Scala analysis: bptemp2
BP tempered using a different generator
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150.224 cents 150.224230 2: 300.448 cents 300.448460 3: 433.686 cents 433.686030 4: 583.910 cents 583.910260 5: 734.134 cents 734.134490 6: 5/3 884.358713 major sixth, BP sixth 7: 9/5 1017.596288 just minor seventh, BP seventh 8: 1167.821 cents 1167.820520 9: 1318.045 cents 1318.044740 10: 1468.269 cents 1468.268970 11: 1601.507 cents 1601.506550 12: 1751.731 cents 1751.730770 13: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 150.2242 cents 150.2242 1: 150.2242 cents 150.2242 2: 150.2242 cents 150.2242 3: 133.2376 cents 133.2376 4: 150.2242 cents 150.2242 5: 150.2242 cents 150.2242 6: 150.2242 cents 150.2242 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 150.2242 cents 150.2242 9: 150.2242 cents 150.2242 10: 150.2242 cents 150.2242 11: 133.2376 cents 133.2376 12: 150.2242 cents 150.2242 13: 150.2242 cents 150.2242
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 133.23757 cents 1: 10 150.22423 cents 2: 6 283.46180 cents 2: 7 300.44846 cents 3: 9 433.68603 cents 3: 4 450.67268 cents 4: 12 583.91026 cents 4: 1 600.89691 cents 5: 2 717.14783 cents 5: 11 734.13449 cents 6: 5 867.37206 cents 6: 8 5/3 884.359 cents major sixth, BP sixth 7: 8 9/5 1017.596 cents just minor seventh, BP seventh 7: 5 1034.58294 cents 8: 11 1167.82052 cents 8: 2 1184.80717 cents 9: 1 1301.05809 cents 9: 12 1318.04474 cents 10: 4 1451.28232 cents 10: 9 1468.26897 cents 11: 7 1601.50655 cents 11: 6 1618.49320 cents 12: 10 1751.73077 cents 12: 3 1768.71743 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 150.2 300.4 433.7 583.9 734.1 884.4 1017.6 1167.8 1318.0 1468.3 1601.5 1751.7 1902.0 150.2 : 150.2 283.5 433.7 583.9 734.1 867.4 1017.6 1167.8 1318.0 1451.3 1601.5 1751.7 1902.0 300.4 : 133.2 283.5 433.7 583.9 717.1 867.4 1017.6 1167.8 1301.1 1451.3 1601.5 1751.7 1902.0 433.7 : 150.2 300.4 450.7 583.9 734.1 884.4 1034.6 1167.8 1318.0 1468.3 1618.5 1768.7 1902.0 583.9 : 150.2 300.4 433.7 583.9 734.1 884.4 1017.6 1167.8 1318.0 1468.3 1618.5 1751.7 1902.0 734.1 : 150.2 283.5 433.7 583.9 734.1 867.4 1017.6 1167.8 1318.0 1468.3 1601.5 1751.7 1902.0 884.4 : 133.2 283.5 433.7 583.9 717.1 867.4 1017.6 1167.8 1318.0 1451.3 1601.5 1751.7 1902.0 1017.6: 150.2 300.4 450.7 583.9 734.1 884.4 1034.6 1184.8 1318.0 1468.3 1618.5 1768.7 1902.0 1167.8: 150.2 300.4 433.7 583.9 734.1 884.4 1034.6 1167.8 1318.0 1468.3 1618.5 1751.7 1902.0 1318.0: 150.2 283.5 433.7 583.9 734.1 884.4 1017.6 1167.8 1318.0 1468.3 1601.5 1751.7 1902.0 1468.3: 133.2 283.5 433.7 583.9 734.1 867.4 1017.6 1167.8 1318.0 1451.3 1601.5 1751.7 1902.0 1601.5: 150.2 300.4 450.7 600.9 734.1 884.4 1034.6 1184.8 1318.0 1468.3 1618.5 1768.7 1902.0 1751.7: 150.2 300.4 450.7 583.9 734.1 884.4 1034.6 1167.8 1318.0 1468.3 1618.5 1751.7 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 150.2242 cents 16.98666 cents 133.23757 cents 2: 283.4618 .. 300.4485 cents 16.98666 cents 133.23757 cents 3: 433.6860 .. 450.6727 cents 16.98665 cents 133.23757 cents 4: 583.9103 .. 600.8969 cents 16.98665 cents 133.23758 cents 5: 717.1478 .. 734.1345 cents 16.98666 cents 116.25092 cents 6: 867.3721 .. 884.3587 cents 16.98666 cents 133.23757 cents 7: 1017.5963 .. 1034.5829 cents 16.98665 cents 27/25, 133.2376 cents 8: 1167.8205 .. 1184.8072 cents 16.98665 cents 133.23758 cents 9: 1301.0581 .. 1318.0447 cents 16.98665 cents 116.25092 cents 10: 1451.2823 .. 1468.2690 cents 16.98665 cents 133.23758 cents 11: 1601.5065 .. 1618.4932 cents 16.98665 cents 133.23758 cents 12: 1751.7308 .. 1768.7174 cents 16.98666 cents 133.23757 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 133.23757 cents, class 1 Average step (divided formal octave): 146.3042 cents Largest one step interval : 150.22423 cents Average / Smallest step : 1.098070 Largest / Average step : 1.026793 Largest / Smallest step : 1.127492 Median interval of one step : 150.22423 cents, amount: 10 Most common interval of one step : 150.22423 cents, amount: 10 Least squares average step : 146.20053 cents, oct.: 1900.60685 cents Scale is strictly proper Scale has Myhill's property chromas: 16.98666 cents and 116.25091 cents, ratio: 6.843659 generators: 4 of 583.91026 cents and 9 of 1318.04474 cents ET pair of linear temperament : 10&13 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1456-tone equal temperament with octave 3/1 degrees: 115 230 332 447 562 677 779 894 1009 1124 1226 1341 1456 generators: 447 and 1009 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAAABAA Step pattern size order : LLSLLLSLLLSLL Scale is a Constant Structure, by a margin of 116.25092 cents Scale diversity : 0.280871 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.892826 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.98665 cents Most common intervals : 583.91026 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 583.910 1167.821 cents Most common triad is 0.0 583.910 1318.045 cents, amount: 11 Number of recognisable fifths : 2, average 717.1478 cents Number of appreciable fifths : 0 Number of recognisable fourths : 0 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 : 13 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 16.9867 cents: 1 2 3 4 5 6 7 8 9 10 11 12 Limited inverse transpositions with margin 16.9867 cents: 1 2 3 4 5 6 7 8 9 10 11 12 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties -- Prime limit : 5 (not all pitches rational)
FIT/MODE
13: 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 4.8891 c. M: 7.8400 c. 62: 5 5 4 5 5 5 4 5 5 5 4 5 5 SP M ME I SD: 3.9403 c. M: 6.3185 c. 75: 6 6 5 6 6 6 5 6 6 6 5 6 6 SP M ME I SD: 2.4098 c. M: 3.8643 c. 88: 7 7 6 7 7 7 6 7 7 7 6 7 7 SP M ME I SD: 1.3316 c. M: 2.1353 c. 101: 8 8 7 8 8 8 7 8 8 8 7 8 8 SP M ME I SD: 0.5309 c. M: 0.8514 c. 114: 9 9 8 9 9 9 8 9 9 9 8 9 9 SP M ME I SD: 0.0872 c. M: 0.1398 c. 443: 35 35 31 35 35 35 31 35 35 35 31 35 35 SP M DE I SD: 0.0538 c. M: 0.0862 c. 557: 44 44 39 44 44 44 39 44 44 44 39 44 44 SP M DE I SD: 0.0249 c. M: 0.0400 c. 671: 53 53 47 53 53 53 47 53 53 53 47 53 53 SP M DE I SD: 0.0059 c. M: 0.0094 c. 1456: 115 115 102 115 115 115 102 115 115 115 102 115 115 SP M DE I SD: 0.0014 c. M: 0.0023 c. 2127: 168 168 149 168 168 168 149 168 168 168 149 168 168 SP M DE I SD: 0.0009 c. M: 0.0014 c.
FIT/HARMONIC
1 x x x x x x x 2 x x x x 3 S SD: 16.0897 cents 2 x x x x 3 x x 4 x x 5 x 6 S SD: 11.9944 cents 3 x x 4 x x 5 x 6 x 7 x 8:9 S SD: 14.9645 cents 4 x x 5 x 6 x 7:8 x 9:10:11:12 S SD: 13.1499 cents 5 x 6 x 7 x 8:9:10:11:12:13:14:15 S SD: 12.0157 cents 6 x 7:8 x 9:10:11:12:13:14:15:17:18 SD: 9.8049 cents 7 x 8:9:10:11:12:13:14:15:16:18:19:21 SD: 11.0695 cents 8:9 x 10:11:12:13:14:16:17:19:20:22:24 SD: 9.7954 cents 9:10:11:12:13:14:15:16:18:19:21:23:25:27 SD: 9.1071 cents 10:11:12:13:14:15:17:18:20:21:23:25:28:30 SD: 6.4894 cents 15:16:18:19:21:23:25:27:29:32:35:38:41:45 SD: 4.3991 cents 20:22:24:26:28:31:33:36:39:43:47:50:55:60 SD: 3.7029 cents 21:23:25:27:29:32:35:38:41:45:49:53:58:63 SD: 2.3602 cents 32:35:38:41:45:49:53:58:63:69:75:81:88:96 SD: 1.9158 cents 36:39:43:46:50:55:60:65:71:77:84:91:99:108 SD: 1.9119 cents 42:46:50:54:59:64:70:76:82:90:98:106:116:126 SD: 1.3990 cents 53:58:63:68:74:81:88:95:104:113:124:134:146:159 SD: 1.2484 cents 57:62:68:73:80:87:95:103:112:122:133:144:157:171 SD: 0.9514 cents 75:82:89:96:105:115:125:135:147:161:175:189:206:225 SD: 0.9411 cents 77:84:92:99:108:118:128:139:151:165:180:194:212:231 SD: 0.9359 cents 78:85:93:100:109:119:130:140:153:167:182:197:215:234 SD: 0.7982 cents 80:87:95:103:112:122:133:144:157:171:187:202:220:240 SD: 0.7603 cents 85:93:101:109:119:130:142:153:167:182:198:214:234:255 SD: 0.7524 cents 99:108:118:127:139:151:165:178:194:212:231:250:272:297 SD: 0.6289 cents 110:120:131:141:154:168:183:198:216:236:257:277:303:330 SD: 0.5864 cents 120:131:143:154:168:183:200:216:236:257:280:303:330:360 SD: 0.5233 cents 132:144:157:170:185:202:220:238:259:283:308:333:363:396 SD: 0.4975 cents 144:157:171:185:202:220:240:259:283:308:336:363:396:432 SD: 0.3815 cents 165:180:196:212:231:252:275:297:324:353:385:416:454:495 SD: 0.2830 cents 221:241:263:284:310:338:368:398:434:473:516:557:608:663 SD: 0.2700 cents 222:242:264:285:311:339:370:400:436:475:518:560:611:666 SD: 0.2682 cents 242:264:288:311:339:370:403:436:475:518:565:610:666:726 SD: 0.2295 cents 264:288:314:339:370:403:440:475:518:565:616:666:726:792 SD: 0.2283 cents 274:299:326:352:384:419:457:493:538:587:640:691:754:822 SD: 0.1957 cents 352:384:419:452:493:538:587:634:691:754:822:888:968:1056 SD: 0.1873 cents 354:386:421:455:496:541:590:637:695:758:827:893:974:1062 SD: 0.1144 cents 496:541:590:637:695:758:827:893:974:1062:1158:1251:1364:1488 SD: 0.0953 cents 576:628:685:740:807:880:960:1037:1131:1233:1345:1453:1584:1728 SD: 0.0910 cents