Scala analysis: sc3_17_3
{153/152, 289/288, 513/512} Fokker block #3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 9/8 203.910002 major whole tone 3: 153/128 308.865411 4: 64/51 393.089590 5: 4/3 498.044999 perfect fourth 6: 24/17 596.999591 1st septendecimal tritone 7: 3/2 701.955001 perfect fifth 8: 51/32 806.910410 9: 27/16 905.865003 Pythagorean major sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 32/17 1095.044590 17th subharmonic 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 17/16 104.9554 17th harmonic 1: 18/17 98.9546 Arabic lute index finger 2: 17/16 104.9554 17th harmonic 3: 17/16 104.9554 17th harmonic 4: 8192/7803 84.2242 5: 17/16 104.9554 17th harmonic 6: 18/17 98.9546 Arabic lute index finger 7: 17/16 104.9554 17th harmonic 8: 17/16 104.9554 17th harmonic 9: 18/17 98.9546 Arabic lute index finger 10: 256/243 90.2250 limma, Pythagorean minor second 11: 18/17 98.9546 Arabic lute index finger 12: 17/16 104.9554 17th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 8192/7803 84.224 cents 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 18/17 98.955 cents Arabic lute index finger 1: 6 17/16 104.955 cents 17th harmonic 2: 4 512/459 189.180 cents 2: 6 9/8 203.910 cents major whole tone 2: 2 289/256 209.911 cents two (17th harmonic) 3: 2 1024/867 288.134 cents 3: 4 32/27 294.135 cents Pythagorean minor third 3: 1 81/68 302.865 cents Persian wosta 3: 5 153/128 308.865 cents 4: 6 64/51 393.090 cents 4: 2 34/27 399.090 cents septendecimal major third 4: 2 81/64 407.820 cents Pythagorean major third 4: 2 2601/2048 413.821 cents 5: 1 384/289 492.044 cents 5: 9 4/3 498.045 cents perfect fourth 5: 2 1377/1024 512.775 cents 6: 6 24/17 597.000 cents 1st septendecimal tritone 6: 6 17/12 603.000 cents 2nd septendecimal tritone 7: 2 2048/1377 687.225 cents 7: 9 3/2 701.955 cents perfect fifth 7: 1 289/192 707.956 cents 8: 2 4096/2601 786.179 cents 8: 2 128/81 792.180 cents Pythagorean minor sixth 8: 2 27/17 800.910 cents septendecimal minor sixth 8: 6 51/32 806.910 cents 9: 5 256/153 891.135 cents 9: 1 136/81 897.135 cents 9: 4 27/16 905.865 cents Pythagorean major sixth 9: 2 867/512 911.866 cents 10: 2 512/289 990.089 cents 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 4 459/256 1010.820 cents 11: 6 32/17 1095.045 cents 17th subharmonic 11: 4 17/9 1101.045 cents septendecimal major seventh 11: 1 243/128 1109.775 cents Pythagorean major seventh 11: 1 7803/4096 1115.776 cents 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 : 99.0 203.9 308.9 393.1 498.0 597.0 702.0 806.9 905.9 996.1 1095.0 1200.0 99.0 : 105.0 209.9 294.1 399.1 498.0 603.0 708.0 806.9 897.1 996.1 1101.0 1200.0 203.9 : 105.0 189.2 294.1 393.1 498.0 603.0 702.0 792.2 891.1 996.1 1095.0 1200.0 308.9 : 84.2 189.2 288.1 393.1 498.0 597.0 687.2 786.2 891.1 990.1 1095.0 1200.0 393.1 : 105.0 203.9 308.9 413.8 512.8 603.0 702.0 806.9 905.9 1010.8 1115.8 1200.0 498.0 : 99.0 203.9 308.9 407.8 498.0 597.0 702.0 800.9 905.9 1010.8 1095.0 1200.0 597.0 : 105.0 209.9 308.9 399.1 498.0 603.0 702.0 806.9 911.9 996.1 1101.0 1200.0 702.0 : 105.0 203.9 294.1 393.1 498.0 597.0 702.0 806.9 891.1 996.1 1095.0 1200.0 806.9 : 99.0 189.2 288.1 393.1 492.0 597.0 702.0 786.2 891.1 990.1 1095.0 1200.0 905.9 : 90.2 189.2 294.1 393.1 498.0 603.0 687.2 792.2 891.1 996.1 1101.0 1200.0 996.1 : 99.0 203.9 302.9 407.8 512.8 597.0 702.0 800.9 905.9 1010.8 1109.8 1200.0 1095.0: 105.0 203.9 308.9 413.8 498.0 603.0 702.0 806.9 911.9 1010.8 1101.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.2242 .. 104.9554 cents 132651/131072, 20.7312 cents 8192/7803, 84.2242 cents 2: 189.1796 .. 209.9108 cents 132651/131072, 20.7312 cents 8192/7803, 84.2242 cents 3: 288.1342 .. 308.8654 cents 132651/131072, 20.7312 cents 262144/250563, 78.2234 cents 4: 393.0896 .. 413.8208 cents 132651/131072, 20.7312 cents 8192/7803, 84.2242 cents 5: 492.0442 .. 512.7754 cents 132651/131072, 20.7312 cents 262144/250563, 78.2234 cents 6: 596.9996 .. 603.0004 cents 289/288, 6.0008 cents 8192/7803, 84.2242 cents 7: 687.2246 .. 707.9558 cents 132651/131072, 20.7312 cents 8192/7803, 84.2242 cents 8: 786.1792 .. 806.9104 cents 132651/131072, 20.7312 cents 262144/250563, 78.2234 cents 9: 891.1346 .. 911.8658 cents 132651/131072, 20.7312 cents 8192/7803, 84.2242 cents 10: 990.0892 .. 1010.8204 cents 132651/131072, 20.7312 cents 262144/250563, 78.2234 cents 11: 1095.0446 .. 1115.7758 cents 132651/131072, 20.7312 cents 8192/7803, 84.2242 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 8192/7803, 84.2242 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 17/16, 104.9554 cents Average / Smallest step : 1.187308 Largest / Average step : 1.049554 Largest / Smallest step : 1.246143 Median interval of one step : 101.95500 cents, amount: 0 Most common interval of one step : 17/16, 104.9554 cents, amount: 6 Least squares average step : 100.00938 cents, oct.: 1200.11253 cents Scale is strictly proper Step pattern alph. order: ABBCBABBADAB Step pattern size order : CDDADCDDCBCD Scale is a Constant Structure, by a margin of 78.22336 cents Scale diversity : 1.147568 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.822239 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 : 289/288, 6.0008 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 Number of appreciable fifths : 10, average 702.5551 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 7 = 58.3333% Limited transpositions with margin 20.7312 cents: 1 2 5 6 7 9 10 Limited inverse transpositions with margin 20.7312 cents: 1 2 5 7 9 10 -- Rational properties -- Prime limit : 17 Odd number limit : 7803 (O: 7803 U: 7803) Highest odd numerator or denominator: 153 Scale harmonicity : 0.011552 Average absolute harmonicity : 0.163095 Specific harmonicity : 0.068453 Fundamental : 1/19584, -14.2574 octaves, 0.0134 Hz. Guide tone : 29376, 14.8424 octaves, 7685512.606 Hz. Exponens Consonantiae : 5.752996E+08, 29.09974 octaves Euler's gradus suavitatis : 56 Sum of Mann's harmonic distance : 352.0, average 29.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.58527, average 1.13211 Sum of Tenney's harmonic distance : 27.65989, average 2.30499 Vogel's harmonic complexity : 29.33333 Wille's k value : 11704 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 413.84247, average 5.30567 Lattice compactness (without 2's) : 159.12354, average 2.04005 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 6 0.16667 42 1 3: -2 .. 3 0.66667 16 5 17: -1 .. 1 -0.16667 6 6 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 22 / 12 = 1.83333 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: 4.8423 c. M: 8.8654 c. Twelve-tone Chromatic (1/11-comma) 46: 4 4 4 3 4 4 4 4 4 3 4 4 SP B ME SD: 3.7758 c. M:-7.1785 c. Diaschismic-12, Pajara-12 58: 5 5 5 4 5 5 5 5 5 4 5 5 SP B ME SD: 2.5170 c. M:-4.4937 c. Diaschismic-12 70: 6 6 6 5 6 6 6 6 6 5 6 6 SP B ME SD: 1.9800 c. M:-3.9026 c. Diaschismic-12 82: 7 7 7 6 7 7 7 7 7 6 7 7 SP B ME SD: 1.8838 c. M:-3.4844 c. Pajaric-12 94: 8 8 8 7 8 8 8 8 8 7 8 8 SP B ME SD: 1.9978 c. M:-3.1731 c. 101: 8 9 9 7 9 8 9 9 8 8 8 9 SP D3 SD: 1.9902 c. M: 3.9051 c. 113: 9 10 10 8 10 9 10 10 9 9 9 10 SP D3 SD: 1.8465 c. M: 3.3794 c. 135: 11 12 12 9 12 11 12 12 11 10 11 12 SP SD: 1.3111 c. M:-2.2457 c. 147: 12 13 13 10 13 12 13 13 12 11 12 13 SP SD: 0.8462 c. M:-1.3387 c. 159: 13 14 14 11 14 13 14 14 13 12 13 14 SP SD: 0.5021 c. M: 0.8414 c. 171: 14 15 15 12 15 14 15 15 14 13 14 15 SP SD: 0.3711 c. M: 0.7090 c. 229: 19 20 20 16 20 19 20 20 19 17 19 20 SP SD: 0.3690 c. M:-0.6852 c. 241: 20 21 21 17 21 20 21 21 20 18 20 21 SP SD: 0.3232 c. M:-0.6305 c. 388: 32 34 34 27 34 32 34 34 32 29 32 34 SP SD: 0.2279 c. M:-0.4129 c. 400: 33 35 35 28 35 33 35 35 33 30 33 35 SP SD: 0.0799 c. M:-0.1350 c. 412: 34 36 36 29 36 34 36 36 34 31 34 36 SP SD: 0.0759 c. M: 0.1275 c. 812: 67 71 71 57 71 67 71 71 67 61 67 71 SP SD: 0.0308 c. M:-0.0602 c. 1383: 114 121 121 97 121 114 121 121 114 104 114 121 SP SD: 0.0239 c. M: 0.0392 c. 1795: 148 157 157 126 157 148 157 157 148 135 148 157 SP SD: 0.0082 c. M: 0.0154 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: 7.0234 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.5289 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.9454 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.9089 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.9570 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.4472 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.7995 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 11.6181 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.8803 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 9.0282 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.9585 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 4.9103 cents 20:21:23:24:25:27:28:30:32:34:36:38:40 SD: 4.8266 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.1988 cents 24:25:27:29:30:32:34:36:38:41:43:45:48 SD: 3.7649 cents 30:32:34:36:38:40:42:45:48:51:53:56:60 SD: 3.0958 cents 31:33:35:37:39:41:44:47:49:52:55:58:62 SD: 2.8988 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 1.8551 cents 48:51:54:57:60:64:68:72:77:81:85:90:96 SD: 1.7986 cents 50:53:56:60:63:67:71:75:80:84:89:94:100 SD: 1.7659 cents 51:54:57:61:64:68:72:77:81:86:91:96:102 SD: 1.5259 cents 54:57:61:65:68:72:76:81:86:91:96:102:108 SD: 1.5224 cents 63:67:71:75:79:84:89:95:100:106:112:119:126 SD: 1.4773 cents 66:70:74:79:83:88:93:99:105:111:117:124:132 SD: 1.0252 cents 82:87:92:98:103:109:116:123:131:138:146:154:164 SD: 0.9837 cents 86:91:97:103:108:115:121:129:137:145:153:162:172 SD: 0.8347 cents 102:108:115:122:128:136:144:153:163:172:181:192:204 SD: 0.5822 cents 134:142:151:160:168:179:189:201:214:226:238:252:268 SD: 0.5778 cents 138:146:155:165:173:184:195:207:220:233:245:260:276 SD: 0.4137 cents 153:162:172:183:192:204:216:230:244:258:272:288:306 SD: 0.3710 cents 216:229:243:258:271:288:305:324:344:365:384:407:432 SD: 0.3443 cents 224:237:252:268:281:299:316:336:357:378:398:422:448 SD: 0.3011 cents 240:254:270:287:301:320:339:360:383:405:427:452:480 SD: 0.2740 cents 256:271:288:306:321:341:361:384:408:432:455:482:512 SD: 0.2520 cents 288:305:324:344:361:384:407:432:459:486:512:542:576 SD: 0.2472 cents 306:324:344:366:384:408:432:459:488:516:544:576:612 SD: 0.1976 cents 342:362:385:409:429:456:483:513:545:577:608:644:684 SD: 0.1626 cents 490:519:551:586:615:653:692:735:781:827:871:922:980 SD: 0.1562 cents 510:540:574:610:640:680:720:765:813:861:907:960:1020 SD: 0.1427 cents 522:553:587:624:655:696:737:783:832:881:928:983:1044 SD: 0.1195 cents 544:576:612:650:683:725:768:816:867:918:967:1024:1088 SD: 0.1127 cents