Scala analysis: zarte84n
Zarlino temperament extraordinaire, 1024-tET mapping
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70.312 cents 70.312500 2: 191.016 cents 191.015620 3: 287.109 cents 287.109380 4: 383.203 cents 383.203130 5: 503.906 cents 503.906250 6: 574.219 cents 574.218750 7: 696.094 cents 696.093750 8: 778.125 cents 778.125000 9: 887.109 cents 887.109380 10: 996.094 cents 996.093750 11: 1079.297 cents 1079.296880 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 120.7031 cents 120.7031 1: 70.3125 cents 70.3125 2: 120.7031 cents 120.7031 3: 96.0938 cents 96.0938 4: 96.0937 cents 96.0937 5: 120.7031 cents 120.7031 6: 70.3125 cents 70.3125 7: 121.8750 cents 121.8750 8: 82.0313 cents 82.0313 9: 108.9844 cents 108.9844 10: 108.9844 cents 108.9844 11: 83.2031 cents 83.2031 12: 120.7031 cents 120.7031
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 70.31250 cents 1: 1 82.03125 cents 1: 1 83.20313 cents 1: 2 96.09376 cents 1: 2 108.98438 cents 1: 3 120.70312 cents 1: 1 121.87500 cents 2: 4 191.01562 cents 2: 3 192.18751 cents 2: 2 203.90625 cents 2: 2 216.79688 cents 2: 1 217.96875 cents 3: 2 274.21875 cents 3: 2 287.10938 cents 3: 1 300.00000 cents 3: 1 301.17188 cents 3: 1 311.71874 cents 3: 5 312.89063 cents 4: 5 383.20313 cents 4: 2 394.92187 cents 4: 1 407.81250 cents 4: 1 408.98437 cents 4: 2 421.87500 cents 4: 1 433.59375 cents 5: 2 491.01562 cents 5: 2 492.18750 cents 5: 6 503.90625 cents 5: 2 505.07813 cents 6: 2 574.21875 cents 6: 1 575.39063 cents 6: 2 587.10938 cents 6: 2 600.00000 cents 6: 2 612.89062 cents 6: 1 624.60937 cents 6: 2 625.78125 cents 7: 2 694.92187 cents 7: 6 696.09375 cents 7: 2 707.81250 cents 7: 2 708.98437 cents 8: 1 766.40625 cents 8: 2 778.12500 cents 8: 1 791.01563 cents 8: 1 792.18750 cents 8: 2 805.07813 cents 8: 5 816.79688 cents 9: 5 887.10938 cents 9: 1 888.28126 cents 9: 1 898.82812 cents 9: 1 900.00000 cents 9: 2 912.89062 cents 9: 2 925.78125 cents 10: 1 982.03125 cents 10: 2 983.20312 cents 10: 2 996.09375 cents 10: 3 1007.81249 cents 10: 4 1008.98438 cents 11: 1 1078.12500 cents 11: 3 1079.29688 cents 11: 2 1091.01562 cents 11: 2 1103.90624 cents 11: 1 1116.79687 cents 11: 1 1117.96875 cents 11: 2 1129.68750 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.72727 = 63/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.3 191.0 287.1 383.2 503.9 574.2 696.1 778.1 887.1 996.1 1079.3 1200.0 70.3 : 120.7 216.8 312.9 433.6 503.9 625.8 707.8 816.8 925.8 1009.0 1129.7 1200.0 191.0 : 96.1 192.2 312.9 383.2 505.1 587.1 696.1 805.1 888.3 1009.0 1079.3 1200.0 287.1 : 96.1 216.8 287.1 409.0 491.0 600.0 709.0 792.2 912.9 983.2 1103.9 1200.0 383.2 : 120.7 191.0 312.9 394.9 503.9 612.9 696.1 816.8 887.1 1007.8 1103.9 1200.0 503.9 : 70.3 192.2 274.2 383.2 492.2 575.4 696.1 766.4 887.1 983.2 1079.3 1200.0 574.2 : 121.9 203.9 312.9 421.9 505.1 625.8 696.1 816.8 912.9 1009.0 1129.7 1200.0 696.1 : 82.0 191.0 300.0 383.2 503.9 574.2 694.9 791.0 887.1 1007.8 1078.1 1200.0 778.1 : 109.0 218.0 301.2 421.9 492.2 612.9 709.0 805.1 925.8 996.1 1118.0 1200.0 887.1 : 109.0 192.2 312.9 383.2 503.9 600.0 696.1 816.8 887.1 1009.0 1091.0 1200.0 996.1 : 83.2 203.9 274.2 394.9 491.0 587.1 707.8 778.1 900.0 982.0 1091.0 1200.0 1079.3: 120.7 191.0 311.7 407.8 503.9 624.6 694.9 816.8 898.8 1007.8 1116.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.3125 .. 121.8750 cents 51.56250 cents 70.31250 cents 2: 191.0156 .. 217.9688 cents 26.95313 cents 69.14062 cents 3: 274.2187 .. 312.8906 cents 38.67188 cents 56.25000 cents 4: 383.2031 .. 433.5938 cents 50.39062 cents 70.31250 cents 5: 491.0156 .. 505.0781 cents 14.06251 cents 57.42187 cents 6: 574.2188 .. 625.7813 cents 51.56250 cents 69.14062 cents 7: 694.9219 .. 708.9844 cents 14.06250 cents 69.14062 cents 8: 766.4063 .. 816.7969 cents 50.39063 cents 57.42188 cents 9: 887.1094 .. 925.7813 cents 38.67187 cents 70.31250 cents 10: 982.0313 .. 1008.9844 cents 26.95313 cents 56.25000 cents 11: 1078.1250 .. 1129.6875 cents 51.56250 cents 69.14062 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 70.31250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 121.87500 cents Average / Smallest step : 1.422222 Largest / Average step : 1.218750 Largest / Smallest step : 1.733333 Median interval of one step : 102.53907 cents, amount: 0 Most common interval of one step : 120.70312 cents, amount: 3 Least squares average step : 98.65565 cents, oct.: 1183.86779 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 60 163 245 327 430 490 594 664 757 850 921 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 851 of 997.266 cents and inv. generated superset size: 626 = 614 more = 5216.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCCBADEFFGB Step pattern size order : AFDDFAGBEECF Scale is a Constant Structure, by a margin of 56.25000 cents Scale diversity : 1.302056 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.654297 Rothenberg efficiency : 0.265290 redundancy: 0.734710 Efficiency x scale size : 3.183478 Number of different interval sizes : 63 = 5.72727 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 5.72727 = 63/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17187 cents Most common intervals : 503.90625 cents & inv., amount: 6 Most common triad is 0.0 503.906 696.094 cents, amount: 3 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 51.5625 cents: 5 7 10 Limited inverse transpositions with margin 51.5625 cents: 1 6 8 11 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.3149 c. M:-29.6875 c. Twelve-tone Chromatic (1/11-comma) 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 15.9879 c. M:-30.5377 c. 18: 1 2 1 2 2 1 1 2 1 2 1 2 P D3 SD: 18.8455 c. M:-29.4271 c. 19: 1 2 1 2 2 1 2 1 2 2 1 2 P M ME SD: 12.7644 c. M: 34.4778 c. 20: 1 2 2 1 2 2 2 1 2 2 1 2 P D3 SD: 17.0334 c. M:-25.7812 c. 21: 1 2 2 2 2 1 2 2 2 1 2 2 P D3 SD: 15.6286 c. M:-27.1763 c. 23: 1 3 2 1 3 1 2 2 2 2 2 2 P D3 SD: 14.6752 c. M:-25.9341 c. 25: 1 3 2 2 2 2 2 2 2 3 1 3 P D3 SD: 15.7493 c. M: 24.0937 c. 26: 1 3 2 2 3 1 3 2 2 2 2 3 P D3 S SD: 14.5779 c. M: 26.8630 c. 27: 2 2 2 3 2 2 3 2 2 2 2 3 SP D3 SD: 14.8906 c. M:-21.8750 c. 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 9.4840 c. M: 18.1439 c. Schismic-12 30: 2 3 2 3 3 1 3 2 3 3 2 3 P D3 SD: 11.6270 c. M: 18.1250 c. 31: 2 3 2 3 3 2 3 2 3 3 2 3 SP M ME SD: 6.6386 c. M: 16.1416 c. 37: 2 4 3 3 4 2 3 3 3 4 2 4 SP SD: 8.8620 c. M:-15.0127 c. 38: 2 4 3 3 4 2 4 3 3 3 3 4 SP D3 S SD: 6.9527 c. M: 17.1464 c. 40: 2 4 4 3 4 2 4 3 4 3 3 4 SP SD: 7.8498 c. M:-12.8906 c. 42: 2 5 3 3 5 2 4 3 4 4 3 4 SP S SD: 7.7526 c. M: 13.1696 c. 43: 3 4 3 4 4 3 4 3 4 4 3 4 SP M ME SD: 7.4471 c. M:-13.4084 c. 46: 3 4 4 4 4 3 5 3 4 4 3 5 SP D3 S SD: 6.2824 c. M: 9.7317 c. 50: 3 5 4 4 5 3 5 3 5 5 3 5 SP D3 S SD: 4.6007 c. M:-11.9062 c. 54: 3 6 4 4 6 3 5 4 5 5 4 5 SP S SD: 5.4287 c. M:-9.5920 c. 57: 3 6 4 5 6 3 6 4 5 5 4 6 SP SD: 5.5798 c. M: 13.4252 c. 60: 4 6 4 5 6 4 6 4 5 6 4 6 SP T3 SD: 5.5462 c. M:-9.6875 c. 62: 4 6 5 5 6 4 6 4 6 6 4 6 SP D3 S SD: 4.8185 c. M:-10.3579 c. 66: 4 7 5 5 7 4 6 5 6 6 4 7 SP SD: 5.0076 c. M:-8.9844 c. 67: 4 7 5 5 7 4 7 4 7 6 4 7 SP SD: 5.0394 c. M:-8.4130 c. 69: 4 7 6 5 7 4 7 5 6 6 5 7 SP SD: 3.1437 c. M:-8.5428 c. 71: 4 7 6 6 7 4 7 5 6 7 5 7 SP SD: 3.6400 c. M: 8.2361 c. 72: 4 7 6 6 7 4 8 5 6 7 5 7 SP SD: 4.5376 c. M: 7.6823 c. 73: 4 8 5 6 8 4 7 5 7 7 5 7 SP SD: 5.1415 c. M: 7.6573 c. 74: 4 8 6 6 7 4 8 5 7 6 6 7 SP SD: 4.7489 c. M:-7.1896 c. 76: 4 8 6 6 8 4 8 5 7 7 5 8 SP S SD: 3.8605 c. M: 7.1546 c. 79: 5 8 6 6 8 5 8 5 7 8 5 8 SP SD: 4.0993 c. M:-6.4527 c. 81: 5 8 6 7 8 5 8 6 7 7 6 8 SP SD: 3.3545 c. M:-7.0602 c. 82: 5 8 7 6 8 5 9 5 8 7 6 8 SP SD: 3.9937 c. M:-6.3453 c. 83: 5 8 7 7 8 5 8 6 7 8 6 8 SP SD: 3.6022 c. M:-7.1583 c. 88: 5 9 7 7 9 5 9 6 8 8 6 9 SP S SD: 1.1495 c. M: 2.1307 c. 100: 6 10 8 8 10 6 10 7 9 9 7 10 SP S SD: 1.0507 c. M:-1.8750 c. 188: 11 19 15 15 19 11 19 13 17 17 13 19 SP S SD: 0.3453 c. M:-0.5984 c. 548: 32 55 44 44 55 32 56 37 50 50 38 55 SP SD: 0.3554 c. M: 0.7527 c. 560: 33 56 45 45 56 33 57 38 51 51 39 56 SP SD: 0.3288 c. M:-0.7031 c. 617: 36 62 50 49 62 36 63 42 56 56 43 62 SP SD: 0.3275 c. M:-0.7350 c. 636: 37 64 51 51 64 37 65 43 58 58 44 64 SP SD: 0.3800 c. M: 0.7665 c. 648: 38 65 52 52 65 38 66 44 59 59 45 65 SP SD: 0.2003 c. M: 0.3472 c. 736: 43 74 59 59 74 43 75 50 67 67 51 74 SP SD: 0.1935 c. M: 0.4076 c. 748: 44 75 60 60 75 44 76 51 68 68 52 75 SP SD: 0.1786 c. M:-0.3823 c. 836: 49 84 67 67 84 49 85 57 76 76 58 84 SP SD: 0.0776 c. M: 0.1346 c. 1024: 60 103 82 82 103 60 104 70 93 93 71 103 SP SD: 0.0000 c. M: 0.0000 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: 2.9306 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.1582 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.0159 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 10.2173 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.1957 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.0705 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 7.6328 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.3016 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.8330 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.5210 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.0522 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 9.3933 cents 14:15:16 x 17:19:20:21:22:23:25:26:28 SD: 8.9370 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 6.8708 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.4940 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.4848 cents 18:19:20:21:22:24:25:27:28:30:32:34:36 SD: 4.6109 cents 21:22:23:25:26:28:29:31:33:35:37:39:42 SD: 4.3311 cents 23:24:26:27:29:31:32:34:36:38:41:43:46 SD: 3.5277 cents 24:25:27:28:30:32:33:36:38:40:43:45:48 SD: 3.4883 cents 27:28:30:32:34:36:38:40:42:45:48:50:54 SD: 3.0642 cents 28:29:31:33:35:37:39:42:44:47:50:52:56 SD: 2.6968 cents 33:34:37:39:41:44:46:49:52:55:59:62:66 SD: 2.5966 cents 41:43:46:48:51:55:57:61:64:68:73:76:82 SD: 2.4327 cents 43:45:48:51:54:58:60:64:67:72:76:80:86 SD: 2.3352 cents 44:46:49:52:55:59:61:66:69:73:78:82:88 SD: 1.5488 cents 51:53:57:60:64:68:71:76:80:85:91:95:102 SD: 1.3662 cents 67:70:75:79:84:90:93:100:105:112:119:125:134 SD: 1.2604 cents 68:71:76:80:85:91:95:102:107:114:121:127:136 SD: 1.2573 cents 69:72:77:81:86:92:96:103:108:115:123:129:138 SD: 1.1935 cents 76:79:85:90:95:102:106:114:119:127:135:142:152 SD: 1.0003 cents 77:80:86:91:96:103:107:115:121:129:137:144:154 SD: 0.9402 cents 94:98:105:111:117:126:131:141:147:157:167:175:188 SD: 0.8231 cents 112:117:125:132:140:150:156:167:176:187:199:209:224 SD: 0.7908 cents 117:122:131:138:146:157:163:175:183:195:208:218:234 SD: 0.7500 cents 118:123:132:139:147:158:164:176:185:197:210:220:236 SD: 0.7110 cents 121:126:135:143:151:162:169:181:190:202:215:226:242 SD: 0.5437 cents 145:151:162:171:181:194:202:217:227:242:258:270:290 SD: 0.4041 cents 190:198:212:224:237:254:265:284:298:317:338:354:380 SD: 0.3715 cents 222:231:248:262:277:297:309:332:348:371:395:414:444 SD: 0.2938 cents 239:249:267:282:298:320:333:357:375:399:425:446:478 SD: 0.2718 cents 266:277:297:314:332:356:371:398:417:444:473:496:532 SD: 0.2167 cents 343:357:383:405:428:459:478:513:538:573:610:640:686 SD: 0.2047 cents 384:400:429:453:479:514:535:574:602:641:683:716:768 SD: 0.1702 cents 432:450:482:510:539:578:602:646:677:721:768:806:864 SD: 0.1436 cents 532:554:594:628:664:712:741:795:834:888:946:992:1064 SD: 0.1198 cents