Scala analysis: 15highschool2
Second 15-note Highschool scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 15/14 119.442808 major diatonic semitone 3: 9/8 203.910002 major whole tone 4: 6/5 315.641287 minor third 5: 5/4 386.313714 major third 6: 4/3 498.044999 perfect fourth 7: 48/35 546.815381 septimal semi-augmented fourth 8: 10/7 617.487807 Euler's tritone 9: 3/2 701.955001 perfect fifth 10: 8/5 813.686286 minor sixth 11: 5/3 884.358713 major sixth, BP sixth 12: 7/4 968.825906 harmonic seventh 13: 9/5 1017.596288 just minor seventh, BP seventh 14: 15/8 1088.268715 classic major seventh 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 21/20 84.4672 minor semitone 4: 16/15 111.7313 minor diatonic semitone 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 16/15 111.7313 minor diatonic semitone 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 21/20 84.4672 minor semitone 10: 16/15 111.7313 minor diatonic semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 21/20 84.4672 minor semitone 13: 36/35 48.7704 septimal diesis, 1/4-tone 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 36/35 48.770 cents septimal diesis, 1/4-tone 1: 5 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 2: 3 15/14 119.443 cents major diatonic semitone 2: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 3 35/32 155.140 cents septimal neutral second 2: 2 192/175 160.502 cents septimal 4/5-tone 2: 4 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 3: 4 9/8 203.910 cents major whole tone 3: 5 8/7 231.174 cents septimal whole tone 3: 5 7/6 266.871 cents septimal minor third 3: 1 32/27 294.135 cents Pythagorean minor third 4: 1 75/64 274.582 cents classic augmented second 4: 1 288/245 279.944 cents 4: 2 25/21 301.847 cents BP second, quasi-equal minor third 4: 6 6/5 315.641 cents minor third 4: 2 175/144 337.543 cents 4: 1 128/105 342.905 cents septimal neutral third 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 1 56/45 378.602 cents septimal narrow major third 5: 1 60/49 350.617 cents smaller approximation to neutral third 5: 1 216/175 364.412 cents 5: 6 5/4 386.314 cents major third 5: 1 63/50 400.108 cents quasi-equal major third 5: 1 80/63 413.578 cents wide major third 5: 1 245/192 422.011 cents 5: 3 32/25 427.373 cents classic diminished fourth 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 6: 3 9/7 435.084 cents septimal major third, BP third 6: 3 21/16 470.781 cents narrow fourth 6: 9 4/3 498.045 cents perfect fourth 7: 1 75/56 505.757 cents marvelous fourth 7: 2 27/20 519.551 cents acute fourth 7: 1 175/128 541.453 cents 7: 3 48/35 546.815 cents septimal semi-augmented fourth 7: 3 25/18 568.717 cents classic augmented fourth 7: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 2 64/45 609.776 cents 2nd tritone 8: 2 45/32 590.224 cents diatonic tritone 8: 3 10/7 617.488 cents Euler's tritone 8: 3 36/25 631.283 cents classic diminished fifth 8: 3 35/24 653.185 cents septimal semi-diminished fifth 8: 1 256/175 658.547 cents 8: 2 40/27 680.449 cents grave fifth 8: 1 112/75 694.243 cents marvelous fifth 9: 9 3/2 701.955 cents perfect fifth 9: 3 32/21 729.219 cents wide fifth 9: 3 14/9 764.916 cents septimal minor sixth 10: 1 54/35 750.725 cents septimal semi-augmented fifth 10: 3 25/16 772.627 cents classic augmented fifth 10: 1 384/245 777.989 cents 10: 1 63/40 786.422 cents narrow minor sixth 10: 1 100/63 799.892 cents quasi-equal minor sixth 10: 6 8/5 813.686 cents minor sixth 10: 1 175/108 835.588 cents 10: 1 49/30 849.383 cents larger approximation to neutral sixth 11: 1 45/28 821.398 cents septimale wide minor sixth 11: 1 80/49 848.662 cents smaller approximation to neutral sixth 11: 1 105/64 857.095 cents septimal neutral sixth 11: 2 288/175 862.457 cents 11: 6 5/3 884.359 cents major sixth, BP sixth 11: 2 42/25 898.153 cents quasi-equal major sixth 11: 1 245/144 920.056 cents 11: 1 128/75 925.418 cents diminished seventh 12: 1 27/16 905.865 cents Pythagorean major sixth 12: 5 12/7 933.129 cents septimal major sixth 12: 5 7/4 968.826 cents harmonic seventh 12: 4 16/9 996.090 cents Pythagorean minor seventh 13: 2 25/14 1003.802 cents middle minor seventh 13: 4 9/5 1017.596 cents just minor seventh, BP seventh 13: 2 175/96 1039.498 cents 13: 3 64/35 1044.860 cents septimal neutral seventh 13: 1 50/27 1066.762 cents grave major seventh 13: 3 28/15 1080.557 cents grave major seventh 14: 4 15/8 1088.269 cents classic major seventh 14: 3 40/21 1115.533 cents acute major seventh 14: 5 48/25 1129.328 cents classic diminished octave 14: 3 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 5.71429 = 40/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 48.8 119.4 203.9 315.6 386.3 498.0 546.8 617.5 702.0 813.7 884.4 968.8 1017.6 1088.3 1200.0 48.8 : 70.7 155.1 266.9 337.5 449.3 498.0 568.7 653.2 764.9 835.6 920.1 968.8 1039.5 1151.2 1200.0 119.4 : 84.5 196.2 266.9 378.6 427.4 498.0 582.5 694.2 764.9 849.4 898.2 968.8 1080.6 1129.3 1200.0 203.9 : 111.7 182.4 294.1 342.9 413.6 498.0 609.8 680.4 764.9 813.7 884.4 996.1 1044.9 1115.5 1200.0 315.6 : 70.7 182.4 231.2 301.8 386.3 498.0 568.7 653.2 702.0 772.6 884.4 933.1 1003.8 1088.3 1200.0 386.3 : 111.7 160.5 231.2 315.6 427.4 498.0 582.5 631.3 702.0 813.7 862.5 933.1 1017.6 1129.3 1200.0 498.0 : 48.8 119.4 203.9 315.6 386.3 470.8 519.6 590.2 702.0 750.7 821.4 905.9 1017.6 1088.3 1200.0 546.8 : 70.7 155.1 266.9 337.5 422.0 470.8 541.5 653.2 702.0 772.6 857.1 968.8 1039.5 1151.2 1200.0 617.5 : 84.5 196.2 266.9 351.3 400.1 470.8 582.5 631.3 702.0 786.4 898.2 968.8 1080.6 1129.3 1200.0 702.0 : 111.7 182.4 266.9 315.6 386.3 498.0 546.8 617.5 702.0 813.7 884.4 996.1 1044.9 1115.5 1200.0 813.7 : 70.7 155.1 203.9 274.6 386.3 435.1 505.8 590.2 702.0 772.6 884.4 933.1 1003.8 1088.3 1200.0 884.4 : 84.5 133.2 203.9 315.6 364.4 435.1 519.6 631.3 702.0 813.7 862.5 933.1 1017.6 1129.3 1200.0 968.8 : 48.8 119.4 231.2 279.9 350.6 435.1 546.8 617.5 729.2 778.0 848.7 933.1 1044.9 1115.5 1200.0 1017.6: 70.7 182.4 231.2 301.8 386.3 498.0 568.7 680.4 729.2 799.9 884.4 996.1 1066.8 1151.2 1200.0 1088.3: 111.7 160.5 231.2 315.6 427.4 498.0 609.8 658.5 729.2 813.7 925.4 996.1 1080.6 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 111.7313 cents 28/27, 62.9609 cents 36/35, 48.7704 cents 2: 119.4428 .. 196.1985 cents 392/375, 76.7557 cents 225/224, 7.7115 cents 3: 203.9100 .. 294.1350 cents 256/243, 90.2250 cents 225/224, 7.7115 cents 4: 274.5824 .. 378.6022 cents 3584/3375, 104.0198 cents 2025/2048,-19.5526 cents 5: 350.6169 .. 449.2746 cents 343/324, 98.6577 cents 675/686,-27.9853 cents 6: 435.0841 .. 498.0450 cents 28/27, 62.9609 cents 243/245,-14.1905 cents 7: 505.7565 .. 609.7763 cents 3584/3375, 104.0198 cents 225/224, 7.7115 cents 8: 590.2237 .. 694.2435 cents 3584/3375, 104.0198 cents 2025/2048,-19.5526 cents 9: 701.9550 .. 764.9159 cents 28/27, 62.9609 cents 225/224, 7.7115 cents 10: 750.7254 .. 849.3831 cents 343/324, 98.6577 cents 243/245,-14.1905 cents 11: 821.3978 .. 925.4176 cents 3584/3375, 104.0198 cents 675/686,-27.9853 cents 12: 905.8650 .. 996.0900 cents 256/243, 90.2250 cents 2025/2048,-19.5526 cents 13: 1003.8015 .. 1080.5572 cents 392/375, 76.7557 cents 225/224, 7.7115 cents 14: 1088.2687 .. 1151.2296 cents 28/27, 62.9609 cents 225/224, 7.7115 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.640340 Largest / Average step : 1.396641 Largest / Smallest step : 2.290966 Median interval of one step : 25/24, 70.6724 cents, amount: 5 Most common interval of one step : 25/24, 70.6724 cents, amount: 5 Least squares average step : 79.13083 cents, oct.: 1186.96244 cents Scale is not proper Step pattern alph. order: ABCDBDABCDBCABD Step pattern size order : ABCDBDABCDBCABD Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.498209 Lumma stability : 0.119842 Lumma impropriety factor : 0.119174 Number of different interval sizes : 80 = 5.71429 / class Number of one step interval sizes : 4 Highest interval variety : 8 Mean interval variety : 5.71429 = 40/7 Median interval variety : 3.5 Lowest interval variety : 3 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 10, average 701.1838 cents Scale contains a complete diamond : 1 3 5 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 46.6667% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval class 3 -- Rational properties -- Prime limit : 7 Odd number limit : 245 (O: 245 U: 245) Highest odd numerator or denominator: 35 Scale harmonicity : 0.020673 Average absolute harmonicity : 0.165446 Specific harmonicity : 0.128557 Fundamental : 1/840, -9.7142 octaves, 0.3115 Hz. Guide tone : 5040, 12.2992 octaves, 1318592.849 Hz. Exponens Consonantiae : 4.233600E+06, 22.01345 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 160.5, average 10.70000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.78912, average 0.85261 Sum of Tenney's harmonic distance : 25.24455, average 1.68297 Vogel's harmonic complexity : 18.53333 Wille's k value : 787 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 385.83879, average 3.21532 Lattice compactness (without 2's) : 218.42099, average 1.82017 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.13333 26 1 3: -1 .. 2 0.60000 13 3 5: -1 .. 1 0.00000 10 6 7: -1 .. 1 -0.20000 5 5 Average exponent except 2's : 6 / 15 = 0.40000 Average absolute exponent except 2's: 28 / 15 = 1.86667 Scale is weakly epimorphic with val: <15 24 32 42| Scale is weakly epimorphic with val: <15 24 34 42| Scale is JI-epimorphic with val: <15 24 35 42| = patent Scale is weakly epimorphic with val: <15 24 37 42| Scale is weakly epimorphic with val: <15 24 38 42|
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 21.9907 c. M:-40.5572 c. 19: 1 1 1 2 1 2 1 1 1 2 1 1 1 1 2 N D3 S SD: 11.7300 c. M:-21.6057 c. 22: 1 1 2 2 1 2 1 1 2 2 1 2 1 1 2 N D3 SD: 10.3044 c. M:-18.7673 c. 31: 1 2 2 3 2 3 1 2 2 3 2 2 1 2 3 N SD: 5.8744 c. M: 11.1447 c. 41: 2 2 3 4 2 4 2 2 3 4 2 3 2 2 4 N SD: 5.3401 c. M:-9.7662 c. 46: 2 3 3 4 3 4 2 3 3 4 3 3 2 3 4 P SD: 4.9841 c. M:-10.9920 c. 52: 2 3 4 5 3 5 2 3 3 5 3 4 2 3 5 N SD: 5.8038 c. M:-9.6473 c. 53: 2 3 4 5 3 5 2 3 4 5 3 4 2 3 5 N SD: 2.9977 c. M: 6.2353 c. 72: 3 4 5 7 4 7 3 4 5 7 4 5 3 4 7 N SD: 2.4862 c. M: 4.9354 c. 94: 4 5 7 9 5 9 4 5 7 9 5 7 4 5 9 N SD: 2.8896 c. M: 4.7218 c. 99: 4 6 7 9 6 9 4 6 7 9 6 7 4 6 9 N SD: 1.3149 c. M:-2.6404 c. 130: 5 8 9 12 8 12 5 8 9 12 8 9 5 8 12 N SD: 1.4192 c. M: 2.6165 c. 140: 6 8 10 13 8 13 6 8 10 13 8 10 6 8 13 N SD: 1.3323 c. M:-2.6582 c. 152: 6 9 11 14 9 14 6 9 11 14 9 11 6 9 14 N SD: 1.1734 c. M:-2.2267 c. 171: 7 10 12 16 10 16 7 10 12 16 10 12 7 10 16 N SD: 0.3111 c. M:-0.5530 c. 270: 11 16 19 25 16 25 11 16 19 25 16 19 11 16 25 N SD: 0.3209 c. M:-0.6202 c. 441: 18 26 31 41 26 41 18 26 31 41 26 31 18 26 41 N SD: 0.1384 c. M:-0.2851 c. 612: 25 36 43 57 36 57 25 36 43 57 36 43 25 36 57 N SD: 0.1223 c. M:-0.2492 c. 935: 38 55 66 87 55 87 38 55 66 87 55 66 38 55 87 N SD: 0.0977 c. M: 0.1616 c. 1106: 45 65 78 103 65 103 45 65 78 103 65 78 45 65 103 N SD: 0.0730 c. M: 0.1280 c. 1277: 52 75 90 119 75 119 52 75 90 119 75 90 52 75 119 N SD: 0.0796 c. M: 0.1033 c. 1376: 56 81 97 128 81 128 56 81 97 128 81 97 56 81 128 N SD: 0.0765 c. M:-0.1598 c. 1407: 57 83 99 131 83 131 57 83 99 131 83 99 57 83 131 N SD: 0.0720 c. M: 0.1563 c. 1547: 63 91 109 144 91 144 63 91 109 144 91 109 63 91 144 N SD: 0.0588 c. M:-0.1154 c. 1578: 64 93 111 147 93 147 64 93 111 147 93 111 64 93 147 N SD: 0.0590 c. M: 0.1077 c. 1848: 75 109 130 172 109 172 75 109 130 172 109 130 75 109 172 N SD: 0.0445 c. M: 0.0691 c. 2019: 82 119 142 188 119 188 82 119 142 188 119 142 82 119 188 N SD: 0.0322 c. M: 0.0629 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: 0.0000 cents 5 x x x 6 x x x 7 x 8 x x 9 x 10 S SD: 6.9951 cents 6 x x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 9.7006 cents 7 x x 8 x 9 x x 10 x 11 x 12 x 13:14 S SD: 10.7321 cents 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16 S SD: 3.4021 cents 9 x x 10:11 x 12 x 13 x 14:15 x 16:17:18 S SD: 7.7315 cents 10 x x 11:12 x 13 x 14:15:16:17 x 18:19:20 S SD: 7.9745 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 8.7118 cents 12 x 13 x 14:15:16 x 17:18:19:20:21:22:23:24 S SD: 6.3136 cents 13 x 14:15 x 16:17:18:19:20:21:22:23 x 24:26 S SD: 8.1893 cents 14 x 15:16:17:18 x 19:20:21:22:23 x 25:26:28 SD: 6.4165 cents 15 x 16:17:18:19:20 x 21:23:24:25:26:27:28:30 SD: 4.7128 cents 16 x 17:18:19:20:21:22:23:24:26:27:28:29:30:32 S SD: 3.7423 cents 17 x 18:19:20:21 x 23:24:26:27:28:30:31:32:34 SD: 5.7513 cents 18 x 19:20:22:23:24:25:26:27:29:30 x 32:34:36 SD: 5.5481 cents 19 x 20:21:23:24:25:26:27:29:30:32:33:34:36:38 SD: 5.2597 cents 20 x 21:23:24:25:27 x 29:30:32:33:35:36:38:40 SD: 5.2322 cents 21:22:23:24:25:26:28:29:30:32:34:35:37:38:39:42 SD: 4.9295 cents 23:24:25:26:28:29:31:32:33:35:37:38:40:41:43:46 SD: 4.4941 cents 24:25:26:27:29:30:32:33:34:36:38:40:42:43:45:48 SD: 2.6771 cents 30:31:32:34:36:38:40:41:43:45:48:50:53:54:56:60 SD: 2.3196 cents 32:33:34:36:38:40:43:44:46:48:51:53:56:58:60:64 SD: 2.2941 cents 39:40:42:44:47:49:52:53:56:59:62:65:68:70:73:78 SD: 2.1107 cents 40:41:43:45:48:50:53:55:57:60:64:67:70:72:75:80 SD: 1.1564 cents 70:72:75:79:84:88:93:96:100:105:112:117:123:126:131:140 SD: 1.0558 cents 72:74:77:81:86:90:96:99:103:108:115:120:126:130:135:144 SD: 0.7893 cents 96:99:103:108:115:120:128:132:137:144:154:160:168:173:180:192 SD: 0.6070 cents 135:139:145:152:162:169:180:185:193:203:216:225:236:243:253:270 SD: 0.4977 cents 144:148:154:162:173:180:192:197:206:216:230:240:252:259:270:288 SD: 0.4755 cents 168:173:180:189:202:210:224:230:240:252:269:280:294:302:315:336 SD: 0.3756 cents 180:185:193:203:216:225:240:247:257:270:288:300:315:324:338:360 SD: 0.3661 cents 200:206:214:225:240:250:267:274:286:300:320:333:350:360:375:400 SD: 0.3336 cents 208:214:223:234:250:260:277:285:297:312:333:347:364:374:390:416 SD: 0.3257 cents 210:216:225:236:252:263:280:288:300:315:336:350:368:378:394:420 SD: 0.3052 cents 240:247:257:270:288:300:320:329:343:360:384:400:420:432:450:480 SD: 0.1157 cents 520:535:557:585:624:650:693:713:743:780:832:867:910:936:975:1040 SD: 0.0889 cents 560:576:600:630:672:700:747:768:800:840:896:933:980:1008:1050:1120 SD: 0.0660 cents 600:617:643:675:720:750:800:823:857:900:960:1000:1050:1080:1125:1200 SD: 0.0463 cents