Scala analysis: xen18-ayers-table-35
7 Generalized Root Mean Squares between 1 and 2.5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 198.289 cents 198.289000 2: 396.578 cents 396.578000 3: 594.868 cents 594.868000 4: 793.157 cents 793.157000 5: 991.446 cents 991.446000 6: 1189.740 cents 1189.740000 7: 1388.020 cents 1388.020000 8: 1586.310 cents 1586.310000
SHOW/INTERVAL
0: 198.2900 cents 198.2900 1: 198.2890 cents 198.2890 2: 198.2890 cents 198.2890 3: 198.2900 cents 198.2900 4: 198.2890 cents 198.2890 5: 198.2890 cents 198.2890 6: 198.2940 cents 198.2940 7: 198.2800 cents 198.2800 8: 198.2900 cents 198.2900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 198.28000 cents 1: 4 198.28900 cents 1: 2 198.29000 cents 1: 1 198.29400 cents 2: 1 396.57000 cents 2: 1 396.57400 cents 2: 2 396.57800 cents 2: 3 396.57900 cents 2: 1 396.58300 cents 3: 1 594.85900 cents 3: 1 594.86300 cents 3: 1 594.86400 cents 3: 4 594.86800 cents 3: 1 594.87200 cents 4: 1 793.14800 cents 4: 1 793.15200 cents 4: 2 793.15300 cents 4: 2 793.15700 cents 4: 1 793.15800 cents 4: 1 793.16200 cents 5: 1 991.43800 cents 5: 4 991.44200 cents 5: 1 991.44600 cents 5: 1 991.44700 cents 5: 1 991.45100 cents 6: 1 1189.72700 cents 6: 3 1189.73100 cents 6: 2 1189.73200 cents 6: 1 1189.73600 cents 6: 1 1189.74000 cents 7: 1 1388.01600 cents 7: 2 1388.02000 cents 7: 4 1388.02100 cents 7: 1 1388.03000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.85714 = 34/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 198.3 396.6 594.9 793.2 991.4 1189.7 1388.0 1586.3 198.3 : 198.3 396.6 594.9 793.2 991.5 1189.7 1388.0 1586.3 396.6 : 198.3 396.6 594.9 793.2 991.4 1189.7 1388.0 1586.3 594.9 : 198.3 396.6 594.9 793.2 991.4 1189.7 1388.0 1586.3 793.2 : 198.3 396.6 594.9 793.2 991.4 1189.7 1388.0 1586.3 991.4 : 198.3 396.6 594.9 793.2 991.4 1189.7 1388.0 1586.3 1189.7: 198.3 396.6 594.9 793.1 991.4 1189.7 1388.0 1586.3 1388.0: 198.3 396.6 594.9 793.2 991.4 1189.7 1388.0 1586.3 1586.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 198.2800 .. 198.2940 cents 0.01400 cents 198.28000 cents 2: 396.5700 .. 396.5830 cents 0.01300 cents 198.27600 cents 3: 594.8590 .. 594.8720 cents 0.01300 cents 198.27600 cents 4: 793.1480 .. 793.1620 cents 0.01400 cents 198.27600 cents 5: 991.4380 .. 991.4510 cents 0.01300 cents 198.27600 cents 6: 1189.7270 .. 1189.7400 cents 0.01300 cents 198.27600 cents 7: 1388.0160 .. 1388.0300 cents 0.01400 cents 198.27600 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 198.28000 cents, class 1 Average step (divided formal octave): 198.2887 cents Largest one step interval : 198.29400 cents Average / Smallest step : 1.000044 Largest / Average step : 1.000026 Largest / Smallest step : 1.000071 Median interval of one step : 198.28900 cents, amount: 4 Most common interval of one step : 198.28900 cents, amount: 4 Least squares average step : 198.28905 cents, oct.: 1586.31243 cents Scale is strictly proper Step pattern alph. order: AABAACDB Step pattern size order : BBCBBDAC Scale is a Constant Structure, by a margin of 198.27600 cents Scale diversity : 0.564620 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.999941 Rothenberg efficiency : 0.366518 redundancy: 0.633482 Efficiency x scale size : 2.932143 Number of different interval sizes : 34 = 4.85714 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.85714 = 34/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 0.00100 cents Most common triad is 0.0 991.442 1388.021 cents, amount: 3 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 12.5000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 1 2 3 4 5 6 7 Limited inverse transpositions : 1 2 3 4 5 6 7 Inversional symmetry on degrees : 0 1 2 3 4 5 6 7 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0030 c. M: 0.0075 c.
FIT/HARMONIC
1 x x x x x 2 x x S SD: 10.2600 cents 2 x x x 3 x 4 x 5 S SD: 30.5924 cents 3 x x 4:5 x 6:7 x S SD: 38.7421 cents 4 x 5 x 6:7:8:9:10 S SD: 16.0663 cents 5 x 6:7:8:9:10:11:12 S SD: 16.5602 cents 6:7 x 8:10:11:12:13:15 SD: 24.0325 cents 7:8:9:10:11:12:14:16:17 S SD: 13.1553 cents 8:9:10:11:13:14:16:18:20 SD: 8.9678 cents 12:13:15:17:19:21:24:27:30 SD: 8.4896 cents 14:16:18:20:22:25:28:31:35 SD: 7.4864 cents 15:17:19:21:24:27:30:33:37 SD: 6.7682 cents 16:18:20:23:25:28:32:36:40 SD: 6.3045 cents 17:19:21:24:27:30:34:38:42 SD: 5.0849 cents 22:25:28:31:35:39:44:49:55 SD: 4.3143 cents 24:27:30:34:38:43:48:54:60 SD: 3.7392 cents 26:29:33:37:41:46:52:58:65 SD: 3.4061 cents 31:35:39:44:49:55:62:69:77 SD: 2.8256 cents 34:38:43:48:54:60:68:76:85 SD: 2.4660 cents 43:48:54:61:68:76:85:96:107 SD: 2.4282 cents 48:54:60:68:76:85:95:107:120 SD: 2.0742 cents 56:63:70:79:89:99:111:125:140 SD: 2.0706 cents 57:64:72:80:90:101:113:127:142 SD: 1.7730 cents 58:65:73:82:92:103:115:129:145 SD: 1.2675 cents 66:74:83:93:104:117:131:147:165 SD: 0.8625 cents 74:83:93:104:117:131:147:165:185 SD: 0.8176 cents 98:110:123:138:155:174:195:218:245 SD: 0.8047 cents 100:112:126:141:158:177:199:223:250 SD: 0.6820 cents 124:139:156:175:196:220:247:276:310 SD: 0.6095 cents 132:148:166:186:209:234:262:294:330 SD: 0.5382 cents 148:166:186:209:234:262:294:330:370 SD: 0.5204 cents 156:175:196:220:247:277:310:348:390 SD: 0.5105 cents 182:204:229:257:288:323:362:406:455 SD: 0.4758 cents 190:213:239:268:300:337:378:424:475 SD: 0.4183 cents 198:222:249:279:313:351:394:441:495 SD: 0.3234 cents 222:249:279:313:351:394:441:495:555 SD: 0.3124 cents 248:278:312:350:392:440:493:553:620 SD: 0.2872 cents 256:287:322:361:405:454:509:571:640 SD: 0.1864 cents 322:361:405:454:509:571:640:718:805 SD: 0.1231 cents 520:583:654:733:822:922:1034:1159:1300 SD: 0.1199 cents 568:637:714:801:898:1007:1129:1266:1420 SD: 0.1126 cents