 1.1139 cents 83:89:93:100:104:111:116:124:133:139:149:155:166 SD: 0.8369 cents 85:91:95:102:106:114:119:127:136:142:152:159:170 SD: 0.7372 cents 100:107:112:120:125:134:140:149:160:167:179:187:200 SD: 0.6039 cents 125:134:140:150:156:167:175:187:200:209:224:233:250 SD: 0.5716 cents 135:145:151:162:169:181:189:202:216:226:242:252:270 SD: 0.5633 cents 140:150:157:168:175:188:196:209:224:234:251:261:280 SD: 0.5250 cents 150:161:168:180:188:201:210:224:240:251:269:280:300 SD: 0.4849 cents 165:177:185:198:206:221:231:246:264:276:296:308:330 SD: 0.4232 cents 180:193:202:216:225:241:252:269:288:301:323:336:360 SD: 0.4143 cents 200:214:224:240:250:268:280:299:320:335:358:373:400 SD: 0.3426 cents 215:230:241:258:269:288:301:321:344:360:385:401:430 SD: 0.3319 cents 225:241:252:270:281:301:315:336:360:377:403:420:450 SD: 0.2557 cents 265:284:297:318:331:355:371:396:424:444:475:495:530 SD: 0.2408 cents 280:300:314:336:350:375:392:418:448:469:502:523:560 SD: 0.2347 cents 292:313:327:350:365:391:409:436:467:489:523:545:584 SD: 0.2224 cents 335:359:375:402:419:449:469:500:536:561:600:625:670 SD: 0.2140 cents 360:386:403:432:450:482:504:538:576:603:645:672:720 SD: 0.1911 cents 365:391:409:438:456:489:511:545:584:611:654:681:730 SD: 0.1411 cents 375:402:420:450:469:502:525:560:600:628:672:700:750 SD: 0.1364 cents 460:493:515:552:575:616:644:687:736:770:824:859:920 SD: 0.1092 cents