Scala analysis: meso-iph7
Neutral diatonic variation based on two Iph fractal series
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 3072/2783 171.044769 2: 3440/2783 366.921188 3: 3712/2783 498.666962 4: 4168/2783 699.257243 5: 4608/2783 872.999770 6: 224/121 1066.190022 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 121/112 133.8100 1: 3072/2783 171.0448 2: 215/192 195.8764 3: 232/215 131.7458 4: 521/464 200.5903 5: 576/521 173.7425 6: 161/144 193.1903 7: 121/112 133.8100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 232/215 131.746 cents 1: 1 121/112 133.810 cents 1: 1 3072/2783 171.045 cents 1: 1 576/521 173.743 cents 1: 1 161/144 193.190 cents 1: 1 215/192 195.876 cents 1: 1 521/464 200.590 cents 2: 1 192/161 304.855 cents 2: 1 2783/2304 327.000 cents 2: 1 29/24 327.622 cents 2: 1 521/430 332.336 cents 2: 1 3440/2783 366.921 cents 2: 1 644/521 366.933 cents 2: 1 36/29 374.333 cents 3: 1 4/3 498.045 cents perfect fourth 3: 1 3712/2783 498.667 cents 3: 1 215/161 500.731 cents 3: 1 2783/2084 500.743 cents 3: 1 288/215 506.079 cents 3: 1 521/384 528.212 cents 3: 1 161/116 567.523 cents 4: 1 232/161 632.477 cents 4: 1 768/521 671.788 cents 4: 1 215/144 693.921 cents 4: 1 4168/2783 699.257 cents 4: 1 322/215 699.269 cents 4: 1 2783/1856 701.333 cents 4: 1 3/2 701.955 cents perfect fifth 5: 1 29/18 825.667 cents 5: 1 521/322 833.067 cents 5: 1 2783/1720 833.079 cents 5: 1 860/521 867.664 cents 5: 1 48/29 872.378 cents 5: 1 4608/2783 873.000 cents 5: 1 161/96 895.145 cents 6: 1 928/521 999.410 cents 6: 1 384/215 1004.124 cents 6: 1 288/161 1006.810 cents 6: 1 521/288 1026.257 cents 6: 1 2783/1536 1028.955 cents 6: 1 224/121 1066.190 cents 6: 1 215/116 1068.254 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 171.0 366.9 498.7 699.3 873.0 1066.2 1200.0 171.0 : 195.9 327.6 528.2 702.0 895.1 1029.0 1200.0 366.9 : 131.7 332.3 506.1 699.3 833.1 1004.1 1200.0 498.7 : 200.6 374.3 567.5 701.3 872.4 1068.3 1200.0 699.3 : 173.7 366.9 500.7 671.8 867.7 999.4 1200.0 873.0 : 193.2 327.0 498.0 693.9 825.7 1026.3 1200.0 1066.2: 133.8 304.9 500.7 632.5 833.1 1006.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 131.7458 .. 200.5903 cents 112015/107648, 68.8445 cents 232/215, 131.7458 cents 2: 304.8547 .. 374.3328 cents 483/464, 69.4781 cents 89088/83881, 104.2645 cents 3: 498.0450 .. 567.5231 cents 483/464, 69.4781 cents 29/27, 123.7122 cents 4: 632.4769 .. 701.9550 cents 483/464, 69.4781 cents 26912/25921, 64.9539 cents 5: 825.6672 .. 895.1453 cents 483/464, 69.4781 cents 29/27, 123.7122 cents 6: 999.4097 .. 1068.2542 cents 112015/107648, 68.8445 cents 89088/83881, 104.2645 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 232/215, 131.7458 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 521/464, 200.5903 cents Average / Smallest step : 1.301207 Largest / Average step : 1.170110 Largest / Smallest step : 1.522556 Median interval of one step : 576/521, 173.7425 cents, amount: 1 Least squares average step : 174.00040 cents, oct.: 1218.00280 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : CFAGDEB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 64.95388 cents Scale diversity : 1.357693 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.653666 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 448063/448060, 0.0116 cents Number of recognisable fifths : 5, average 699.1471 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 68.8561 cents: 2 -- Rational properties -- Prime limit : 521 Odd number limit : 2783 (O: 2783 U: 2783) Highest odd numerator or denominator: 2783 Scale harmonicity : 0.006078 Fundamental : 1/2783, -11.4424 octaves, 0.0940 Hz. Guide tone : too high to compute Exponens Consonantiae : 5.832139E+14, 49.05102 octaves Euler's gradus suavitatis : 657 Sum of Mann's harmonic distance : 16631.5, average 2375.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 19.30535, average 2.75791 Sum of Tenney's harmonic distance : 39.83366, average 5.69052 Vogel's harmonic complexity : 103.00000 Wille's k value : 1391 Wilson's harmonic complexity : 656 Rectangular lattice diameter : 10 Triangular lattice diameter : 3 Lattice compactness : 136.61485, average 4.87910 Lattice compactness (without 2's) : 53.41584, average 1.90771 Number of different primes : 9 Prime exponents' range, average, count, tones@limit: 2: 1 .. 10 5.57143 39 1 3: 0 .. 2 0.42857 3 5: 0 .. 1 0.14286 1 7: 0 .. 1 0.14286 1 11: -2 .. 0 -1.71429 12 1 23: -1 .. 0 -0.71429 5 2 29: 0 .. 1 0.14286 1 1 43: 0 .. 1 0.14286 1 1 521: 0 .. 1 0.14286 1 1 Average exponent except 2's :-9 / 7 =-1.28571 Average absolute exponent except 2's: 25 / 7 = 3.57143
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 19.5418 c. M: 37.6186 c. Lebeng 12: 2 2 1 2 2 2 1 P M ME S SD: 23.3210 c. M:-33.8100 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 15: 2 3 1 3 2 2 2 SP D3 S SD: 19.7478 c. M:-33.0788 c. 16: 2 3 2 2 3 2 2 SP M ME S SD: 19.9325 c. M:-27.0002 c. Mavila-7, Antiaeolian 17: 2 3 2 3 2 3 2 SP M ME I SD: 16.3853 c. M: 29.8683 c. Neutral Dorian, Maqamic-7 19: 3 3 2 3 3 3 2 SP M ME S SD: 10.2123 c. M:-18.4289 c. Nineteen-tone Major, Ionian 26: 4 4 3 4 4 4 3 SP M ME S SD: 7.1342 c. M:-13.5706 c. Twenty-six tone Major 29: 4 5 3 5 4 5 3 SP T3 SD: 5.2452 c. M:-9.6720 c. 36: 5 6 4 6 5 6 4 SP T3 SD: 2.9736 c. M: 6.3331 c. 55: 8 9 6 9 8 9 6 SP T3 SD: 2.6114 c. M:-3.9879 c. 62: 9 10 7 10 9 10 7 SP T3 SD: 2.5204 c. M:-4.5588 c. 89: 13 14 10 15 13 14 10 SP SD: 2.4606 c. M:-4.2361 c. 91: 13 15 10 15 13 15 10 SP T3 SD: 1.7898 c. M: 2.6701 c. 118: 17 19 13 20 17 19 13 SP SD: 1.4728 c. M:-2.4377 c. 125: 18 20 14 21 18 20 14 SP SD: 1.2509 c. M: 2.1212 c. 154: 22 25 17 26 22 25 17 SP SD: 0.9758 c. M:-2.0415 c. 161: 23 26 18 27 23 26 18 SP SD: 0.9594 c. M: 1.7038 c. 209: 30 34 23 35 30 34 23 SP SD: 1.0080 c. M:-1.7526 c. 216: 31 35 24 36 31 35 24 SP SD: 0.8117 c. M:-1.3330 c. 268: 38 44 29 45 39 43 30 SP SD: 0.7963 c. M: 1.6520 c. 275: 39 45 30 46 40 44 31 SP SD: 0.9045 c. M: 1.4627 c. 287: 41 47 31 48 42 46 32 SP SD: 0.7718 c. M: 1.1060 c. 294: 42 48 32 49 43 47 33 SP SD: 0.7088 c. M: 1.2981 c. 323: 46 53 35 54 47 52 36 SP SD: 0.5542 c. M:-0.8807 c. 330: 47 54 36 55 48 53 37 SP SD: 0.5541 c. M: 1.0754 c. 359: 51 59 39 60 52 58 40 SP SD: 0.5426 c. M:-0.7668 c. 366: 52 60 40 61 53 59 41 SP SD: 0.5883 c. M: 0.8966 c. 385: 55 63 42 64 56 62 43 SP SD: 0.5586 c. M: 1.0754 c. 386: 55 63 42 65 56 62 43 SP SD: 0.5333 c. M: 1.2576 c. 393: 56 64 43 66 57 63 44 SP SD: 0.4707 c. M: 0.9570 c. 422: 60 69 46 71 61 68 47 SP SD: 0.4417 c. M: 1.0366 c. 429: 61 70 47 72 62 69 48 SP SD: 0.4275 c. M: 0.7649 c. 441: 63 72 48 74 64 71 49 SP SD: 0.4278 c. M: 0.7078 c. 448: 64 73 49 75 65 72 50 SP SD: 0.2498 c. M: 0.4527 c. 484: 69 79 53 81 70 78 54 SP SD: 0.1649 c. M: 0.3199 c. 1023: 146 167 112 171 148 165 114 SP SD: 0.1772 c. M: 0.2725 c. 1086: 155 177 119 182 157 175 121 SP SD: 0.1750 c. M: 0.3244 c. 1093: 156 178 120 183 158 176 122 SP SD: 0.1729 c. M:-0.2270 c. 1102: 157 180 121 184 160 177 123 SP SD: 0.1512 c. M:-0.3215 c. 1131: 161 185 124 189 164 182 126 SP SD: 0.1447 c. M: 0.2225 c. 1138: 162 186 125 190 165 183 127 SP SD: 0.1211 c. M: 0.2188 c. 1256: 179 205 138 210 182 202 140 SP SD: 0.1080 c. M:-0.2486 c. 1263: 180 206 139 211 183 203 141 SP SD: 0.1215 c. M: 0.1753 c. 1292: 184 211 142 216 187 208 144 SP SD: 0.0898 c. M: 0.1469 c. 1586: 226 259 174 265 230 255 177 SP SD: 0.0915 c. M:-0.1402 c. 1622: 231 265 178 271 235 261 181 SP SD: 0.0818 c. M: 0.1446 c. 1740: 248 284 191 291 252 280 194 SP SD: 0.0489 c. M:-0.1037 c. 1776: 253 290 195 297 257 286 198 SP SD: 0.0491 c. M: 0.0988 c. 2224: 317 363 244 372 322 358 248 SP SD: 0.0422 c. M: 0.1058 c. 2260: 322 369 248 378 327 364 252 SP SD: 0.0532 c. M: 0.0829 c. 2279: 325 372 250 381 330 367 254 SP SD: 0.0522 c. M:-0.0829 c. 2286: 326 373 251 382 331 368 255 SP SD: 0.0431 c. M:-0.0838 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: 1.3489 cents 3 x x 4 x 5 x 6 S SD: 3.7920 cents 4 x 5 x 6:7 x 8 S SD: 24.4515 cents 5 x 6:7 x 8:9:10 S SD: 24.9312 cents 6:7 x 8:9:10:11:12 S SD: 16.3320 cents 7:8 x 9:10:12:13:14 S SD: 22.3548 cents 8:9:10:11:12:13:15:16 SD: 10.8586 cents 12:13:15:16:18:20:22:24 SD: 6.1451 cents 18:20:22:24:27:30:33:36 S SD: 4.3557 cents 20:22:25:27:30:33:37:40 SD: 4.2710 cents 26:29:32:35:39:43:48:52 SD: 3.6920 cents 29:32:36:39:43:48:54:58 SD: 3.6708 cents 30:33:37:40:45:50:56:60 SD: 2.8370 cents 38:42:47:51:57:63:70:76 SD: 2.0543 cents 47:52:58:63:70:78:87:94 SD: 2.0490 cents 56:62:69:75:84:93:104:112 SD: 1.8720 cents 58:64:72:77:87:96:107:116 SD: 1.8333 cents 59:65:73:79:88:98:109:118 SD: 1.7628 cents 60:66:74:80:90:99:111:120 SD: 1.4054 cents 68:75:84:91:102:113:126:136 SD: 1.3174 cents 76:84:94:101:114:126:141:152 SD: 1.2161 cents 87:96:108:116:130:144:161:174 SD: 1.2127 cents 88:97:109:117:132:146:163:176 SD: 1.1948 cents 93:103:115:124:139:154:172:186 SD: 1.0026 cents 96:106:119:128:144:159:178:192 SD: 0.9003 cents 105:116:130:140:157:174:194:210 SD: 0.8065 cents 114:126:141:152:171:189:211:228 SD: 0.6196 cents 135:149:167:180:202:224:250:270 SD: 0.6125 cents 153:169:189:204:229:253:283:306 SD: 0.4818 cents 165:182:204:220:247:273:305:330 SD: 0.4761 cents 174:192:215:232:261:288:322:348 SD: 0.4336 cents 183:202:226:244:274:303:339:366 SD: 0.2959 cents 203:224:251:271:304:336:376:406 SD: 0.2922 cents 221:244:273:295:331:366:409:442 SD: 0.2681 cents 288:318:356:384:431:477:533:576 SD: 0.2427 cents 317:350:392:423:475:525:587:634 SD: 0.2204 cents 348:384:430:464:521:576:644:696 SD: 0.2176 cents 386:426:477:515:578:639:715:772 SD: 0.1927 cents 416:459:514:555:623:689:770:832 SD: 0.1783 cents 432:477:534:576:647:715:800:864 SD: 0.1732 cents 444:490:549:592:665:735:822:888 SD: 0.1445 cents 462:510:571:616:692:765:855:924 SD: 0.1266 cents