Scala analysis: xen14-darreg-telephone-14
Streched 14-tone equal temperament approximating push-button telephone tones
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 86.790 cents 86.790000 2: 173.570 cents 173.570000 3: 260.360 cents 260.360000 4: 347.140 cents 347.140000 5: 433.930 cents 433.930000 6: 520.710 cents 520.710000 7: 607.500 cents 607.500000 8: 694.290 cents 694.290000 9: 781.070 cents 781.070000 10: 867.860 cents 867.860000 11: 954.640 cents 954.640000 12: 1041.430 cents 1041.430000 13: 1128.210 cents 1128.210000 14: 1215.000 cents 1215.000000
SHOW/INTERVAL
0: 86.7900 cents 86.7900 1: 86.7900 cents 86.7900 2: 86.7800 cents 86.7800 3: 86.7900 cents 86.7900 4: 86.7800 cents 86.7800 5: 86.7900 cents 86.7900 6: 86.7800 cents 86.7800 7: 86.7900 cents 86.7900 8: 86.7900 cents 86.7900 9: 86.7800 cents 86.7800 10: 86.7900 cents 86.7900 11: 86.7800 cents 86.7800 12: 86.7900 cents 86.7900 13: 86.7800 cents 86.7800 14: 86.7900 cents 86.7900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 86.78000 cents 1: 8 86.79000 cents 2: 12 173.57000 cents 2: 2 173.58000 cents 3: 4 260.35000 cents 3: 10 260.36000 cents 4: 10 347.14000 cents 4: 4 347.15000 cents 5: 2 433.92000 cents 5: 12 433.93000 cents 6: 8 520.71000 cents 6: 6 520.72000 cents 7: 14 607.50000 cents 8: 6 694.28000 cents 8: 8 694.29000 cents 9: 12 781.07000 cents 9: 2 781.08000 cents 10: 4 867.85000 cents 10: 10 867.86000 cents 11: 10 954.64000 cents 11: 4 954.65000 cents 12: 2 1041.42000 cents 12: 12 1041.43000 cents 13: 8 1128.21000 cents 13: 6 1128.22000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.92308 = 25/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.6 1041.4 1128.2 1215.0 86.8 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.6 1041.4 1128.2 1215.0 173.6 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.6 1041.4 1128.2 1215.0 260.4 : 86.8 173.6 260.3 347.1 433.9 520.7 607.5 694.3 781.1 867.8 954.6 1041.4 1128.2 1215.0 347.1 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.6 1041.4 1128.2 1215.0 433.9 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.6 1041.4 1128.2 1215.0 520.7 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.7 1041.4 1128.2 1215.0 607.5 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.6 1041.4 1128.2 1215.0 694.3 : 86.8 173.6 260.3 347.1 433.9 520.7 607.5 694.3 781.1 867.8 954.6 1041.4 1128.2 1215.0 781.1 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.6 1041.4 1128.2 1215.0 867.9 : 86.8 173.6 260.3 347.1 433.9 520.7 607.5 694.3 781.1 867.8 954.6 1041.4 1128.2 1215.0 954.6 : 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.7 1041.4 1128.2 1215.0 1041.4: 86.8 173.6 260.4 347.1 433.9 520.7 607.5 694.3 781.1 867.9 954.6 1041.4 1128.2 1215.0 1128.2: 86.8 173.6 260.4 347.2 433.9 520.7 607.5 694.3 781.1 867.9 954.7 1041.4 1128.2 1215.0 1215.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 86.7800 .. 86.7900 cents 0.01000 cents 86.78000 cents 2: 173.5700 .. 173.5800 cents 0.01000 cents 86.78000 cents 3: 260.3500 .. 260.3600 cents 0.01000 cents 86.77000 cents 4: 347.1400 .. 347.1500 cents 0.01000 cents 86.78000 cents 5: 433.9200 .. 433.9300 cents 0.01000 cents 86.77000 cents 6: 520.7100 .. 520.7200 cents 0.01000 cents 86.78000 cents 7: 607.5000 .. 607.5000 cents 1/1, 0.0000 cents 86.78000 cents 8: 694.2800 .. 694.2900 cents 0.01000 cents 86.78000 cents 9: 781.0700 .. 781.0800 cents 0.01000 cents 86.78000 cents 10: 867.8500 .. 867.8600 cents 0.01000 cents 86.77000 cents 11: 954.6400 .. 954.6500 cents 0.01000 cents 86.78000 cents 12: 1041.4200 .. 1041.4300 cents 0.01000 cents 86.77000 cents 13: 1128.2100 .. 1128.2200 cents 0.01000 cents 86.78000 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 86.78000 cents, class 1 Average step (divided formal octave): 86.7857 cents Largest one step interval : 86.79000 cents Average / Smallest step : 1.000066 Largest / Average step : 1.000049 Largest / Smallest step : 1.000115 Median interval of one step : 86.79000 cents, amount: 8 Most common interval of one step : 86.79000 cents, amount: 8 Least squares average step : 86.78567 cents, oct.: 1214.99945 cents Scale is strictly proper Scale has 2 repeating blocks of 7 notes Blocks have Myhill's property chromas: 0.01000 cents and 86.77000 cents, ratio: 8677.000000 generators: 2 of 173.57000 cents and 5 of 433.93000 cents ET pair of linear temperament : 121500&121500 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 14-tone equal temperament with octave 1215.000 cents degrees: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Least number of segments generator : 9 of 781.071 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 9 of 781.071 cents and inv. generated superset size: 14 = 0 more = 100.000% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABABABAABABABA Step pattern size order : LSLSLSLLSLSLSL Interval vector is [ 8 2 10 4 12 6 7 ] Scale is a Constant Structure, by a margin of 86.77000 cents Scale diversity : 0.989909 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.999901 Number of different interval sizes : 25 = 1.92308 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.92308 = 25/13 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 0.01000 cents Most common intervals : 607.50000 cents & inv., amount: 14 Number of recognisable fifths : 14, average 694.2857 cents Number of recognisable fourths : 0 Scale contains two identical disjunct heptachords Formal octave complements present : 14 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 1 2 3 4 5 6 7 8 9 10 11 12 13 Limited inverse transpositions : 1 2 3 4 5 6 7 8 9 10 11 12 13 Inversional symmetry on degrees : 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 -- Rational properties --
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0029 c. M: 0.0043 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x 2 S SD: 15.0000 cents 2 x x x x x x x 3 x x x x x 4 S SD: 8.4225 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 10.5983 cents 4 x x x 5 x x x 6 x x 7 x x 8 S SD: 11.2349 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 11.7872 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 5.7130 cents 7 x x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 7.2267 cents 8 x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 9.8578 cents 9 x 10 x 11 x 12:13 x 14:15:16 x 17:18 S SD: 7.5799 cents 10 x 11 x 12:13 x 14:15:16 x 17:18:19:20 S SD: 7.4848 cents 11 x 12:13 x 14:15:16 x 17:18:19:20:21:22 S SD: 6.4202 cents 12 x 13:14:15 x 16:17:18:19:20:21:22:23:24 S SD: 5.5084 cents 13:14 x 15:16:17:18 x 19:20:21:23:24:25:26 SD: 8.5684 cents 14:15 x 16:17:18:19:20:21:22:23:24:26:27:28 S SD: 4.8757 cents 15:16:17 x 18:19:20:21:22:24:25:26:27:29:30 SD: 7.0932 cents 16:17:18:19:20:21:22:23:24:25:26:28:29:31:32 SD: 6.6312 cents 17:18:19:20:21:22:23:24:25:27:28:30:31:33:34 SD: 4.5968 cents 18:19:20:21:22:23:24:26:27:28:30:31:33:35:36 SD: 4.0484 cents 23:24:25:27:28:30:31:33:34:36:38:40:42:44:46 SD: 3.8946 cents 26:27:29:30:32:33:35:37:39:41:43:45:47:50:52 SD: 3.3255 cents 31:33:34:36:38:40:42:44:46:49:51:54:57:59:63 SD: 2.8713 cents 35:37:39:41:43:45:47:50:52:55:58:61:64:67:71 SD: 2.3147 cents 37:39:41:43:45:48:50:53:55:58:61:64:68:71:75 SD: 2.1753 cents 38:40:42:44:46:49:51:54:57:60:63:66:69:73:77 SD: 2.0567 cents 45:47:50:52:55:58:61:64:67:71:74:78:82:86:91 SD: 1.7526 cents 49:52:54:57:60:63:66:70:73:77:81:85:89:94:99 SD: 1.6418 cents 54:57:60:63:66:69:73:77:81:85:89:94:99:104:109 SD: 1.6319 cents 55:58:61:64:67:71:74:78:82:86:91:95:100:106:111 SD: 1.5345 cents 57:60:63:66:70:73:77:81:85:89:94:99:104:109:115 SD: 1.2176 cents 63:66:70:73:77:81:85:89:94:99:104:109:115:121:127 SD: 1.1929 cents 74:78:82:86:90:95:100:105:111:116:122:128:135:142:149 SD: 1.0819 cents 77:81:85:89:94:99:104:109:115:121:127:134:141:148:155 SD: 1.0616 cents 85:89:94:99:104:109:115:121:127:133:140:148:155:163:171 SD: 1.0378 cents 91:96:101:106:111:117:123:129:136:143:150:158:166:175:184 SD: 0.9093 cents 95:100:105:110:116:122:128:135:142:149:157:165:173:182:192 SD: 0.7579 cents 98:103:108:114:120:126:132:139:146:154:162:170:179:188:198 SD: 0.7527 cents 112:118:124:130:137:144:151:159:167:176:185:194:204:215:226 SD: 0.6256 cents 131:138:145:152:160:168:177:186:196:206:216:227:239:251:264 SD: 0.6252 cents 134:141:148:156:164:172:181:190:200:210:221:233:245:257:270 SD: 0.5994 cents 140:147:155:163:171:180:189:199:209:220:231:243:255:269:282 SD: 0.5233 cents 154:162:170:179:188:198:208:219:230:242:254:267:281:295:311 SD: 0.4261 cents 172:181:190:200:210:221:232:244:257:270:284:299:314:330:347 SD: 0.3709 cents 197:207:218:229:241:253:266:280:294:309:325:342:360:378:397 SD: 0.3603 cents 211:222:233:245:258:271:285:300:315:331:348:366:385:405:426 SD: 0.3307 cents 217:228:240:252:265:279:293:308:324:341:358:377:396:416:438 SD: 0.3068 cents 235:247:260:273:287:302:317:334:351:369:388:408:429:451:474 SD: 0.2571 cents 284:299:314:330:347:365:384:403:424:446:469:493:518:545:573 SD: 0.2549 cents 314:330:347:365:384:403:424:446:469:493:518:545:573:602:633 SD: 0.2473 cents 330:347:365:384:403:424:446:469:493:518:545:573:602:633:666 SD: 0.2342 cents 333:350:368:387:407:428:450:473:497:523:550:578:608:639:672 SD: 0.1494 cents 407:428:450:473:497:523:550:578:608:639:672:706:743:781:821 SD: 0.1467 cents 464:488:513:539:567:596:627:659:693:729:766:805:847:890:936 SD: 0.1466 cents 481:506:532:559:588:618:650:683:718:755:794:835:878:923:970 SD: 0.1460 cents 504:530:557:586:616:648:681:716:753:791:832:875:920:967:1017 SD: 0.1433 cents 505:531:558:587:617:649:682:717:754:793:834:877:922:969:1019 SD: 0.1388 cents 519:546:574:603:634:667:701:737:775:815:857:901:947:996:1047 SD: 0.1318 cents 530:557:586:616:648:681:716:753:791:832:875:920:967:1017:1069 SD: 0.1293 cents 559:588:618:650:683:718:755:794:835:878:923:970:1020:1073:1128 SD: 0.1285 cents 568:597:628:660:694:730:767:807:848:892:938:986:1037:1090:1146 SD: 0.1238 cents 590:620:652:686:721:758:797:838:881:926:974:1024:1077:1132:1190 SD: 0.1139 cents