Scala analysis: nonepi
Non epimorphic scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 2701/2400 204.551081 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 98415/65536 703.908722 5: 5/3 884.358713 major sixth, BP sixth 6: 2401/1280 1088.989912 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 2560/2401 111.0101 1: 2701/2400 204.5511 2: 3000/2701 181.7626 3: 16/15 111.7313 minor diatonic semitone 4: 295245/262144 205.8637 5: 65536/59049 180.4500 Pythagorean diminished third 6: 7203/6400 204.6312 7: 2560/2401 111.0101
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2560/2401 111.010 cents 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 65536/59049 180.450 cents Pythagorean diminished third 1: 1 3000/2701 181.763 cents 1: 1 2701/2400 204.551 cents 1: 1 7203/6400 204.631 cents 1: 1 295245/262144 205.864 cents 2: 1 3200/2701 293.494 cents 2: 1 43216/36015 315.561 cents 2: 1 6/5 315.641 cents minor third 2: 1 19683/16384 317.595 cents Pythagorean augmented second 2: 1 614656/492075 385.081 cents 2: 2 5/4 386.314 cents major third 3: 1 131072/98415 496.091 cents 3: 1 3200/2401 497.324 cents 3: 2 4/3 498.045 cents perfect fourth 3: 1 7381125/5531648 499.358 cents 3: 1 2701/2000 520.192 cents 3: 1 7203/5120 590.945 cents 4: 1 10240/7203 609.055 cents 4: 1 4000/2701 679.808 cents 4: 1 11063296/7381125 700.642 cents 4: 2 3/2 701.955 cents perfect fifth 4: 1 2401/1600 702.676 cents two (larger approximation to neutral third) 4: 1 98415/65536 703.909 cents 5: 2 8/5 813.686 cents minor sixth 5: 1 492075/307328 814.919 cents 5: 1 32768/19683 882.405 cents Pythagorean diminished seventh 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 36015/21608 884.439 cents 5: 1 2701/1600 906.506 cents 6: 1 524288/295245 994.136 cents 6: 1 12800/7203 995.369 cents 6: 1 4800/2701 995.449 cents 6: 1 2701/1500 1018.237 cents 6: 1 59049/32768 1019.550 cents Pythagorean augmented sixth 6: 1 15/8 1088.269 cents classic major seventh 6: 1 2401/1280 1088.990 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.33333 = 19/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 204.6 386.3 498.0 703.9 884.4 1089.0 1200.0 204.6 : 181.8 293.5 499.4 679.8 884.4 995.4 1200.0 386.3 : 111.7 317.6 498.0 702.7 813.7 1018.2 1200.0 498.0 : 205.9 386.3 590.9 702.0 906.5 1088.3 1200.0 703.9 : 180.4 385.1 496.1 700.6 882.4 994.1 1200.0 884.4 : 204.6 315.6 520.2 702.0 813.7 1019.6 1200.0 1089.0: 111.0 315.6 497.3 609.1 814.9 995.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.0101 .. 205.8637 cents 141776649/134217728, 94.8536 cents 2560/2401, 111.0101 cents 2: 293.4939 .. 386.3137 cents 2701/2560, 92.8198 cents 167772160/159491349, 87.6302 cents 3: 496.0913 .. 590.9449 cents 141776649/134217728, 94.8536 cents 524288/492075, 109.7776 cents 4: 609.0551 .. 703.9087 cents 141776649/134217728, 94.8536 cents 52428800/51883209, 18.1102 cents 5: 813.6863 .. 906.5061 cents 2701/2560, 92.8198 cents 524288/492075, 109.7776 cents 6: 994.1363 .. 1088.9899 cents 141776649/134217728, 94.8536 cents 167772160/159491349, 87.6302 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 2560/2401, 111.0101 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 295245/262144, 205.8637 cents Average / Smallest step : 1.544261 Largest / Average step : 1.200872 Largest / Smallest step : 1.854460 Median interval of one step : 3000/2701, 181.7626 cents, amount: 1 Least squares average step : 176.01915 cents, oct.: 1232.13407 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : EDBGCFA Scale is a Constant Structure, by a margin of 18.11017 cents Scale diversity : 1.392164 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.529122 Rothenberg efficiency : 0.312925 redundancy: 0.687075 Efficiency x scale size : 2.190476 Number of different interval sizes : 38 = 6.33333 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.33333 = 19/3 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 21609/21608, 0.0801 cents Number of recognisable fifths : 5, average 702.2275 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 94.8536 cents: 2 -- Rational properties -- Prime limit : 73 Odd number limit : 7381125 (O: 7381125 U: 7381125) Highest odd numerator or denominator: 98415 Scale harmonicity : 0.009523 Fundamental : 1/4915200, -22.2288 octaves, 0.0001 Hz. Guide tone : too high to compute Exponens Consonantiae : 1.254814E+19, 63.44411 octaves Euler's gradus suavitatis : 183 Sum of Mann's harmonic distance : 86380.0, average 12340.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.68004, average 1.95429 Sum of Tenney's harmonic distance : 26.96621, average 3.85232 Vogel's harmonic complexity : 47.28571 Wille's k value : 3690562 Wilson's harmonic complexity : 183 Rectangular lattice diameter : 19 Triangular lattice diameter : 13 Lattice compactness : 224.70519, average 8.02519 Lattice compactness (without 2's) : 116.31409, average 4.15407 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -16 .. 2 -4.00000 34 1 3: -1 .. 9 0.85714 12 1 5: -2 .. 1 0.00000 6 3 7: 0 .. 4 0.57143 4 1 37: 0 .. 1 0.14286 1 73: 0 .. 1 0.14286 1 1 Average exponent except 2's : 12 / 7 = 1.71429 Average absolute exponent except 2's: 24 / 7 = 3.42857 Scale is weakly epimorphic with val: <7 11 15 19 38 44| Scale is weakly epimorphic with val: <7 11 15 21 37 44| Scale is weakly epimorphic with val: <7 11 15 21 38 43| Scale is weakly epimorphic with val: <7 12 15 19 34 42| Scale is weakly epimorphic with val: <7 12 15 21 38 44| Scale is weakly epimorphic with val: <7 12 17 21 38 44|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.7458 c. M: 60.4185 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 25.5849 c. M: 44.3587 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 2 2 1 P M ME S SD: 9.2040 c. M:-15.6413 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 19: 3 3 2 3 3 3 2 SP M ME S SD: 9.6518 c. M: 15.3057 c. Nineteen-tone Major, Ionian 22: 4 3 2 4 3 4 2 P T3 SD: 7.7713 c. M:-13.6307 c. Twenty-two tone "Just" Major 31: 5 5 3 5 5 5 3 SP M DE S SD: 6.1084 c. M: 11.0027 c. Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian 34: 6 5 3 6 5 6 3 P T3 SD: 3.8797 c. M:-7.2136 c. Thirty-four tone "Just" Major 41: 7 6 4 7 6 7 4 SP T3 SD: 4.0181 c. M: 6.3099 c. Forty-one tone "Just" Major 46: 8 7 4 8 7 8 4 P T3 SD: 3.7633 c. M:-6.6623 c. Forty-six tone "Just" Major 53: 9 8 5 9 8 9 5 SP T3 SD: 1.3786 c. M: 2.1975 c. Fifty-three tone "Just" Major 65: 11 10 6 11 10 11 6 SP T3 SD: 1.3704 c. M: 2.3703 c. Sixty-five tone "Just" Major 87: 15 13 8 15 13 15 8 SP T3 SD: 1.2511 c. M:-2.3455 c. 99: 17 15 9 17 15 17 9 SP T3 SD: 1.2294 c. M:-1.9192 c. 118: 20 18 11 20 18 20 11 SP T3 SD: 1.0151 c. M: 2.2138 c. 140: 24 21 13 24 21 24 13 SP T3 SD: 0.9306 c. M: 1.5016 c. 152: 26 23 14 26 23 26 14 SP T3 SD: 0.6688 c. M: 1.2771 c. 205: 35 31 19 35 31 35 19 SP T3 SD: 0.6272 c. M: 1.4697 c. 251: 43 38 23 43 38 43 23 SP T3 SD: 0.8447 c. M: 1.1199 c. 258: 44 39 24 44 39 44 24 SP T3 SD: 0.7085 c. M: 1.5831 c. 270: 46 41 25 46 41 46 25 SP T3 SD: 0.6622 c. M: 1.6865 c. 327: 56 49 31 56 49 56 30 SP SD: 0.7816 c. M:-1.0376 c. 335: 57 51 31 58 50 57 31 SP SD: 0.7314 c. M:-1.7629 c. 345: 59 52 32 59 52 59 32 SP T3 SD: 0.7045 c. M: 1.3000 c. 357: 61 54 33 61 54 61 33 SP T3 SD: 0.6162 c. M: 1.3877 c. 388: 66 59 36 67 58 66 36 SP SD: 0.5302 c. M:-1.2459 c. 392: 67 59 37 67 59 67 36 SP SD: 0.5767 c. M:-0.9346 c. 404: 69 61 38 69 61 69 37 SP SD: 0.6522 c. M:-1.1091 c. 407: 69 62 38 70 61 69 38 SP SD: 0.6501 c. M: 1.1113 c. 410: 70 62 38 71 61 70 38 SP SD: 0.6230 c. M:-1.4571 c. 411: 70 62 39 70 62 70 38 SP SD: 0.6013 c. M:-1.2251 c. 422: 72 64 39 73 63 72 39 SP SD: 0.5470 c. M:-1.3045 c. 434: 74 66 40 75 65 74 40 SP SD: 0.5907 c. M:-1.1604 c. 441: 75 67 41 76 66 75 41 SP SD: 0.4259 c. M:-0.8532 c. 445: 76 67 42 76 67 76 41 SP SD: 0.4716 c. M:-0.8314 c. 453: 77 69 42 78 68 77 42 SP SD: 0.4288 c. M:-0.7270 c. 475: 81 72 44 82 71 81 44 SP SD: 0.3958 c. M:-0.9334 c. 487: 83 74 45 84 73 83 45 SP SD: 0.4012 c. M:-0.8141 c. 494: 84 75 46 85 74 84 46 SP SD: 0.3993 c. M: 0.7308 c. 506: 86 77 47 87 76 86 47 SP SD: 0.3523 c. M: 0.5985 c. 528: 90 80 49 91 79 90 49 SP SD: 0.3175 c. M:-0.6367 c. 540: 92 82 50 93 81 92 50 SP SD: 0.2704 c. M:-0.5357 c. 581: 99 88 54 100 87 99 54 SP SD: 0.3056 c. M: 0.5218 c. 593: 101 90 55 102 89 101 55 SP SD: 0.2075 c. M:-0.3071 c. 646: 110 98 60 111 97 110 60 SP SD: 0.2170 c. M: 0.4450 c. 658: 112 100 61 113 99 112 61 SP SD: 0.2042 c. M:-0.3124 c. 745: 127 113 69 128 112 127 69 SP SD: 0.1681 c. M: 0.3269 c. 798: 136 121 74 137 120 136 74 SP SD: 0.1818 c. M: 0.3006 c. 985: 168 149 92 169 148 168 91 SP SD: 0.1599 c. M:-0.2537 c. 1038: 177 157 97 178 156 177 96 SP SD: 0.1252 c. M:-0.2209 c. 1050: 179 159 98 180 158 179 97 SP SD: 0.1394 c. M:-0.2407 c. 1091: 186 165 102 187 164 186 101 SP SD: 0.1285 c. M: 0.2459 c. 1103: 188 167 103 189 166 188 102 SP SD: 0.1096 c. M:-0.2324 c. 1137: 194 172 106 195 171 194 105 SP SD: 0.1177 c. M:-0.1983 c. 1156: 197 175 108 198 174 197 107 SP SD: 0.1175 c. M:-0.2249 c. 1190: 203 180 111 204 179 203 110 SP SD: 0.0876 c. M:-0.1548 c. 1243: 212 188 116 213 187 212 115 SP SD: 0.0968 c. M: 0.1512 c. 1631: 278 247 152 280 245 278 151 SP SD: 0.0868 c. M:-0.1992 c. 1643: 280 249 153 282 247 280 152 SP SD: 0.0870 c. M:-0.1692 c. 1696: 289 257 158 291 255 289 157 SP SD: 0.0665 c. M:-0.1007 c. 1730: 295 262 161 297 260 295 160 SP SD: 0.0636 c. M:-0.1375 c. 1783: 304 270 166 306 268 304 165 SP SD: 0.0364 c. M:-0.0733 c. 1848: 315 280 172 317 278 315 171 SP SD: 0.0312 c. M:-0.0569 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: 0.9769 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 21.1224 cents 5 x 6:7 x 8:9:10 S SD: 29.8134 cents 6:7 x 8:9:10:11:12 S SD: 12.3129 cents 7:8:9 x 11:12:13:14 SD: 18.2118 cents 8:9:10:11:12:13:15:16 SD: 9.8602 cents 10:11 x 13:15:17:19:20 SD: 11.9693 cents 12:14:15:16:18:20:23:24 SD: 10.3816 cents 14:16:18:19:21:23:26:28 SD: 10.0504 cents 15:17:19:20:23:25:28:30 SD: 6.4637 cents 16:18:20:21:24:27:30:32 S SD: 4.9705 cents 24:27:30:32:36:40:45:48 S SD: 0.3113 cents 231:260:289:308:347:385:433:462 SD: 0.2881 cents 255:287:319:340:383:425:478:510 SD: 0.2606 cents 279:314:349:372:419:465:523:558 SD: 0.2408 cents 303:341:379:404:455:505:568:606 SD: 0.2269 cents 327:368:409:436:491:545:613:654 SD: 0.2173 cents 351:395:439:468:527:585:658:702 SD: 0.2109 cents 375:422:469:500:563:625:703:750 SD: 0.2070 cents 384:432:480:512:577:640:720:768 SD: 0.2036 cents 408:459:510:544:613:680:765:816 SD: 0.1859 cents 432:486:540:576:649:720:810:864 SD: 0.1716 cents 456:513:570:608:685:760:855:912 SD: 0.1605 cents 480:540:600:640:721:800:900:960 SD: 0.1520 cents 492:554:615:656:739:820:923:984 SD: 0.1464 cents 504:567:630:672:757:840:945:1008 SD: 0.1459 cents 516:581:645:688:775:860:968:1032 SD: 0.1302 cents 540:608:675:720:811:900:1013:1080 SD: 0.1165 cents 564:635:705:752:847:940:1058:1128 SD: 0.1050 cents 588:662:735:784:883:980:1103:1176 SD: 0.0957 cents