Scala analysis: sk3_17_4
{289/288, 2187/2176} block #4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 9/8 203.910002 major whole tone 3: 81/68 302.864594 Persian wosta 4: 34/27 399.090407 septendecimal major third 5: 4/3 498.044999 perfect fourth 6: 17/12 603.000409 2nd septendecimal tritone 7: 3/2 701.955001 perfect fifth 8: 27/17 800.909593 septendecimal minor sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 17/9 1101.045408 septendecimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 18/17 98.9546 Arabic lute index finger 1: 17/16 104.9554 17th harmonic 2: 18/17 98.9546 Arabic lute index finger 3: 18/17 98.9546 Arabic lute index finger 4: 2312/2187 96.2258 5: 18/17 98.9546 Arabic lute index finger 6: 17/16 104.9554 17th harmonic 7: 18/17 98.9546 Arabic lute index finger 8: 18/17 98.9546 Arabic lute index finger 9: 17/16 104.9554 17th harmonic 10: 256/243 90.2250 limma, Pythagorean minor second 11: 17/16 104.9554 17th harmonic 12: 18/17 98.9546 Arabic lute index finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 2312/2187 96.226 cents 1: 6 18/17 98.955 cents Arabic lute index finger 1: 4 17/16 104.955 cents 17th harmonic 2: 4 272/243 195.180 cents Persian whole tone 2: 2 324/289 197.909 cents two (Arabic lute index finger) 2: 6 9/8 203.910 cents major whole tone 3: 4 32/27 294.135 cents Pythagorean minor third 3: 2 289/243 300.136 cents 3: 5 81/68 302.865 cents Persian wosta 3: 1 153/128 308.865 cents 4: 2 64/51 393.090 cents 4: 6 34/27 399.090 cents septendecimal major third 4: 2 729/578 401.819 cents 4: 2 81/64 407.820 cents Pythagorean major third 5: 9 4/3 498.045 cents perfect fourth 5: 1 289/216 504.046 cents 5: 2 729/544 506.775 cents 6: 6 24/17 597.000 cents 1st septendecimal tritone 6: 6 17/12 603.000 cents 2nd septendecimal tritone 7: 2 1088/729 693.225 cents 7: 1 432/289 695.954 cents 7: 9 3/2 701.955 cents perfect fifth 8: 2 128/81 792.180 cents Pythagorean minor sixth 8: 2 1156/729 798.181 cents two (septendecimal major third) 8: 6 27/17 800.910 cents septendecimal minor sixth 8: 2 51/32 806.910 cents 9: 1 256/153 891.135 cents 9: 5 136/81 897.135 cents 9: 2 486/289 899.864 cents 9: 4 27/16 905.865 cents Pythagorean major sixth 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 2 289/162 1002.091 cents 10: 4 243/136 1004.820 cents 11: 4 32/17 1095.045 cents 17th subharmonic 11: 6 17/9 1101.045 cents septendecimal major seventh 11: 1 2187/1156 1103.774 cents 11: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 105.0 203.9 302.9 399.1 498.0 603.0 702.0 800.9 905.9 996.1 1101.0 1200.0 105.0 : 99.0 197.9 294.1 393.1 498.0 597.0 696.0 800.9 891.1 996.1 1095.0 1200.0 203.9 : 99.0 195.2 294.1 399.1 498.0 597.0 702.0 792.2 897.1 996.1 1101.0 1200.0 302.9 : 96.2 195.2 300.1 399.1 498.0 603.0 693.2 798.2 897.1 1002.1 1101.0 1200.0 399.1 : 99.0 203.9 302.9 401.8 506.8 597.0 702.0 800.9 905.9 1004.8 1103.8 1200.0 498.0 : 105.0 203.9 302.9 407.8 498.0 603.0 702.0 806.9 905.9 1004.8 1101.0 1200.0 603.0 : 99.0 197.9 302.9 393.1 498.0 597.0 702.0 800.9 899.9 996.1 1095.0 1200.0 702.0 : 99.0 203.9 294.1 399.1 498.0 603.0 702.0 800.9 897.1 996.1 1101.0 1200.0 800.9 : 105.0 195.2 300.1 399.1 504.0 603.0 702.0 798.2 897.1 1002.1 1101.0 1200.0 905.9 : 90.2 195.2 294.1 399.1 498.0 597.0 693.2 792.2 897.1 996.1 1095.0 1200.0 996.1 : 105.0 203.9 308.9 407.8 506.8 603.0 702.0 806.9 905.9 1004.8 1109.8 1200.0 1101.0: 99.0 203.9 302.9 401.8 498.0 597.0 702.0 800.9 899.9 1004.8 1095.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 104.9554 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 2: 195.1804 .. 203.9100 cents 2187/2176, 8.7296 cents 256/243, 90.2250 cents 3: 294.1350 .. 308.8654 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 4: 393.0896 .. 407.8200 cents 4131/4096, 14.7304 cents 8192/7803, 84.2242 cents 5: 498.0450 .. 506.7746 cents 2187/2176, 8.7296 cents 256/243, 90.2250 cents 6: 596.9996 .. 603.0004 cents 289/288, 6.0008 cents 256/243, 90.2250 cents 7: 693.2254 .. 701.9550 cents 2187/2176, 8.7296 cents 256/243, 90.2250 cents 8: 792.1800 .. 806.9104 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 9: 891.1346 .. 905.8650 cents 4131/4096, 14.7304 cents 8192/7803, 84.2242 cents 10: 996.0900 .. 1004.8196 cents 2187/2176, 8.7296 cents 256/243, 90.2250 cents 11: 1095.0446 .. 1109.7750 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 17/16, 104.9554 cents Average / Smallest step : 1.108340 Largest / Average step : 1.049554 Largest / Smallest step : 1.163263 Median interval of one step : 18/17, 98.9546 cents, amount: 6 Most common interval of one step : 18/17, 98.9546 cents, amount: 6 Least squares average step : 100.11093 cents, oct.: 1201.33116 cents Scale is strictly proper Step pattern alph. order: ABBCBABBADAB Step pattern size order : DCCBCDCCDADC Scale is a Constant Structure, by a margin of 84.22418 cents Scale diversity : 1.088629 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.892249 Rothenberg efficiency : 0.409689 redundancy: 0.590311 Efficiency x scale size : 4.916270 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 19683/19652, 2.7288 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 : 12, average 700.0000 cents Scale is a well-temperament. It has 3 different sizes of fifth Best fifths form a closed circle Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 7 = 58.3333% Limited transpositions with margin 14.7304 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 14.7304 cents: 1 2 3 4 5 6 7 8 9 10 11 -- Rational properties -- Prime limit : 17 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.011507 Average absolute harmonicity : 0.163244 Specific harmonicity : 0.067704 Fundamental : 1/7344, -12.8424 octaves, 0.0356 Hz. Guide tone : 22032, 14.4273 octaves, 5764134.455 Hz. Exponens Consonantiae : 1.618030E+08, 27.26966 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 221.0, average 18.41667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.75665, average 1.06305 Sum of Tenney's harmonic distance : 25.10408, average 2.09201 Vogel's harmonic complexity : 33.16667 Wille's k value : 6196 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 330.36262, average 4.23542 Lattice compactness (without 2's) : 216.46430, average 2.77518 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.66667 24 1 3: -3 .. 4 0.33333 22 5 17: -1 .. 1 0.16667 6 6 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 28 / 12 = 2.33333 Scale is weakly epimorphic with val: <12 17 47| Scale is JI-epimorphic with val: <12 19 49| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 3.1242 c. M: 5.8650 c. Twelve-tone Chromatic (1/11-comma) 70: 6 6 6 5 6 6 6 6 6 5 6 6 SP B ME SD: 3.1994 c. M:-5.7068 c. Diaschismic-12 82: 7 7 7 6 7 7 7 7 7 6 7 7 SP B ME SD: 2.6339 c. M:-4.4525 c. Pajaric-12 87: 8 7 7 7 7 8 7 7 8 6 8 7 SP D3 SD: 2.8042 c. M:-5.3894 c. 94: 8 8 8 7 8 8 8 8 8 7 8 8 SP B ME SD: 2.2804 c. M:-3.5184 c. 99: 9 8 8 8 8 9 8 8 9 7 9 8 SP D3 SD: 2.1225 c. M:-4.1355 c. 106: 9 9 9 8 9 9 9 9 9 8 9 9 SP B ME SD: 2.0681 c. M: 3.0686 c. 111: 10 9 9 9 9 10 9 9 10 8 10 9 SP D3 SD: 1.6014 c. M:-3.1527 c. 123: 11 10 10 10 10 11 10 10 11 9 11 10 SP D3 SD: 1.2018 c. M:-2.3617 c. 135: 12 11 11 11 11 12 11 11 12 10 12 11 SP D3 SD: 0.9047 c. M:-1.7113 c. 147: 13 12 12 12 12 13 12 12 13 11 13 12 SP D3 SD: 0.7068 c. M:-1.1670 c. 159: 14 13 13 13 13 14 13 13 14 12 14 13 SP D3 SD: 0.6125 c. M: 0.9778 c. 229: 20 19 19 18 19 20 19 19 20 17 20 19 SP SD: 0.5821 c. M:-1.0655 c. 241: 21 20 20 19 20 21 20 20 21 18 21 20 SP SD: 0.4971 c. M:-0.8698 c. 253: 22 21 21 20 21 22 21 21 22 19 22 21 SP SD: 0.4635 c. M:-0.6927 c. 265: 23 22 22 21 22 23 22 22 23 20 23 22 SP SD: 0.4766 c. M: 0.8045 c. 352: 31 29 29 28 29 31 29 29 31 26 31 29 SP SD: 0.5017 c. M:-0.9532 c. 364: 32 30 30 29 30 32 30 30 32 27 32 30 SP SD: 0.3829 c. M:-0.7284 c. 376: 33 31 31 30 31 33 31 31 33 28 33 31 SP SD: 0.2723 c. M:-0.5180 c. 388: 34 32 32 31 32 34 32 32 34 29 34 32 SP SD: 0.1700 c. M:-0.3206 c. 400: 35 33 33 32 33 35 33 33 35 30 35 33 SP SD: 0.0802 c. M:-0.1354 c. 412: 36 34 34 33 34 36 34 34 36 31 36 34 SP SD: 0.0552 c. M: 0.1010 c. 812: 71 67 67 65 67 71 67 67 71 61 71 67 SP SD: 0.0506 c. M:-0.0911 c. 971: 85 80 80 78 80 85 80 80 85 73 85 80 SP SD: 0.0617 c. M:-0.0909 c. 1212: 106 100 100 97 100 106 100 100 106 91 106 100 SP SD: 0.0579 c. M:-0.1057 c. 1224: 107 101 101 98 101 107 101 101 107 92 107 101 SP SD: 0.0475 c. M:-0.0766 c. 1371: 120 113 113 110 113 120 113 113 120 103 120 113 SP SD: 0.0398 c. M:-0.0774 c. 1383: 121 114 114 111 114 121 114 114 121 104 121 114 SP SD: 0.0284 c. M: 0.0446 c. 1783: 156 147 147 143 147 156 147 147 156 134 156 147 SP SD: 0.0183 c. M:-0.0362 c. 1795: 157 148 148 144 148 157 148 148 157 135 157 148 SP SD: 0.0128 c. M: 0.0234 c. 2195: 192 181 181 176 181 192 181 181 192 165 192 181 SP SD: 0.0064 c. M:-0.0120 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: 7.5273 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.9535 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.0920 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.2498 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.1091 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.1155 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0071 cents 11:12 x 13:14:15:16 x 17:19:20:21:22 SD: 10.9211 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.0727 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.3490 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.7223 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.1715 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.7729 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.1634 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.2838 cents 30:32:34:36:38:40:43:45:48:51:53:57:60 SD: 3.1545 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.6004 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2781 cents 42:45:47:50:53:56:60:63:67:71:75:79:84 SD: 2.2021 cents 46:49:52:55:58:61:65:69:73:78:82:87:92 SD: 1.5443 cents 48:51:54:57:60:64:68:72:76:81:85:91:96 SD: 1.4596 cents 58:62:65:69:73:77:82:87:92:98:103:110:116 SD: 1.4211 cents 62:66:70:74:78:83:88:93:98:105:110:117:124 SD: 1.3045 cents 63:67:71:75:79:84:89:95:100:106:112:119:126 SD: 1.1789 cents 78:83:88:93:98:104:111:117:124:132:139:147:156 SD: 1.0860 cents 80:85:90:95:101:107:113:120:127:135:142:151:160 SD: 0.8867 cents 96:102:108:114:121:128:136:144:152:162:171:181:192 SD: 0.7517 cents 112:119:126:133:141:149:159:168:178:189:199:212:224 SD: 0.7094 cents 126:134:142:150:159:168:179:189:200:213:224:238:252 SD: 0.6452 cents 142:151:160:169:179:189:201:213:226:240:252:268:284 SD: 0.6343 cents 144:153:162:172:181:192:204:216:229:243:256:272:288 SD: 0.5109 cents 158:168:178:188:199:211:224:237:251:267:281:298:316 SD: 0.4833 cents 162:172:182:193:204:216:230:243:257:273:288:306:324 SD: 0.4644 cents 177:188:199:211:223:236:251:266:281:299:315:334:354 SD: 0.4390 cents 189:201:213:225:238:252:268:284:300:319:336:357:378 SD: 0.4251 cents 192:204:216:229:242:256:272:288:305:324:341:363:384 SD: 0.3003 cents 224:238:252:267:282:299:317:336:356:378:398:423:448 SD: 0.2765 cents 240:255:270:286:302:320:340:360:381:405:427:453:480 SD: 0.2079 cents 288:306:324:343:363:384:408:432:457:486:512:544:576 SD: 0.1872 cents 336:357:378:400:423:448:476:504:534:567:597:635:672 SD: 0.1731 cents 432:459:486:515:544:576:612:648:686:729:768:816:864 SD: 0.1180 cents 528:561:594:629:665:704:748:792:839:891:939:997:1056 SD: 0.1036 cents 576:612:648:686:725:768:816:864:915:972:1024:1088:1152 SD: 0.0761 cents