Scala analysis: reflections
7-limit (slightly tempered) "reflections" scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 383.743 cents 383.743000 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 1083.128 cents 1083.128000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.8720 cents 116.8720 1: 28/27 62.9609 Archytas' 1/3-tone 2: 243/224 140.9491 Archytas' 2/3-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 116.8721 cents 116.8721 5: 114.3020 cents 114.3020 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 15/14 119.4428 major diatonic semitone 10: 21/20 84.4672 minor semitone 11: 114.3021 cents 114.3021 12: 116.8720 cents 116.8720
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 28/27 62.961 cents Archytas' 1/3-tone 1: 2 21/20 84.467 cents minor semitone 1: 2 114.30200 cents 1: 2 116.87209 cents 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 243/224 140.949 cents Archytas' 2/3-tone 2: 2 179.83300 cents 2: 2 10/9 182.404 cents minor whole tone 2: 2 198.76919 cents 2: 4 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 2 32/27 294.135 cents Pythagorean minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 2 6/5 315.641 cents minor third 3: 2 318.21200 cents 3: 2 320.78210 cents 4: 2 56/45 378.602 cents septimal narrow major third 4: 2 381.17290 cents 4: 2 383.74300 cents 4: 2 5/4 386.314 cents major third 4: 4 9/7 435.084 cents septimal major third, BP third 5: 1 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 500.61500 cents 5: 2 500.61571 cents 5: 2 27/20 519.551 cents acute fourth 6: 2 112/81 561.006 cents 6: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 585.08291 cents 6: 2 614.91709 cents 6: 2 10/7 617.488 cents Euler's tritone 6: 2 81/56 638.994 cents 7: 2 40/27 680.449 cents grave fifth 7: 2 699.38429 cents 7: 1 699.38500 cents 7: 6 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 8: 4 14/9 764.916 cents septimal minor sixth 8: 2 8/5 813.686 cents minor sixth 8: 2 816.25709 cents 8: 2 818.82710 cents 8: 2 45/28 821.398 cents septimale wide minor sixth 9: 2 879.21800 cents 9: 2 881.78800 cents 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 3 12/7 933.129 cents septimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 1001.23081 cents 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 1020.16710 cents 11: 1 448/243 1059.051 cents 11: 2 28/15 1080.557 cents grave major seventh 11: 2 1083.12800 cents 11: 2 1085.69800 cents 11: 2 40/21 1115.533 cents acute major seventh 11: 3 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.45455 = 60/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 63.0 203.9 266.9 383.7 498.0 582.5 702.0 764.9 884.4 968.8 1083.1 1200.0 63.0 : 140.9 203.9 320.8 435.1 519.6 639.0 702.0 821.4 905.9 1020.2 1137.0 1200.0 203.9 : 63.0 179.8 294.1 378.6 498.0 561.0 680.4 764.9 879.2 996.1 1059.1 1200.0 266.9 : 116.9 231.2 315.6 435.1 498.0 617.5 702.0 816.3 933.1 996.1 1137.0 1200.0 383.7 : 114.3 198.8 318.2 381.2 500.6 585.1 699.4 816.3 879.2 1020.2 1083.1 1200.0 498.0 : 84.5 203.9 266.9 386.3 470.8 585.1 702.0 764.9 905.9 968.8 1085.7 1200.0 582.5 : 119.4 182.4 301.8 386.3 500.6 617.5 680.4 821.4 884.4 1001.2 1115.5 1200.0 702.0 : 63.0 182.4 266.9 381.2 498.0 561.0 702.0 764.9 881.8 996.1 1080.6 1200.0 764.9 : 119.4 203.9 318.2 435.1 498.0 639.0 702.0 818.8 933.1 1017.6 1137.0 1200.0 884.4 : 84.5 198.8 315.6 378.6 519.6 582.5 699.4 813.7 898.2 1017.6 1080.6 1200.0 968.8 : 114.3 231.2 294.1 435.1 498.0 614.9 729.2 813.7 933.1 996.1 1115.5 1200.0 1083.1: 116.9 179.8 320.8 383.7 500.6 614.9 699.4 818.8 881.8 1001.2 1085.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 140.9491 cents 6561/6272, 77.9882 cents 28/27, 62.9609 cents 2: 179.8330 .. 231.1741 cents 51.34110 cents 38.88390 cents 3: 266.8709 .. 320.7821 cents 53.91119 cents 49/48, 35.6968 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 57.82009 cents 5: 470.7809 .. 519.5513 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 6: 561.0059 .. 638.9941 cents 6561/6272, 77.9882 cents 2240/2187, 41.4546 cents 7: 680.4487 .. 729.2191 cents 36/35, 48.7704 cents 2240/2187, 41.4546 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 9: 879.2180 .. 933.1291 cents 53.91110 cents 57.82019 cents 10: 968.8259 .. 1020.1671 cents 51.34119 cents 49/48, 35.6968 cents 11: 1059.0509 .. 1137.0391 cents 6561/6272, 77.9882 cents 38.88381 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 243/224, 140.9491 cents Average / Smallest step : 1.588287 Largest / Average step : 1.409491 Largest / Smallest step : 2.238677 Median interval of one step : 114.30200 cents, amount: 2 Most common interval of one step : 28/27, 62.9609 cents, amount: 3 Least squares average step : 98.13319 cents, oct.: 1177.59824 cents Scale is strictly proper Step pattern alph. order: ABACDEFAFEDC Step pattern size order : AFADCBEAEBCD Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.415147 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.454189 Rothenberg efficiency : 0.266763 redundancy: 0.733237 Efficiency x scale size : 3.201154 Number of different interval sizes : 60 = 5.45455 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.45455 = 60/11 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.00071 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 9, average 701.0982 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 25.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 7-8 -- Rational properties -- Prime limit : 7 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 21.9744 c. M:-37.0391 c. Twelve-tone Chromatic (1/11-comma) 16: 1 2 1 1 2 1 1 1 2 1 1 2 P D3 SD: 20.6668 c. M:-33.1291 c. 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 17.9473 c. M:-33.2883 c. 18: 1 2 1 2 1 2 2 0 2 2 1 2 P D3 SD: 20.6592 c. M: 31.5826 c. 19: 1 2 1 2 2 1 2 1 2 1 2 2 P M ME SD: 10.5510 c. M: 21.4575 c. Mandelbaum Twelve out of 19 22: 1 3 1 2 2 2 2 1 2 2 2 2 P D3 SD: 9.5151 c. M:-17.4878 c. 31: 2 3 2 3 3 2 3 2 3 2 3 3 SP M ME SD: 6.6142 c. M:-14.4585 c. 41: 2 5 2 4 4 3 4 2 4 3 4 4 SP SD: 3.1075 c. M: 6.3099 c. 53: 3 6 3 5 5 4 5 3 5 4 5 5 SP SD: 3.5260 c. M:-6.1671 c. 72: 4 8 4 7 7 5 7 4 7 5 7 7 SP SD: 1.9657 c. M: 3.9100 c. 94: 5 11 5 9 9 7 9 5 9 7 9 9 SP SD: 1.9260 c. M:-4.7218 c. 113: 6 13 6 11 11 8 11 6 11 8 11 11 SP SD: 1.5452 c. M: 2.9428 c. 147: 8 17 8 14 14 10 15 8 14 11 14 14 SP SD: 1.9836 c. M: 2.9204 c. 152: 8 18 8 15 14 11 15 8 15 11 14 15 SP SD: 1.4669 c. M:-3.0991 c. 157: 8 19 8 15 15 11 16 8 16 11 15 15 SP SD: 1.6285 c. M:-2.4594 c. 166: 9 19 9 16 16 12 16 9 16 12 16 16 SP SD: 1.4975 c. M:-3.0300 c. 171: 9 20 9 17 16 12 17 9 17 12 16 17 SP SD: 0.9719 c. M: 2.4262 c. 193: 10 23 10 19 18 14 19 10 19 14 18 19 SP SD: 1.1223 c. M:-1.9438 c. 212: 11 25 11 21 20 15 21 11 21 15 20 21 SP SD: 0.9125 c. M: 1.9959 c. 229: 12 27 12 22 22 16 23 12 23 16 22 22 SP SD: 0.7682 c. M:-1.5882 c. 265: 14 31 14 26 25 19 26 14 26 19 25 26 SP SD: 0.7678 c. M:-1.6388 c. 270: 14 32 14 26 26 19 27 14 27 19 26 26 SP SD: 0.6695 c. M: 1.5208 c. 284: 15 33 15 28 27 20 28 15 28 20 27 28 SP SD: 0.8421 c. M: 1.4379 c. 301: 16 35 16 29 29 21 30 16 30 21 29 29 SP SD: 0.6355 c. M:-1.2574 c. 328: 17 39 17 32 31 23 33 17 33 23 31 32 SP SD: 0.6089 c. M:-1.0071 c. 342: 18 40 18 33 33 24 34 18 34 24 33 33 SP SD: 0.5275 c. M: 1.2869 c. 381: 20 45 20 37 36 27 38 20 38 27 36 37 SP SD: 0.6011 c. M:-1.2528 c. 400: 21 47 21 39 38 28 40 21 40 28 38 39 SP SD: 0.2620 c. M:-0.6413 c. 441: 23 52 23 43 42 31 44 23 44 31 42 43 SP SD: 0.1798 c. M: 0.3759 c. 841: 44 99 44 82 80 59 84 44 84 59 80 82 SP SD: 0.1609 c. M: 0.3481 c. 894: 47 105 47 87 85 63 89 47 89 63 85 87 SP SD: 0.1569 c. M:-0.3016 c. 913: 48 107 48 89 87 64 91 48 91 64 87 89 SP SD: 0.1334 c. M: 0.2559 c. 935: 49 110 49 91 89 66 93 49 93 66 89 91 SP SD: 0.0965 c. M:-0.1616 c. 1335: 70 157 70 130 127 94 133 70 133 94 127 130 SP SD: 0.0874 c. M:-0.1629 c. 1376: 72 162 72 134 131 97 137 72 137 97 131 134 SP SD: 0.0848 c. M: 0.1702 c. 1407: 74 165 74 137 134 99 140 74 140 99 134 137 SP SD: 0.0719 c. M:-0.1521 c. 1448: 76 170 76 141 138 102 144 76 144 102 138 141 SP SD: 0.0462 c. M: 0.1046 c. 1848: 97 217 97 180 176 130 184 97 184 130 176 180 SP SD: 0.0248 c. M:-0.0569 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: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.6427 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 16.8946 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 5.6275 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 11.3536 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 6.7630 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.4434 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 11.1954 cents 11 x 12:13:14:15 x x 17:18:19:21:22 SD: 10.5172 cents 12 x x 14:15:16:17:18:19:20:21:22:24 S SD: 5.0054 cents 13:14 x 15:16:17:18 x 20:22:23:24:26 S SD: 9.2809 cents 14:15:16 x 17:19:20:21:22:23:25:26:28 SD: 9.3800 cents 15:16:17:18:19:20:21 x 23:25:26:28:30 SD: 7.3137 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.8772 cents 17:18:19:20:21:23:24 x 26:28:30:32:34 SD: 6.0553 cents 18:19:20:21:22:24:25:27:28:30:32:34:36 SD: 5.2549 cents 20:21 x 23:25:27:28:30:31:33:35:37:40 SD: 4.2841 cents 23:24:26:27:29:31:32:35:36:38:40:43:46 SD: 3.8684 cents 24:25:27:28:30:32:34:36:37:40:42:45:48 SD: 2.2873 cents 47:49:53:55:59:63:66:71:73:78:82:88:94 SD: 2.0159 cents 48:50:54:56:60:64:67:72:75:80:84:90:96 SD: 1.1137 cents 72:75:81:84:90:96:101:108:112:120:126:135:144 SD: 0.8510 cents 102:106:115:119:127:136:143:153:159:170:179:191:204 SD: 0.8169 cents 108:112:122:126:135:144:151:162:168:180:189:202:216 SD: 0.6622 cents 120:124:135:140:150:160:168:180:187:200:210:224:240 SD: 0.6515 cents 128:133:144:149:160:171:179:192:199:213:224:239:256 SD: 0.6496 cents 132:137:149:154:165:176:185:198:205:220:231:247:264 SD: 0.6267 cents 137:142:154:160:171:183:192:206:213:228:240:256:274 SD: 0.5775 cents 138:143:155:161:172:184:193:207:215:230:242:258:276 SD: 0.5196 cents 144:149:162:168:180:192:202:216:224:240:252:269:288 SD: 0.4930 cents 160:166:180:187:200:213:224:240:249:267:280:299:320 SD: 0.4546 cents 162:168:182:189:202:216:227:243:252:270:284:303:324 SD: 0.3814 cents 168:174:189:196:210:224:235:252:261:280:294:314:336 SD: 0.3601 cents 192:199:216:224:240:256:269:288:299:320:336:359:384 SD: 0.3009 cents 216:224:243:252:270:288:302:324:336:360:378:404:432 SD: 0.2958 cents 240:249:270:280:300:320:336:360:373:400:420:449:480 SD: 0.2796 cents 270:280:304:315:337:360:378:405:420:450:473:505:540 SD: 0.2062 cents 360:373:405:420:449:480:504:540:560:600:630:673:720 SD: 0.1673 cents 408:423:459:476:509:544:571:612:635:680:714:763:816 SD: 0.1306 cents 432:448:486:504:539:576:605:648:672:720:756:808:864 SD: 0.1012 cents 600:622:675:700:749:800:840:900:933:1000:1050:1122:1200 SD: 0.0874 cents