Scala analysis: xen18-erlich-dimisept-08
4L 4s MOS for Dimisept, L=197.08, s=101.45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 101.450 cents 101.450000 2: 298.530 cents 298.530000 3: 399.980 cents 399.980000 4: 597.060 cents 597.060000 5: 698.510 cents 698.510000 6: 895.590 cents 895.590000 7: 997.040 cents 997.040000 8: 1194.120 cents 1194.120000
SHOW/INTERVAL
0: 197.0800 cents 197.0800 1: 101.4500 cents 101.4500 2: 197.0800 cents 197.0800 3: 101.4500 cents 101.4500 4: 197.0800 cents 197.0800 5: 101.4500 cents 101.4500 6: 197.0800 cents 197.0800 7: 101.4500 cents 101.4500 8: 197.0800 cents 197.0800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 101.45000 cents 1: 4 197.08000 cents 2: 8 298.53000 cents 3: 4 399.98000 cents 3: 4 495.61000 cents 4: 8 597.06000 cents 5: 4 698.51000 cents 5: 4 794.14000 cents 6: 8 895.59000 cents 7: 4 997.04000 cents 7: 4 1092.67000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.57143 = 11/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 101.5 298.5 400.0 597.1 698.5 895.6 997.0 1194.1 101.5 : 197.1 298.5 495.6 597.1 794.1 895.6 1092.7 1194.1 298.5 : 101.5 298.5 400.0 597.1 698.5 895.6 997.0 1194.1 400.0 : 197.1 298.5 495.6 597.1 794.1 895.6 1092.7 1194.1 597.1 : 101.5 298.5 400.0 597.1 698.5 895.6 997.0 1194.1 698.5 : 197.1 298.5 495.6 597.1 794.1 895.6 1092.7 1194.1 895.6 : 101.4 298.5 400.0 597.1 698.5 895.6 997.0 1194.1 997.0 : 197.1 298.5 495.6 597.1 794.1 895.6 1092.7 1194.1 1194.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.4500 .. 197.0800 cents 95.63000 cents 101.45000 cents 2: 298.5300 .. 298.5300 cents 1/1, 0.0000 cents 101.45000 cents 3: 399.9800 .. 495.6100 cents 95.63000 cents 101.45000 cents 4: 597.0600 .. 597.0600 cents 1/1, 0.0000 cents 101.45000 cents 5: 698.5100 .. 794.1400 cents 95.63000 cents 101.45000 cents 6: 895.5900 .. 895.5900 cents 1/1, 0.0000 cents 101.45000 cents 7: 997.0400 .. 1092.6700 cents 95.63000 cents 101.45000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 101.45000 cents, class 1 Average step (divided formal octave): 149.2650 cents Largest one step interval : 197.08000 cents Average / Smallest step : 1.471316 Largest / Average step : 1.320336 Largest / Smallest step : 1.942632 Median interval of one step : 149.26500 cents, amount: 0 Least squares average step : 145.51480 cents, oct.: 1164.11843 cents Scale is strictly proper Scale has 4 repeating blocks of 2 notes Blocks have Myhill's property chromas: 95.63000 cents and 5.82000 cents, ratio: 16.431271 generator: 1 of 101.45000 cents ET pair of linear temperament : 200&412 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1024-tone equal temperament with octave 1194.120 cents degrees: 87 256 343 512 599 768 855 1024 Least number of segments generator : 513 of 598.226 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 599 of 698.514 cents and inv. generated superset size: 770 = 762 more = 9625.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABAB Step pattern size order : SLSLSLSL Scale is a Constant Structure, by a margin of 101.45000 cents Scale diversity : 1.199307 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.679664 Rothenberg efficiency (ambiguous key): 1.000000 redundancy: 0.000000 Efficiency x scale size : 8.000000 Number of different interval sizes : 11 = 1.57143 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.57143 = 11/7 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 95.63000 cents Scale is a chain of 4 triads 0.0 698.510 895.590 cents Most common triad is 0.0 298.530 597.060 cents, amount: 8 Number of recognisable fifths : 4, average 698.5100 cents Number of recognisable fourths : 4, average 495.6100 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle Formal octave complements present : 4 = 50.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 2 4 6 Limited inverse transpositions : 1 3 5 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: 33.8103 c. M:-47.8150 c. 12: 1 2 1 2 1 2 1 2 SP B ME SD: 1.3718 c. M: 1.9400 c. Octatonic, Messiaen mode 2, Dominant Diminished, Diminished Blues, Half-Whole step scale 104: 9 17 9 17 9 17 9 17 SP B DE SD: 1.3345 c. M:-1.8873 c. 116: 10 19 10 19 10 19 10 19 SP B DE SD: 1.0546 c. M:-1.4914 c. 128: 11 21 11 21 11 21 11 21 SP B DE SD: 0.8271 c. M:-1.1697 c. 140: 12 23 12 23 12 23 12 23 SP B DE SD: 0.6386 c. M:-0.9031 c. 152: 13 25 13 25 13 25 13 25 SP B DE SD: 0.4799 c. M:-0.6787 c. 164: 14 27 14 27 14 27 14 27 SP B DE SD: 0.3444 c. M:-0.4871 c. 176: 15 29 15 29 15 29 15 29 SP B DE SD: 0.2274 c. M:-0.3216 c. 188: 16 31 16 31 16 31 16 31 SP B DE SD: 0.1253 c. M:-0.1772 c. 200: 17 33 17 33 17 33 17 33 SP B DE SD: 0.0355 c. M:-0.0502 c. 412: 35 68 35 68 35 68 35 68 SP B DE SD: 0.0055 c. M: 0.0078 c. 1024: 87 169 87 169 87 169 87 169 SP B DE SD: 0.0025 c. M:-0.0036 c. 1436: 122 237 122 237 122 237 122 237 SP B DE SD: 0.0002 c. M:-0.0003 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 5.8800 cents 2 x x x x 3 x x 4 S SD: 3.4074 cents 3 x x 4 x x 5 x 6 S SD: 32.9603 cents 4 x x 5 x 6 x 7:8 S SD: 8.0205 cents 5 x 6 x 7 x 8:9:10 S SD: 17.5155 cents 6 x 7:8 x 9:10:11:12 S SD: 19.3859 cents 7 x 8:9:10 x 12 x 14 S SD: 17.4702 cents 8 x x 10:11:12:13:14:16 S SD: 13.0740 cents 9:10:11 x 13 x 15:16:18 SD: 17.2151 cents 10:11:12:13:14:15:17:18:20 SD: 11.5144 cents 11:12:13:14 x 16:18:20:22 S SD: 13.2637 cents 12:13:14:15:17:18:20:21:24 SD: 7.4698 cents 15:16:18:19:21:22:25:27:30 SD: 6.2957 cents 16:17:19:20:23:24:27:28:32 SD: 5.7588 cents 20:21:24:25:28:30:34:36:40 SD: 5.5622 cents 22:23:26:28:31:33:37:39:44 SD: 4.1568 cents 27:29:32:34:38:40:45:48:54 SD: 4.0172 cents 30:32:36:38:42:45:50:53:60 SD: 3.9684 cents 31:33:37:39:44:46:52:55:62 SD: 2.7545 cents 32:34:38:40:45:48:54:57:64 SD: 2.5148 cents 46:49:55:58:65:69:77:82:92 SD: 2.0095 cents 49:52:58:62:69:73:82:87:98 SD: 1.9870 cents 53:56:63:67:75:79:89:94:106 SD: 1.7991 cents 63:67:75:79:89:94:106:112:126 SD: 1.7701 cents 65:69:77:82:92:97:109:116:130 SD: 1.5431 cents 68:72:81:86:96:102:114:121:136 SD: 1.3484 cents 80:85:95:101:113:120:134:142:159 SD: 1.1418 cents 85:90:101:107:120:127:143:151:169 SD: 1.0331 cents 99:105:118:125:140:148:166:176:197 SD: 1.0240 cents 100:106:119:126:141:150:168:178:199 SD: 0.7898 cents 112:119:133:141:158:168:188:199:223 SD: 0.7620 cents 127:135:151:160:179:190:213:226:253 SD: 0.6970 cents 131:139:156:165:185:196:220:233:261 SD: 0.5848 cents 149:158:177:188:210:223:250:265:297 SD: 0.4955 cents 165:175:196:208:233:247:277:293:329 SD: 0.4347 cents 185:196:220:233:261:277:310:329:369 SD: 0.4214 cents 235:249:279:296:332:352:394:418:468 SD: 0.3809 cents 250:265:297:315:353:374:419:445:498 SD: 0.3284 cents 281:298:334:354:397:421:471:500:560 SD: 0.3131 cents 282:299:335:355:398:422:473:502:562 SD: 0.2766 cents 330:350:392:416:466:494:554:587:658 SD: 0.2364 cents 350:371:416:441:494:524:587:623:698 SD: 0.2292 cents 362:384:430:456:511:542:607:644:722 SD: 0.2084 cents 415:440:493:523:586:621:696:738:827 SD: 0.1531 cents 447:474:531:563:631:669:750:795:891 SD: 0.1175 cents