Scala analysis: phi_6
Phi equal division by 6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 138.848 cents 138.848380 2: 277.697 cents 277.696770 3: 416.545 cents 416.545150 4: 555.394 cents 555.393530 5: 694.242 cents 694.241910 6: 833.090 cents 833.090300
SHOW/INTERVAL
0: 138.8484 cents 138.8484 1: 138.8484 cents 138.8484 2: 138.8484 cents 138.8484 3: 138.8484 cents 138.8484 4: 138.8484 cents 138.8484 5: 138.8484 cents 138.8484 6: 138.8484 cents 138.8484
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 138.84838 cents 2: 6 277.69677 cents 3: 6 416.54515 cents 4: 6 555.39353 cents 5: 6 694.24191 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 138.8 277.7 416.5 555.4 694.2 833.1 138.8: 138.8 277.7 416.5 555.4 694.2 833.1 277.7: 138.8 277.7 416.5 555.4 694.2 833.1 416.5: 138.8 277.7 416.5 555.4 694.2 833.1 555.4: 138.8 277.7 416.5 555.4 694.2 833.1 694.2: 138.8 277.7 416.5 555.4 694.2 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.8484 .. 138.8484 cents 1/1, 0.0000 cents 138.84838 cents 2: 277.6968 .. 277.6968 cents 1/1, 0.0000 cents 138.84839 cents 3: 416.5452 .. 416.5452 cents 1/1, 0.0000 cents 138.84838 cents 4: 555.3935 .. 555.3935 cents 1/1, 0.0000 cents 138.84838 cents 5: 694.2419 .. 694.2419 cents 1/1, 0.0000 cents 138.84838 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 138.84838 cents, class 1 Average step (divided formal octave): 138.8484 cents Largest one step interval : 138.84838 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 138.84838 cents, amount: 6 Most common interval of one step : 138.84838 cents, amount: 6 Least squares average step : 138.84838 cents, oct.: 833.09030 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 138.84838 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.166667 redundancy: 0.833333 Efficiency x scale size : 1.000000 Number of different interval sizes : 5 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 6, average 694.2419 cents Number of recognisable fourths : 0 Best fifths form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M:-0.0000 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic
FIT/HARMONIC
1 x x x x x 2 S SD: 366.9097 cents 2 x x x x 3 x S SD: 7.7131 cents 3 x x x 4 x 5 S SD: 38.4620 cents 4 x x 5 x 6 x S SD: 15.5999 cents 5 x 6 x 7 x 8 S SD: 16.8382 cents 6 x 7 x 8:9:10 S SD: 19.5160 cents 7 x 8:9:10 x 11 S SD: 23.6166 cents 8:9 x 10:11:12:13 S SD: 14.5305 cents 9:10 x 11:12:13:15 SD: 25.2308 cents 10:11:12:13:14:15:16 H SD: 11.4434 cents 11:12:13:14:15:16:18 S SD: 9.2325 cents 16:17:19:20:22:24:26 SD: 8.4767 cents 18:20:21:23:25:27:29 SD: 8.1095 cents 21:23:25:27:29:31:34 SD: 6.8451 cents 22:24:26:28:30:33:36 S SD: 5.4068 cents 23:25:27:29:32:34:37 SD: 5.1049 cents 29:31:34:37:40:43:47 SD: 4.5366 cents 34:37:40:43:47:51:55 SD: 2.6676 cents 45:49:53:57:62:67:73 SD: 2.3867 cents 47:51:55:60:65:70:76 SD: 1.9289 cents 58:63:68:74:80:87:94 SD: 1.8301 cents 63:68:74:80:87:94:102 SD: 1.3794 cents 81:88:95:103:112:121:131 SD: 1.2612 cents 97:105:114:123:134:145:157 SD: 1.2381 cents 108:117:127:137:149:161:175 SD: 1.1708 cents 109:118:128:139:150:163:176 SD: 1.1446 cents 110:119:129:140:152:164:178 SD: 1.0504 cents 121:131:142:154:167:181:196 SD: 0.7710 cents 132:143:155:168:182:197:214 SD: 0.6295 cents 154:167:181:196:212:230:249 SD: 0.5922 cents 180:195:211:229:248:269:291 SD: 0.5543 cents 191:207:224:243:263:285:309 SD: 0.4712 cents 217:235:255:276:299:324:351 SD: 0.3414 cents 264:286:310:336:364:394:427 SD: 0.2960 cents 298:323:350:379:411:445:482 SD: 0.2818 cents 312:338:366:397:430:466:505 SD: 0.2706 cents 357:387:419:454:492:533:578 SD: 0.2606 cents 397:430:466:505:547:593:642 SD: 0.2256 cents 442:479:519:562:609:660:715 SD: 0.1817 cents 489:530:574:622:674:730:791 SD: 0.1593 cents 529:573:621:673:729:790:856 SD: 0.1082 cents