Scala analysis: prop19_g
Seventh 7-note 19-et strictly proper scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 126.316 cents 126.315789 2: 378.947 cents 378.947368 3: 442.105 cents 442.105263 4: 694.737 cents 694.736842 5: 821.053 cents 821.052632 6: 1010.526 cents 1010.526316 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 189.4737 cents 189.4737 1: 126.3158 cents 126.3158 2: 252.6316 cents 252.6316 3: 63.1579 cents 63.1579 4: 252.6316 cents 252.6316 5: 126.3158 cents 126.3158 6: 189.4737 cents 189.4737 7: 189.4737 cents 189.4737
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 63.15790 cents 1: 2 126.31579 cents 1: 2 189.47368 cents 1: 2 252.63158 cents 2: 4 315.78947 cents 2: 3 378.94737 cents 3: 2 442.10526 cents 3: 2 505.26316 cents 3: 3 568.42105 cents 4: 3 631.57895 cents 4: 2 694.73684 cents 4: 2 757.89474 cents 5: 3 821.05263 cents 5: 4 884.21053 cents 6: 2 947.36842 cents 6: 2 1010.52632 cents 6: 2 1073.68421 cents 6: 1 1136.84210 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 126.3 378.9 442.1 694.7 821.1 1010.5 1200.0 126.3 : 252.6 315.8 568.4 694.7 884.2 1073.7 1200.0 378.9 : 63.2 315.8 442.1 631.6 821.1 947.4 1200.0 442.1 : 252.6 378.9 568.4 757.9 884.2 1136.8 1200.0 694.7 : 126.3 315.8 505.3 631.6 884.2 947.4 1200.0 821.1 : 189.5 378.9 505.3 757.9 821.1 1073.7 1200.0 1010.5: 189.5 315.8 568.4 631.6 884.2 1010.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.1579 .. 252.6316 cents 189.47368 cents 63.15790 cents 2: 315.7895 .. 378.9474 cents 63.15789 cents 63.15790 cents 3: 442.1053 .. 568.4211 cents 126.31579 cents 63.15790 cents 4: 631.5789 .. 757.8947 cents 126.31579 cents 63.15790 cents 5: 821.0526 .. 884.2105 cents 63.15789 cents 63.15790 cents 6: 947.3684 .. 1136.8421 cents 189.47368 cents 63.15789 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 63.15790 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 252.63158 cents Average / Smallest step : 2.714286 Largest / Average step : 1.473684 Largest / Smallest step : 4.000000 Median interval of one step : 189.47368 cents, amount: 2 Least squares average step : 168.27068 cents, oct.: 1177.89474 cents Scale is strictly proper Scale is a mode of a 19-tone equal temperament with octave 1200.000 cents degrees: 2 6 7 11 13 16 19 Least number of segments generator : 12 of 757.895 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 12 of 757.895 cents and inv. generated superset size: 11 = 4 more = 157.143% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABCBADD Step pattern size order : BDADBCC Interval vector is [ 1 2 2 2 4 3 2 2 3 ] Scale is a Constant Structure, by a margin of 63.15789 cents Scale diversity : 1.513142 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.368421 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.00000 = 3 Median interval variety : 2.5 Lowest interval variety : 2 Smallest interval difference : 63.15789 cents Most common intervals : 315.78947 cents & inv., amount: 4 Most common triad is 0.0 315.789 884.211 cents, amount: 3 Number of recognisable fifths : 2, average 694.7368 cents Best fifths form a closed circle Formal octave complements present : 3 = 42.8571% Limited inverse transpositions : 5 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 38.2795 c. M:-72.1805 c. Lebeng 9: 1 2 0 2 1 2 1 N D3 SD: 30.8179 c. M:-56.1404 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 27.7361 c. M: 50.5263 c. 12: 1 3 0 3 1 2 2 P S SD: 22.3297 c. M: 42.1053 c. 16: 2 3 1 3 2 2 3 P D3 SD: 18.1505 c. M: 35.5263 c. 17: 2 3 1 4 2 2 3 P SD: 19.0475 c. M:-26.0062 c. 19: 2 4 1 4 2 3 3 SP S SD: 0.0000 c. M:-0.0000 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: 3.6091 cents 3 x x 4 x 5 x 6 S SD: 28.1601 cents 4 x 5 x 6 x 7:8 S SD: 10.7392 cents 5 x 6 x 7:8:9:10 S SD: 25.8506 cents 6 x 7:8:9:10:11:12 S SD: 24.3005 cents 7:8 x 9:10:11:13:14 SD: 24.8559 cents 8:9:10 x 12:13:14:16 S SD: 15.1341 cents 10:11:12:13:15:16:18:20 SD: 10.8866 cents 11:12 x 14:16:18:20:22 S SD: 11.6799 cents 12:13:15 x 18:19:22:24 SD: 8.1902 cents 13:14:16:17:19:21:23:26 SD: 7.7067 cents 15:16:19 x 22:24:27:30 SD: 7.8863 cents 16:17:20:21:24:26:29:32 SD: 6.5887 cents 20:22:25:26:30:32:36:40 SD: 6.1512 cents 23:25:29:30:34:37:41:46 SD: 5.6605 cents 24:26:30:31:36:39:43:48 SD: 3.6077 cents 28:30:35:36:42:45:50:56 SD: 2.2508 cents 38:41:47:49:57:61:68:76 SD: 2.0980 cents 49:53:61:63:73:79:88:98 SD: 2.0472 cents 53:57:66:68:79:85:95:106 SD: 1.6836 cents 65:70:81:84:97:104:117:130 SD: 1.5551 cents 66:71:82:85:99:106:118:132 SD: 1.4361 cents 69:74:86:89:103:111:124:138 SD: 1.0916 cents 79:85:98:102:118:127:142:158 SD: 1.0732 cents 93:100:116:120:139:149:167:186 SD: 1.0039 cents 106:114:132:137:158:170:190:212 SD: 0.7758 cents 107:115:133:138:160:172:192:214 SD: 0.5904 cents 130:140:162:168:194:209:233:260 SD: 0.5579 cents 158:170:197:204:236:254:283:316 SD: 0.4946 cents 168:181:209:217:251:270:301:336 SD: 0.4586 cents 172:185:214:222:257:276:308:344 SD: 0.4510 cents 188:202:234:243:281:302:337:376 SD: 0.4502 cents 196:211:244:253:293:315:351:392 SD: 0.3775 cents 213:229:265:275:318:342:382:426 SD: 0.3045 cents 237:255:295:306:354:381:425:474 SD: 0.1609 cents 409:440:509:528:611:657:733:818 SD: 0.1104 cents 478:514:595:617:714:768:857:956 SD: 0.0994 cents