Scala analysis: xen11-chalmers-tetrachordal-10-02
Eight Tone Fourth Modular Diamond
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 16/15 111.731285 minor diatonic semitone 3: 5/4 386.313714 major third 4: 9/7 435.084095 septimal major third, BP third 5: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 6: 4/3 498.044999 perfect fourth 7: 48/35 546.815381 septimal semi-augmented fourth 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 35/24 653.1846 septimal semi-diminished fifth 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 75/64 274.5824 classic augmented second 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 245/243 14.1905 minor BP diesis, Sensamagic comma 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 35/24 653.1846 septimal semi-diminished fifth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 245/243 14.191 cents minor BP diesis, Sensamagic comma 1: 4 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 75/64 274.582 cents classic augmented second 1: 1 35/24 653.185 cents septimal semi-diminished fifth 2: 2 28/27 62.961 cents Archytas' 1/3-tone 2: 1 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 135/112 323.353 cents septimal wide minor third 2: 1 3/2 701.955 cents perfect fifth 2: 1 245/162 716.146 cents 3: 2 16/15 111.731 cents minor diatonic semitone 3: 1 175/144 337.543 cents 3: 1 243/196 372.123 cents 3: 1 5/4 386.314 cents major third 3: 1 54/35 750.725 cents septimal semi-augmented fifth 3: 2 14/9 764.916 cents septimal minor sixth 4: 1 192/175 160.502 cents septimal 4/5-tone 4: 2 5/4 386.314 cents major third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 14/9 764.916 cents septimal minor sixth 4: 2 8/5 813.686 cents minor sixth 4: 1 175/96 1039.498 cents 5: 2 9/7 435.084 cents septimal major third, BP third 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 5: 1 8/5 813.686 cents minor sixth 5: 1 392/243 827.877 cents 5: 1 288/175 862.457 cents 5: 2 15/8 1088.269 cents classic major seventh 6: 1 324/245 483.854 cents 6: 1 4/3 498.045 cents perfect fourth 6: 2 224/135 876.647 cents narrow septimal major sixth 6: 1 15/8 1088.269 cents classic major seventh 6: 1 1225/648 1102.459 cents 6: 2 27/14 1137.039 cents septimal major seventh 7: 1 48/35 546.815 cents septimal semi-augmented fourth 7: 1 128/75 925.418 cents diminished seventh 7: 1 27/14 1137.039 cents septimal major seventh 7: 4 35/18 1151.230 cents septimal semi-diminished octave 7: 1 486/245 1185.809 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.71429 = 40/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 63.0 111.7 386.3 435.1 449.3 498.0 546.8 1200.0 63.0 : 48.8 323.4 372.1 386.3 435.1 483.9 1137.0 1200.0 111.7 : 274.6 323.4 337.5 386.3 435.1 1088.3 1151.2 1200.0 386.3 : 48.8 63.0 111.7 160.5 813.7 876.6 925.4 1200.0 435.1 : 14.2 63.0 111.7 764.9 827.9 876.6 1151.2 1200.0 449.3 : 48.8 97.5 750.7 813.7 862.5 1137.0 1185.8 1200.0 498.0 : 48.8 702.0 764.9 813.7 1088.3 1137.0 1151.2 1200.0 546.8 : 653.2 716.1 764.9 1039.5 1088.3 1102.5 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.1905 .. 653.1846 cents 81/56, 638.9941 cents 245/243, 14.1905 cents 2: 62.9609 .. 716.1455 cents 35/24, 653.1846 cents 32/45,-590.2237 cents 3: 111.7313 .. 764.9159 cents 35/24, 653.1846 cents 864/1225,-604.4142 cents 4: 160.5017 .. 1039.4983 cents 30625/18432, 878.9967 cents 864/1225,-604.4142 cents 5: 435.0841 .. 1088.2687 cents 35/24, 653.1846 cents 864/1225,-604.4142 cents 6: 483.8545 .. 1137.0391 cents 35/24, 653.1846 cents 864/1225,-604.4142 cents 7: 546.8154 .. 1185.8095 cents 81/56, 638.9941 cents 32/45,-590.2237 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 245/243, 14.1905 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 35/24, 653.1846 cents Average / Smallest step : 10.570435 Largest / Average step : 4.354564 Largest / Smallest step : 46.029638 Median interval of one step : 36/35, 48.7704 cents, amount: 4 Most common interval of one step : 36/35, 48.7704 cents, amount: 4 Least squares average step : 107.09829 cents, oct.: 856.78634 cents Scale is not proper Step pattern alph. order: ABCBDBBE Step pattern size order : CBDBABBE Scale is not a Constant Structure Scale diversity : 1.462806 Lumma stability : 0.023651 Lumma impropriety factor : 0.895065 Rothenberg efficiency : 0.356250 redundancy: 0.643750 Efficiency x scale size : 2.850000 Number of different interval sizes : 32 = 4.57143 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.71429 = 40/7 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 36/35, 48.7704 cents & inv., amount: 4 Number of recognisable fifths : 2, average 709.0503 cents Number of appreciable fifths : 1, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 12.5000% -- Rational properties -- Prime limit : 7 Odd number limit : 1225 (O: 1225 U: 1225) Highest odd numerator or denominator: 35 Scale harmonicity : 0.018974 Average absolute harmonicity : 0.200814 Specific harmonicity : 0.109775 Fundamental : 1/3780, -11.8842 octaves, 0.0692 Hz. Guide tone : 5040, 12.2992 octaves, 1318592.849 Hz. Exponens Consonantiae : 1.905120E+07, 24.18338 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 133.0, average 16.62500 Mersenne's string divisions : 142647120 Sum of van Prooijen's expressibility: 7.82592, average 0.97824 Sum of Tenney's harmonic distance : 15.94006, average 1.99251 Vogel's harmonic complexity : 22.50000 Wille's k value : 2362 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 132.33995, average 3.67611 Lattice compactness (without 2's) : 87.80830, average 2.43912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.37500 15 1 3: -3 .. 2 -0.62500 11 1 5: -1 .. 1 0.00000 4 2 7: -1 .. 1 0.00000 4 4 Average exponent except 2's :-5 / 8 =-0.62500 Average absolute exponent except 2's: 19 / 8 = 2.37500 Scale is weakly epimorphic with val: <8 12 21 21|
FIT/MODE
8: 0 1 2 0 0 0 1 4 N SD: 43.0762 c. M:-63.6863 c. 9: 0 1 2 0 0 1 0 5 N SD: 34.8281 c. M: 62.9609 c. 10: 1 0 2 1 0 0 1 5 N SD: 35.5843 c. M:-57.0391 c. 11: 1 0 3 0 0 1 0 6 N SD: 29.7023 c. M:-50.0499 c. 13: 1 0 3 1 0 0 1 7 N SD: 21.6874 c. M: 36.5065 c. 15: 1 0 4 0 1 0 1 8 N SD: 22.8005 c. M: 35.0841 c. 16: 1 0 4 1 0 1 0 9 N SD: 19.5180 c. M: 36.7313 c. 17: 1 0 4 1 0 1 1 9 N SD: 22.3508 c. M: 41.1430 c. 18: 1 1 4 1 0 1 0 10 N SD: 20.5994 c. M:-35.2883 c. 19: 1 1 4 1 0 1 1 10 N SD: 10.5274 c. M:-21.6057 c. 22: 1 1 5 1 0 1 1 12 N SD: 6.3157 c. M: 12.9110 c. 41: 2 2 9 2 0 2 2 22 N SD: 6.0108 c. M: 10.2502 c. 50: 3 2 11 2 1 2 2 27 N SD: 5.8365 c. M:-9.0391 c. 53: 3 2 12 2 1 2 2 29 N SD: 3.1045 c. M:-4.9636 c. 72: 4 3 16 3 1 3 3 39 N SD: 2.8401 c. M:-4.9354 c. 74: 4 3 17 3 1 3 3 40 N SD: 3.3122 c. M:-4.7794 c. 75: 4 3 17 3 1 3 3 41 N SD: 1.9284 c. M: 3.0841 c. 77: 4 3 18 3 1 3 3 42 N SD: 1.9136 c. M:-3.2967 c. 96: 5 4 22 4 1 4 4 52 N SD: 1.6784 c. M:-3.1846 c. 99: 5 4 23 4 1 4 4 54 N SD: 1.5904 c. M: 2.6404 c. 118: 6 5 27 5 1 5 5 64 N SD: 1.4791 c. M:-2.3372 c. 149: 8 6 34 6 2 6 6 81 N SD: 1.0397 c. M:-1.7321 c. 152: 8 6 35 6 2 6 6 83 N SD: 0.9898 c. M: 2.0785 c. 171: 9 7 39 7 2 7 7 93 N SD: 0.3224 c. M:-0.5530 c. 419: 22 17 96 17 5 17 17 228 N SD: 0.2290 c. M:-0.3674 c. 441: 23 18 101 18 5 18 18 240 N SD: 0.2149 c. M: 0.3759 c. 494: 26 20 113 20 6 20 20 269 N SD: 0.1584 c. M: 0.2663 c. 590: 31 24 135 24 7 24 24 321 N SD: 0.1863 c. M:-0.3033 c. 612: 32 25 140 25 7 25 25 333 N SD: 0.1649 c. M: 0.2550 c. 665: 35 27 152 27 8 27 27 362 N SD: 0.1257 c. M:-0.1970 c. 913: 48 37 209 37 11 37 37 497 N SD: 0.1081 c. M:-0.2325 c. 935: 49 38 214 38 11 38 38 509 N SD: 0.0598 c. M: 0.0774 c. 1106: 58 45 253 45 13 45 45 602 N SD: 0.0420 c. M: 0.0884 c. 1525: 80 62 349 62 18 62 62 830 N SD: 0.0440 c. M:-0.0699 c. 1848: 97 75 423 75 22 75 75 1006 N SD: 0.0434 c. M:-0.0760 c. 2019: 106 82 462 82 24 82 82 1099 N SD: 0.0277 c. M:-0.0567 c. 2190: 115 89 501 89 26 89 89 1192 N SD: 0.0350 c. M:-0.0528 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3:4 S SD: 77.5698 cents 3 x x x x x 4 x 6 S SD: 0.0000 cents 4 x x 5 x x x 6:8 S SD: 51.7132 cents 5 x x 6 x x x 7:10 SD: 26.3920 cents 6 x x x x x 8 x 12 S SD: 0.0000 cents 7 x 8 x 9 x x 10:14 SD: 34.6962 cents 8 x 9:10 x x x 11:16 SD: 23.0722 cents 9 x 10:11 x x 12 x 18 S SD: 20.1684 cents 10 x 11 x x 13 x 14:20 SD: 16.0792 cents 11 x 12 x 14 x x 15:22 SD: 10.9541 cents 12 x 13:15 x x 16 x 24 SD: 6.7103 cents 13 x 14:16 x 17 x 18:26 SD: 7.7434 cents 14 x 15 x 18 x x 19:28 SD: 4.9251 cents 15 x 16:19 x x 20:21:30 SD: 8.4855 cents 16 x 17:20 x 21 x 22:32 SD: 4.5987 cents 17 x 18:21 x 22 x 23:34 SD: 6.7634 cents 18 x 19 x 23 x 24:25:36 SD: 6.0770 cents 19 x 20:24 x x 25:26:38 SD: 7.4691 cents 20:21 x 25 x 26:27 x 40 SD: 6.1626 cents 21:22 x 26:27 x 28:29:42 SD: 4.4936 cents 22:23 x x 28 x 29:30:44 SD: 6.3042 cents 23:24:25:29 x 30:31:32:46 SD: 7.1278 cents 24:25:26:30 x 31:32:33:48 SD: 4.1369 cents 25:26:27:31:32 x 33:34:50 SD: 5.0556 cents 26:27:28 x 33:34:35:36:52 SD: 5.6382 cents 27:28:29:34 x 35:36:37:54 SD: 2.5095 cents 28:29:30:35:36 x 37:38:56 SD: 3.5972 cents 30:31:32:38 x 39:40:41:60 SD: 3.5710 cents 31:32:33:39:40 x 41:43:62 SD: 4.0952 cents 32:33:34:40:41 x 43:44:64 SD: 2.7768 cents 34:35:36:43 x 44:45:47:68 SD: 4.7313 cents 35:36:37:44:45 x 47:48:70 SD: 3.7569 cents 37:38:39:46 x 48:49:51:74 SD: 4.5405 cents 38:39:41:48:49 x 51:52:76 SD: 4.9774 cents 39:40:42:49:50:51:52:53:78 SD: 4.3701 cents 40:41:43:50:51:52:53:55:80 SD: 3.8779 cents 41:43:44:51 x 53:55:56:82 SD: 3.9026 cents 42:44:45:53:54 x 56:58:84 SD: 3.9929 cents 43:45:46:54:55:56:57:59:86 SD: 3.0241 cents 44:46:47:55 x 57:59:60:88 SD: 2.8453 cents 45:47:48:56:58 x 60:62:90 SD: 2.4473 cents 48:50:51:60 x 62:64:66:96 SD: 1.8296 cents 51:53:54:64 x 66:68:70:102 SD: 2.1799 cents 52:54:55:65:67 x 69:71:104 SD: 2.7156 cents 53:55:57:66:68:69:71:73:106 SD: 2.6149 cents 54:56:58:68:69:70:72:74:108 SD: 2.5723 cents 55:57:59:69:71 x 73:75:110 SD: 2.6543 cents 56:58:60:70:72:73:75:77:112 SD: 1.9283 cents 57:59:61:71:73:74:76:78:114 SD: 1.5151 cents 58:60:62:73 x 75:77:80:116 SD: 2.6584 cents 59:61:63:74:76 x 79:81:118 SD: 1.6461 cents 60:62:64:75:77:78:80:82:120 SD: 1.3070 cents 62:64:66:78:80 x 83:85:124 SD: 2.4216 cents 63:65:67:79:81:82:84:86:126 SD: 1.9741 cents 64:66:68:80:82:83:85:88:128 SD: 1.9478 cents 65:67:69:81 x 84:87:89:130 SD: 2.4267 cents 67:69:71:84:86:87:89:92:134 SD: 2.3838 cents 69:72:74:86:89 x 92:95:138 SD: 2.4957 cents 70:73:75:88:90:91:93:96:140 SD: 2.2129 cents 71:74:76:89:91:92:95:97:142 SD: 1.9643 cents 72:75:77:90 x 93:96:99:144 SD: 1.6805 cents 73:76:78:91:94:95:97:100:146 SD: 1.6246 cents 75:78:80:94:96:97:100:103:150 SD: 1.4064 cents 77:80:82:96:99:100:103:106:154 SD: 1.3870 cents 79:82:84:99 x 102:105:108:158 SD: 1.8046 cents 80:83:85:100:103:104:107:110:160 SD: 1.4039 cents 81:84:86:101:104:105:108:111:162 SD: 1.1878 cents 84:87:90:105:108:109:112:115:168 SD: 1.0934 cents 86:89:92:108:111 x 115:118:172 SD: 1.8820 cents 87:90:93:109:112:113:116:119:174 SD: 1.1543 cents 88:91:94:110:113:114:117:121:176 SD: 1.1241 cents 104:108:111:130:134:135:139:143:208 SD: 0.9967 cents 105:109:112:131:135:136:140:144:210 SD: 0.5002 cents 108:112:115:135:139:140:144:148:216 SD: 0.4678 cents 165:171:176:206:212:214:220:226:330 SD: 0.4442 cents 192:199:205:240:247:249:256:263:384 SD: 0.3886 cents 213:221:227:266:274:276:284:292:426 SD: 0.3420 cents 240:249:256:300:309:311:320:329:480 SD: 0.3381 cents 267:277:285:334:343:346:356:366:534 SD: 0.3232 cents 297:308:317:371:382:385:396:407:594 SD: 0.2727 cents 347:360:370:434:446:450:463:476:694 SD: 0.2632 cents 372:386:397:465:478:482:496:510:744 SD: 0.2437 cents 375:389:400:469:482:486:500:514:750 SD: 0.1953 cents 452:469:482:565:581:586:603:620:904 SD: 0.1934 cents 465:482:496:581:598:603:620:638:930 SD: 0.1925 cents 480:498:512:600:617:622:640:658:960 SD: 0.1632 cents 540:560:576:675:694:700:720:741:1080 SD: 0.1537 cents 567:588:605:709:729:735:756:778:1134 SD: 0.1527 cents