Scala analysis: bptemp
Tempered version of the Bohlen-Pierce scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 142.698 cents 142.697920 2: 297.116 cents 297.116350 3: 439.814 cents 439.814270 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 75/49 736.930616 BP fifth 6: 879.629 cents 879.628540 7: 1022.326 cents 1022.326460 8: 49/25 1165.024385 BP eighth 9: 15/7 1319.442808 septimal minor ninth, BP ninth 10: 1462.141 cents 1462.140730 11: 1604.839 cents 1604.838650 12: 1759.257 cents 1759.257080 13: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 142.6979 cents 142.6979 1: 142.6979 cents 142.6979 2: 154.4184 cents 154.4184 3: 142.6979 cents 142.6979 4: 142.6979 cents 142.6979 5: 375/343 154.4184 BP major semitone, minor BP chroma 6: 142.6979 cents 142.6979 7: 142.6979 cents 142.6979 8: 142.6979 cents 142.6979 9: 375/343 154.4184 BP major semitone, minor BP chroma 10: 142.6979 cents 142.6979 11: 142.6979 cents 142.6979 12: 154.4184 cents 154.4184 13: 142.6979 cents 142.6979
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 142.69792 cents 1: 4 154.41843 cents 2: 5 285.39584 cents 2: 8 297.11635 cents 3: 1 2401/1875 428.094 cents 3: 12 439.81427 cents 4: 10 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 3 594.23270 cents 5: 6 725.21011 cents 5: 7 75/49 736.931 cents BP fifth 6: 2 867.90804 cents 6: 11 879.62854 cents 7: 11 1022.32646 cents 7: 2 1034.04697 cents 8: 7 49/25 1165.024 cents BP eighth 8: 6 1176.74489 cents 9: 3 1307.72230 cents 9: 10 15/7 1319.443 cents septimal minor ninth, BP ninth 10: 12 1462.14073 cents 10: 1 5625/2401 1473.861 cents 11: 8 1604.83865 cents 11: 5 1616.55916 cents 12: 4 1747.53657 cents 12: 9 1759.25708 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 : 142.7 297.1 439.8 582.5 736.9 879.6 1022.3 1165.0 1319.4 1462.1 1604.8 1759.3 1902.0 142.7 : 154.4 297.1 439.8 594.2 736.9 879.6 1022.3 1176.7 1319.4 1462.1 1616.6 1759.3 1902.0 297.1 : 142.7 285.4 439.8 582.5 725.2 867.9 1022.3 1165.0 1307.7 1462.1 1604.8 1747.5 1902.0 439.8 : 142.7 297.1 439.8 582.5 725.2 879.6 1022.3 1165.0 1319.4 1462.1 1604.8 1759.3 1902.0 582.5 : 154.4 297.1 439.8 582.5 736.9 879.6 1022.3 1176.7 1319.4 1462.1 1616.6 1759.3 1902.0 736.9 : 142.7 285.4 428.1 582.5 725.2 867.9 1022.3 1165.0 1307.7 1462.1 1604.8 1747.5 1902.0 879.6 : 142.7 285.4 439.8 582.5 725.2 879.6 1022.3 1165.0 1319.4 1462.1 1604.8 1759.3 1902.0 1022.3: 142.7 297.1 439.8 582.5 736.9 879.6 1022.3 1176.7 1319.4 1462.1 1616.6 1759.3 1902.0 1165.0: 154.4 297.1 439.8 594.2 736.9 879.6 1034.0 1176.7 1319.4 1473.9 1616.6 1759.3 1902.0 1319.4: 142.7 285.4 439.8 582.5 725.2 879.6 1022.3 1165.0 1319.4 1462.1 1604.8 1747.5 1902.0 1462.1: 142.7 297.1 439.8 582.5 736.9 879.6 1022.3 1176.7 1319.4 1462.1 1604.8 1759.3 1902.0 1604.8: 154.4 297.1 439.8 594.2 736.9 879.6 1034.0 1176.7 1319.4 1462.1 1616.6 1759.3 1902.0 1759.3: 142.7 285.4 439.8 582.5 725.2 879.6 1022.3 1165.0 1307.7 1462.1 1604.8 1747.5 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 142.6979 .. 154.4184 cents 11.72051 cents 142.69792 cents 2: 285.3958 .. 297.1164 cents 11.72051 cents 130.97741 cents 3: 428.0938 .. 439.8143 cents 11.72050 cents 130.97742 cents 4: 582.5122 .. 594.2327 cents 11.72050 cents 142.69792 cents 5: 725.2101 .. 736.9306 cents 11.72051 cents 130.97741 cents 6: 867.9080 .. 879.6285 cents 11.72050 cents 130.97742 cents 7: 1022.3265 .. 1034.0470 cents 11.72051 cents 142.69792 cents 8: 1165.0244 .. 1176.7449 cents 11.72050 cents 130.97742 cents 9: 1307.7223 .. 1319.4428 cents 11.72051 cents 130.97741 cents 10: 1462.1407 .. 1473.8612 cents 11.72050 cents 142.69792 cents 11: 1604.8386 .. 1616.5592 cents 11.72051 cents 130.97742 cents 12: 1747.5366 .. 1759.2571 cents 11.72051 cents 130.97741 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 142.69792 cents, class 1 Average step (divided formal octave): 146.3042 cents Largest one step interval : 154.41843 cents Average / Smallest step : 1.025272 Largest / Average step : 1.055461 Largest / Smallest step : 1.082135 Median interval of one step : 142.69792 cents, amount: 9 Most common interval of one step : 142.69792 cents, amount: 9 Least squares average step : 146.28992 cents, oct.: 1901.76896 cents Scale is strictly proper Scale has Myhill's property chromas: 11.72051 cents and 130.97741 cents, ratio: 11.175061 generators: 3 of 439.81427 cents and 10 of 1462.14073 cents ET pair of linear temperament : 13&160 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 973-tone equal temperament with octave 3/1 degrees: 73 152 225 298 377 450 523 596 675 748 821 900 973 generators: 225 and 748 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABAABA Step pattern size order : SLSSLSSSLSSLS Scale is a Constant Structure, by a margin of 130.97741 cents Scale diversity : 0.272979 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.926052 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 : 11.72050 cents Most common intervals : 439.81427 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 736.931 1462.141 cents Most common triad is 0.0 439.814 1462.141 cents, amount: 11 Number of recognisable 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 11.7205 cents: 1 2 3 4 5 6 7 8 9 10 11 12 Limited inverse transpositions with margin 11.7205 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 : 7 (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: 3.3734 c. M: 5.4095 c. 82: 6 7 6 6 7 6 6 6 7 6 6 7 6 SP M ME I SD: 3.3025 c. M: 5.2957 c. 95: 7 8 7 7 8 7 7 7 8 7 7 8 7 SP M ME I SD: 2.3889 c. M:-3.8308 c. 108: 8 9 8 8 9 8 8 8 9 8 8 9 8 SP M ME I SD: 1.6953 c. M:-2.7186 c. 121: 9 10 9 9 10 9 9 9 10 9 9 10 9 SP M ME I SD: 1.1507 c. M:-1.8453 c. 134: 10 11 10 10 11 10 10 10 11 10 10 11 10 SP M ME I SD: 0.7118 c. M:-1.1415 c. 147: 11 12 11 11 12 11 11 11 12 11 11 12 11 SP M ME I SD: 0.3506 c. M:-0.5621 c. 160: 12 13 12 12 13 12 12 12 13 12 12 13 12 SP M ME I SD: 0.0480 c. M: 0.0769 c. 493: 37 40 37 37 40 37 37 37 40 37 37 40 37 SP M DE I SD: 0.0422 c. M: 0.0677 c. 653: 49 53 49 49 53 49 49 49 53 49 49 53 49 SP M DE I SD: 0.0201 c. M:-0.0323 c. 813: 61 66 61 61 66 61 61 61 66 61 61 66 61 SP M DE I SD: 0.0067 c. M:-0.0108 c. 973: 73 79 73 73 79 73 73 73 79 73 73 79 73 SP M DE I SD: 0.0023 c. M:-0.0036 c. 1786: 134 145 134 134 145 134 134 134 145 134 134 145 134 SP M DE I SD: 0.0018 c. M: 0.0029 c.
FIT/HARMONIC
1 x x x x x x x 2 x x x x 3 S SD: 17.4878 cents 2 x x x x 3 x x 4 x x 5 x 6 S SD: 13.2045 cents 3 x x 4 x x 5 x 6 x 7 x 8:9 S SD: 15.2805 cents 4 x x 5 x 6 x 7:8 x 9:10:11:12 S SD: 13.6749 cents 5 x 6 x 7 x 8:9:10:11:12:13:14:15 S SD: 11.7703 cents 6 x 7:8 x 9:10:11:12:13:14:15:17:18 SD: 9.1591 cents 7 x 8:9:10:11:12:13:14:15:16:18:19:21 SD: 10.8659 cents 8:9 x 10:11:12:13:14:16:17:19:20:22:24 SD: 10.6352 cents 9:10:11:12:13:14:15:16:18:19:21:23:25:27 SD: 9.1993 cents 10:11:12:13:14:15:17:18:20:21:23:25:28:30 SD: 6.6855 cents 11:12:13:14:15:17:18:20:22:24:26:28:30:33 SD: 6.6425 cents 13:14:15:17:18:20:22:23:25:28:30:33:36:39 SD: 6.5775 cents 14:15:17:18:20:21:23:25:27:30:33:35:39:42 SD: 6.4878 cents 15:16:18:19:21:23:25:27:29:32:35:38:41:45 SD: 4.4158 cents 20:22:24:26:28:31:33:36:39:43:47:51:55:60 SD: 3.7838 cents 21:23:25:27:29:32:35:38:41:45:49:53:58:63 SD: 2.4324 cents 32:35:38:41:45:49:53:58:63:69:74:81:88:96 SD: 2.1551 cents 38:41:45:49:53:58:63:69:74:81:88:96:105:114 SD: 1.9090 cents 42:46:50:54:59:64:70:76:82:90:98:106:116:126 SD: 1.6712 cents 45:49:53:58:63:69:75:81:88:96:105:114:124:135 SD: 1.5474 cents 47:51:56:61:66:72:78:85:92:101:109:119:130:141 SD: 1.3361 cents 55:60:65:71:77:84:91:99:108:118:128:139:152:165 SD: 1.2040 cents 58:63:69:75:81:89:96:105:114:124:135:147:160:174 SD: 1.1656 cents 68:74:81:88:95:104:113:123:133:146:158:172:188:204 SD: 0.9567 cents 70:76:83:90:98:107:116:126:137:150:163:177:193:210 SD: 0.7808 cents 80:87:95:103:112:122:133:144:157:171:186:202:221:240 SD: 0.7784 cents 92:100:109:119:129:141:153:166:180:197:214:232:254:276 SD: 0.7159 cents 103:112:122:133:144:158:171:186:202:221:240:260:285:309 SD: 0.6718 cents 107:116:127:138:150:164:178:193:210:229:249:270:296:321 SD: 0.5142 cents 118:128:140:152:165:181:196:213:231:253:275:298:326:354 SD: 0.4854 cents 128:139:152:165:179:196:213:231:251:274:298:323:354:384 SD: 0.3641 cents 175:190:208:226:245:268:291:316:343:375:407:442:483:525 SD: 0.3344 cents 198:215:235:255:277:303:329:357:388:424:461:500:547:594 SD: 0.2727 cents 245:266:291:316:343:375:407:442:480:525:570:619:677:735 SD: 0.1466 cents 370:402:439:477:518:566:615:668:725:793:861:935:1022:1110 SD: 0.1466 cents 373:405:443:481:522:571:620:673:731:799:868:943:1030:1119 SD: 0.1394 cents 405:440:481:522:567:620:673:731:794:868:942:1023:1119:1215 SD: 0.1296 cents 477:518:566:615:668:730:793:861:935:1022:1110:1205:1318:1431 SD: 0.1022 cents 560:608:665:722:784:857:931:1011:1098:1200:1303:1415:1547:1680 SD: 0.0810 cents