Scala analysis: prop19_7c

Harmonic major (inverse 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:        378.947 cents     378.947368
  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:        189.4737 cents    189.4737
  3:        126.3158 cents    126.3158
  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   : 189.5 378.9 505.3 694.7 821.1 1073.7 1200.0
 189.5 : 189.5 315.8 505.3 631.6 884.2 1010.5 1200.0
 378.9 : 126.3 315.8 442.1 694.7 821.1 1010.5 1200.0
 505.3 : 189.5 315.8 568.4 694.7 884.2 1073.7 1200.0
 694.7 : 126.3 378.9 505.3 694.7 884.2 1010.5 1200.0
 821.1 : 252.6 378.9 568.4 757.9 884.2 1073.7 1200.0
 1073.7: 126.3 315.8 505.3 631.6 821.1 947.4  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                     63.15790 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      63.15790 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          : 172.78195 cents, oct.:  1209.47368 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 6 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: AABABCB
Step pattern size order : MMSMSLS
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   : 5 = 71.4286%
-- Rational properties --
FIT/MODE
  7:  1 1 1 1 1 1 1  SP B ME I SD: 27.0677 c. M: 45.1128 c.  Lebeng
 10:  2 1 1 2 1 2 1   P M ME S SD: 25.5993 c. M:-50.5263 c.  Sethares Neutral, Beatles-7, Dichotic-7
 12:  2 2 1 2 1 3 1   P   D3   SD: 15.7895 c. M:-26.3158 c.  Harmonic Major, Mischung 2, Mela Sarasangi, Raga Anand Leela, Haripriya, Nat Bhairav, Simhavahini, Ethiopian, Tabahaniotikos: Greece
 17:  3 2 2 3 2 3 2  SP M ME S SD: 18.2005 c. M:-26.0062 c.  Beatles-7, Dichotic-7
 19:  3 3 2 3 2 4 2  SP   D3   SD: 0.0000 c. M: 0.0000 c.  Nineteen-tone Harmonic Major
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: 26.3411 cents
 5 x 6:7 x 8:9:10  S SD: 22.9566 cents
 6:7 x 8:9:10:11:12  S SD: 17.2351 cents
 7:8:9 x 10:11:13:14    SD: 18.5206 cents
 8:9:10:11:12:13:15:16    SD: 7.8608 cents
 15:17:19:20:22:24:28:30    SD: 7.5811 cents
 16:18:20:21:24:26:30:32    SD: 6.5400 cents
 18:20:22:24:27:29:33:36    SD: 5.9962 cents
 20:22:25:27:30:32:37:40    SD: 4.6035 cents
 24:27:30:32:36:39:45:48    SD: 4.4236 cents
 26:29:32:35:39:42:48:52    SD: 3.9223 cents
 33:37:41:44:49:53:61:66    SD: 2.6550 cents
 36:40:45:48:54:58:67:72    SD: 2.1791 cents
 41:46:51:55:61:66:76:82    SD: 1.9802 cents
 53:59:66:71:79:85:99:106    SD: 1.4652 cents
 61:68:76:82:91:98:113:122    SD: 1.4157 cents
 69:77:86:92:103:111:128:138    SD: 1.2659 cents
 77:86:96:103:115:124:143:154    SD: 0.8225 cents
 115:128:143:154:172:185:214:230    SD: 0.7893 cents
 122:136:152:163:182:196:227:244    SD: 0.7169 cents
 127:142:158:170:190:204:236:254    SD: 0.6944 cents
 130:145:162:174:194:209:242:260    SD: 0.5110 cents
 148:165:184:198:221:238:275:296    SD: 0.4724 cents
 156:174:194:209:233:251:290:312    SD: 0.4332 cents
 180:201:224:241:269:289:335:360    SD: 0.4040 cents
 233:260:290:312:348:374:433:466    SD: 0.2917 cents
 257:287:320:344:384:413:478:514    SD: 0.2866 cents
 269:300:335:360:402:432:500:538    SD: 0.2719 cents
 277:309:345:371:414:445:515:554    SD: 0.2321 cents
 310:346:386:415:463:498:576:620    SD: 0.2260 cents
 328:366:408:439:490:527:610:656    SD: 0.1994 cents
 363:405:452:486:542:583:675:726    SD: 0.1890 cents
 389:434:484:521:581:625:723:778    SD: 0.1559 cents
 425:474:529:569:635:683:790:850    SD: 0.1230 cents
 519:579:646:695:775:834:965:1038    SD: 0.0947 cents