Scala analysis: buzurg1
Variant of Buzurg (Qutb al Din al-Shirazi, Persian theorist, c. 1300)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 56/39 626.343244 5: 3/2 701.955001 perfect fifth 6: 18/11 852.592059 undecimal neutral sixth 7: 21/11 1119.462965 undecimal major seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 14/13 128.2982 2/3-tone 2: 8/7 231.1741 septimal whole tone 3: 13/12 138.5727 tridecimal 2/3-tone 4: 14/13 128.2982 2/3-tone 5: 117/112 75.6118 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 7/6 266.8709 septimal minor third 8: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 117/112 75.612 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 2 14/13 128.298 cents 2/3-tone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 44/39 208.835 cents 2: 1 351/308 226.249 cents 2: 1 7/6 266.871 cents septimal minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 26/21 369.747 cents 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 352/273 440.009 cents 3: 1 154/117 475.706 cents 3: 1 117/88 493.120 cents tridecimal gentle fourth 3: 3 4/3 498.045 cents perfect fourth 4: 1 117/88 493.120 cents tridecimal gentle fourth 4: 2 39/28 573.657 cents 4: 1 88/63 578.582 cents 4: 1 63/44 621.418 cents 4: 2 56/39 626.343 cents 4: 1 176/117 706.880 cents 5: 3 3/2 701.955 cents perfect fifth 5: 1 176/117 706.880 cents 5: 1 117/77 724.294 cents 5: 1 273/176 759.991 cents 5: 1 44/27 845.453 cents neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 6: 1 11/7 782.492 cents undecimal augmented fifth 6: 1 21/13 830.253 cents 6: 1 13/8 840.528 cents tridecimal neutral sixth 6: 1 18/11 852.592 cents undecimal neutral sixth 6: 1 12/7 933.129 cents septimal major sixth 6: 1 616/351 973.751 cents 6: 1 39/22 991.165 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 7: 1 12/7 933.129 cents septimal major sixth 7: 1 7/4 968.826 cents harmonic seventh 7: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 7: 1 24/13 1061.427 cents tridecimal neutral seventh 7: 2 13/7 1071.702 cents 16/3-tone 7: 1 21/11 1119.463 cents undecimal major seventh 7: 1 224/117 1124.388 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.85714 = 48/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 128.3 359.5 498.0 626.3 702.0 852.6 1119.5 1200.0 128.3 : 231.2 369.7 498.0 573.7 724.3 991.2 1071.7 1200.0 359.5 : 138.6 266.9 342.5 493.1 760.0 840.5 968.8 1200.0 498.0 : 128.3 203.9 354.5 621.4 702.0 830.3 1061.4 1200.0 626.3 : 75.6 226.2 493.1 573.7 702.0 933.1 1071.7 1200.0 702.0 : 150.6 417.5 498.0 626.3 857.5 996.1 1124.4 1200.0 852.6 : 266.9 347.4 475.7 706.9 845.5 973.8 1049.4 1200.0 1119.5: 80.5 208.8 440.0 578.6 706.9 782.5 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.6118 .. 266.8709 cents 392/351, 191.2591 cents 117/112, 75.6118 cents 2: 203.9100 .. 417.5080 cents 112/99, 213.5980 cents 27/28,-62.9609 cents 3: 342.4827 .. 498.0450 cents 128/117, 155.5623 cents 429/448,-75.0253 cents 4: 493.1197 .. 706.8803 cents 15488/13689, 213.7606 cents 351/352,-4.9253 cents 5: 701.9550 .. 857.5173 cents 128/117, 155.5623 cents 351/352,-4.9253 cents 6: 782.4920 .. 996.0900 cents 112/99, 213.5980 cents 429/448,-75.0253 cents 7: 933.1291 .. 1124.3882 cents 392/351, 191.2591 cents 27/28,-62.9609 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 117/112, 75.6118 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.983818 Largest / Average step : 1.779139 Largest / Smallest step : 3.529490 Median interval of one step : 133.43545 cents, amount: 0 Most common interval of one step : 14/13, 128.2982 cents, amount: 2 Least squares average step : 151.51137 cents, oct.: 1212.09094 cents Scale is not proper Step pattern alph. order: ABCADEFG Step pattern size order : CFDCAEGB Scale is not a Constant Structure Scale diversity : 1.533026 Lumma stability : 0.126020 Lumma impropriety factor : 0.238186 Rothenberg efficiency : 0.303571 redundancy: 0.696429 Efficiency x scale size : 2.428571 Number of different interval sizes : 44 = 6.28571 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.85714 = 48/7 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 352/351, 4.9253 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Number of recognisable fifths : 5, average 703.9251 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 37.5000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 351 (O: 351 U: 351) Highest odd numerator or denominator: 39 Scale harmonicity : 0.015718 Average absolute harmonicity : 0.206788 Specific harmonicity : 0.080108 Fundamental : 1/858, -9.7448 octaves, 0.3049 Hz. Guide tone : 1008, 9.9773 octaves, 263718.570 Hz. Exponens Consonantiae : 8.648640E+05, 19.72211 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 113.5, average 14.18750 Mersenne's string divisions : 16662240 Sum of van Prooijen's expressibility: 7.13681, average 0.89210 Sum of Tenney's harmonic distance : 14.73603, average 1.84200 Vogel's harmonic complexity : 25.12500 Wille's k value : 643 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 95.96583, average 2.66572 Lattice compactness (without 2's) : 60.39450, average 1.67763 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.37500 13 1 3: -1 .. 2 0.25000 6 2 7: 0 .. 1 0.37500 3 11: -1 .. 0 -0.25000 2 2 13: -1 .. 0 -0.37500 3 3 Average exponent except 2's : 0 / 8 = 0.00000 Average absolute exponent except 2's: 14 / 8 = 1.75000
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 45.2647 c. M: 69.4630 c. 9: 1 2 1 1 0 1 2 1 N SD: 37.6459 c. M: 52.7963 c. 10: 1 2 1 1 1 1 2 1 P D3 I SD: 19.7808 c. M: 39.4630 c. 16: 2 3 2 1 1 2 4 1 N SD: 21.3634 c. M: 27.5921 c. 17: 2 3 2 2 1 2 4 1 N SD: 7.4922 c. M:-12.8782 c. 27: 3 5 3 3 2 3 6 2 N SD: 6.7220 c. M: 9.1561 c. 31: 3 6 4 3 2 4 7 2 N SD: 6.9297 c. M: 12.1692 c. 36: 4 7 4 4 2 5 8 2 N SD: 8.0940 c. M:-14.0746 c. 38: 4 7 5 4 2 5 8 3 N SD: 7.7757 c. M: 14.1998 c. 41: 4 8 5 4 3 5 9 3 N SD: 7.0625 c. M: 11.7091 c. 44: 5 8 5 5 3 5 10 3 N SD: 5.5297 c. M:-8.0654 c. 46: 5 9 5 5 3 6 10 3 N SD: 3.9177 c. M:-8.2775 c. 56: 6 11 6 6 4 7 12 4 N SD: 4.3119 c. M:-5.1879 c. 58: 6 11 7 6 4 7 13 4 N SD: 4.1432 c. M: 7.7482 c. 63: 7 12 7 7 4 8 14 4 N SD: 3.3837 c. M:-5.0351 c. 73: 8 14 8 8 5 9 16 5 N SD: 3.0280 c. M: 4.8943 c. 77: 8 15 9 8 5 10 17 5 N SD: 2.5347 c. M:-4.5508 c. 86: 9 17 10 9 5 11 19 6 N SD: 2.9509 c. M:-4.2806 c. 87: 9 17 10 9 6 11 19 6 N SD: 2.8734 c. M: 5.6536 c. 94: 10 18 11 10 6 12 21 6 N SD: 1.8775 c. M:-3.9413 c. 101: 11 19 12 11 6 13 22 7 N SD: 2.3231 c. M:-3.3597 c. 103: 11 20 12 11 6 13 23 7 N SD: 2.0379 c. M:-2.9259 c. 104: 11 20 12 11 7 13 23 7 N SD: 1.7503 c. M: 3.2663 c. 121: 13 23 14 13 8 15 27 8 N SD: 1.5729 c. M: 2.4475 c. 149: 16 29 17 16 9 19 33 10 N SD: 1.4529 c. M:-2.9438 c. 159: 17 31 18 17 10 20 35 11 N SD: 1.3241 c. M:-2.7918 c. 166: 18 32 19 18 10 21 37 11 N SD: 1.4218 c. M:-2.5724 c. 176: 19 34 20 19 11 22 39 12 N SD: 0.9963 c. M:-1.8913 c. 197: 21 38 23 21 12 25 44 13 N SD: 0.9579 c. M:-1.4474 c. 207: 22 40 24 22 13 26 46 14 N SD: 0.4641 c. M: 0.7620 c. 224: 24 43 26 24 14 28 50 15 N SD: 0.4040 c. M: 0.8063 c. 270: 29 52 31 29 17 34 60 18 N SD: 0.4627 c. M:-0.7413 c. 400: 43 77 46 43 25 50 89 27 N SD: 0.4705 c. M:-0.7018 c. 431: 46 83 50 46 27 54 96 29 N SD: 0.3166 c. M: 0.6199 c. 460: 49 89 53 49 29 58 102 31 N SD: 0.3490 c. M:-0.5277 c. 477: 51 92 55 51 30 60 106 32 N SD: 0.1363 c. M:-0.2761 c. 684: 73 132 79 73 43 86 152 46 N SD: 0.1554 c. M: 0.2281 c. 701: 75 135 81 75 44 88 156 47 N SD: 0.1002 c. M:-0.1903 c. 1178: 126 227 136 126 74 148 262 79 N SD: 0.0854 c. M:-0.1423 c. 1282: 137 247 148 137 81 161 285 86 N SD: 0.0822 c. M:-0.1380 c. 1506: 161 290 174 161 95 189 335 101 N SD: 0.0509 c. M: 0.1098 c. 1713: 183 330 198 183 108 215 381 115 N SD: 0.0626 c. M: 0.1028 c. 1983: 212 382 229 212 125 249 441 133 N SD: 0.0293 c. M:-0.0554 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 4 x x 5 x 6 S SD: 10.5889 cents 4 x 5 x x 6:7 x 8 S SD: 29.8232 cents 5 x 6 x 7 x 8 x 10 S SD: 18.2961 cents 6 x 7:8 x 9:10:11:12 S SD: 20.0681 cents 7:8 x 9:10 x 11:13:14 SD: 24.6199 cents 8:9:10:11 x 12:13:15:16 SD: 14.5646 cents 9:10:11:12:13:14:15:17:18 SD: 11.5183 cents 12:13:15:16:17:18:20:23:24 SD: 6.1581 cents 14:15:17:19:20:21:23:27:28 SD: 5.5854 cents 22:24:27:29:32:33:36:42:44 SD: 4.7000 cents 25:27:31:33:36:38:41:48:50 SD: 4.2514 cents 26:28:32:35:37:39:43:50:52 SD: 3.9799 cents 27:29:33:36:39:41:44:52:54 SD: 3.9635 cents 30:32:37:40:43:45:49:57:60 SD: 2.4226 cents 39:42:48:52:56:59:64:74:78 SD: 2.3510 cents 42:45:52:56:60:63:69:80:84 SD: 2.2530 cents 48:52:59:64:69:72:79:92:96 SD: 2.0202 cents 52:56:64:69:75:78:85:99:104 SD: 1.5572 cents 64:69:79:85:92:96:105:122:128 SD: 1.2866 cents 66:71:81:88:95:99:108:126:132 SD: 0.8432 cents 78:84:96:104:112:117:128:149:156 SD: 0.6297 cents 142:153:175:189:204:213:232:271:284 SD: 0.6089 cents 144:155:177:192:207:216:236:275:288 SD: 0.5155 cents 156:168:192:208:224:234:255:298:312 SD: 0.2664 cents 234:252:288:312:336:351:383:447:468 SD: 0.1417 cents 468:504:576:624:672:702:766:893:936 SD: 0.1215 cents 558:601:687:744:801:837:913:1065:1116 SD: 0.1161 cents 594:640:731:792:853:891:972:1134:1188 SD: 0.1083 cents