Scala analysis: O3-quasi-meso-iph7_Cs
Disjunct tetrachords ~1/1-56/51-26/21-4/3 a bit like Dudon's meso-iph7.scl
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 161.719 cents 161.718750 2: 369.141 cents 369.140620 3: 495.703 cents 495.703130 4: 704.297 cents 704.296870 5: 866.016 cents 866.015630 6: 1073.438 cents 1073.437500 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 126.5625 cents 126.5625 1: 161.7187 cents 161.7187 2: 207.4219 cents 207.4219 3: 126.5625 cents 126.5625 4: 208.5937 cents 208.5937 5: 161.7188 cents 161.7188 6: 207.4219 cents 207.4219 7: 126.5625 cents 126.5625
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 126.56251 cents 1: 2 161.71875 cents 1: 2 207.42187 cents 1: 1 208.59374 cents 2: 1 288.28125 cents 2: 2 333.98438 cents 2: 1 335.15625 cents 2: 2 369.14062 cents 2: 1 370.31250 cents 3: 4 495.70313 cents 3: 1 496.87501 cents 3: 1 542.57812 cents 3: 1 577.73437 cents 4: 1 622.26563 cents 4: 1 657.42188 cents 4: 1 703.12499 cents 4: 4 704.29687 cents 5: 1 829.68750 cents 5: 2 830.85938 cents 5: 1 864.84375 cents 5: 2 866.01563 cents 5: 1 911.71875 cents 6: 1 991.40626 cents 6: 2 992.57813 cents 6: 2 1038.28125 cents 6: 2 1073.43750 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 161.7 369.1 495.7 704.3 866.0 1073.4 1200.0 161.7 : 207.4 334.0 542.6 704.3 911.7 1038.3 1200.0 369.1 : 126.6 335.2 496.9 704.3 830.9 992.6 1200.0 495.7 : 208.6 370.3 577.7 704.3 866.0 1073.4 1200.0 704.3 : 161.7 369.1 495.7 657.4 864.8 991.4 1200.0 866.0 : 207.4 334.0 495.7 703.1 829.7 1038.3 1200.0 1073.4: 126.6 288.3 495.7 622.3 830.9 992.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.5625 .. 208.5937 cents 82.03123 cents 126.56251 cents 2: 288.2812 .. 370.3125 cents 82.03125 cents 79.68751 cents 3: 495.7031 .. 577.7344 cents 82.03124 cents 125.39063 cents 4: 622.2656 .. 704.2969 cents 82.03124 cents 44.53126 cents 5: 829.6875 .. 911.7188 cents 82.03125 cents 125.39063 cents 6: 991.4063 .. 1073.4375 cents 82.03124 cents 79.68751 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 126.56250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 208.59374 cents Average / Smallest step : 1.354497 Largest / Average step : 1.216797 Largest / Smallest step : 1.648148 Median interval of one step : 161.71875 cents, amount: 2 Least squares average step : 174.10714 cents, oct.: 1218.75000 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 138 315 423 601 739 916 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 565 of 662.109 cents and inv. generated superset size: 116 = 109 more = 1657.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDABC Step pattern size order : BCADBCA Scale is a Constant Structure, by a margin of 44.53126 cents Scale diversity : 1.381264 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.589844 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17187 cents Most common intervals : 495.70313 cents & inv., amount: 4 Number of recognisable fifths : 5, average 704.0625 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 22.5750 c. M: 44.8661 c. Lebeng 10: 1 2 1 2 1 2 1 P M ME I SD: 20.8294 c. M: 41.7187 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 24.8285 c. M:-38.2813 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 14: 2 2 2 2 2 3 1 P T3 SD: 21.4577 c. M:-40.8482 c. 15: 2 3 1 3 2 2 2 SP D3 S SD: 19.8640 c. M: 33.4375 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 13.4290 c. M: 20.5423 c. Neutral Dorian, Maqamic-7 22: 3 4 2 4 3 4 2 P T3 SD: 8.9496 c. M:-17.4716 c. Raga Jogiya 29: 4 5 3 5 4 5 3 SP T3 SD: 2.4250 c. M:-3.7985 c. 68: 9 12 7 12 9 12 7 SP T3 SD: 1.9428 c. M:-3.0331 c. Tiby 4th Byzantine Liturgical mode 75: 10 13 8 13 10 13 8 SP T3 SD: 1.2283 c. M: 2.0156 c. 104: 14 18 11 18 14 18 11 SP T3 SD: 0.3732 c. M: 0.6310 c. 237: 32 41 25 41 32 41 25 SP T3 SD: 0.3506 c. M: 0.4994 c. 341: 46 59 36 59 46 59 36 SP T3 SD: 0.3266 c. M:-0.4846 c. 445: 60 77 47 77 60 77 47 SP T3 SD: 0.3250 c. M:-0.4766 c. 511: 69 88 54 89 69 88 54 SP SD: 0.3207 c. M:-0.5206 c. 513: 69 89 54 89 69 89 54 SP T3 SD: 0.3194 c. M: 0.5186 c. 540: 73 93 57 94 73 93 57 SP SD: 0.3370 c. M:-0.6510 c. 542: 73 94 57 94 73 94 57 SP T3 SD: 0.3221 c. M:-0.6011 c. 549: 74 95 58 95 74 95 58 SP T3 SD: 0.3281 c. M:-0.4717 c. 550: 74 95 58 96 74 95 58 SP SD: 0.3021 c. M: 0.4304 c. 579: 78 100 61 101 78 100 61 SP SD: 0.2498 c. M: 0.3663 c. 608: 82 105 64 106 82 105 64 SP SD: 0.2554 c. M:-0.4317 c. 615: 83 106 65 107 83 106 65 SP SD: 0.2325 c. M: 0.3601 c. 654: 88 113 69 114 88 113 69 SP SD: 0.2223 c. M: 0.3333 c. 683: 92 118 72 119 92 118 72 SP SD: 0.1631 c. M:-0.2419 c. 712: 96 123 75 124 96 123 75 SP SD: 0.1636 c. M:-0.2765 c. 758: 102 131 80 132 102 131 80 SP SD: 0.1754 c. M: 0.2752 c. 787: 106 136 83 137 106 136 83 SP SD: 0.1056 c. M: 0.1504 c. 816: 110 141 86 142 110 141 86 SP SD: 0.0951 c. M:-0.1608 c. 891: 120 154 94 155 120 154 94 SP SD: 0.0746 c. M: 0.1171 c. 920: 124 159 97 160 124 159 97 SP SD: 0.0422 c. M:-0.0713 c. 1024: 138 177 108 178 138 177 108 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 1.1709 cents 3 x x 4 x 5 x 6 S SD: 6.1640 cents 4 x 5 x 6:7 x 8 S SD: 26.0652 cents 5 x 6:7 x 8:9:10 S SD: 25.4987 cents 6 x 7:8:9:10:11:12 S SD: 17.7843 cents 7:8 x 9:11:12:13:14 SD: 23.0461 cents 8:9:10:11:12:13:15:16 SD: 11.1053 cents 9:10:11:12:14:15:17:18 SD: 10.7656 cents 12:13:15:16:18:20:22:24 SD: 5.9892 cents 20:22:25:27:30:33:37:40 SD: 4.4066 cents 22:24:27:29:33:36:41:44 SD: 4.1510 cents 28:31:35:37:42:46:52:56 SD: 3.8608 cents 30:33:37:40:45:49:56:60 SD: 2.8063 cents 42:46:52:56:63:69:78:84 SD: 1.2399 cents 72:79:89:96:108:119:134:144 SD: 0.8521 cents 100:110:124:133:150:165:186:200 SD: 0.8165 cents 114:125:141:152:171:188:212:228 SD: 0.6008 cents 142:156:176:189:213:234:264:284 SD: 0.5519 cents 151:166:187:201:227:249:281:302 SD: 0.4905 cents 163:179:202:217:245:269:303:326 SD: 0.4116 cents 185:203:229:246:278:305:344:370 SD: 0.3913 cents 193:212:239:257:290:318:359:386 SD: 0.3301 cents 205:225:254:273:308:338:381:410 SD: 0.3036 cents 257:282:318:342:386:424:478:514 SD: 0.2689 cents 265:291:328:353:398:437:493:530 SD: 0.2152 cents 416:457:515:554:625:686:773:832 SD: 0.2063 cents 428:470:530:570:643:706:796:856 SD: 0.1997 cents 438:481:542:583:658:722:814:876 SD: 0.1776 cents 450:494:557:599:676:742:837:900 SD: 0.1645 cents 468:514:579:623:703:772:870:936 SD: 0.1602 cents 488:536:604:650:733:805:907:976 SD: 0.1580 cents 510:560:631:679:766:841:948:1020 SD: 0.0956 cents