Scala analysis: pseudo_Odo_octatonics
pyth. 3-limit 5ths chain of 8 pitch-classes: Bb-F-C-G-D-A-E-B
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 32/27 294.134997 Pythagorean minor third 3: 81/64 407.820003 Pythagorean major third 4: 4/3 498.044999 perfect fourth 5: 3/2 701.955001 perfect fifth 6: 27/16 905.865003 Pythagorean major sixth 7: 16/9 996.089998 Pythagorean minor seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 9/8 203.9100 major whole tone 2: 256/243 90.2250 limma, Pythagorean minor second 3: 2187/2048 113.6850 apotome 4: 256/243 90.2250 limma, Pythagorean minor second 5: 9/8 203.9100 major whole tone 6: 9/8 203.9100 major whole tone 7: 256/243 90.2250 limma, Pythagorean minor second 8: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 256/243 90.225 cents limma, Pythagorean minor second 1: 1 2187/2048 113.685 cents apotome 1: 4 9/8 203.910 cents major whole tone 2: 2 9/8 203.910 cents major whole tone 2: 4 32/27 294.135 cents Pythagorean minor third 2: 2 81/64 407.820 cents Pythagorean major third 3: 1 32/27 294.135 cents Pythagorean minor third 3: 2 81/64 407.820 cents Pythagorean major third 3: 5 4/3 498.045 cents perfect fourth 4: 2 4/3 498.045 cents perfect fourth 4: 2 1024/729 588.270 cents Pythagorean diminished fifth 4: 2 729/512 611.730 cents Pythagorean tritone 4: 2 3/2 701.955 cents perfect fifth 5: 5 3/2 701.955 cents perfect fifth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 128/81 792.180 cents Pythagorean minor sixth 6: 4 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 7: 4 16/9 996.090 cents Pythagorean minor seventh 7: 1 4096/2187 1086.315 cents Pythagorean diminished octave 7: 3 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.14286 = 22/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 203.9 294.1 407.8 498.0 702.0 905.9 996.1 1200.0 203.9 : 90.2 203.9 294.1 498.0 702.0 792.2 996.1 1200.0 294.1 : 113.7 203.9 407.8 611.7 702.0 905.9 1109.8 1200.0 407.8 : 90.2 294.1 498.0 588.3 792.2 996.1 1086.3 1200.0 498.0 : 203.9 407.8 498.0 702.0 905.9 996.1 1109.8 1200.0 702.0 : 203.9 294.1 498.0 702.0 792.2 905.9 996.1 1200.0 905.9 : 90.2 294.1 498.0 588.3 702.0 792.2 996.1 1200.0 996.1 : 203.9 407.8 498.0 611.7 702.0 905.9 1109.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 203.9100 .. 407.8200 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 3: 294.1350 .. 498.0450 cents 9/8, 203.9100 cents 2048/2187,-113.6850 cents 4: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 5: 701.9550 .. 905.8650 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 6: 792.1800 .. 996.0900 cents 9/8, 203.9100 cents 2048/2187,-113.6850 cents 7: 996.0900 .. 1109.7750 cents 2187/2048, 113.6850 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.662510 Largest / Average step : 1.359400 Largest / Smallest step : 2.260017 Median interval of one step : 158.79750 cents, amount: 0 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 144.73243 cents, oct.: 1157.85941 cents Scale is not proper Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 113 163 226 276 389 502 552 665 Least number of segments generator : 333 of 600.902 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 389 of 701.955 cents and inv. generated superset size: 8 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBAABA Step pattern size order : LSMSLLSL Scale is not a Constant Structure Scale diversity : 1.241641 Lumma stability : 0.150375 Lumma impropriety factor : 0.189475 Rothenberg efficiency : 0.750000 redundancy: 0.250000 Efficiency x scale size : 6.000000 Number of different interval sizes : 14 = 2.00000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.14286 = 22/7 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 531441/524288, 23.4600 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Scale has Generated (pseudo-Myhill) property, generator: 701.955 cents and inv. Scale is a chain of 4 triads 0.0 294.135 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 7, average 701.9550 cents Scale is a complete genus musicum : 2^m 3^7 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 : 7 = 87.5000% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties -- Prime limit : 3 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.033708 Average absolute harmonicity : 0.241801 Specific harmonicity : 0.189843 Fundamental : 1/1728, -10.7549 octaves, 0.1514 Hz. Guide tone : 2592, 11.3399 octaves, 678133.465 Hz. Exponens Consonantiae : 4.478976E+06, 22.09474 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 152.0, average 19.00000 Mersenne's string divisions : 656639025 Sum of van Prooijen's expressibility: 7.63394, average 0.95424 Sum of Tenney's harmonic distance : 15.46072, average 1.93259 Vogel's harmonic complexity : 16.25000 Wille's k value : 1093 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 189.14626, average 5.25406 Lattice compactness (without 2's) : 100.00000, average 2.77778 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -6 .. 5 -0.25000 26 1 3: -3 .. 4 0.50000 16 7 Average exponent except 2's : 4 / 8 = 0.50000 Average absolute exponent except 2's: 16 / 8 = 2.00000 Scale is weakly epimorphic with val: <8 13| = patent
FIT/MODE
8: 1 1 1 0 2 1 1 1 N T3 SD: 39.1746 c. M:-53.9100 c. 10: 2 0 1 1 2 1 1 2 N SD: 40.0184 c. M: 65.8650 c. 12: 2 1 1 1 2 2 1 2 N D3 SD: 4.5849 c. M: 7.8200 c. Minor Bebop, Dorian Bebop, Raga Khokhar, Zilla, Mixolydian/Dorian mixed 29: 5 2 3 2 5 5 2 5 N G SD: 3.5020 c. M:-5.9731 c. 41: 7 3 4 3 7 7 3 7 N G SD: 1.1351 c. M:-1.9361 c. 53: 9 4 5 4 9 9 4 9 N G SD: 0.1600 c. M: 0.2728 c. 200: 34 15 19 15 34 34 15 34 N G SD: 0.1055 c. M:-0.1800 c. 253: 43 19 24 19 43 43 19 43 N G SD: 0.0499 c. M:-0.0851 c. 306: 52 23 29 23 52 52 23 52 N G SD: 0.0136 c. M:-0.0231 c. 359: 61 27 34 27 61 61 27 61 N G SD: 0.0121 c. M: 0.0206 c. 665: 113 50 63 50 113 113 50 113 N G SD: 0.0003 c. M: 0.0005 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x x 4 x 5 x 6 S SD: 7.1688 cents 4 x x 5 x 6 x 7:8 S SD: 8.6813 cents 5 x 6 x 7 x 8:9:10 S SD: 25.7345 cents 6 x 7 x 8:9:10:11:12 S SD: 10.5986 cents 7:8 x 9 x 11:12 x 14 SD: 18.6721 cents 8:9 x 10:11:12 x 14:16 S SD: 10.5986 cents 9:10:11 x 12:14:15:16:18 S SD: 12.5577 cents 10:11:12 x 13:15:17:18:20 SD: 9.6077 cents 12 x 14:15:16:18:20:21:24 S SD: 7.0156 cents 13:15 x 16:17:20:22:23:26 SD: 12.2922 cents 14:16:17:18:19:21:24:25:28 SD: 8.8317 cents 15:17:18:19:20:23:25:27:30 SD: 6.8473 cents 16:18:19:20:21:24:27:28:32 S SD: 5.5348 cents 18:20:21:23:24:27:30:32:36 SD: 5.5086 cents 22:25:26:28:29:33:37:39:44 SD: 3.6884 cents 26:29:31:33:35:39:44:46:52 SD: 3.3565 cents 32:36:38:41:43:48:54:57:64 SD: 3.2005 cents 33:37:39:42:44:50:56:59:66 SD: 3.1746 cents 38:43:45:48:51:57:64:68:76 SD: 2.4511 cents 42:47:50:53:56:63:71:75:84 SD: 1.9307 cents 48:54:57:61:64:72:81:85:96 SD: 1.2983 cents 64:72:76:81:85:96:108:114:128 SD: 1.0363 cents 80:90:95:101:107:120:135:142:160 SD: 1.0173 cents 86:97:102:109:115:129:145:153:172 SD: 0.9418 cents 90:101:107:114:120:135:152:160:180 SD: 0.8975 cents 102:115:121:129:136:153:172:181:204 SD: 0.6851 cents 135:152:160:171:180:203:228:240:270 SD: 0.6164 cents 144:162:171:182:192:216:243:256:288 SD: 0.5163 cents 162:182:192:205:216:243:273:288:324 SD: 0.4214 cents 216:243:256:273:288:324:365:384:432 SD: 0.4198 cents 222:250:263:281:296:333:375:395:444 SD: 0.3689 cents 234:263:277:296:312:351:395:416:468 SD: 0.3574 cents 248:279:294:314:331:372:419:441:496 SD: 0.3573 cents 264:297:313:334:352:396:446:469:528 SD: 0.3083 cents 282:317:334:357:376:423:476:501:564 SD: 0.2775 cents 297:334:352:376:396:446:501:528:594 SD: 0.2757 cents 320:360:379:405:427:480:540:569:640 SD: 0.2286 cents 336:378:398:425:448:504:567:597:672 SD: 0.2130 cents 384:432:455:486:512:576:648:683:768 SD: 0.1181 cents 432:486:512:547:576:648:729:768:864 SD: 0.0989 cents