Scala analysis: met24-xenonajdi6_Fup
Curious hexatonic like Najdi (17: 3 3 2 2 3 2 2), 3 3 2 3 3 3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 207.422 cents 207.421870 2: 438.281 cents 438.281250 3: 564.844 cents 564.843750 4: 772.266 cents 772.265620 5: 992.578 cents 992.578120 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 207.4219 cents 207.4219 1: 207.4219 cents 207.4219 2: 230.8594 cents 230.8594 3: 126.5625 cents 126.5625 4: 207.4219 cents 207.4219 5: 220.3125 cents 220.3125 6: 207.4219 cents 207.4219
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 126.56250 cents 1: 3 207.42187 cents 1: 1 220.31250 cents 1: 1 230.85938 cents 2: 1 333.98437 cents 2: 1 357.42188 cents 2: 1 414.84375 cents 2: 2 427.73437 cents 2: 1 438.28125 cents 3: 1 554.29687 cents 3: 2 564.84375 cents 3: 2 635.15625 cents 3: 1 645.70313 cents 4: 1 761.71875 cents 4: 2 772.26562 cents 4: 1 785.15625 cents 4: 1 842.57812 cents 4: 1 866.01563 cents 5: 1 969.14062 cents 5: 1 979.68750 cents 5: 3 992.57812 cents 5: 1 1073.43750 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.40000 = 22/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 207.4 438.3 564.8 772.3 992.6 1200.0 207.4 : 230.9 357.4 564.8 785.2 992.6 1200.0 438.3 : 126.6 334.0 554.3 761.7 969.1 1200.0 564.8 : 207.4 427.7 635.2 842.6 1073.4 1200.0 772.3 : 220.3 427.7 635.2 866.0 992.6 1200.0 992.6 : 207.4 414.8 645.7 772.3 979.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.5625 .. 230.8594 cents 104.29688 cents 126.56250 cents 2: 333.9844 .. 438.2813 cents 104.29688 cents 103.12499 cents 3: 554.2969 .. 645.7031 cents 91.40626 cents 116.01562 cents 4: 761.7188 .. 866.0156 cents 104.29688 cents 116.01562 cents 5: 969.1406 .. 1073.4375 cents 104.29688 cents 103.12499 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 126.56250 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 230.85938 cents Average / Smallest step : 1.580247 Largest / Average step : 1.154297 Largest / Smallest step : 1.824074 Median interval of one step : 207.42187 cents, amount: 3 Most common interval of one step : 207.42187 cents, amount: 3 Least squares average step : 198.13702 cents, oct.: 1188.82211 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 177 374 482 659 847 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 721 of 844.922 cents and inv. generated superset size: 173 = 167 more = 2883.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCADA Step pattern size order : BDABCB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 103.12499 cents Scale diversity : 1.449438 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.576172 Rothenberg efficiency : 0.427778 redundancy: 0.572222 Efficiency x scale size : 2.566667 Number of different interval sizes : 22 = 4.40000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.40000 = 22/5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 10.54687 cents Most common intervals : 207.42187 cents & inv., amount: 3 Number of recognisable fifths : 0 Formal octave complements present : 3 = 50.0000% Limited inverse transpositions with margin 104.2969 cents: 5 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 24.4294 c. M: 38.2813 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 11: 2 2 1 2 2 2 SP M ME SD: 10.6898 c. M: 19.3892 c. Machine-6 17: 3 3 2 3 3 3 SP M ME SD: 6.7458 c. M: 14.7518 c. Machine-6 28: 5 5 3 5 5 5 SP M DE SD: 6.4357 c. M: 9.7098 c. Machine-6 36: 6 7 4 6 7 6 SP SD: 5.3123 c. M:-7.4219 c. 40: 7 8 4 7 7 7 SP SD: 6.2853 c. M:-11.7188 c. 41: 7 8 4 7 8 7 SP SD: 6.0202 c. M: 11.2900 c. 46: 8 9 5 8 8 8 SP SD: 6.0482 c. M:-10.3431 c. 47: 8 9 5 8 9 8 SP SD: 3.8228 c. M: 6.3082 c. 58: 10 11 6 10 11 10 SP SD: 4.0671 c. M: 6.7484 c. 64: 11 12 7 11 12 11 SP SD: 3.4166 c. M: 7.0313 c. 68: 12 13 7 12 12 12 SP SD: 3.2610 c. M:-4.3428 c. 70: 12 14 7 12 13 12 SP SD: 3.2285 c. M:-7.4330 c. 75: 13 14 8 13 14 13 SP SD: 3.6919 c. M: 6.2812 c. 76: 13 15 8 13 14 13 SP SD: 2.5414 c. M:-3.8240 c. 87: 15 17 9 15 16 15 SP SD: 1.3308 c. M:-3.0981 c. 93: 16 18 10 16 17 16 SP SD: 1.5375 c. M:-2.8982 c. 98: 17 19 10 17 18 17 SP SD: 1.3365 c. M:-2.5351 c. 104: 18 20 11 18 19 18 SP SD: 0.4339 c. M:-0.8113 c. 219: 38 42 23 38 40 38 SP SD: 0.5168 c. M:-0.7973 c. 255: 44 49 27 44 47 44 SP SD: 0.3949 c. M: 0.6342 c. 323: 56 62 34 56 59 56 SP SD: 0.4201 c. M:-0.6277 c. 342: 59 66 36 59 63 59 SP SD: 0.3011 c. M:-0.4043 c. 359: 62 69 38 62 66 62 SP SD: 0.2005 c. M: 0.3982 c. 446: 77 86 47 77 82 77 SP SD: 0.1996 c. M:-0.2838 c. 457: 79 88 48 79 84 79 SP SD: 0.1891 c. M: 0.2923 c. 463: 80 89 49 80 85 80 SP SD: 0.1414 c. M: 0.2683 c. 550: 95 106 58 95 101 95 SP SD: 0.1756 c. M:-0.2642 c. 561: 97 108 59 97 103 97 SP SD: 0.1167 c. M:-0.2214 c. 578: 100 111 61 100 106 100 SP SD: 0.1540 c. M: 0.2190 c. 665: 115 128 70 115 122 115 SP SD: 0.1082 c. M:-0.2150 c. 682: 118 131 72 118 125 118 SP SD: 0.1510 c. M:-0.2028 c. 769: 133 148 81 133 141 133 SP SD: 0.1310 c. M:-0.2103 c. 816: 141 157 86 141 150 141 SP SD: 0.1106 c. M: 0.2068 c. 909: 157 175 96 157 167 157 SP SD: 0.1168 c. M:-0.1728 c. 920: 159 177 97 159 169 159 SP SD: 0.0490 c. M: 0.0917 c. 1024: 177 197 108 177 188 177 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 35.1553 cents 3 x 4 x x 5:6 S SD: 41.2083 cents 4 x 5 x 6:7:8 S SD: 22.6500 cents 5:6 x 7:8:9:10 S SD: 23.9710 cents 6:7:8 x 9:11:12 SD: 24.7176 cents 7:8:9:10:11:12:14 S SD: 13.9289 cents 9:10:12 x 14:16:18 S SD: 13.0598 cents 10:11:13:14:16:18:20 SD: 11.4344 cents 13:15:17:18:20:23:26 SD: 9.1832 cents 14:16:18:19:22:25:28 SD: 7.6598 cents 16:18:21:22:25:28:32 SD: 7.1020 cents 18:20:23:25:28:32:36 SD: 5.0026 cents 21:24:27:29:33:37:42 SD: 4.8873 cents 23:26:30:32:36:41:46 SD: 4.1531 cents 31:35:40:43:48:55:62 SD: 2.6581 cents 39:44:50:54:61:69:78 SD: 1.6520 cents 55:62:71:76:86:98:110 SD: 1.6411 cents 62:70:80:86:97:110:124 SD: 0.8431 cents 80:90:103:111:125:142:160 SD: 0.7135 cents 101:114:130:140:158:179:202 SD: 0.6657 cents 125:141:161:173:195:222:250 SD: 0.6493 cents 132:149:170:183:206:234:264 SD: 0.5514 cents 142:160:183:197:222:252:284 SD: 0.4436 cents 181:204:233:251:283:321:362 SD: 0.3880 cents 205:231:264:284:320:364:410 SD: 0.3587 cents 212:239:273:294:331:376:424 SD: 0.2911 cents 267:301:344:370:417:474:534 SD: 0.2045 cents 306:345:394:424:478:543:612 SD: 0.1385 cents 368:415:474:510:575:653:736 SD: 0.1358 cents 448:505:577:621:700:795:896 SD: 0.1216 cents