Scala analysis: prop19_7b
Harmonic minor
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 189.474 cents 189.473684 2: 315.789 cents 315.789474 3: 505.263 cents 505.263158 4: 694.737 cents 694.736842 5: 821.053 cents 821.052632 6: 1073.684 cents 1073.684211 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 126.3158 cents 126.3158 1: 189.4737 cents 189.4737 2: 126.3158 cents 126.3158 3: 189.4737 cents 189.4737 4: 189.4737 cents 189.4737 5: 126.3158 cents 126.3158 6: 252.6316 cents 252.6316 7: 126.3158 cents 126.3158
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 126.31579 cents 1: 3 189.47368 cents 1: 1 252.63158 cents 2: 4 315.78947 cents 2: 3 378.94737 cents 3: 1 442.10526 cents 3: 4 505.26316 cents 3: 2 568.42105 cents 4: 2 631.57895 cents 4: 4 694.73684 cents 4: 1 757.89474 cents 5: 3 821.05263 cents 5: 4 884.21053 cents 6: 1 947.36842 cents 6: 3 1010.52632 cents 6: 3 1073.68421 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.66667 = 8/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 189.5 315.8 505.3 694.7 821.1 1073.7 1200.0 189.5 : 126.3 315.8 505.3 631.6 884.2 1010.5 1200.0 315.8 : 189.5 378.9 505.3 757.9 884.2 1073.7 1200.0 505.3 : 189.5 315.8 568.4 694.7 884.2 1010.5 1200.0 694.7 : 126.3 378.9 505.3 694.7 821.1 1010.5 1200.0 821.1 : 252.6 378.9 568.4 694.7 884.2 1073.7 1200.0 1073.7: 126.3 315.8 442.1 631.6 821.1 947.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.3158 .. 252.6316 cents 126.31579 cents 126.31579 cents 2: 315.7895 .. 378.9474 cents 63.15789 cents 63.15789 cents 3: 442.1053 .. 568.4211 cents 126.31579 cents 63.15789 cents 4: 631.5789 .. 757.8947 cents 126.31579 cents 63.15790 cents 5: 821.0526 .. 884.2105 cents 63.15790 cents 63.15790 cents 6: 947.3684 .. 1073.6842 cents 126.31579 cents 63.15789 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 126.31579 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 252.63158 cents Average / Smallest step : 1.357143 Largest / Average step : 1.473684 Largest / Smallest step : 2.000000 Median interval of one step : 189.47368 cents, amount: 3 Least squares average step : 171.87970 cents, oct.: 1203.15790 cents Scale is strictly proper Scale is 3-distributional even Scale is a mode of a 19-tone equal temperament with octave 1200.000 cents degrees: 3 5 8 11 13 17 19 Least number of segments generator : 11 of 694.737 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 11 of 694.737 cents and inv. generated superset size: 10 = 3 more = 142.857% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 19-tone equal temperament Step pattern alph. order: ABAABCB Step pattern size order : MSMMSLS Interval vector is [ 0 3 3 1 4 3 1 4 2 ] Scale is a Constant Structure, by a margin of 63.15789 cents Scale diversity : 1.414959 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.473684 Rothenberg efficiency : 0.521088 redundancy: 0.478912 Efficiency x scale size : 3.647619 Number of different interval sizes : 16 = 2.66667 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.66667 = 8/3 Median interval variety : 2.5 Lowest interval variety : 2 Smallest interval difference : 63.15789 cents Number of recognisable fifths : 4, average 694.7368 cents Best fifths form a closed circle Formal octave complements present : 3 = 42.8571% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 25.5196 c. M: 45.1128 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 29.7197 c. M:-50.5263 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 1 2 2 1 3 1 P D3 SD: 14.8865 c. M:-26.3158 c. Harmonic Minor, Mischung 4, Pilu That, Mela Kiravani, Raga Kiranavali, Kirvani (Kirwani), Kalyana Vasantha, Deshi(3), Maqam Bayat-e-Esfahan, Sultani Yakah, Zhalibny Minor, Armoniko minore: Greece 19: 3 2 3 3 2 4 2 SP D3 SD: 0.0000 c. M: 0.0000 c. Nineteen-tone Harmonic Minor
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: 21.2388 cents 4 x 5 x 6 x 7:8 S SD: 31.6436 cents 5 x 6:7 x 8:9:10 S SD: 19.1495 cents 6 x 7:8:9:10:11:12 S SD: 14.0400 cents 7:8 x 9:10:11:13:14 SD: 19.8062 cents 8:9:10:11:12:13:15:16 SD: 12.7353 cents 10:11:12:13:15:16:19:20 SD: 9.8131 cents 14:16:17:19:21:23:26:28 SD: 9.2930 cents 15:17:18:20:22:24:28:30 SD: 6.2242 cents 18:20:22:24:27:29:33:36 SD: 6.0046 cents 20:22:24:27:30:32:37:40 SD: 4.4817 cents 26:29:31:35:39:42:48:52 SD: 3.2002 cents 35:39:42:47:52:56:65:70 SD: 1.8963 cents 50:56:60:67:75:80:93:100 SD: 1.7733 cents 51:57:61:68:76:82:95:102 SD: 1.5919 cents 59:66:71:79:88:95:110:118 SD: 1.3275 cents 71:79:85:95:106:114:132:142 SD: 0.9373 cents 79:88:95:106:118:127:147:158 SD: 0.8553 cents 115:128:138:154:172:185:214:230 SD: 0.7518 cents 120:134:144:161:179:193:223:240 SD: 0.7071 cents 130:145:156:174:194:209:242:260 SD: 0.4212 cents 180:201:216:241:269:289:335:360 SD: 0.4015 cents 241:269:289:323:360:387:448:482 SD: 0.3724 cents 251:280:301:336:375:403:467:502 SD: 0.3246 cents 269:300:323:360:402:432:500:538 SD: 0.2723 cents 310:346:372:415:463:498:576:620 SD: 0.2071 cents 354:395:425:474:529:569:658:708 SD: 0.1768 cents 389:434:467:521:581:625:723:778 SD: 0.1501 cents 425:474:510:569:635:683:790:850 SD: 0.1248 cents 484:540:581:648:723:778:900:968 SD: 0.1196 cents 519:579:623:695:775:834:965:1038 SD: 0.1111 cents 555:619:666:743:829:892:1032:1110 SD: 0.1068 cents