Scala analysis: tedorian
Eb Dorian in temperament extraordinaire -- neo-medieval style
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 213.686 cents 213.686280 2: 289.735 cents 289.735280 3: 493.157 cents 493.156850 4: 706.843 cents 706.843140 5: 910.265 cents 910.264710 6: 986.314 cents 986.313710 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 213.6863 cents 213.6863 1: 213.6863 cents 213.6863 2: 76.0490 cents 76.0490 3: 203.4216 cents 203.4216 4: 213.6863 cents 213.6863 5: 203.4216 cents 203.4216 6: 76.0490 cents 76.0490 7: 213.6863 cents 213.6863
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 76.04900 cents 1: 2 203.42157 cents 1: 3 213.68628 cents 2: 2 279.47057 cents 2: 2 289.73528 cents 2: 2 417.10786 cents 2: 1 427.37257 cents 3: 4 493.15685 cents 3: 2 503.42157 cents 3: 1 620.52943 cents 4: 1 579.47057 cents 4: 2 696.57843 cents 4: 4 706.84314 cents 5: 1 772.62743 cents 5: 2 782.89214 cents 5: 2 910.26471 cents 5: 2 920.52943 cents 6: 3 986.31371 cents 6: 2 996.57843 cents 6: 2 1123.95100 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 213.7 289.7 493.2 706.8 910.3 986.3 1200.0 213.7 : 76.0 279.5 493.2 696.6 772.6 986.3 1200.0 289.7 : 203.4 417.1 620.5 696.6 910.3 1124.0 1200.0 493.2 : 213.7 417.1 493.2 706.8 920.5 996.6 1200.0 706.8 : 203.4 279.5 493.2 706.8 782.9 986.3 1200.0 910.3 : 76.0 289.7 503.4 579.5 782.9 996.6 1200.0 986.3 : 213.7 427.4 503.4 706.8 920.5 1124.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.0490 .. 213.6863 cents 137.63728 cents 76.04900 cents 2: 279.4706 .. 427.3726 cents 147.90200 cents 65.78429 cents 3: 493.1568 .. 620.5294 cents 127.37258 cents 65.78428 cents 4: 579.4706 .. 706.8431 cents 127.37257 cents -41.05886 cents 5: 772.6274 .. 920.5294 cents 147.90200 cents 65.78429 cents 6: 986.3137 .. 1123.9510 cents 137.63729 cents 65.78428 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 76.04900 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 213.68628 cents Average / Smallest step : 2.254186 Largest / Average step : 1.246503 Largest / Smallest step : 2.809850 Median interval of one step : 203.42157 cents, amount: 2 Most common interval of one step : 213.68628 cents, amount: 3 Least squares average step : 171.20861 cents, oct.: 1198.46029 cents Scale is not proper Scale is a mode of a 1988-tone equal temperament with octave 2/1 degrees: 354 480 817 1171 1508 1634 1988 Least number of segments generator : 995 of 600.604 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1145 of 691.147 cents and inv. generated superset size: 297 = 290 more = 4242.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCACBA Step pattern size order : LSMLMSL Scale is a Constant Structure, by a margin of 41.05886 cents Scale diversity : 1.331763 Lumma stability : 0.346029 Lumma impropriety factor : 0.034216 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 10.26471 cents Most common intervals : 493.15685 cents & inv., amount: 4 Most common triad is 0.0 493.157 706.843 cents, amount: 3 Number of recognisable fifths : 6, average 703.4216 cents Best major thirds form a closed circle Formal octave complements present : 7 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 38.0003 c. M:-53.1219 c. Lebeng 10: 2 0 2 2 2 0 2 N M DE I SD: 30.8874 c. M:-49.7353 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 9.8490 c. M:-13.6863 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 17: 3 1 3 3 3 1 3 N M DE I SD: 4.1097 c. M:-7.3823 c. Supra-7 29: 5 2 5 5 5 2 5 N M DE I SD: 4.0579 c. M:-6.7897 c. 46: 8 3 8 8 8 3 8 N M DE I SD: 3.3319 c. M:-4.9906 c. 61: 11 4 10 11 10 4 11 N I SD: 3.2841 c. M:-5.3467 c. 63: 11 4 11 11 11 4 11 N M DE I SD: 3.2875 c. M:-4.1625 c. 66: 12 4 11 12 11 4 12 N I SD: 2.7589 c. M:-4.4955 c. 78: 14 5 13 14 13 5 14 N I SD: 1.7090 c. M:-2.5724 c. 95: 17 6 16 17 16 6 17 N I SD: 0.7569 c. M:-1.0506 c. 112: 20 7 19 20 19 7 20 N I SD: 0.4314 c. M:-0.5994 c. 219: 39 14 37 39 37 14 39 N I SD: 0.3612 c. M:-0.6757 c. 236: 42 15 40 42 40 15 42 N I SD: 0.0914 c. M:-0.1270 c. 348: 62 22 59 62 59 22 62 N I SD: 0.0769 c. M:-0.1068 c. 584: 104 37 99 104 99 37 104 N I SD: 0.0089 c. M:-0.0124 c. 1404: 250 89 238 250 238 89 250 N I SD: 0.0080 c. M:-0.0111 c. 1988: 354 126 337 354 337 126 354 N I SD: 0.0030 c. M:-0.0042 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: 2.4441 cents 3 x x 4 x 5 x 6 S SD: 8.7877 cents 4 x 5 x 6 x 7:8 S SD: 24.5677 cents 5 x 6:7 x 8:9:10 S SD: 27.5401 cents 6 x 7:8:9:10:11:12 S SD: 12.0380 cents 7:8 x 9:11:12 x 14 SD: 19.9237 cents 8:9 x 11:12 x 14:16 SD: 12.3418 cents 10:11:12:13:15:17:18:20 SD: 10.7193 cents 11:12:13:15:17:19 x 22 SD: 16.1366 cents 12 x 14:16:18:20:21:24 S SD: 6.5564 cents 13:15 x 17:20:22:23:26 SD: 9.8657 cents 14:16:17:19:21:24:25:28 SD: 9.6607 cents 15:17:18:20:23:25:27:30 SD: 8.3952 cents 16:18:19:21:24:27:28:32 SD: 4.5307 cents 19 x 22:25:29:32:34:38 SD: 8.7552 cents 20:23:24:27:30:34:35:40 SD: 7.2381 cents 21:24:25:28:32:36:37:42 SD: 5.5932 cents 22:25:26:29:33:37:39:44 SD: 2.9712 cents 38:43:45:51:57:64:67:76 SD: 2.7757 cents 39:44:46:52:59:66:69:78 SD: 1.8197 cents 55:62:65:73:83:93:97:110 SD: 1.4071 cents 61:69:72:81:92:103:108:122 SD: 1.0241 cents 91:103:108:121:137:154:161:182 SD: 1.0194 cents 99:112:117:132:149:167:175:198 SD: 1.0155 cents 100:113:118:133:150:169:177:200 SD: 0.9788 cents 115:130:136:153:173:195:203:230 SD: 0.7217 cents 121:137:143:161:182:205:214:242 SD: 0.4633 cents 137:155:162:182:206:232:242:274 SD: 0.3854 cents 176:199:208:234:265:298:311:352 SD: 0.3684 cents 182:206:215:242:274:308:322:364 SD: 0.3666 cents 198:224:234:263:298:335:350:396 SD: 0.2859 cents 236:267:279:314:355:399:417:472 SD: 0.2645 cents 319:361:377:424:480:540:564:638 SD: 0.2098 cents 357:404:422:475:537:604:631:714 SD: 0.1937 cents 367:415:434:488:552:621:649:734 SD: 0.1828 cents 373:422:441:496:561:631:659:746 SD: 0.1532 cents 434:491:513:577:653:734:767:868 SD: 0.1264 cents 516:584:610:686:776:873:912:1032 SD: 0.1198 cents 555:628:656:738:835:939:981:1110 SD: 0.0812 cents