Scala analysis: edo-09

9 equal divisions of the octave

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        133.333 cents     133.333333
  2:        266.667 cents     266.666667
  3:        400.000 cents     400.000000
  4:        533.333 cents     533.333333
  5:        666.667 cents     666.666667
  6:        800.000 cents     800.000000
  7:        933.333 cents     933.333333
  8:       1066.667 cents    1066.666667
  9:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        133.3333 cents    133.3333
  1:        133.3333 cents    133.3333
  2:        133.3333 cents    133.3333
  3:        133.3333 cents    133.3333
  4:        133.3333 cents    133.3333
  5:        133.3333 cents    133.3333
  6:        133.3333 cents    133.3333
  7:        133.3333 cents    133.3333
  8:        133.3333 cents    133.3333
  9:        133.3333 cents    133.3333
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   9 133.33333 cents
  2:   9 266.66667 cents
  3:   9 400.00000 cents
  4:   9 533.33333 cents
  5:   9 666.66667 cents
  6:   9 800.00000 cents
  7:   9 933.33333 cents
  8:   9 1066.66667 cents
Only one interval per interval class, scale is equal tempered
Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5     6     7     8      9     
 0.0   : 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 133.3 : 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 266.7 : 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 400.0 : 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 533.3 : 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 666.7 : 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 800.0 : 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 933.3 : 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 1066.7: 133.3 266.7 400.0 533.3 666.7 800.0 933.3 1066.7 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  133.3333  .. 133.3333 cents      1/1, 0.0000 cents                  133.33333 cents
  2:  266.6667  .. 266.6667 cents      1/1, 0.0000 cents                  133.33333 cents
  3:  400.0000  .. 400.0000 cents      1/1, 0.0000 cents                  133.33333 cents
  4:  533.3333  .. 533.3333 cents      1/1, 0.0000 cents                  133.33333 cents
  5:  666.6667  .. 666.6667 cents      1/1, 0.0000 cents                  133.33333 cents
  6:  800.0000  .. 800.0000 cents      1/1, 0.0000 cents                  133.33333 cents
  7:  933.3333  .. 933.3333 cents      1/1, 0.0000 cents                  133.33333 cents
  8:  1066.6667 .. 1066.6667 cents     1/1, 0.0000 cents                  133.33333 cents
SHOW DATA
Number of notes                     : 9
-- Interval properties --
Smallest interval                   : 133.33333 cents, class 1
Average step (divided formal octave): 133.3333 cents
Largest one step interval           : 133.33333 cents
Average / Smallest step             : 1.000000
Largest / Average step              : 1.000000
Largest / Smallest step             : 1.000000
Median interval of one step         : 133.33333 cents, amount: 9
Most common interval of one step    : 133.33333 cents, amount: 9
Least squares average step          : 133.33333 cents, oct.:  1200.00000 cents
Scale is strictly proper
Scale is equal tempered
Scale is maximally even for L / S <= 2
Scale is distributional even
Scale is a Constant Structure, by a margin of 133.33333 cents
Scale diversity                     : 1.000000
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 1.000000
Rothenberg efficiency               : 0.111111   redundancy: 0.888889
Efficiency x scale size             : 1.000000
Number of different interval sizes  : 8 = 1.00000 / class
Number of one step interval sizes   : 1
Mean interval variety               : 1.00000 = 1
Lowest interval variety             : 1
Number of recognisable fifths       : 0
Scale contains two identical disjunct pentachords
Best fifths form a closed circle
Best minor thirds form a closed circle
Limited transpositions              : all
Inversional symmetry on degrees     : all
Inversional symmetry on intervals   : all
-- Rational properties --
FIT/MODE
  9:  1 1 1 1 1 1 1 1 1  SP B ME I SD: 0.0000 c. M: 0.0000 c.  Pelog Nawanada: Sunda
FIT/HARMONIC
 1 x x x x x x x x 2  S SD: 0.0000 cents
 2 x x x x 3 x x x 4  S SD: 17.6442 cents
 3 x x x 4 x x 5 x 6  S SD: 20.1212 cents
 4 x x 5 x 6 x 7 x 8  S SD: 12.9719 cents
 5 x 6 x 7 x 8 x 9:10  S SD: 17.2189 cents
 6 x 7 x 8:9 x 10:11:12  S SD: 12.0052 cents
 7 x 8:9 x 10:11:12:13:14  S SD: 10.3422 cents
 8 x 9:10:11:12:13:14:15:16  S SD: 11.9002 cents
 9:10 x 11:12:13:14:15:17:18    SD: 13.7689 cents
 10:11:12:13:14:15:16:17:19:20    SD: 12.3682 cents
 11:12:13:14:15:16:17:19:20:22    SD: 7.6728 cents
 12:13:14:15:16:18:19:21:22:24    SD: 7.2727 cents
 14:15:16:18:19:21:22:24:26:28    SD: 7.2711 cents
 17:18:20:21:23:25:27:29:31:34    SD: 6.5268 cents
 19:21:22:24:26:28:30:33:35:38    SD: 5.6277 cents
 22:24:26:28:30:32:35:38:41:44    SD: 4.6526 cents
 24:26:28:30:33:35:38:41:44:48    SD: 3.6480 cents
 34:37:40:43:46:50:54:58:63:68    SD: 2.7411 cents
 36:39:42:45:49:53:57:62:67:72    SD: 2.1666 cents
 42:45:49:53:57:62:67:72:78:84    SD: 2.1593 cents
 47:51:55:59:64:69:75:81:87:94    SD: 1.9360 cents
 49:53:57:62:67:72:78:84:91:98    SD: 1.5813 cents
 53:57:62:67:72:78:84:91:98:106    SD: 1.3410 cents
 61:66:71:77:83:90:97:105:113:122    SD: 1.2965 cents
 66:71:77:83:90:97:105:113:122:132    SD: 1.1163 cents
 73:79:85:92:99:107:116:125:135:146    SD: 1.0657 cents
 77:83:90:97:105:113:122:132:143:154    SD: 0.9895 cents
 85:92:99:107:116:125:135:146:157:170    SD: 0.9883 cents
 89:96:104:112:121:131:141:153:165:178    SD: 0.8940 cents
 100:108:117:126:136:147:159:171:185:200    SD: 0.8526 cents
 113:122:132:142:154:166:179:194:209:226    SD: 0.8384 cents
 119:129:139:150:162:175:189:204:220:238    SD: 0.8358 cents
 122:132:142:154:166:179:194:209:226:244    SD: 0.8248 cents
 126:136:147:159:171:185:200:216:233:252    SD: 0.6943 cents
 127:137:148:160:173:187:202:218:235:254    SD: 0.6901 cents
 136:147:159:171:185:200:216:233:252:272    SD: 0.6481 cents
 138:149:161:174:188:203:219:237:256:276    SD: 0.5726 cents
 150:162:175:189:204:220:238:257:278:300    SD: 0.4760 cents
 162:175:189:204:220:238:257:278:300:324    SD: 0.4648 cents
 174:188:203:219:237:256:276:298:322:348    SD: 0.4432 cents
 211:228:246:266:287:310:335:362:391:422    SD: 0.2859 cents
 277:299:323:349:377:407:440:475:513:554    SD: 0.2017 cents
 385:416:449:485:524:566:611:660:713:770    SD: 0.1300 cents
 438:473:511:552:596:644:695:751:811:876    SD: 0.1288 cents
 577:623:673:727:785:848:916:989:1068:1154    SD: 0.1257 cents
 588:635:686:741:800:864:933:1008:1089:1176    SD: 0.1188 cents