Scala analysis: ramx15
Untempered version of the 5-limit minor third chain
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 10/9 182.403712 minor whole tone 3: 125/108 253.076139 semi-augmented whole tone 4: 6/5 315.641287 minor third 5: 5/4 386.313714 major third 6: 4/3 498.044999 perfect fourth 7: 25/18 568.717426 classic augmented fourth 8: 36/25 631.282574 classic diminished fifth 9: 3/2 701.955001 perfect fifth 10: 8/5 813.686286 minor sixth 11: 5/3 884.358713 major sixth, BP sixth 12: 216/125 946.923861 semi-augmented sixth 13: 9/5 1017.596288 just minor seventh, BP seventh 14: 48/25 1129.327573 classic diminished octave 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 16/15 111.7313 minor diatonic semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 648/625 62.5651 major diesis 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 16/15 111.7313 minor diatonic semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma 8: 648/625 62.5651 major diesis 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 16/15 111.7313 minor diatonic semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 648/625 62.5651 major diesis 13: 25/24 70.6724 classic chromatic semitone, minor chroma 14: 16/15 111.7313 minor diatonic semitone 15: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 648/625 62.565 cents major diesis 1: 8 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 4 16/15 111.731 cents minor diatonic semitone 2: 6 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 8 10/9 182.404 cents minor whole tone 3: 3 9/8 203.910 cents major whole tone 3: 6 144/125 244.969 cents classic diminished third 3: 6 125/108 253.076 cents semi-augmented whole tone 4: 12 6/5 315.641 cents minor third 4: 2 3125/2592 323.749 cents 4: 1 100/81 364.807 cents grave major third 5: 2 3888/3125 378.206 cents 5: 8 5/4 386.314 cents major third 5: 3 32/25 427.373 cents classic diminished fourth 5: 2 625/486 435.480 cents 6: 4 162/125 448.879 cents 6: 2 125/96 456.986 cents classic augmented third 6: 8 4/3 498.045 cents perfect fourth 6: 1 15625/11664 506.152 cents two (semi-augmented whole tone) 7: 2 27/20 519.551 cents acute fourth 7: 4 864/625 560.610 cents 7: 9 25/18 568.717 cents classic augmented fourth 8: 9 36/25 631.283 cents classic diminished fifth 8: 4 625/432 639.390 cents 8: 2 40/27 680.449 cents grave fifth 9: 1 23328/15625 693.848 cents 9: 8 3/2 701.955 cents perfect fifth 9: 2 192/125 743.014 cents classic diminished sixth 9: 4 125/81 751.121 cents 10: 2 972/625 764.520 cents 10: 3 25/16 772.627 cents classic augmented fifth 10: 8 8/5 813.686 cents minor sixth 10: 2 3125/1944 821.794 cents 11: 1 81/50 835.193 cents acute minor sixth 11: 2 5184/3125 876.251 cents 11: 12 5/3 884.359 cents major sixth, BP sixth 12: 6 216/125 946.924 cents semi-augmented sixth 12: 6 125/72 955.031 cents classic augmented sixth 12: 3 16/9 996.090 cents Pythagorean minor seventh 13: 8 9/5 1017.596 cents just minor seventh, BP seventh 13: 1 1152/625 1058.655 cents 13: 6 50/27 1066.762 cents grave major seventh 14: 4 15/8 1088.269 cents classic major seventh 14: 8 48/25 1129.328 cents classic diminished octave 14: 3 625/324 1137.435 cents octave - major diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.28571 = 23/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 70.7 182.4 253.1 315.6 386.3 498.0 568.7 631.3 702.0 813.7 884.4 946.9 1017.6 1129.3 1200.0 70.7 : 111.7 182.4 245.0 315.6 427.4 498.0 560.6 631.3 743.0 813.7 876.3 946.9 1058.7 1129.3 1200.0 182.4 : 70.7 133.2 203.9 315.6 386.3 448.9 519.6 631.3 702.0 764.5 835.2 946.9 1017.6 1088.3 1200.0 253.1 : 62.6 133.2 245.0 315.6 378.2 448.9 560.6 631.3 693.8 764.5 876.3 946.9 1017.6 1129.3 1200.0 315.6 : 70.7 182.4 253.1 315.6 386.3 498.0 568.7 631.3 702.0 813.7 884.4 955.0 1066.8 1137.4 1200.0 386.3 : 111.7 182.4 245.0 315.6 427.4 498.0 560.6 631.3 743.0 813.7 884.4 996.1 1066.8 1129.3 1200.0 498.0 : 70.7 133.2 203.9 315.6 386.3 448.9 519.6 631.3 702.0 772.6 884.4 955.0 1017.6 1088.3 1200.0 568.7 : 62.6 133.2 245.0 315.6 378.2 448.9 560.6 631.3 702.0 813.7 884.4 946.9 1017.6 1129.3 1200.0 631.3 : 70.7 182.4 253.1 315.6 386.3 498.0 568.7 639.4 751.1 821.8 884.4 955.0 1066.8 1137.4 1200.0 702.0 : 111.7 182.4 245.0 315.6 427.4 498.0 568.7 680.4 751.1 813.7 884.4 996.1 1066.8 1129.3 1200.0 813.7 : 70.7 133.2 203.9 315.6 386.3 457.0 568.7 639.4 702.0 772.6 884.4 955.0 1017.6 1088.3 1200.0 884.4 : 62.6 133.2 245.0 315.6 386.3 498.0 568.7 631.3 702.0 813.7 884.4 946.9 1017.6 1129.3 1200.0 946.9 : 70.7 182.4 253.1 323.7 435.5 506.2 568.7 639.4 751.1 821.8 884.4 955.0 1066.8 1137.4 1200.0 1017.6: 111.7 182.4 253.1 364.8 435.5 498.0 568.7 680.4 751.1 813.7 884.4 996.1 1066.8 1129.3 1200.0 1129.3: 70.7 141.3 253.1 323.7 386.3 457.0 568.7 639.4 702.0 772.6 884.4 955.0 1017.6 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.5651 .. 111.7313 cents 250/243, 49.1661 cents 648/625, 62.5651 cents 2: 133.2376 .. 182.4037 cents 250/243, 49.1661 cents 81/80, 21.5063 cents 3: 203.9100 .. 253.0761 cents 250/243, 49.1661 cents 81/80, 21.5063 cents 4: 315.6413 .. 364.8074 cents 250/243, 49.1661 cents 648/625, 62.5651 cents 5: 378.2064 .. 435.4799 cents 1953125/1889568, 57.2734 cents 78732/78125, 13.3990 cents 6: 448.8789 .. 506.1523 cents 1953125/1889568, 57.2734 cents 78732/78125, 13.3990 cents 7: 519.5513 .. 568.7174 cents 250/243, 49.1661 cents 78732/78125, 13.3990 cents 8: 631.2826 .. 680.4487 cents 250/243, 49.1661 cents 648/625, 62.5651 cents 9: 693.8477 .. 751.1211 cents 1953125/1889568, 57.2734 cents 78732/78125, 13.3990 cents 10: 764.5201 .. 821.7936 cents 1953125/1889568, 57.2734 cents 78732/78125, 13.3990 cents 11: 835.1926 .. 884.3587 cents 250/243, 49.1661 cents 78732/78125, 13.3990 cents 12: 946.9239 .. 996.0900 cents 250/243, 49.1661 cents 648/625, 62.5651 cents 13: 1017.5963 .. 1066.7624 cents 250/243, 49.1661 cents 81/80, 21.5063 cents 14: 1088.2687 .. 1137.4349 cents 250/243, 49.1661 cents 81/80, 21.5063 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 648/625, 62.5651 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.278667 Largest / Average step : 1.396641 Largest / Smallest step : 1.785839 Median interval of one step : 25/24, 70.6724 cents, amount: 8 Most common interval of one step : 25/24, 70.6724 cents, amount: 8 Least squares average step : 79.83324 cents, oct.: 1197.49866 cents Scale is strictly proper Step pattern alph. order: ABACABACABACABA Step pattern size order : MLMSMLMSMLMSMLM Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.261508 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.399371 Number of different interval sizes : 46 = 3.28571 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.28571 = 23/7 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 12 Most common triad is 0.0 315.641 884.359 cents, amount: 9 Number of recognisable fifths : 9, average 701.0542 cents Scale contains two identical disjunct heptachords Best minor thirds form a closed circle Scale contains a complete diamond : 3 5 9 25 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 15 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties -- Prime limit : 5 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 125 Scale harmonicity : 0.016287 Average absolute harmonicity : 0.157376 Specific harmonicity : 0.108973 Fundamental : 1/27000, -14.7207 octaves, 0.0097 Hz. Guide tone : 54000, 15.7207 octaves, 14127780.526 Hz. Exponens Consonantiae : 1.458000E+09, 30.44134 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 444.5, average 29.63333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.44419, average 1.02961 Sum of Tenney's harmonic distance : 31.34861, average 2.08991 Vogel's harmonic complexity : 27.53333 Wille's k value : 14062 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 12 Triangular lattice diameter : 6 Lattice compactness : 465.95454, average 3.88295 Lattice compactness (without 2's) : 337.30150, average 2.81085 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.53333 26 1 3: -3 .. 3 0.00000 20 2 5: -3 .. 3 0.00000 20 12 Average exponent except 2's : 0 / 15 = 0.00000 Average absolute exponent except 2's: 40 / 15 = 2.66667 Scale is JI-epimorphic with val: <15 24 35| = patent Scale is weakly epimorphic with val: <15 25 33| Scale is weakly epimorphic with val: <15 25 36|
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.5048 c. M: 22.4037 c. 19: 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 P M ME I SD: 5.3307 c. M: 7.5145 c. 34: 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 SP M ME I SD: 3.8410 c. M: 6.0173 c. 53: 3 5 3 3 3 5 3 3 3 5 3 3 3 5 3 SP M DE I SD: 2.1996 c. M: 4.0195 c. 72: 4 7 4 4 4 7 4 4 4 7 4 4 4 7 4 SP M DE I SD: 2.4313 c. M: 4.0058 c. 84: 5 8 5 4 5 8 5 4 5 8 5 4 5 8 5 P I SD: 2.3506 c. M: 4.0667 c. 99: 6 9 6 5 6 9 6 5 6 9 6 5 6 9 6 SP I SD: 1.2399 c. M:-2.0548 c. 118: 7 11 7 6 7 11 7 6 7 11 7 6 7 11 7 SP I SD: 0.6180 c. M:-1.1611 c. 152: 9 14 9 8 9 14 9 8 9 14 9 8 9 14 9 SP I SD: 0.4992 c. M: 0.8248 c. 171: 10 16 10 9 10 16 10 9 10 16 10 9 10 16 10 SP I SD: 0.3096 c. M: 0.4970 c. 270: 16 25 16 14 16 25 16 14 16 25 16 14 16 25 16 SP I SD: 0.2644 c. M:-0.4387 c. 289: 17 27 17 15 17 27 17 15 17 27 17 15 17 27 17 SP I SD: 0.1781 c. M: 0.2952 c. 441: 26 41 26 23 26 41 26 23 26 41 26 23 26 41 26 SP I SD: 0.0614 c. M: 0.0908 c. 730: 43 68 43 38 43 68 43 38 43 68 43 38 43 68 43 SP I SD: 0.0435 c. M: 0.0745 c. 1171: 69 109 69 61 69 109 69 61 69 109 69 61 69 109 69 SP I SD: 0.0246 c. M: 0.0409 c. 1342: 79 125 79 70 79 125 79 70 79 125 79 70 79 125 79 SP I SD: 0.0190 c. M: 0.0316 c. 1783: 105 166 105 93 105 166 105 93 105 166 105 93 105 166 105 SP I SD: 0.0109 c. M:-0.0195 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 0.0000 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 5.4755 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 2.7590 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 5.7721 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 12.0706 cents 8 x 9 x x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.5532 cents 9 x 10 x 11 x 12 x 13 x 14:15 x 16:17:18 S SD: 7.6000 cents 10 x 11 x 12 x 13:14 x 15:16 x 17:18:19:20 S SD: 5.9521 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 8.1684 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 5.7360 cents 13 x 14:15 x 16:17:18:19:20:21:22 x 23:25:26 SD: 8.0314 cents 14:15 x 16:17:18:19 x 20:21:22:23:24:25:27:28 SD: 7.2240 cents 15:16:17 x 18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.6271 cents 16:17:18 x 19:20:21:22:23:24:26:27:28:29:31:32 SD: 5.0883 cents 17:18:19:20 x 21:23:24 x 26:27:28:29:31:33:34 SD: 6.2672 cents 18:19:20:21:22:23:24:25:26:27:29:30:31:32:35:36 SD: 4.3822 cents 20:21:22:23:24:25:27:28:29:30:32:33:35:36:38:40 SD: 3.3493 cents 24:25:27:28:29:30:32:33:35:36:38:40:41:43:46:48 SD: 3.2481 cents 25:26:28:29:30:31:33:35:36:38:40:42:43:45:48:50 SD: 2.7325 cents 30:31:33:35:36:38:40:42:43:45:48:50:52:54:58:60 SD: 2.6990 cents 36:38:40:42:43:45:48:50:52:54:58:60:62:65:69:72 SD: 2.1331 cents 44:46:49:51:53:55:59:61:63:66:70:73:76:79:84:88 SD: 1.6112 cents 45:47:50:52:54:56:60:63:65:68:72:75:78:81:86:90 SD: 1.5824 cents 51:53:57:59:61:64:68:71:73:77:82:85:88:92:98:102 SD: 1.5558 cents 52:54:58:60:62:65:69:72:75:78:83:87:90:94:100:104 SD: 1.4333 cents 64:67:71:74:77:80:85:89:92:96:102:107:111:115:123:128 SD: 1.1401 cents 70:73:78:81:84:88:93:97:101:105:112:117:121:126:134:140 SD: 1.0392 cents 72:75:80:83:86:90:96:100:104:108:115:120:124:130:138:144 SD: 0.9918 cents 75:78:83:87:90:94:100:104:108:113:120:125:130:135:144:150 SD: 0.9121 cents 90:94:100:104:108:113:120:125:130:135:144:150:156:162:173:180 SD: 0.8133 cents 96:100:107:111:115:120:128:133:138:144:154:160:166:173:184:192 SD: 0.6791 cents 100:104:111:116:120:125:133:139:144:150:160:167:173:180:192:200 SD: 0.5265 cents 120:125:133:139:144:150:160:167:173:180:192:200:207:216:230:240 SD: 0.4934 cents 144:150:160:167:173:180:192:200:207:216:230:240:249:259:276:288 SD: 0.4535 cents 164:171:182:190:197:205:219:228:236:246:262:273:283:295:315:328 SD: 0.4393 cents 165:172:183:191:198:206:220:229:238:248:264:275:285:297:317:330 SD: 0.4215 cents 180:188:200:208:216:225:240:250:259:270:288:300:311:324:346:360 SD: 0.3932 cents 190:198:211:220:228:238:253:264:274:285:304:317:328:342:365:380 SD: 0.3907 cents 195:203:217:226:234:244:260:271:281:293:312:325:337:351:374:390 SD: 0.3755 cents 196:204:218:227:235:245:261:272:282:294:314:327:339:353:376:392 SD: 0.3728 cents 210:219:233:243:252:263:280:292:302:315:336:350:363:378:403:420 SD: 0.3728 cents 216:225:240:250:259:270:288:300:311:324:346:360:373:389:415:432 SD: 0.2036 cents 336:350:373:389:403:420:448:467:484:504:538:560:581:605:645:672 SD: 0.1965 cents 360:375:400:417:432:450:480:500:518:540:576:600:622:648:691:720 SD: 0.1334 cents 504:525:560:583:605:630:672:700:726:756:806:840:871:907:968:1008 SD: 0.1131 cents 576:600:640:667:691:720:768:800:829:864:922:960:995:1037:1106:1152 SD: 0.1128 cents 600:625:667:694:720:750:800:833:864:900:960:1000:1037:1080:1152:1200 SD: 0.1068 cents