Scala analysis: mavila9
9-note scale of mavila temperament (TOP tuning)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 163.508 cents 163.507700 2: 327.015 cents 327.015400 3: 358.013 cents 358.012580 4: 521.520 cents 521.520280 5: 685.028 cents 685.027980 6: 848.536 cents 848.535680 7: 879.533 cents 879.532870 8: 1043.041 cents 1043.040570 9: 1206.548 cents 1206.548260
SHOW/INTERVAL
0: 163.5077 cents 163.5077 1: 163.5077 cents 163.5077 2: 163.5077 cents 163.5077 3: 30.9972 cents 30.9972 4: 163.5077 cents 163.5077 5: 163.5077 cents 163.5077 6: 163.5077 cents 163.5077 7: 30.9972 cents 30.9972 8: 163.5077 cents 163.5077 9: 163.5077 cents 163.5077
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 30.99718 cents 1: 7 163.50770 cents 2: 4 194.50488 cents 2: 5 327.01540 cents 3: 6 358.01258 cents 3: 3 490.52310 cents 4: 8 521.52028 cents 4: 1 654.03079 cents 5: 1 552.51747 cents 5: 8 685.02798 cents 6: 3 716.02517 cents 6: 6 848.53568 cents 7: 5 879.53287 cents 7: 4 1012.04338 cents 8: 7 1043.04057 cents 8: 2 1175.55108 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 163.5 327.0 358.0 521.5 685.0 848.5 879.5 1043.0 1206.5 163.5 : 163.5 194.5 358.0 521.5 685.0 716.0 879.5 1043.0 1206.5 327.0 : 31.0 194.5 358.0 521.5 552.5 716.0 879.5 1043.0 1206.5 358.0 : 163.5 327.0 490.5 521.5 685.0 848.5 1012.0 1175.6 1206.5 521.5 : 163.5 327.0 358.0 521.5 685.0 848.5 1012.0 1043.0 1206.5 685.0 : 163.5 194.5 358.0 521.5 685.0 848.5 879.5 1043.0 1206.5 848.5 : 31.0 194.5 358.0 521.5 685.0 716.0 879.5 1043.0 1206.5 879.5 : 163.5 327.0 490.5 654.0 685.0 848.5 1012.0 1175.6 1206.5 1043.0: 163.5 327.0 490.5 521.5 685.0 848.5 1012.0 1043.0 1206.5 1206.5
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.9972 .. 163.5077 cents 132.51052 cents 30.99718 cents 2: 194.5049 .. 327.0154 cents 132.51052 cents 30.99718 cents 3: 358.0126 .. 490.5231 cents 132.51052 cents 30.99718 cents 4: 521.5203 .. 654.0308 cents 132.51051 cents 30.99718 cents 5: 552.5175 .. 685.0280 cents 132.51051 cents -101.51332 cents 6: 716.0252 .. 848.5357 cents 132.51051 cents 30.99719 cents 7: 879.5329 .. 1012.0434 cents 132.51051 cents 30.99719 cents 8: 1043.0406 .. 1175.5511 cents 132.51051 cents 30.99719 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 30.99718 cents, class 1 Average step (divided formal octave): 134.0609 cents Largest one step interval : 163.50770 cents Average / Smallest step : 4.324939 Largest / Average step : 1.219652 Largest / Smallest step : 5.274922 Median interval of one step : 163.50770 cents, amount: 7 Most common interval of one step : 163.50770 cents, amount: 7 Least squares average step : 132.82105 cents, oct.: 1195.38948 cents Scale is not proper Scale has Myhill's property chromas: 132.51052 cents and 101.51334 cents, ratio: 1.305351 generators: 4 of 521.52028 cents and 5 of 685.02798 cents ET pair of linear temperament : 37&118 Scale is distributional even Scale is a mode of a 1129-tone equal temperament with octave 1206.548 cents degrees: 153 306 335 488 641 794 823 976 1129 generators: 488 and 641 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAA Step pattern size order : LLSLLLSLL Scale is a Constant Structure, by a margin of 30.99718 cents Scale diversity : 1.114694 Lumma stability : 0.205526 Lumma impropriety factor : 0.084135 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 30.99718 cents Most common intervals : 521.52028 cents & inv., amount: 8 Scale is a chain of 4 triads 0.0 521.520 1043.041 cents Most common triad is 0.0 521.520 685.028 cents, amount: 7 Number of recognisable fifths : 3, average 716.0252 cents Number of appreciable fifths : 0 Number of recognisable fourths : 3, average 490.5231 cents Scale contains two identical conjunct pentachords Formal octave complements present : 9 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 38.0156 c. M: 58.8936 c. Pelog Nawanada: Sunda 10: 1 2 0 1 2 1 0 2 1 N D3 I SD: 31.9260 c. M: 42.8529 c. 11: 1 2 0 2 1 2 0 1 2 N T3 SD: 31.8870 c. M: 55.8647 c. 12: 2 1 1 1 2 1 1 1 2 N D3 I SD: 31.1296 c. M:-44.1702 c. Houseini: Greece, Raga Rudra Manjiri, Modes of Major Pentatonic mixed 13: 2 2 0 2 1 2 0 2 2 N I SD: 29.3257 c. M: 44.2302 c. 14: 2 2 0 2 2 2 0 2 2 N M DE I SD: 11.4335 c. M: 17.7127 c. 21: 3 3 0 3 3 3 0 3 3 N M DE I SD: 11.4335 c. M: 17.7127 c. 23: 3 3 1 3 3 3 1 3 3 N M DE I SD: 7.9162 c. M: 12.2637 c. 30: 4 4 1 4 4 4 1 4 4 N M DE I SD: 3.4012 c. M: 5.2692 c. 37: 5 5 1 5 5 5 1 5 5 N M DE I SD: 0.5947 c. M: 0.9213 c. 81: 11 11 2 11 11 11 2 11 11 N M DE I SD: 0.4448 c. M: 0.6891 c. 118: 16 16 3 16 16 16 3 16 16 N M DE I SD: 0.1189 c. M: 0.1841 c. 155: 21 21 4 21 21 21 4 21 21 N M DE I SD: 0.0515 c. M: 0.0797 c. 273: 37 37 7 37 37 37 7 37 37 N M DE I SD: 0.0222 c. M: 0.0343 c. 428: 58 58 11 58 58 58 11 58 58 N M DE I SD: 0.0045 c. M: 0.0070 c. 1129: 153 153 29 153 153 153 29 153 153 N M DE I SD: 0.0019 c. M: 0.0030 c. 1557: 211 211 40 211 211 211 40 211 211 N M DE I SD: 0.0002 c. M: 0.0003 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 6.5483 cents 2 x x x x 3 x x x 4 S SD: 9.0747 cents 3 x x x 4 x x 5 x 6 S SD: 8.2816 cents 4 x x 5 x 6 x x 7:8 S SD: 20.3687 cents 5 x 6 x 7 x 8 x 9:10 S SD: 15.1712 cents 6 x 7 x 8:9 x 10:11:12 S SD: 11.2560 cents 7:8 x 9 x 10:11:12:13:14 S SD: 21.7495 cents 8:9 x 10:11:12:13 x 15:16 SD: 10.8424 cents 9:10 x 11:12:13 x 15:16:18 SD: 10.7235 cents 10:11:12 x 14:15:16:17:18:20 S SD: 10.8775 cents 11:12:13:14:15:16:18 x 20:22 S SD: 10.3212 cents 12:13 x 15:16:18 x 20:22:24 SD: 6.9495 cents 13:14 x 16:18:19:21:22:24:26 SD: 9.2474 cents 14:15:17 x 19:21:23 x 26:28 SD: 8.2636 cents 15:16:18 x 20:22:24:25:27:30 SD: 9.4970 cents 16:18:19:20:22:24:26:27:29:32 SD: 8.2100 cents 17:19 x 21:23:25:28 x 31:34 SD: 5.5258 cents 18:20 x 22:24:27:29:30:33:36 SD: 5.5003 cents 19:21:23 x 26:28:31:32:35:38 SD: 4.9101 cents 20:22:24:25:27:30 x 33:37:40 SD: 5.4594 cents 21:23:25:26:28:31:34:35:38:42 SD: 4.9850 cents 22:24 x 27:30:33:36:37:40:44 SD: 4.4129 cents 23:25:28 x 31:34 x 38:42:46 SD: 4.0193 cents 27:30 x 33:36:40:44:45:49:54 SD: 4.4086 cents 28:31:34 x 38:42:46:47:51:56 SD: 4.0752 cents 29:32:35:36:39:43:47:48:53:58 SD: 2.8411 cents 32:35:39 x 43:48:52:53:58:64 SD: 3.9931 cents 33:36:40:41:45:49:54:55:60:66 SD: 3.3404 cents 35:38:42:43:47:52:57:58:64:70 SD: 3.1291 cents 38:42:46:47:51:56:62:63:69:76 SD: 2.9670 cents 39:43:47:48:53:58:64:65:71:78 SD: 1.9999 cents 41:45 x 50:55:61:67:68:75:82 SD: 2.6663 cents 43:47:52:53:58:64:70:71:79:86 SD: 2.3035 cents 48:53:58:59:65:71:78:80:88:96 SD: 1.9257 cents 52:57:63:64:70:77:85:86:95:104 SD: 1.7489 cents 57:63:69:70:77:85:93:95:104:114 SD: 1.6941 cents 62:68:75:76:84:92:101:103:113:124 SD: 1.3295 cents 82:90:99:101:111:122:134:136:150:165 SD: 0.9113 cents 91:100:110:112:123:135:149:151:166:183 SD: 0.8372 cents 109:120:132:134:147:162:178:181:199:219 SD: 0.7766 cents 122:134:147:150:165:181:199:203:223:245 SD: 0.6405 cents 130:143:157:160:176:193:212:216:237:261 SD: 0.6017 cents 139:153:168:171:188:206:227:231:254:279 SD: 0.5730 cents 169:186:204:208:228:251:276:281:309:339 SD: 0.5536 cents 174:191:210:214:235:258:284:289:318:349 SD: 0.5268 cents 183:201:221:225:247:272:299:304:334:367 SD: 0.4464 cents 202:222:244:248:273:300:330:336:369:406 SD: 0.4374 cents 213:234:257:262:288:316:348:354:389:428 SD: 0.4142 cents 222:244:268:273:300:330:362:369:406:446 SD: 0.3935 cents 231:254:279:284:312:343:377:384:422:464 SD: 0.2183 cents 313:344:378:385:423:465:511:520:572:628 SD: 0.1777 cents 375:412:453:461:507:557:612:623:685:753 SD: 0.1583 cents 495:544:598:609:669:735:808:823:904:994 SD: 0.1531 cents 515:566:622:633:696:765:841:856:941:1034 SD: 0.1282 cents 544:598:657:669:735:808:888:904:994:1092 SD: 0.1080 cents