Scala analysis: buzurg_al-erin10
Decatonic with septimal Buzurg, Rastlike modes (cf. Secor, blarney.txt)
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: 8/7 231.174094 septimal whole tone 3: 16/13 359.472338 tridecimal neutral third 4: 4/3 498.044999 perfect fourth 5: 56/39 626.343244 6: 3/2 701.955001 perfect fifth 7: 21/13 830.253246 8: 12/7 933.129094 septimal major sixth 9: 24/13 1061.427339 tridecimal neutral seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 14/13 128.2982 2/3-tone 2: 52/49 102.8758 3: 14/13 128.2982 2/3-tone 4: 13/12 138.5727 tridecimal 2/3-tone 5: 14/13 128.2982 2/3-tone 6: 117/112 75.6118 7: 14/13 128.2982 2/3-tone 8: 52/49 102.8758 9: 14/13 128.2982 2/3-tone 10: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 117/112 75.612 cents 1: 2 52/49 102.876 cents 1: 5 14/13 128.298 cents 2/3-tone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 2: 2 9/8 203.910 cents major whole tone 2: 4 8/7 231.174 cents septimal whole tone 2: 4 7/6 266.871 cents septimal minor third 3: 1 117/98 306.786 cents 3: 1 63/52 332.208 cents 3: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 2 16/13 359.472 cents tridecimal neutral third 3: 3 26/21 369.747 cents 3: 2 49/39 395.169 cents 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 21/16 470.781 cents narrow fourth 4: 6 4/3 498.045 cents perfect fourth 5: 1 18/13 563.382 cents tridecimal augmented fourth 5: 3 39/28 573.657 cents 5: 1 147/104 599.079 cents 5: 1 208/147 600.921 cents 5: 3 56/39 626.343 cents 5: 1 13/9 636.618 cents tridecimal diminished fifth 6: 6 3/2 701.955 cents perfect fifth 6: 2 32/21 729.219 cents wide fifth 6: 2 14/9 764.916 cents septimal minor sixth 7: 2 78/49 804.831 cents 7: 3 21/13 830.253 cents 7: 2 13/8 840.528 cents tridecimal neutral sixth 7: 1 64/39 857.517 cents 39th subharmonic 7: 1 104/63 867.792 cents 7: 1 196/117 893.214 cents 8: 4 12/7 933.129 cents septimal major sixth 8: 4 7/4 968.826 cents harmonic seventh 8: 2 16/9 996.090 cents Pythagorean minor seventh 9: 2 24/13 1061.427 cents tridecimal neutral seventh 9: 5 13/7 1071.702 cents 16/3-tone 9: 2 49/26 1097.124 cents 9: 1 224/117 1124.388 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.22222 = 38/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 128.3 231.2 359.5 498.0 626.3 702.0 830.3 933.1 1061.4 1200.0 128.3 : 102.9 231.2 369.7 498.0 573.7 702.0 804.8 933.1 1071.7 1200.0 231.2 : 128.3 266.9 395.2 470.8 599.1 702.0 830.3 968.8 1097.1 1200.0 359.5 : 138.6 266.9 342.5 470.8 573.7 702.0 840.5 968.8 1071.7 1200.0 498.0 : 128.3 203.9 332.2 435.1 563.4 702.0 830.3 933.1 1061.4 1200.0 626.3 : 75.6 203.9 306.8 435.1 573.7 702.0 804.8 933.1 1071.7 1200.0 702.0 : 128.3 231.2 359.5 498.0 626.3 729.2 857.5 996.1 1124.4 1200.0 830.3 : 102.9 231.2 369.7 498.0 600.9 729.2 867.8 996.1 1071.7 1200.0 933.1 : 128.3 266.9 395.2 498.0 626.3 764.9 893.2 968.8 1097.1 1200.0 1061.4: 138.6 266.9 369.7 498.0 636.6 764.9 840.5 968.8 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.6118 .. 138.5727 cents 28/27, 62.9609 cents 117/112, 75.6118 cents 2: 203.9100 .. 266.8709 cents 28/27, 62.9609 cents 27/26, 65.3373 cents 3: 306.7859 .. 395.1692 cents 4802/4563, 88.3833 cents 351/343, 39.9149 cents 4: 435.0841 .. 498.0450 cents 28/27, 62.9609 cents 351/343, 39.9149 cents 5: 563.3823 .. 636.6177 cents 169/162, 73.2353 cents 27/26, 65.3373 cents 6: 701.9550 .. 764.9159 cents 28/27, 62.9609 cents 27/26, 65.3373 cents 7: 804.8308 .. 893.2141 cents 4802/4563, 88.3833 cents 351/343, 39.9149 cents 8: 933.1291 .. 996.0900 cents 28/27, 62.9609 cents 351/343, 39.9149 cents 9: 1061.4273 .. 1124.3882 cents 28/27, 62.9609 cents 27/26, 65.3373 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 117/112, 75.6118 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 13/12, 138.5727 cents Average / Smallest step : 1.587055 Largest / Average step : 1.154772 Largest / Smallest step : 1.832687 Median interval of one step : 14/13, 128.2982 cents, amount: 5 Most common interval of one step : 14/13, 128.2982 cents, amount: 5 Least squares average step : 119.05024 cents, oct.: 1190.50237 cents Scale is strictly proper Step pattern alph. order: ABACADABAC Step pattern size order : CBCDCACBCD Scale is a Constant Structure, by a margin of 39.91494 cents Scale diversity : 1.450489 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.476861 Rothenberg efficiency : 0.362698 redundancy: 0.637302 Efficiency x scale size : 3.626984 Number of different interval sizes : 38 = 4.22222 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.22222 = 38/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 21632/21609, 1.8417 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Number of recognisable fifths : 6, average 701.9550 cents Scale contains two identical disjunct pentachords Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 3 = 30.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval class 2 -- Rational properties -- Prime limit : 13 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 39 Scale harmonicity : 0.018847 Average absolute harmonicity : 0.178797 Specific harmonicity : 0.091577 Fundamental : 1/546, -9.0928 octaves, 0.4792 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 1.834560E+05, 17.48507 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 135.5, average 13.55000 Mersenne's string divisions : 655034310 Sum of van Prooijen's expressibility: 8.89955, average 0.88996 Sum of Tenney's harmonic distance : 18.67853, average 1.86785 Vogel's harmonic complexity : 20.60000 Wille's k value : 409 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 142.12096, average 2.58402 Lattice compactness (without 2's) : 84.32583, average 1.53320 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.80000 20 1 3: -1 .. 1 0.20000 6 2 7: -1 .. 1 0.10000 5 2 13: -1 .. 0 -0.50000 5 5 Average exponent except 2's :-2 / 10 =-0.20000 Average absolute exponent except 2's: 16 / 10 = 1.60000 Scale is weakly epimorphic with val: <10 16 28 35| Scale is JI-epimorphic with val: <10 16 28 37| = patent Scale is weakly epimorphic with val: <10 16 28 39| Scale is weakly epimorphic with val: <10 17 31 36| Scale is weakly epimorphic with val: <10 18 29 34|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.2918 c. M:-26.8709 c. 17: 2 1 2 2 2 1 2 1 2 2 P D3 SD: 11.0684 c. M: 19.4094 c. 19: 2 2 2 2 2 1 2 2 2 2 SP M ME SD: 11.8865 c. M:-21.4575 c. 26: 3 2 3 3 3 1 3 2 3 3 P SD: 9.3734 c. M:-19.8106 c. 27: 3 2 3 3 3 2 3 2 3 3 SP D3 SD: 7.3100 c. M:-14.1912 c. 36: 4 3 4 4 4 2 4 3 4 4 SP SD: 4.1864 c. M:-7.1943 c. 58: 6 5 6 7 6 4 6 5 6 7 SP SD: 4.2103 c. M: 7.7482 c. 63: 7 5 7 7 7 4 7 5 7 7 SP SD: 3.8439 c. M:-7.8420 c. 67: 7 6 7 8 7 4 7 6 7 8 SP SD: 3.2086 c. M: 6.3726 c. 77: 8 7 8 9 8 5 8 7 8 9 SP SD: 2.3553 c. M: 4.2792 c. 94: 10 8 10 11 10 6 10 8 10 11 SP SD: 1.1080 c. M: 2.0255 c. 130: 14 11 14 15 14 8 14 11 14 15 SP SD: 0.6657 c. M:-1.3491 c. 207: 22 18 22 24 22 13 22 18 22 24 SP SD: 0.6020 c. M: 1.2677 c. 224: 24 19 24 26 24 14 24 19 24 26 SP SD: 0.5275 c. M: 0.9862 c. 234: 25 20 25 27 25 15 25 20 25 27 SP SD: 0.4445 c. M: 0.7022 c. 270: 29 23 29 31 29 17 29 23 29 31 SP SD: 0.4783 c. M:-0.8579 c. 337: 36 29 36 39 36 21 36 29 36 39 SP SD: 0.3403 c. M: 0.5797 c. 347: 37 30 37 40 37 22 37 30 37 40 SP SD: 0.3297 c. M:-0.5885 c. 364: 39 31 39 42 39 23 39 31 39 42 SP SD: 0.2607 c. M:-0.5160 c. 441: 47 38 47 51 47 28 47 38 47 51 SP SD: 0.2659 c. M: 0.4929 c. 477: 51 41 51 55 51 30 51 41 51 55 SP SD: 0.1594 c. M:-0.2761 c. 571: 61 49 61 66 61 36 61 49 61 66 SP SD: 0.0795 c. M: 0.1314 c. 1048: 112 90 112 121 112 66 112 90 112 121 SP SD: 0.0663 c. M:-0.1236 c. 1272: 136 109 136 147 136 80 136 109 136 147 SP SD: 0.0674 c. M: 0.1102 c. 1412: 151 121 151 163 151 89 151 121 151 163 SP SD: 0.0295 c. M:-0.0584 c. 1983: 212 170 212 229 212 125 212 170 212 229 SP SD: 0.0107 c. M: 0.0195 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x x 5 x 6 S SD: 16.2568 cents 4 x x 5 x x 6 x 7 x 8 S SD: 11.1656 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 15.5408 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 10.2718 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.4546 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 10.0016 cents 9 x 10:11:12:13:14 x 15:17:18 SD: 12.8342 cents 10:11 x 12:13:14:15:16:17:18:20 S SD: 10.8391 cents 12:13:14:15:16:17:18:19:21:22:24 SD: 7.2586 cents 13:14:15:16:17:19:20:21:22:24:26 SD: 6.9020 cents 14:15:16:17:19:20:21:23:24:26:28 SD: 5.0976 cents 21:23:24:26:28:30:32:34:36:39:42 SD: 4.3596 cents 26:28:30:32:35:37:39:42:45:48:52 SD: 3.2626 cents 34:37:39:42:45:49:51:55:58:63:68 SD: 2.7022 cents 36:39:41:44:48:52:54:58:62:66:72 SD: 2.4969 cents 39:42:45:48:52:56:59:63:67:72:78 SD: 2.2477 cents 42:45:48:52:56:60:63:68:72:78:84 SD: 1.9579 cents 48:52:55:59:64:69:72:78:82:89:96 SD: 1.8240 cents 52:56:59:64:69:75:78:84:89:96:104 SD: 1.7140 cents 60:65:69:74:80:86:90:97:103:111:120 SD: 1.6282 cents 62:67:71:76:83:89:93:100:106:114:124 SD: 1.4943 cents 64:69:73:79:85:92:96:103:110:118:128 SD: 1.2549 cents 78:84:89:96:104:112:117:126:134:144:156 SD: 0.4622 cents 156:168:178:192:208:224:234:252:267:288:312 SD: 0.3927 cents 168:181:192:207:224:241:252:271:288:310:336 SD: 0.3712 cents 182:196:208:224:243:261:273:294:312:336:364 SD: 0.3245 cents 234:252:267:288:312:336:351:378:401:432:468 SD: 0.2844 cents 260:280:297:320:347:373:390:420:446:480:520 SD: 0.2662 cents 273:294:312:336:364:392:410:441:468:504:546 SD: 0.2113 cents 351:378:401:432:468:504:527:567:602:648:702 SD: 0.1938 cents 364:392:416:448:485:523:546:588:624:672:728 SD: 0.1623 cents 390:420:446:480:520:560:585:630:669:720:780 SD: 0.1569 cents 442:476:505:544:589:635:663:714:758:816:884 SD: 0.1566 cents 468:504:535:576:624:672:702:756:802:864:936 SD: 0.0771 cents 546:588:624:672:728:784:819:882:936:1008:1092 SD: 0.0000 cents