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