Scala analysis: omaha
Omaha 2.3.11 scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 9/8 203.910002 major whole tone 3: 32/27 294.134997 Pythagorean minor third 4: 11/9 347.407941 undecimal neutral third 5: 4/3 498.044999 perfect fourth 6: 11/8 551.317942 undecimal semi-augmented fourth 7: 3/2 701.955001 perfect fifth 8: 18/11 852.592059 undecimal neutral sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 3: 256/243 90.2250 limma, Pythagorean minor second 4: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone 8: 12/11 150.6371 undecimal neutral second, 3/4-tone 9: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 10: 256/243 90.2250 limma, Pythagorean minor second 11: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 12: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 4 88/81 143.498 cents 2nd undecimal neutral second 2: 6 9/8 203.910 cents major whole tone 2: 2 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 3: 2 121/108 196.771 cents 3: 1 297/256 257.183 cents 3: 4 32/27 294.135 cents Pythagorean minor third 3: 5 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 5 11/9 347.408 cents undecimal neutral third 4: 3 81/64 407.820 cents Pythagorean major third 4: 3 128/99 444.772 cents 4: 1 162/121 505.184 cents 5: 1 121/96 400.681 cents 5: 9 4/3 498.045 cents perfect fourth 5: 2 243/176 558.457 cents 6: 5 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 1024/729 588.270 cents Pythagorean diminished fifth 6: 1 729/512 611.730 cents Pythagorean tritone 6: 5 16/11 648.682 cents undecimal semi-diminished fifth 7: 2 352/243 641.543 cents 7: 9 3/2 701.955 cents perfect fifth 7: 1 192/121 799.319 cents 8: 1 121/81 694.816 cents two (undecimal neutral third) 8: 3 99/64 755.228 cents 8: 3 128/81 792.180 cents Pythagorean minor sixth 8: 5 18/11 852.592 cents undecimal neutral sixth 9: 5 44/27 845.453 cents neutral sixth 9: 4 27/16 905.865 cents Pythagorean major sixth 9: 1 512/297 942.817 cents 9: 2 216/121 1003.229 cents 10: 2 121/72 898.726 cents 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 4 81/44 1056.502 cents 2nd undecimal neutral seventh 11: 5 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 2 243/128 1109.775 cents Pythagorean major seventh 11: 5 64/33 1146.727 cents 33rd subharmonic Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 150.6 203.9 294.1 347.4 498.0 551.3 702.0 852.6 905.9 996.1 1049.4 1200.0 150.6 : 53.3 143.5 196.8 347.4 400.7 551.3 702.0 755.2 845.5 898.7 1049.4 1200.0 203.9 : 90.2 143.5 294.1 347.4 498.0 648.7 702.0 792.2 845.5 996.1 1146.7 1200.0 294.1 : 53.3 203.9 257.2 407.8 558.5 611.7 702.0 755.2 905.9 1056.5 1109.8 1200.0 347.4 : 150.6 203.9 354.5 505.2 558.5 648.7 702.0 852.6 1003.2 1056.5 1146.7 1200.0 498.0 : 53.3 203.9 354.5 407.8 498.0 551.3 702.0 852.6 905.9 996.1 1049.4 1200.0 551.3 : 150.6 301.3 354.5 444.8 498.0 648.7 799.3 852.6 942.8 996.1 1146.7 1200.0 702.0 : 150.6 203.9 294.1 347.4 498.0 648.7 702.0 792.2 845.5 996.1 1049.4 1200.0 852.6 : 53.3 143.5 196.8 347.4 498.0 551.3 641.5 694.8 845.5 898.7 1049.4 1200.0 905.9 : 90.2 143.5 294.1 444.8 498.0 588.3 641.5 792.2 845.5 996.1 1146.7 1200.0 996.1 : 53.3 203.9 354.5 407.8 498.0 551.3 702.0 755.2 905.9 1056.5 1109.8 1200.0 1049.4: 150.6 301.3 354.5 444.8 498.0 648.7 702.0 852.6 1003.2 1056.5 1146.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 150.6371 cents 128/121, 97.3641 cents 33/32, 53.2729 cents 2: 143.4979 .. 301.2741 cents 1458/1331, 157.7762 cents 242/243,-7.1391 cents 3: 196.7709 .. 354.5471 cents 1458/1331, 157.7762 cents 14641/15552,-104.5032 cents 4: 347.4079 .. 505.1841 cents 1458/1331, 157.7762 cents 242/243,-7.1391 cents 5: 400.6809 .. 558.4571 cents 1458/1331, 157.7762 cents 14641/15552,-104.5032 cents 6: 551.3179 .. 648.6821 cents 128/121, 97.3641 cents 242/243,-7.1391 cents 7: 641.5429 .. 799.3191 cents 1458/1331, 157.7762 cents 242/243,-7.1391 cents 8: 694.8159 .. 852.5921 cents 1458/1331, 157.7762 cents 14641/15552,-104.5032 cents 9: 845.4529 .. 1003.2291 cents 1458/1331, 157.7762 cents 242/243,-7.1391 cents 10: 898.7259 .. 1056.5021 cents 1458/1331, 157.7762 cents 14641/15552,-104.5032 cents 11: 1049.3629 .. 1146.7271 cents 128/121, 97.3641 cents 242/243,-7.1391 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 12/11, 150.6371 cents Average / Smallest step : 1.877125 Largest / Average step : 1.506371 Largest / Smallest step : 2.827647 Median interval of one step : 256/243, 90.2250 cents, amount: 2 Least squares average step : 99.10727 cents, oct.: 1189.28724 cents Scale is not proper Step pattern alph. order: ABCBABAABCBA Step pattern size order : LSMSLSLLSMSL Scale is a Constant Structure, by a margin of 7.13912 cents Scale diversity : 1.344622 Lumma stability : 0.088788 Lumma impropriety factor : 0.384040 Rothenberg efficiency : 0.406055 redundancy: 0.593945 Efficiency x scale size : 4.872655 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 10, average 701.2411 cents Scale contains two identical disjunct hexachords Scale contains a complete diamond : 1 3 9 27 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 91.6667% -- Rational properties -- Prime limit : 11 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.016296 Average absolute harmonicity : 0.174539 Specific harmonicity : 0.103758 Fundamental : 1/4752, -12.2143 octaves, 0.0551 Hz. Guide tone : 9504, 13.2143 octaves, 2486489.373 Hz. Exponens Consonantiae : 4.516301E+07, 25.42864 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 133.5, average 11.12500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.93242, average 0.91103 Sum of Tenney's harmonic distance : 21.92296, average 1.82691 Vogel's harmonic complexity : 25.16667 Wille's k value : 4009 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 323.23976, average 4.14410 Lattice compactness (without 2's) : 183.57153, average 2.35348 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.25000 27 1 3: -3 .. 3 0.00000 18 6 11: -1 .. 1 0.08333 5 5 Average exponent except 2's : 1 / 12 = 0.08333 Average absolute exponent except 2's: 23 / 12 = 1.91667 Scale is weakly epimorphic with val: <12 17 42| Scale is JI-epimorphic with val: <12 19 42| = patent
FIT/MODE
12: 2 0 1 1 1 1 1 2 0 1 1 1 N T3 SD: 32.2635 c. M:-52.5921 c. 13: 2 0 1 1 1 1 2 1 1 1 0 2 N SD: 24.6144 c. M:-36.5065 c. 14: 2 0 1 1 2 0 2 2 0 1 1 2 N SD: 29.4900 c. M: 53.2329 c. 16: 2 1 1 1 2 0 2 2 1 1 1 2 N T3 SD: 19.6376 c. M: 27.5921 c. 17: 2 1 1 1 2 1 2 2 1 1 1 2 N D3 SD: 8.4229 c. M:-13.3879 c. 24: 3 1 2 1 3 1 3 3 1 2 1 3 N SD: 3.2016 c. M:-5.8650 c. 41: 5 2 3 2 5 2 5 5 2 3 2 5 N SD: 2.8191 c. M:-4.7796 c. 65: 8 3 5 3 8 3 8 8 3 5 3 8 N SD: 2.0654 c. M: 3.3613 c. 89: 11 4 7 4 11 4 11 11 4 7 4 11 N SD: 2.0868 c. M: 3.1539 c. 94: 12 4 7 4 12 4 12 12 4 7 4 12 N SD: 1.6939 c. M: 2.7271 c. 111: 14 5 8 5 14 5 14 14 5 8 5 14 N SD: 1.3213 c. M:-2.2431 c. 118: 15 5 9 5 15 5 15 15 5 9 5 15 N SD: 1.2668 c. M: 2.1654 c. 135: 17 6 10 6 17 6 17 17 6 10 6 17 N SD: 0.5470 c. M:-0.8017 c. 159: 20 7 12 7 20 7 20 20 7 12 7 20 N SD: 0.2183 c. M: 0.3745 c. 359: 45 16 27 16 45 16 45 45 16 27 16 45 N SD: 0.1424 c. M: 0.2244 c. 494: 62 22 37 22 62 22 62 62 22 37 22 62 N SD: 0.1115 c. M:-0.2079 c. 518: 65 23 39 23 65 23 65 65 23 39 23 65 N SD: 0.0564 c. M: 0.0824 c. 1012: 127 45 76 45 127 45 127 127 45 76 45 127 N SD: 0.0427 c. M:-0.0655 c. 1171: 147 52 88 52 147 52 147 147 52 88 52 147 N SD: 0.0150 c. M:-0.0274 c. 1689: 212 75 127 75 212 75 212 212 75 127 75 212 N SD: 0.0103 c. M: 0.0166 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.8769 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.6821 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 5.7876 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 17.6371 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.8224 cents 9 x 10 x 11:12 x 14 x 15:16:17:18 S SD: 10.8687 cents 10:11 x 12 x 13:14:15:16:17:18 x 20 S SD: 8.3906 cents 11:12 x 13 x x 15:17:18:19 x 20:22 SD: 8.6011 cents 12:13 x 14:15:16:17:18 x 20:21:22:24 S SD: 7.9243 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 7.3299 cents 14:15:16 x 17 x 19:21:23:24:25:26:28 SD: 6.0865 cents 15:16:17:18 x 20:21:23 x 25:27:28:30 SD: 8.0365 cents 16:17:18:19:20:21:22:24:26:27:28:29:32 SD: 6.2559 cents 17 x 19:20:21:23 x 26:28:29:30:31:34 SD: 5.5934 cents 18 x 20:21:22:24:25:27:29:30:32:33:36 SD: 4.7203 cents 19:21 x x 23:25:26:29:31:32:34:35:38 SD: 5.0248 cents 20:22:23:24 x 27:28:30:33:34:36:37:40 SD: 6.1859 cents 21:23:24:25:26:28:29:32:34:35:37:39:42 SD: 5.0621 cents 22:24:25:26:27:29:30:33:36:37:39:40:44 SD: 2.9352 cents 32:35:36:38:39:43:44:48:52:54:57:59:64 SD: 1.8458 cents 42:46:47:50:51:56:58:63:69:71:75:77:84 SD: 1.8442 cents 48:52:54:57:59:64:66:72:79:81:85:88:96 SD: 1.6643 cents 54:59:61:64:66:72:74:81:88:91:96:99:108 SD: 1.0151 cents 80:87:90:95:98:107:110:120:131:135:142:147:160 SD: 0.8725 cents 86:94:97:102:105:115:118:129:141:145:153:158:172 SD: 0.8466 cents 90:98:101:107:110:120:124:135:147:152:160:165:180 SD: 0.7561 cents 96:105:108:114:117:128:132:144:157:162:171:176:192 SD: 0.6890 cents 112:122:126:133:137:149:154:168:183:189:199:205:224 SD: 0.5921 cents 144:157:162:171:176:192:198:216:236:243:256:264:288 SD: 0.3684 cents 198:216:223:235:242:264:272:297:324:334:352:363:396 SD: 0.2977 cents 234:255:263:277:286:312:322:351:383:395:416:429:468 SD: 0.2975 cents 264:288:297:313:323:352:363:396:432:446:469:484:528 SD: 0.2480 cents 288:314:324:341:352:384:396:432:471:486:512:528:576 SD: 0.1839 cents 352:384:396:417:430:469:484:528:576:594:626:645:704 SD: 0.1684 cents 384:419:432:455:469:512:528:576:628:648:683:704:768 SD: 0.1570 cents 432:471:486:512:528:576:594:648:707:729:768:792:864 SD: 0.0855 cents