Scala analysis: xen18-erlich-miracle-10
1L 9s MOS for Miracle, L=150.15, s=116.72
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.720 cents 116.720000 2: 233.440 cents 233.440000 3: 350.160 cents 350.160000 4: 466.880 cents 466.880000 5: 617.030 cents 617.030000 6: 733.750 cents 733.750000 7: 850.470 cents 850.470000 8: 967.190 cents 967.190000 9: 1083.910 cents 1083.910000 10: 1200.630 cents 1200.630000
SHOW/INTERVAL
0: 116.7200 cents 116.7200 1: 116.7200 cents 116.7200 2: 116.7200 cents 116.7200 3: 116.7200 cents 116.7200 4: 116.7200 cents 116.7200 5: 150.1500 cents 150.1500 6: 116.7200 cents 116.7200 7: 116.7200 cents 116.7200 8: 116.7200 cents 116.7200 9: 116.7200 cents 116.7200 10: 116.7200 cents 116.7200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 116.72000 cents 1: 1 150.15000 cents 2: 8 233.44000 cents 2: 2 266.87000 cents 3: 7 350.16000 cents 3: 3 383.59000 cents 4: 6 466.88000 cents 4: 4 500.31000 cents 5: 5 583.60000 cents 5: 5 617.03000 cents 6: 4 700.32000 cents 6: 6 733.75000 cents 7: 3 817.04000 cents 7: 7 850.47000 cents 8: 2 933.76000 cents 8: 8 967.19000 cents 9: 1 1050.48000 cents 9: 9 1083.91000 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 10 0.0 : 116.7 233.4 350.2 466.9 617.0 733.7 850.5 967.2 1083.9 1200.6 116.7 : 116.7 233.4 350.2 500.3 617.0 733.7 850.5 967.2 1083.9 1200.6 233.4 : 116.7 233.4 383.6 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 350.2 : 116.7 266.9 383.6 500.3 617.0 733.8 850.5 967.2 1083.9 1200.6 466.9 : 150.1 266.9 383.6 500.3 617.0 733.7 850.5 967.2 1083.9 1200.6 617.0 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 933.8 1050.5 1200.6 733.7 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 933.8 1083.9 1200.6 850.5 : 116.7 233.4 350.2 466.9 583.6 700.3 817.0 967.2 1083.9 1200.6 967.2 : 116.7 233.4 350.2 466.9 583.6 700.3 850.5 967.2 1083.9 1200.6 1083.9: 116.7 233.4 350.2 466.9 583.6 733.7 850.5 967.2 1083.9 1200.6 1200.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.7200 .. 150.1500 cents 33.43000 cents 116.72000 cents 2: 233.4400 .. 266.8700 cents 33.43000 cents 83.29000 cents 3: 350.1600 .. 383.5900 cents 33.43000 cents 83.29000 cents 4: 466.8800 .. 500.3100 cents 33.43000 cents 83.29000 cents 5: 583.6000 .. 617.0300 cents 33.43000 cents 83.29000 cents 6: 700.3200 .. 733.7500 cents 33.43000 cents 83.29000 cents 7: 817.0400 .. 850.4700 cents 33.43000 cents 83.29000 cents 8: 933.7600 .. 967.1900 cents 33.43000 cents 83.29000 cents 9: 1050.4800 .. 1083.9100 cents 33.43000 cents 83.29000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 116.72000 cents, class 1 Average step (divided formal octave): 120.0630 cents Largest one step interval : 150.15000 cents Average / Smallest step : 1.028641 Largest / Average step : 1.250593 Largest / Smallest step : 1.286412 Median interval of one step : 116.72000 cents, amount: 9 Most common interval of one step : 116.72000 cents, amount: 9 Least squares average step : 120.62740 cents, oct.: 1206.27403 cents Scale is strictly proper Scale has Myhill's property chromas: 33.43000 cents and 83.29000 cents, ratio: 2.491475 generators: 1 of 116.72000 cents and 9 of 1083.91000 cents ET pair of linear temperament : 10&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1831-tone equal temperament with octave 1200.630 cents degrees: 178 356 534 712 941 1119 1297 1475 1653 1831 generators: 178 and 1653 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAAA Step pattern size order : SSSSLSSSSS Scale is a Constant Structure, by a margin of 83.29000 cents Scale diversity : 1.190566 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.749407 Rothenberg efficiency : 0.733333 redundancy: 0.266667 Efficiency x scale size : 7.333333 Number of different interval sizes : 18 = 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 : 33.43000 cents Most common intervals : 116.72000 cents & inv., amount: 9 Scale is a chain of 5 triads 0.0 466.880 1083.910 cents Number of recognisable fifths : 4, average 700.3200 cents Number of recognisable fourths : 4, average 500.3100 cents Scale contains two identical disjunct pentachords Best major thirds form a closed circle Formal octave complements present : 9 = 90.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 9-10 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.7464 c. M: 16.7150 c. 21: 2 2 2 2 3 2 2 2 2 2 SP M ME SD: 6.9222 c. M:-11.8714 c. 31: 3 3 3 3 4 3 3 3 3 3 SP M ME SD: 1.5452 c. M:-2.6500 c. 41: 4 4 4 4 5 4 4 4 4 4 SP M ME SD: 1.2089 c. M: 2.0732 c. 72: 7 7 7 7 9 7 7 7 7 7 SP M DE SD: 0.0231 c. M: 0.0396 c. 1111: 108 108 108 108 139 108 108 108 108 108 SP M DE SD: 0.0207 c. M:-0.0355 c. 1183: 115 115 115 115 148 115 115 115 115 115 SP M DE SD: 0.0180 c. M:-0.0309 c. 1255: 122 122 122 122 157 122 122 122 122 122 SP M DE SD: 0.0157 c. M:-0.0269 c. 1327: 129 129 129 129 166 129 129 129 129 129 SP M DE SD: 0.0136 c. M:-0.0232 c. 1399: 136 136 136 136 175 136 136 136 136 136 SP M DE SD: 0.0117 c. M:-0.0200 c. 1471: 143 143 143 143 184 143 143 143 143 143 SP M DE SD: 0.0100 c. M:-0.0171 c. 1543: 150 150 150 150 193 150 150 150 150 150 SP M DE SD: 0.0084 c. M:-0.0145 c. 1615: 157 157 157 157 202 157 157 157 157 157 SP M DE SD: 0.0070 c. M:-0.0120 c. 1687: 164 164 164 164 211 164 164 164 164 164 SP M DE SD: 0.0057 c. M:-0.0098 c. 1759: 171 171 171 171 220 171 171 171 171 171 SP M DE SD: 0.0046 c. M:-0.0078 c. 1831: 178 178 178 178 229 178 178 178 178 178 SP M DE SD: 0.0035 c. M:-0.0060 c. 1903: 185 185 185 185 238 185 185 185 185 185 SP M DE SD: 0.0025 c. M:-0.0042 c. 1975: 192 192 192 192 247 192 192 192 192 192 SP M DE SD: 0.0015 c. M:-0.0026 c. 2047: 199 199 199 199 256 199 199 199 199 199 SP M DE SD: 0.0007 c. M:-0.0011 c. 2119: 206 206 206 206 265 206 206 206 206 206 SP M DE SD: 0.0001 c. M: 0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.6300 cents 2 x x x x x 3 x x x 4 S SD: 15.9006 cents 3 x x x 4 x x 5 x x 6 S SD: 15.3482 cents 4 x x 5 x x 6 x 7 x 8 S SD: 12.0444 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 15.8458 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 12.2951 cents 7 x 8 x 9:10:11 x 12:13:14 S SD: 9.7956 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 10.9180 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 9.4387 cents 10:11 x 12:13:14:15:16:17:19:20 SD: 11.2989 cents 11:12:13 x 14:16:17:18:19:21:22 SD: 11.0024 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 8.6176 cents 13:14:15:16:17:19:20:21:23:24:26 SD: 5.9243 cents 19:20:22:23:25:27:29:31:33:36:38 SD: 4.8599 cents 23:25:26:28:30:33:35:38:40:43:46 SD: 4.3588 cents 26:28:30:32:34:37:40:42:45:49:52 SD: 3.8789 cents 27:29:31:33:35:39:41:44:47:51:54 SD: 3.5643 cents 28:30:32:34:37:40:43:46:49:52:56 SD: 2.7692 cents 39:42:45:48:51:56:60:64:68:73:78 SD: 2.7151 cents 40:43:46:49:52:57:61:65:70:75:80 SD: 2.1271 cents 44:47:50:54:58:63:67:72:77:82:88 SD: 2.0008 cents 49:52:56:60:64:70:75:80:86:92:98 SD: 1.7921 cents 55:59:63:67:72:79:84:90:96:103:110 SD: 1.4644 cents 61:65:70:75:80:87:93:100:107:114:122 SD: 1.4611 cents 68:73:78:83:89:97:104:111:119:127:136 SD: 1.0097 cents 84:90:96:103:110:120:128:137:147:157:168 SD: 0.7675 cents 103:110:118:126:135:147:157:168:180:193:206 SD: 0.7550 cents 112:120:128:137:147:160:171:183:196:209:224 SD: 0.7046 cents 116:124:133:142:152:166:177:190:203:217:232 SD: 0.6922 cents 117:125:134:143:153:167:179:191:205:219:234 SD: 0.6905 cents 129:138:148:158:169:184:197:211:226:241:258 SD: 0.6713 cents 131:140:150:160:172:187:200:214:229:245:262 SD: 0.6593 cents 146:156:167:179:191:209:223:239:255:273:292 SD: 0.6510 cents 152:163:174:186:199:217:232:248:266:284:304 SD: 0.6085 cents 159:170:182:195:208:227:243:260:278:297:318 SD: 0.4598 cents 187:200:214:229:245:267:286:306:327:350:374 SD: 0.3365 cents 214:229:245:262:280:306:327:350:374:400:428 SD: 0.3318 cents 255:273:292:312:334:364:390:417:446:477:510 SD: 0.3176 cents 262:280:300:321:343:374:400:428:458:490:524 SD: 0.3109 cents 271:290:310:332:355:387:414:443:474:507:542 SD: 0.2045 cents 388:415:444:475:508:554:593:634:678:726:776 SD: 0.1659 cents 472:505:540:578:618:674:721:771:825:883:944 SD: 0.1592 cents 500:535:572:612:655:714:764:817:874:935:1000 SD: 0.1307 cents 588:629:673:720:770:840:898:961:1028:1100:1176 SD: 0.1244 cents