Scala analysis: dialeastsquares
Least squares diatonic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 192.227 cents 192.227060 2: 309.537 cents 309.537140 3: 504.948 cents 504.947610 4: 695.052 cents 695.052390 5: 890.463 cents 890.462860 6: 1007.773 cents 1007.772940 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 192.2271 cents 192.2271 1: 192.2271 cents 192.2271 2: 117.3101 cents 117.3101 3: 195.4105 cents 195.4105 4: 190.1048 cents 190.1048 5: 195.4105 cents 195.4105 6: 117.3101 cents 117.3101 7: 192.2271 cents 192.2271
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 117.31008 cents 1: 1 190.10478 cents 1: 2 192.22706 cents 1: 2 195.41047 cents 2: 2 309.53714 cents 2: 2 312.72055 cents 2: 1 384.45412 cents 2: 2 385.51525 cents 3: 2 501.76420 cents 3: 2 502.82533 cents 3: 2 504.94761 cents 3: 1 580.92572 cents 4: 1 619.07428 cents 4: 2 695.05239 cents 4: 2 697.17467 cents 4: 2 698.23580 cents 5: 2 814.48475 cents 5: 1 815.54588 cents 5: 2 887.27945 cents 5: 2 890.46286 cents 6: 2 1004.58953 cents 6: 2 1007.77294 cents 6: 1 1009.89522 cents 6: 2 1082.68992 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 192.2 309.5 504.9 695.1 890.5 1007.8 1200.0 192.2 : 117.3 312.7 502.8 698.2 815.5 1007.8 1200.0 309.5 : 195.4 385.5 580.9 698.2 890.5 1082.7 1200.0 504.9 : 190.1 385.5 502.8 695.1 887.3 1004.6 1200.0 695.1 : 195.4 312.7 504.9 697.2 814.5 1009.9 1200.0 890.5 : 117.3 309.5 501.8 619.1 814.5 1004.6 1200.0 1007.8: 192.2 384.5 501.8 697.2 887.3 1082.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 117.3101 .. 195.4105 cents 78.10039 cents 117.31008 cents 2: 309.5371 .. 385.5152 cents 75.97811 cents 114.12667 cents 3: 501.7642 .. 580.9257 cents 79.16152 cents 116.24895 cents 4: 619.0743 .. 698.2358 cents 79.16152 cents 38.14856 cents 5: 814.4847 .. 890.4629 cents 75.97811 cents 116.24895 cents 6: 1004.5895 .. 1082.6899 cents 78.10039 cents 114.12667 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 117.31008 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 195.41047 cents Average / Smallest step : 1.461329 Largest / Average step : 1.139894 Largest / Smallest step : 1.665760 Median interval of one step : 192.22706 cents, amount: 2 Least squares average step : 171.46647 cents, oct.: 1200.26528 cents Scale is strictly proper Step pattern alph. order: ABCDCBA Step pattern size order : CADBDAC Scale is a Constant Structure, by a margin of 38.14856 cents Scale diversity : 1.300858 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.611267 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.06113 cents Number of recognisable fifths : 6, average 696.8210 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 7 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.5804 c. M: 33.3200 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 7.0883 c. M:-9.5371 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 19: 3 2 3 3 3 2 3 SP M ME I SD: 3.6556 c. M:-6.2523 c. Nineteen-tone Dorian 31: 5 3 5 5 5 3 5 SP M DE I SD: 1.1625 c. M:-1.7218 c. Intense Diatonic Phrygian, M.Dorian 81: 13 8 13 13 13 8 13 SP M DE I SD: 1.0900 c. M:-1.5740 c. 112: 18 11 18 18 18 11 18 SP M DE I SD: 1.0249 c. M:-1.3762 c. 143: 23 14 23 23 23 14 23 SP M DE I SD: 1.0171 c. M:-1.4511 c. 193: 31 19 31 31 31 19 31 SP M DE I SD: 1.0446 c. M:-1.3437 c. 205: 33 20 33 33 33 20 33 SP M DE I SD: 1.0337 c. M:-1.5330 c. 225: 36 22 37 35 37 22 36 SP I SD: 0.9332 c. M:-1.7191 c. 237: 38 23 39 37 39 23 38 SP I SD: 0.8277 c. M:-1.3815 c. 245: 39 24 40 39 40 24 39 SP I SD: 0.8616 c. M:-1.2067 c. 249: 40 24 41 39 41 24 40 SP I SD: 0.8738 c. M: 1.1034 c. 256: 41 25 42 40 42 25 41 SP I SD: 0.7018 c. M:-1.3024 c. 268: 43 26 44 42 44 26 43 SP I SD: 0.6504 c. M:-1.0225 c. 276: 44 27 45 44 45 27 44 SP I SD: 0.7405 c. M:-0.9227 c. 280: 45 27 46 44 46 27 45 SP I SD: 0.7402 c. M:-0.9657 c. 287: 46 28 47 45 47 28 46 SP I SD: 0.5292 c. M:-0.9757 c. 299: 48 29 49 47 49 29 48 SP I SD: 0.5275 c. M:-0.7380 c. 306: 49 30 50 48 50 30 49 SP I SD: 0.5209 c. M:-0.9347 c. 318: 51 31 52 50 52 31 51 SP I SD: 0.4034 c. M:-0.7128 c. 330: 53 32 54 52 54 32 53 SP I SD: 0.4492 c. M:-0.5069 c. 337: 54 33 55 53 55 33 54 SP I SD: 0.3946 c. M:-0.6904 c. 349: 56 34 57 55 57 34 56 SP I SD: 0.3196 c. M:-0.4965 c. 368: 59 36 60 58 60 36 59 SP I SD: 0.3045 c. M:-0.4872 c. 380: 61 37 62 60 62 37 61 SP I SD: 0.2763 c. M:-0.4045 c. 399: 64 39 65 63 65 39 64 SP I SD: 0.2510 c. M:-0.3155 c. 430: 69 42 70 68 70 42 69 SP I SD: 0.2337 c. M:-0.3311 c. 644: 103 63 105 102 105 63 103 SP I SD: 0.2000 c. M: 0.3016 c. 675: 108 66 110 107 110 66 108 SP I SD: 0.1661 c. M:-0.2271 c. 694: 111 68 113 110 113 68 111 SP I SD: 0.1611 c. M:-0.2962 c. 706: 113 69 115 112 115 69 113 SP I SD: 0.1495 c. M:-0.1887 c. 725: 116 71 118 115 118 71 116 SP I SD: 0.1377 c. M:-0.2271 c. 756: 121 74 123 120 123 74 121 SP I SD: 0.1325 c. M:-0.1857 c. 1012: 162 99 165 160 165 99 162 SP I SD: 0.1270 c. M:-0.1907 c. 1024: 164 100 167 162 167 100 164 SP I SD: 0.1132 c. M:-0.1621 c. 1043: 167 102 170 165 170 102 167 SP I SD: 0.0893 c. M:-0.1339 c. 1074: 172 105 175 170 175 105 172 SP I SD: 0.0545 c. M:-0.0803 c. 1105: 177 108 180 175 180 108 177 SP I SD: 0.0251 c. M:-0.0349 c. 1136: 182 111 185 180 185 111 182 SP I SD: 0.0235 c. M:-0.0301 c. 2241: 359 219 365 355 365 219 359 SP I SD: 0.0182 c. M: 0.0325 c. 2260: 362 221 368 358 368 221 362 SP I SD: 0.0141 c. M:-0.0204 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 3.4513 cents 3 x x 4 x 5 x 6 S SD: 3.0715 cents 4 x 5 x 6 x 7:8 S SD: 21.5916 cents 5 x 6:7 x 8:9:10 S SD: 21.9496 cents 6 x 7:8:9:10:11:12 S SD: 10.1142 cents 7:8 x 9:10:12:13:14 S SD: 22.5594 cents 8:9:10:11:12:13:14:16 S SD: 15.8045 cents 9:10:11:12:13:15:16:18 SD: 10.2685 cents 10:11:12:13:15:17:18:20 SD: 9.3573 cents 14:16:17:19:21:23:25:28 SD: 8.8212 cents 15:17:18:20:22:25:27:30 SD: 6.1298 cents 18:20:22:24:27:30:32:36 S SD: 6.0605 cents 20:22:24:27:30:33:36:40 S SD: 5.8696 cents 24:27:29:32:36:40:43:48 SD: 3.4973 cents 35:39:42:47:52:59:63:70 SD: 3.0789 cents 36:40:43:48:54:60:64:72 SD: 2.7452 cents 41:46:49:55:61:69:73:82 SD: 2.5213 cents 42:47:50:56:63:70:75:84 SD: 2.0884 cents 51:57:61:68:76:85:91:102 SD: 1.6501 cents 61:68:73:82:91:102:109:122 SD: 1.3274 cents 67:75:80:90:100:112:120:134 SD: 1.0750 cents 77:86:92:103:115:129:138:154 SD: 0.6112 cents 138:154:165:185:206:231:247:276 SD: 0.5662 cents 144:161:172:193:215:241:258:288 SD: 0.5478 cents 153:171:183:205:229:256:274:306 SD: 0.5340 cents 162:181:194:217:242:271:290:324 SD: 0.4022 cents 180:201:215:241:269:301:322:360 SD: 0.3607 cents 204:228:244:273:305:341:365:408 SD: 0.2675 cents 271:303:324:363:405:453:485:542 SD: 0.2673 cents 281:314:336:376:420:470:503:562 SD: 0.1534 cents 419:468:501:561:626:701:750:838 SD: 0.1393 cents 537:600:642:719:802:898:961:1074 SD: 0.1300 cents 561:627:671:751:838:938:1004:1122 SD: 0.1223 cents