Scala analysis: xen18-erlich-dimipent-08
4L 4s MOS for Dimipent, L=197.49, s=101.67
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 101.670 cents 101.670000 2: 299.160 cents 299.160000 3: 400.830 cents 400.830000 4: 598.320 cents 598.320000 5: 699.990 cents 699.990000 6: 897.480 cents 897.480000 7: 999.150 cents 999.150000 8: 1196.640 cents 1196.640000
SHOW/INTERVAL
0: 197.4900 cents 197.4900 1: 101.6700 cents 101.6700 2: 197.4900 cents 197.4900 3: 101.6700 cents 101.6700 4: 197.4900 cents 197.4900 5: 101.6700 cents 101.6700 6: 197.4900 cents 197.4900 7: 101.6700 cents 101.6700 8: 197.4900 cents 197.4900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 101.67000 cents 1: 4 197.49000 cents 2: 8 299.16000 cents 3: 4 400.83000 cents 3: 4 496.65000 cents 4: 8 598.32000 cents 5: 4 699.99000 cents 5: 4 795.81000 cents 6: 8 897.48000 cents 7: 4 999.15000 cents 7: 4 1094.97000 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 : 101.7 299.2 400.8 598.3 700.0 897.5 999.1 1196.6 101.7 : 197.5 299.2 496.7 598.3 795.8 897.5 1095.0 1196.6 299.2 : 101.7 299.2 400.8 598.3 700.0 897.5 999.1 1196.6 400.8 : 197.5 299.2 496.7 598.3 795.8 897.5 1095.0 1196.6 598.3 : 101.7 299.2 400.8 598.3 700.0 897.5 999.1 1196.6 700.0 : 197.5 299.2 496.6 598.3 795.8 897.5 1095.0 1196.6 897.5 : 101.7 299.2 400.8 598.3 700.0 897.5 999.1 1196.6 999.1 : 197.5 299.2 496.7 598.3 795.8 897.5 1095.0 1196.6 1196.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.6700 .. 197.4900 cents 95.82000 cents 101.67000 cents 2: 299.1600 .. 299.1600 cents 1/1, 0.0000 cents 101.67000 cents 3: 400.8300 .. 496.6500 cents 95.82000 cents 101.67000 cents 4: 598.3200 .. 598.3200 cents 1/1, 0.0000 cents 101.67000 cents 5: 699.9900 .. 795.8100 cents 95.82000 cents 101.67000 cents 6: 897.4800 .. 897.4800 cents 1/1, 0.0000 cents 101.67000 cents 7: 999.1500 .. 1094.9700 cents 95.82000 cents 101.67000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 101.67000 cents, class 1 Average step (divided formal octave): 149.5800 cents Largest one step interval : 197.49000 cents Average / Smallest step : 1.471230 Largest / Average step : 1.320297 Largest / Smallest step : 1.942461 Median interval of one step : 149.58000 cents, amount: 0 Least squares average step : 145.82235 cents, oct.: 1166.57882 cents Scale is strictly proper Scale has 4 repeating blocks of 2 notes Blocks have Myhill's property chromas: 95.82000 cents and 5.85000 cents, ratio: 16.379487 generator: 1 of 101.67000 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 612-tone equal temperament with octave 1196.640 cents degrees: 52 153 205 306 358 459 511 612 Least number of segments generator : 307 of 600.275 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 407 of 795.805 cents and inv. generated superset size: 461 = 453 more = 5762.500% 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 101.67000 cents Scale diversity : 1.197326 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.679703 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 : 95.82000 cents Scale is a chain of 4 triads 0.0 699.990 897.480 cents Most common triad is 0.0 299.160 598.320 cents, amount: 8 Number of recognisable fifths : 4, average 699.9900 cents Number of recognisable fourths : 4, average 496.6500 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: 33.8775 c. M:-47.9100 c. 12: 1 2 1 2 1 2 1 2 SP B ME SD: 1.3789 c. M: 1.9500 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: 1.3332 c. M:-1.8854 c. 116: 10 19 10 19 10 19 10 19 SP B DE SD: 1.0526 c. M:-1.4886 c. 128: 11 21 11 21 11 21 11 21 SP B DE SD: 0.8247 c. M:-1.1663 c. 140: 12 23 12 23 12 23 12 23 SP B DE SD: 0.6358 c. M:-0.8991 c. 152: 13 25 13 25 13 25 13 25 SP B DE SD: 0.4767 c. M:-0.6742 c. 164: 14 27 14 27 14 27 14 27 SP B DE SD: 0.3410 c. M:-0.4822 c. 176: 15 29 15 29 15 29 15 29 SP B DE SD: 0.2237 c. M:-0.3164 c. 188: 16 31 16 31 16 31 16 31 SP B DE SD: 0.1214 c. M:-0.1717 c. 200: 17 33 17 33 17 33 17 33 SP B DE SD: 0.0314 c. M:-0.0444 c. 412: 35 68 35 68 35 68 35 68 SP B DE SD: 0.0097 c. M: 0.0137 c. 612: 52 101 52 101 52 101 52 101 SP B DE SD: 0.0037 c. M:-0.0053 c. 1024: 87 169 87 169 87 169 87 169 SP B DE SD: 0.0017 c. M: 0.0023 c. 1636: 139 270 139 270 139 270 139 270 SP B DE SD: 0.0004 c. M:-0.0005 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 3.3600 cents 2 x x x x 3 x x 4 S SD: 1.9462 cents 3 x x 4 x x 5 x 6 S SD: 32.7180 cents 4 x x 5 x 6 x 7:8 S SD: 8.4610 cents 5 x 6 x 7 x 8:9:10 S SD: 17.7702 cents 6 x 7:8 x 9:10:11:12 S SD: 19.1500 cents 7 x 8:9:10:11:12 x 14 S SD: 19.8967 cents 8 x x 10:11:12:13:14:16 S SD: 13.5382 cents 9:10:11 x 13 x 15:16:18 SD: 17.0826 cents 10:11:12:13:14:15:17:18:20 SD: 11.3094 cents 11:12:13:14:16 x 18:20:22 S SD: 13.2653 cents 12:13:14:15:17:18:20:21:24 SD: 7.6484 cents 15:16:18:19:21:22:25:27:30 SD: 6.3515 cents 16:17:19:20:23:24:27:28:32 SD: 5.7643 cents 20:21:24:25:28:30:34:36:40 SD: 5.3494 cents 22:23:26:28:31:33:37:39:44 SD: 4.1354 cents 30:32:36:38:42:45:50:53:60 SD: 4.0974 cents 31:33:37:39:44:46:52:55:62 SD: 2.8170 cents 32:34:38:40:45:48:54:57:64 SD: 2.4217 cents 46:49:55:58:65:69:77:82:92 SD: 1.8243 cents 54:57:64:68:76:81:91:96:108 SD: 1.7611 cents 63:67:75:79:89:94:106:112:126 SD: 1.7517 cents 65:69:77:82:92:97:109:116:130 SD: 1.4109 cents 68:72:81:86:96:102:114:121:136 SD: 1.1307 cents 84:89:100:106:119:126:141:150:168 SD: 1.0651 cents 96:102:114:121:136:144:161:171:192 SD: 0.9366 cents 100:106:119:126:141:150:168:178:200 SD: 0.7255 cents 150:159:178:189:212:225:252:267:299 SD: 0.5685 cents 165:175:196:208:233:247:277:294:329 SD: 0.3764 cents 196:208:233:247:277:294:329:349:391 SD: 0.3465 cents 233:247:277:294:329:349:391:415:465 SD: 0.3227 cents 249:264:296:314:352:373:418:443:497 SD: 0.2889 cents 265:281:315:334:374:397:445:472:529 SD: 0.2392 cents 281:298:334:354:397:421:472:500:561 SD: 0.2363 cents 349:370:415:440:493:523:586:622:697 SD: 0.2337 cents 361:383:429:455:510:541:606:643:721 SD: 0.1917 cents 446:473:530:562:630:668:749:794:890 SD: 0.1648 cents 499:529:593:629:705:748:838:889:996 SD: 0.1554 cents 514:545:611:648:726:770:863:915:1026 SD: 0.1344 cents 530:562:630:668:749:794:890:944:1058 SD: 0.0775 cents