Scala analysis: zarte84
Temperament extraordinaire, Zarlino's 2/7-comma meantone (F-C#)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70.672 cents 70.672430 2: 191.621 cents 191.620690 3: 287.431 cents 287.431040 4: 383.241 cents 383.241390 5: 504.190 cents 504.189650 6: 574.862 cents 574.862080 7: 695.810 cents 695.810350 8: 779.052 cents 779.051730 9: 887.431 cents 887.431040 10: 995.810 cents 995.810350 11: 1079.052 cents 1079.051730 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 120.9483 cents 120.9483 1: 70.6724 cents 70.6724 2: 120.9483 cents 120.9483 3: 95.8104 cents 95.8104 4: 95.8104 cents 95.8104 5: 120.9483 cents 120.9483 6: 70.6724 cents 70.6724 7: 120.9483 cents 120.9483 8: 83.2414 cents 83.2414 9: 108.3793 cents 108.3793 10: 108.3793 cents 108.3793 11: 83.2414 cents 83.2414 12: 120.9483 cents 120.9483
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 70.67243 cents 1: 2 83.24138 cents 1: 2 95.81035 cents 1: 2 108.37931 cents 1: 4 120.94826 cents 2: 7 191.62069 cents 2: 2 204.18965 cents 2: 3 216.75861 cents 3: 2 274.86208 cents 3: 2 287.43104 cents 3: 2 300.00000 cents 3: 6 312.56896 cents 4: 5 383.24139 cents 4: 2 395.81034 cents 4: 2 408.37931 cents 4: 2 420.94827 cents 4: 1 433.51722 cents 5: 4 491.62069 cents 5: 8 504.18965 cents 6: 3 574.86208 cents 6: 2 587.43104 cents 6: 2 600.00000 cents 6: 2 612.56896 cents 6: 3 625.13792 cents 7: 8 695.81035 cents 7: 4 708.37930 cents 8: 1 766.48278 cents 8: 2 779.05173 cents 8: 2 791.62069 cents 8: 2 804.18966 cents 8: 5 816.75861 cents 9: 6 887.43104 cents 9: 2 900.00000 cents 9: 2 912.56896 cents 9: 2 925.13792 cents 10: 3 983.24139 cents 10: 2 995.81035 cents 10: 7 1008.37930 cents 11: 4 1079.05173 cents 11: 2 1091.62069 cents 11: 2 1104.18965 cents 11: 2 1116.75862 cents 11: 2 1129.32757 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.90909 = 43/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 191.6 287.4 383.2 504.2 574.9 695.8 779.1 887.4 995.8 1079.1 1200.0 70.7 : 120.9 216.8 312.6 433.5 504.2 625.1 708.4 816.8 925.1 1008.4 1129.3 1200.0 191.6 : 95.8 191.6 312.6 383.2 504.2 587.4 695.8 804.2 887.4 1008.4 1079.1 1200.0 287.4 : 95.8 216.8 287.4 408.4 491.6 600.0 708.4 791.6 912.6 983.2 1104.2 1200.0 383.2 : 120.9 191.6 312.6 395.8 504.2 612.6 695.8 816.8 887.4 1008.4 1104.2 1200.0 504.2 : 70.7 191.6 274.9 383.2 491.6 574.9 695.8 766.5 887.4 983.2 1079.1 1200.0 574.9 : 120.9 204.2 312.6 420.9 504.2 625.1 695.8 816.8 912.6 1008.4 1129.3 1200.0 695.8 : 83.2 191.6 300.0 383.2 504.2 574.9 695.8 791.6 887.4 1008.4 1079.1 1200.0 779.1 : 108.4 216.8 300.0 420.9 491.6 612.6 708.4 804.2 925.1 995.8 1116.8 1200.0 887.4 : 108.4 191.6 312.6 383.2 504.2 600.0 695.8 816.8 887.4 1008.4 1091.6 1200.0 995.8 : 83.2 204.2 274.9 395.8 491.6 587.4 708.4 779.1 900.0 983.2 1091.6 1200.0 1079.1: 120.9 191.6 312.6 408.4 504.2 625.1 695.8 816.8 900.0 1008.4 1116.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 120.9483 cents 50.27583 cents 70.67243 cents 2: 191.6207 .. 216.7586 cents 25.13792 cents 70.67243 cents 3: 274.8621 .. 312.5690 cents 37.70688 cents 58.10347 cents 4: 383.2414 .. 433.5172 cents 50.27583 cents 70.67243 cents 5: 491.6207 .. 504.1897 cents 12.56896 cents 58.10347 cents 6: 574.8621 .. 625.1379 cents 50.27584 cents 70.67243 cents 7: 695.8104 .. 708.3793 cents 12.56895 cents 70.67243 cents 8: 766.4828 .. 816.7586 cents 50.27583 cents 58.10348 cents 9: 887.4310 .. 925.1379 cents 37.70688 cents 70.67243 cents 10: 983.2414 .. 1008.3793 cents 25.13791 cents 58.10347 cents 11: 1079.0517 .. 1129.3276 cents 50.27584 cents 70.67243 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 70.67243 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 120.94826 cents Average / Smallest step : 1.414979 Largest / Average step : 1.209483 Largest / Smallest step : 1.711392 Median interval of one step : 102.09483 cents, amount: 0 Most common interval of one step : 120.94826 cents, amount: 4 Least squares average step : 98.67220 cents, oct.: 1184.06643 cents Scale is strictly proper Step pattern alph. order: ABCCBABDEEDB Step pattern size order : AECCEAEBDDBE Scale is a Constant Structure, by a margin of 58.10347 cents Scale diversity : 1.289021 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.664828 Rothenberg efficiency : 0.314478 redundancy: 0.685522 Efficiency x scale size : 3.773737 Number of different interval sizes : 43 = 3.90909 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 3.90909 = 43/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 12.56895 cents Most common intervals : 504.18965 cents & inv., amount: 8 Most common triad is 0.0 504.190 695.810 cents, amount: 7 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 50.2758 cents: 5 7 10 Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 9 -- 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: 16.0452 c. M:-29.3276 c. Twelve-tone Chromatic (1/11-comma) 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 15.9215 c. M: 30.3002 c. 18: 1 2 1 2 2 1 1 2 1 2 1 2 P D3 SD: 18.6410 c. M: 29.1437 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 11.6579 c. M:-28.3584 c. Meantone Chromatic (1/3-comma) 20: 1 2 2 1 2 2 2 1 2 2 1 2 P D3 SD: 17.0641 c. M:-25.1379 c. 21: 1 2 2 2 2 1 2 2 2 1 2 2 P D3 SD: 15.5163 c. M:-26.8547 c. 23: 1 3 2 1 3 1 2 2 2 2 2 2 P D3 SD: 14.5494 c. M:-25.6124 c. 27: 2 2 2 3 2 2 3 2 2 2 2 3 SP D3 SD: 14.8091 c. M:-20.9483 c. 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 9.3441 c. M: 18.4655 c. Schismic-12 31: 2 3 2 3 3 2 3 2 3 3 2 3 SP M ME SD: 6.7012 c. M: 16.4633 c. 35: 2 4 2 3 4 2 3 3 3 3 2 4 SP SD: 9.3631 c. M: 16.1946 c. 37: 2 4 3 3 4 2 3 3 3 4 2 4 SP SD: 8.7520 c. M: 14.7293 c. 38: 2 4 3 3 4 2 4 3 3 3 3 4 SP D3 S SD: 6.8668 c. M: 16.8630 c. 40: 2 4 4 3 4 2 4 3 4 3 3 4 SP SD: 7.8385 c. M:-12.5690 c. 42: 2 5 3 3 5 2 4 3 4 4 3 4 SP S SD: 7.8231 c. M: 13.5296 c. 43: 3 4 3 4 4 3 4 3 4 4 3 4 SP M ME SD: 7.3229 c. M:-13.0485 c. 46: 3 4 4 4 4 3 5 3 4 4 3 5 SP D3 S SD: 6.2842 c. M: 9.4865 c. 50: 3 5 4 4 5 3 5 3 5 4 4 5 SP D3 SD: 4.7172 c. M: 11.8103 c. 60: 4 6 4 5 6 4 6 4 5 6 4 6 SP T3 SD: 5.4698 c. M:-9.3276 c. 62: 4 6 5 5 6 4 6 4 6 6 4 6 SP D3 S SD: 4.7975 c. M:-10.6413 c. 65: 4 6 6 5 6 4 7 4 6 6 4 7 SP SD: 4.9940 c. M: 8.2825 c. 66: 4 7 5 5 7 4 6 5 6 6 4 7 SP SD: 4.6752 c. M:-8.3793 c. 69: 4 7 6 5 7 4 7 5 6 6 5 7 SP SD: 2.9449 c. M:-8.2211 c. 76: 4 8 6 6 8 4 8 5 7 7 5 8 SP S SD: 4.1112 c. M: 7.5145 c. 77: 5 7 6 7 7 5 8 5 7 7 5 8 SP SD: 4.4972 c. M:-7.2496 c. 79: 5 8 6 6 8 5 8 5 7 8 5 8 SP SD: 4.1236 c. M:-6.7213 c. 81: 5 8 6 7 8 5 8 6 7 7 6 8 SP SD: 3.1181 c. M:-6.1335 c. 88: 5 9 7 7 9 5 9 6 8 8 6 9 SP S SD: 1.3626 c. M: 2.4906 c. 100: 6 10 8 8 10 6 10 7 9 9 7 10 SP S SD: 0.7263 c. M:-1.3276 c. 188: 11 19 15 15 19 11 19 13 17 17 13 19 SP S SD: 0.2515 c. M: 0.4597 c. 288: 17 29 23 23 29 17 29 20 26 26 20 29 SP S SD: 0.0880 c. M:-0.1609 c. 476: 28 48 38 38 48 28 48 33 43 43 33 48 SP S SD: 0.0461 c. M: 0.0842 c. 764: 45 77 61 61 77 45 77 53 69 69 53 77 SP S SD: 0.0045 c. M:-0.0082 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: 3.0723 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.2900 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9613 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 10.0569 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.2118 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.9546 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 7.6705 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.3175 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.8203 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.5734 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.0447 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 9.4077 cents 14:15:16 x 17:19:20:21:22:23:25:26:28 SD: 8.8748 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 6.7913 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.4898 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.4221 cents 18:19:20:21:22:24:25:27:28:30:32:34:36 SD: 4.6576 cents 21:22:23:25:26:28:29:31:33:35:37:39:42 SD: 4.3463 cents 23:24:26:27:29:31:32:34:36:38:41:43:46 SD: 3.5125 cents 24:25:27:28:30:32:33:36:38:40:43:45:48 SD: 3.5050 cents 27:28:30:32:34:36:38:40:42:45:48:50:54 SD: 3.0691 cents 28:29:31:33:35:37:39:42:44:47:50:52:56 SD: 2.7366 cents 33:34:37:39:41:44:46:49:52:55:59:62:66 SD: 2.5947 cents 40:42:45:47:50:54:56:60:63:67:71:75:80 SD: 2.5372 cents 41:43:46:48:51:55:57:61:64:68:73:76:82 SD: 2.4433 cents 43:45:48:51:54:58:60:64:67:72:76:80:86 SD: 2.3097 cents 44:46:49:52:55:59:61:66:69:73:78:82:88 SD: 1.5834 cents 51:53:57:60:64:68:71:76:80:85:91:95:102 SD: 1.3911 cents 67:70:75:79:84:90:93:100:105:112:119:125:134 SD: 1.2463 cents 68:71:76:80:85:91:95:102:107:114:121:127:136 SD: 1.2082 cents 76:79:85:90:95:102:106:114:119:127:135:142:152 SD: 0.9944 cents 77:80:86:91:96:103:107:115:121:129:137:144:154 SD: 0.9387 cents 93:97:104:110:116:124:130:139:146:155:165:173:186 SD: 0.9317 cents 94:98:105:111:117:126:131:141:147:157:167:175:188 SD: 0.8467 cents 104:108:116:123:130:139:145:155:163:174:185:194:208 SD: 0.8283 cents 109:114:122:129:136:146:152:163:171:182:194:203:218 SD: 0.8097 cents 112:117:125:132:140:150:156:167:176:187:199:209:224 SD: 0.7439 cents 118:123:132:139:147:158:164:176:185:197:210:220:236 SD: 0.7221 cents 121:126:135:143:151:162:169:181:190:202:215:226:242 SD: 0.4913 cents 145:151:162:171:181:194:202:217:227:242:258:270:290 SD: 0.4615 cents 172:179:192:203:215:230:240:257:270:287:306:321:344 SD: 0.4272 cents 190:198:212:224:237:254:265:284:298:317:338:354:380 SD: 0.3822 cents 215:224:240:254:268:288:300:321:337:359:382:401:430 SD: 0.3563 cents 221:230:247:261:276:296:308:330:347:369:393:412:442 SD: 0.3423 cents 238:248:266:281:297:318:332:356:373:397:423:444:476 SD: 0.3279 cents 239:249:267:282:298:320:333:357:375:399:425:446:478 SD: 0.2327 cents 266:277:297:314:332:356:371:398:417:444:473:496:532 SD: 0.2221 cents 343:357:383:405:428:459:478:513:538:573:610:640:686 SD: 0.2075 cents 360:375:402:425:449:482:502:538:565:601:640:671:720 SD: 0.1965 cents 376:392:420:444:469:503:524:562:590:628:668:701:752 SD: 0.1918 cents 384:400:429:453:479:514:535:574:602:641:683:716:768 SD: 0.1883 cents 408:425:456:482:509:546:569:610:640:681:725:761:816 SD: 0.1698 cents 459:478:513:542:573:614:640:686:720:766:816:856:918 SD: 0.1533 cents 477:497:533:563:595:638:665:713:748:796:848:890:954 SD: 0.1472 cents 503:524:562:594:628:673:701:752:789:840:894:938:1006 SD: 0.1155 cents 554:577:619:654:691:741:772:828:869:925:985:1033:1108 SD: 0.1140 cents