Scala analysis: meanred
171-et Hahn reduced rational Meantone[12]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 672/625 125.526052 2: 125/112 190.115235 classic augmented semitone 3: 6/5 315.641287 minor third 4: 56/45 378.602191 septimal narrow major third 5: 75/56 505.756522 marvelous fourth 6: 25/18 568.717426 classic augmented fourth 7: 112/75 694.243478 marvelous fifth 8: 45/28 821.397809 septimale wide minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 224/125 1009.884765 11: 625/336 1074.473948 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 672/625 125.5261 1: 672/625 125.5261 2: 78125/75264 64.5892 3: 672/625 125.5261 4: 28/27 62.9609 Archytas' 1/3-tone 5: 3375/3136 127.1543 6: 28/27 62.9609 Archytas' 1/3-tone 7: 672/625 125.5261 8: 3375/3136 127.1543 9: 28/27 62.9609 Archytas' 1/3-tone 10: 672/625 125.5261 11: 78125/75264 64.5892 12: 672/625 125.5261
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 28/27 62.961 cents Archytas' 1/3-tone 1: 2 78125/75264 64.589 cents 1: 5 672/625 125.526 cents 1: 2 3375/3136 127.154 cents 2: 3 6272/5625 188.487 cents 2: 7 125/112 190.115 cents classic augmented semitone 2: 1 451584/390625 251.052 cents 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 3 125/108 253.076 cents semi-augmented whole tone 3: 9 6/5 315.641 cents minor third 4: 5 56/45 378.602 cents septimal narrow major third 4: 3 15625/12544 380.230 cents two (classic augmented semitone) 4: 3 4032/3125 441.167 cents 4: 1 2025/1568 442.796 cents 5: 1 15625/12096 443.191 cents 5: 4 12544/9375 504.128 cents 5: 7 75/56 505.757 cents marvelous fourth 6: 6 25/18 568.717 cents classic augmented fourth 6: 6 36/25 631.283 cents classic diminished fifth 7: 7 112/75 694.243 cents marvelous fifth 7: 4 9375/6272 695.872 cents 7: 1 24192/15625 756.809 cents 8: 1 3136/2025 757.204 cents two (septimal narrow major third) 8: 3 3125/2016 758.833 cents 8: 3 25088/15625 819.770 cents 8: 5 45/28 821.398 cents septimale wide minor sixth 9: 9 5/3 884.359 cents major sixth, BP sixth 9: 3 216/125 946.924 cents semi-augmented sixth 10: 1 140/81 947.320 cents 10: 1 390625/225792 948.948 cents 10: 7 224/125 1009.885 cents 10: 3 5625/3136 1011.513 cents two (marvelous fourth) 11: 2 6272/3375 1072.846 cents 11: 5 625/336 1074.474 cents 11: 2 150528/78125 1135.411 cents 11: 3 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 125.5 190.1 315.6 378.6 505.8 568.7 694.2 821.4 884.4 1009.9 1074.5 1200.0 125.5 : 64.6 190.1 253.1 380.2 443.2 568.7 695.9 758.8 884.4 948.9 1074.5 1200.0 190.1 : 125.5 188.5 315.6 378.6 504.1 631.3 694.2 819.8 884.4 1009.9 1135.4 1200.0 315.6 : 63.0 190.1 253.1 378.6 505.8 568.7 694.2 758.8 884.4 1009.9 1074.5 1200.0 378.6 : 127.2 190.1 315.6 442.8 505.8 631.3 695.9 821.4 946.9 1011.5 1137.0 1200.0 505.8 : 63.0 188.5 315.6 378.6 504.1 568.7 694.2 819.8 884.4 1009.9 1072.8 1200.0 568.7 : 125.5 252.7 315.6 441.2 505.8 631.3 756.8 821.4 946.9 1009.9 1137.0 1200.0 694.2 : 127.2 190.1 315.6 380.2 505.8 631.3 695.9 821.4 884.4 1011.5 1074.5 1200.0 821.4 : 63.0 188.5 253.1 378.6 504.1 568.7 694.2 757.2 884.4 947.3 1072.8 1200.0 884.4 : 125.5 190.1 315.6 441.2 505.8 631.3 694.2 821.4 884.4 1009.9 1137.0 1200.0 1009.9: 64.6 190.1 315.6 380.2 505.8 568.7 695.9 758.8 884.4 1011.5 1074.5 1200.0 1074.5: 125.5 251.1 315.6 441.2 504.1 631.3 694.2 819.8 946.9 1009.9 1135.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 127.1543 cents 91125/87808, 64.1934 cents 28/27, 62.9609 cents 2: 188.4870 .. 252.6804 cents 91125/87808, 64.1934 cents 19668992/18984375, 61.3326 cents 3: 253.0761 .. 315.6413 cents 648/625, 62.5651 cents 4375/4374, 0.3958 cents 4: 378.6022 .. 442.7956 cents 91125/87808, 64.1934 cents 28/27, 62.9609 cents 5: 443.1914 .. 505.7565 cents 648/625, 62.5651 cents 4375/4374, 0.3958 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 28/27, 62.9609 cents 7: 694.2435 .. 756.8086 cents 648/625, 62.5651 cents 28/27, 62.9609 cents 8: 757.2044 .. 821.3978 cents 91125/87808, 64.1934 cents 4375/4374, 0.3958 cents 9: 884.3587 .. 946.9239 cents 648/625, 62.5651 cents 28/27, 62.9609 cents 10: 947.3196 .. 1011.5130 cents 91125/87808, 64.1934 cents 4375/4374, 0.3958 cents 11: 1072.8457 .. 1137.0391 cents 91125/87808, 64.1934 cents 19668992/18984375, 61.3326 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 3375/3136, 127.1543 cents Average / Smallest step : 1.588287 Largest / Average step : 1.271543 Largest / Smallest step : 2.019576 Median interval of one step : 672/625, 125.5261 cents, amount: 5 Most common interval of one step : 672/625, 125.5261 cents, amount: 5 Least squares average step : 99.40977 cents, oct.: 1192.91728 cents Scale is strictly proper Step pattern alph. order: ABACDCADCABA Step pattern size order : CBCADACDACBC Scale is a Constant Structure, by a margin of 0.39576 cents Scale diversity : 1.201151 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.418345 Rothenberg efficiency : 0.419108 redundancy: 0.580892 Efficiency x scale size : 5.029293 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 4375/4374, 0.3958 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 9 Most common triad is 0.0 315.641 884.359 cents, amount: 6 Number of recognisable fifths : 11, average 694.8356 cents Best fifths form a closed circle Scale contains a complete diamond : 7 45 75 Formal octave complements present : 11 = 91.6667% Limited inverse transpositions with margin 64.1934 cents: 7 -- Rational properties -- Prime limit : 7 Odd number limit : 390625 (O: 390625 U: 390625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.010936 Average absolute harmonicity : 0.126434 Specific harmonicity : 0.062354 Fundamental : 1/630000, -19.2650 octaves, 0.0004 Hz. Guide tone : 1260000, 20.2650 octaves, 329648212.279 Hz. Exponens Consonantiae : 7.938000E+11, 39.52998 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 1700.5, average 141.70833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 19.63801, average 1.63650 Sum of Tenney's harmonic distance : 39.19551, average 3.26629 Vogel's harmonic complexity : 37.75000 Wille's k value : 585937 Wilson's harmonic complexity : 66 Rectangular lattice diameter : 14 Triangular lattice diameter : 8 Lattice compactness : 410.66486, average 5.26493 Lattice compactness (without 2's) : 275.41910, average 3.53101 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.41667 33 1 3: -2 .. 2 -0.16667 12 5: -4 .. 4 0.16667 24 3 7: -1 .. 1 0.00000 8 8 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 44 / 12 = 3.66667 Scale is weakly epimorphic with val: <12 17 26 31| Scale is weakly epimorphic with val: <12 17 26 32| Scale is weakly epimorphic with val: <12 17 26 34| Scale is weakly epimorphic with val: <12 17 26 35| Scale is weakly epimorphic with val: <12 17 26 37| Scale is JI-epimorphic with val: <12 18 27 31| Scale is weakly epimorphic with val: <12 18 27 32| Scale is weakly epimorphic with val: <12 18 27 34| Scale is weakly epimorphic with val: <12 18 27 35| Scale is weakly epimorphic with val: <12 18 27 37| Scale is weakly epimorphic with val: <12 19 28 31| Scale is weakly epimorphic with val: <12 19 28 32| Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 19 28 35| Scale is weakly epimorphic with val: <12 19 28 37| Scale is weakly epimorphic with val: <12 20 29 31| Scale is weakly epimorphic with val: <12 20 29 32| Scale is weakly epimorphic with val: <12 20 29 34| Scale is weakly epimorphic with val: <12 20 29 35| Scale is JI-epimorphic with val: <12 20 29 37| Scale is weakly epimorphic with val: <12 21 30 31| Scale is weakly epimorphic with val: <12 21 30 32| Scale is weakly epimorphic with val: <12 21 30 34| Scale is weakly epimorphic with val: <12 21 30 35| Scale is weakly epimorphic with val: <12 21 30 37|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.1395 c. M:-31.2826 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 0.4939 c. M: 0.7897 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 327: 34 18 34 17 35 17 34 35 17 34 18 34 P SD: 0.5641 c. M:-0.7554 c. 346: 36 19 36 18 37 18 36 37 18 36 19 36 P SD: 0.5070 c. M: 0.6706 c. 365: 38 20 38 19 39 19 38 39 19 38 20 38 P SD: 0.4559 c. M:-0.5945 c. 384: 40 21 40 20 41 20 40 41 20 40 21 40 P SD: 0.4100 c. M: 0.5261 c. 403: 42 22 42 21 43 21 42 43 21 42 22 42 P SD: 0.3685 c. M:-0.4640 c. 422: 44 23 44 22 45 22 44 45 22 44 23 44 P SD: 0.3310 c. M:-0.4076 c. 441: 46 24 46 23 47 23 46 47 23 46 24 46 P SD: 0.2968 c. M: 0.3709 c. 460: 48 25 48 24 49 24 48 49 24 48 25 48 P SD: 0.2657 c. M: 0.3413 c. 479: 50 26 50 25 51 25 50 51 25 50 26 50 P SD: 0.2372 c. M: 0.3141 c. 498: 52 27 52 26 53 26 52 53 26 52 27 52 P SD: 0.2112 c. M: 0.2889 c. 517: 54 28 54 27 55 27 54 55 27 54 28 54 P SD: 0.1874 c. M: 0.2656 c. 536: 56 29 56 28 57 28 56 57 28 56 29 56 P SD: 0.1658 c. M: 0.2440 c. 555: 58 30 58 29 59 29 58 59 29 58 30 58 P SD: 0.1461 c. M: 0.2238 c. 574: 60 31 60 30 61 30 60 61 30 60 31 60 P SD: 0.1284 c. M: 0.2050 c. 593: 62 32 62 31 63 31 62 63 31 62 32 62 P SD: 0.1127 c. M: 0.1874 c. 612: 64 33 64 32 65 32 64 65 32 64 33 64 P SD: 0.0991 c. M: 0.1708 c. 631: 66 34 66 33 67 33 66 67 33 66 34 66 P SD: 0.0877 c. M: 0.1553 c. 650: 68 35 68 34 69 34 68 69 34 68 35 68 P SD: 0.0788 c. M: 0.1407 c. 669: 70 36 70 35 71 35 70 71 35 70 36 70 P SD: 0.0727 c. M: 0.1269 c. 688: 72 37 72 36 73 36 72 73 36 72 37 72 P SD: 0.0693 c. M: 0.1138 c. 707: 74 38 74 37 75 37 74 75 37 74 38 74 P SD: 0.0688 c. M: 0.1177 c. 1395: 146 75 146 73 148 73 146 148 73 146 75 146 P SD: 0.0688 c. M: 0.1153 c. 1540: 161 83 161 81 163 81 161 163 81 161 83 161 SP SD: 0.0666 c. M:-0.1137 c. 1559: 163 84 163 82 165 82 163 165 82 163 84 163 SP SD: 0.0650 c. M:-0.1087 c. 1578: 165 85 165 83 167 83 165 167 83 165 85 165 SP SD: 0.0639 c. M: 0.1050 c. 1597: 167 86 167 84 169 84 167 169 84 167 86 167 SP SD: 0.0634 c. M: 0.1079 c. 2038: 213 110 213 107 216 107 213 216 107 213 110 213 SP SD: 0.0611 c. M:-0.1090 c. 2057: 215 111 215 108 218 108 215 218 108 215 111 215 SP SD: 0.0564 c. M:-0.1007 c. 2076: 217 112 217 109 220 109 217 220 109 217 112 217 SP SD: 0.0519 c. M:-0.0925 c. 2095: 219 113 219 110 222 110 219 222 110 219 113 219 SP SD: 0.0476 c. M:-0.0845 c. 2114: 221 114 221 111 224 111 221 224 111 221 114 221 SP SD: 0.0435 c. M:-0.0767 c. 2133: 223 115 223 112 226 112 223 226 112 223 115 223 SP SD: 0.0396 c. M:-0.0689 c. 2152: 225 116 225 113 228 113 225 228 113 225 116 225 SP SD: 0.0359 c. M:-0.0614 c. 2171: 227 117 227 114 230 114 227 230 114 227 117 227 SP SD: 0.0326 c. M:-0.0539 c. 2190: 229 118 229 115 232 115 229 232 115 229 118 229 SP SD: 0.0297 c. M:-0.0497 c. 2209: 231 119 231 116 234 116 231 234 116 231 119 231 SP SD: 0.0272 c. M:-0.0467 c. 2228: 233 120 233 117 236 117 233 236 117 233 120 233 SP SD: 0.0253 c. M:-0.0438 c. 2247: 235 121 235 118 238 118 235 238 118 235 121 235 SP SD: 0.0240 c. M:-0.0409 c. 2266: 237 122 237 119 240 119 237 240 119 237 122 237 SP SD: 0.0235 c. M: 0.0386 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 3.8558 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.5705 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.6206 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 3.5170 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.3215 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 15.0878 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.6779 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 10.2435 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.8613 cents 11:12 x 13:14:15 x 16:18 x 20 x 22 S SD: 10.8220 cents 12:13 x 14:15:16:17:18:19:20 x 22:24 S SD: 7.2116 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.2604 cents 14:15:16:17 x 19 x 21 x 23:25:26:28 SD: 6.4723 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.7244 cents 18:19:20 x 22:24:25:27:29:30:32:33:36 SD: 4.9873 cents 20 x 22:24:25:27:28:30:32:33:36:37:40 SD: 3.6826 cents 21:23 x 25:26:28:29:31:34:35:38:39:42 SD: 4.3625 cents 24:26:27:29:30:32:33:36:39:40:43:45:48 SD: 3.2719 cents 26:28:29:31:32:35:36:39:42:43:47:48:52 SD: 3.0280 cents 29:31:32:35:36:39:40:43:47:48:52:54:58 SD: 3.0173 cents 33:35:37:40:41:44:46:49:53:55:59:61:66 SD: 2.9642 cents 35:38:39:42:44:47:49:52:56:58:63:65:70 SD: 2.7832 cents 36:39:40:43:45:48:50:54:58:60:65:67:72 SD: 2.1440 cents 41:44:46:49:51:55:57:61:66:68:73:76:82 SD: 1.7402 cents 51:55:57:61:63:68:71:76:82:85:91:95:102 SD: 1.6234 cents 53:57:59:64:66:71:74:79:85:88:95:99:106 SD: 1.5403 cents 54:58:60:65:67:72:75:81:87:90:97:100:108 SD: 1.5176 cents 65:70:73:78:81:87:90:97:104:108:116:121:130 SD: 1.4493 cents 66:71:74:79:82:88:92:99:106:110:118:123:132 SD: 1.3883 cents 67:72:75:80:83:90:93:100:108:112:120:125:134 SD: 1.3772 cents 69:74:77:83:86:92:96:103:111:115:124:128:138 SD: 1.0615 cents 77:83:86:92:96:103:107:115:124:128:138:143:154 SD: 0.9608 cents 94:101:105:113:117:126:131:140:151:157:168:175:188 SD: 0.8690 cents 95:102:106:114:118:127:132:142:153:158:170:177:190 SD: 0.6995 cents 120:129:134:144:149:161:167:179:193:200:215:223:240 SD: 0.5627 cents 130:140:145:156:162:174:181:194:209:217:233:242:260 SD: 0.5553 cents 144:155:161:173:179:193:200:215:231:240:258:268:288 SD: 0.4849 cents 172:185:192:206:214:230:239:257:276:287:308:320:344 SD: 0.4836 cents 180:194:201:216:224:241:250:269:289:300:323:335:360 SD: 0.4511 cents 188:202:210:226:234:252:261:281:302:313:337:350:376 SD: 0.4145 cents 200:215:223:240:249:268:278:299:321:333:358:372:400 SD: 0.3913 cents 201:216:224:241:250:269:279:300:323:335:360:374:402 SD: 0.3224 cents 241:259:269:289:300:323:335:360:387:402:432:448:482 SD: 0.2877 cents 250:269:279:300:311:335:347:373:402:417:448:465:500 SD: 0.2542 cents 265:285:296:318:330:355:368:396:426:442:475:493:530 SD: 0.2252 cents 336:361:375:403:418:450:467:502:540:560:602:625:672 SD: 0.1864 cents 371:399:414:445:462:497:515:554:596:618:665:690:742 SD: 0.1854 cents 414:445:462:497:515:554:575:618:665:690:742:770:828 SD: 0.1820 cents 430:462:480:516:535:576:597:642:691:717:771:800:860 SD: 0.1713 cents 450:484:502:540:560:603:625:672:723:750:806:837:900 SD: 0.1403 cents 466:501:520:559:580:624:647:696:749:777:835:867:932 SD: 0.1122 cents 519:558:579:623:646:695:721:775:834:865:930:965:1038 SD: 0.1105 cents 586:630:654:703:729:785:814:875:942:977:1050:1090:1172 SD: 0.0986 cents