Scala analysis: kelletat
Herbert Kelletat's Bach-tuning (1967)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 90.000 cents 90.000000 2: 196.000 cents 196.000000 3: 294.000 cents 294.000000 4: 386.900 cents 386.900000 5: 498.000 cents 498.000000 6: 588.000 cents 588.000000 7: 700.000 cents 700.000000 8: 792.000 cents 792.000000 9: 892.000 cents 892.000000 10: 996.000 cents 996.000000 11: 1086.000 cents 1086.000000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 114.0000 cents 114.0000 1: 90.0000 cents 90.0000 2: 106.0000 cents 106.0000 3: 98.0000 cents 98.0000 4: 92.9000 cents 92.9000 5: 111.1000 cents 111.1000 6: 90.0000 cents 90.0000 7: 112.0000 cents 112.0000 8: 92.0000 cents 92.0000 9: 100.0000 cents 100.0000 10: 104.0000 cents 104.0000 11: 90.0000 cents 90.0000 12: 114.0000 cents 114.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 90.00000 cents 1: 1 92.00000 cents 1: 1 92.90000 cents 1: 1 98.00000 cents 1: 1 100.00000 cents 1: 1 104.00000 cents 1: 1 106.00000 cents 1: 1 111.10000 cents 1: 1 112.00000 cents 1: 1 114.00000 cents 2: 1 190.90000 cents 2: 1 192.00000 cents 2: 1 194.00000 cents 2: 1 196.00000 cents 2: 1 201.10000 cents 2: 1 202.00000 cents 2: 6 204.00000 cents 3: 5 294.00000 cents 3: 1 296.00000 cents 3: 1 296.90000 cents 3: 1 302.00000 cents 3: 1 304.00000 cents 3: 1 308.00000 cents 3: 1 310.00000 cents 3: 1 313.10000 cents 4: 1 386.00000 cents 4: 1 386.90000 cents 4: 1 392.00000 cents 4: 1 394.00000 cents 4: 1 398.00000 cents 4: 1 400.00000 cents 4: 1 405.10000 cents 4: 1 406.00000 cents 4: 4 408.00000 cents 5: 7 498.00000 cents 5: 1 500.00000 cents 5: 1 500.90000 cents 5: 2 504.00000 cents 5: 1 505.10000 cents 6: 2 588.00000 cents 6: 1 590.00000 cents 6: 1 590.90000 cents 6: 1 596.00000 cents 6: 1 598.00000 cents 6: 1 602.00000 cents 6: 1 604.00000 cents 6: 1 609.10000 cents 6: 1 610.00000 cents 6: 2 612.00000 cents 7: 1 694.90000 cents 7: 2 696.00000 cents 7: 1 699.10000 cents 7: 1 700.00000 cents 7: 7 702.00000 cents 8: 4 792.00000 cents 8: 1 794.00000 cents 8: 1 794.90000 cents 8: 1 800.00000 cents 8: 1 802.00000 cents 8: 1 806.00000 cents 8: 1 808.00000 cents 8: 1 813.10000 cents 8: 1 814.00000 cents 9: 1 886.90000 cents 9: 1 890.00000 cents 9: 1 892.00000 cents 9: 1 896.00000 cents 9: 1 898.00000 cents 9: 1 903.10000 cents 9: 1 904.00000 cents 9: 5 906.00000 cents 10: 6 996.00000 cents 10: 1 998.00000 cents 10: 1 998.90000 cents 10: 1 1004.00000 cents 10: 1 1006.00000 cents 10: 1 1008.00000 cents 10: 1 1009.10000 cents 11: 1 1086.00000 cents 11: 1 1088.00000 cents 11: 1 1088.90000 cents 11: 1 1094.00000 cents 11: 1 1096.00000 cents 11: 1 1100.00000 cents 11: 1 1102.00000 cents 11: 1 1107.10000 cents 11: 1 1108.00000 cents 11: 3 1110.00000 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 90.0 196.0 294.0 386.9 498.0 588.0 700.0 792.0 892.0 996.0 1086.0 1200.0 90.0 : 106.0 204.0 296.9 408.0 498.0 610.0 702.0 802.0 906.0 996.0 1110.0 1200.0 196.0 : 98.0 190.9 302.0 392.0 504.0 596.0 696.0 800.0 890.0 1004.0 1094.0 1200.0 294.0 : 92.9 204.0 294.0 406.0 498.0 598.0 702.0 792.0 906.0 996.0 1102.0 1200.0 386.9 : 111.1 201.1 313.1 405.1 505.1 609.1 699.1 813.1 903.1 1009.1 1107.1 1200.0 498.0 : 90.0 202.0 294.0 394.0 498.0 588.0 702.0 792.0 898.0 996.0 1088.9 1200.0 588.0 : 112.0 204.0 304.0 408.0 498.0 612.0 702.0 808.0 906.0 998.9 1110.0 1200.0 700.0 : 92.0 192.0 296.0 386.0 500.0 590.0 696.0 794.0 886.9 998.0 1088.0 1200.0 792.0 : 100.0 204.0 294.0 408.0 498.0 604.0 702.0 794.9 906.0 996.0 1108.0 1200.0 892.0 : 104.0 194.0 308.0 398.0 504.0 602.0 694.9 806.0 896.0 1008.0 1100.0 1200.0 996.0 : 90.0 204.0 294.0 400.0 498.0 590.9 702.0 792.0 904.0 996.0 1096.0 1200.0 1086.0: 114.0 204.0 310.0 408.0 500.9 612.0 702.0 814.0 906.0 1006.0 1110.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.0000 .. 114.0000 cents 24.00000 cents 90.00000 cents 2: 190.9000 .. 204.0000 cents 13.10000 cents 76.90000 cents 3: 294.0000 .. 313.1000 cents 19.10000 cents 90.00000 cents 4: 386.0000 .. 408.0000 cents 22.00000 cents 72.90000 cents 5: 498.0000 .. 505.1000 cents 7.10000 cents 90.00000 cents 6: 588.0000 .. 612.0000 cents 24.00000 cents 82.90000 cents 7: 694.9000 .. 702.0000 cents 7.10000 cents 82.90000 cents 8: 792.0000 .. 814.0000 cents 22.00000 cents 90.00000 cents 9: 886.9000 .. 906.0000 cents 19.10000 cents 72.90000 cents 10: 996.0000 .. 1009.1000 cents 13.10000 cents 90.00000 cents 11: 1086.0000 .. 1110.0000 cents 24.00000 cents 76.90000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 90.00000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 114.00000 cents Average / Smallest step : 1.111111 Largest / Average step : 1.140000 Largest / Smallest step : 1.266667 Median interval of one step : 99.00000 cents, amount: 0 Most common interval of one step : 90.00000 cents, amount: 3 Least squares average step : 99.23015 cents, oct.: 1190.76185 cents Scale is strictly proper Step pattern alph. order: ABCDEAFGHIAJ Step pattern size order : AGDCHAIBEFAJ Scale is a Constant Structure, by a margin of 72.90000 cents Scale diversity : 1.136596 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.837833 Rothenberg efficiency : 0.236652 redundancy: 0.763348 Efficiency x scale size : 2.839827 Number of different interval sizes : 88 = 8.00000 / class Number of one step interval sizes : 10 Highest interval variety : 10 Mean interval variety : 8.00000 = 8 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.90000 cents Most common intervals : 498.00000 cents & inv., amount: 7 Most common triad is 0.0 498.000 702.000 cents, amount: 6 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 24.0000 cents: 2 5 7 9 10 Limited inverse transpositions with margin 24.0000 cents: 1 2 4 6 9 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: 8.2240 c. M:-14.0000 c. Twelve-tone Chromatic (1/11-comma) 39: 3 3 4 3 3 3 4 3 3 3 3 4 SP D3 SD: 8.5301 c. M:-13.6923 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 5.3813 c. M: 13.9512 c. Schismic-12 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 6.0867 c. M:-12.9767 c. Meantone Chromatic (1/5-comma) 49: 4 4 4 4 4 4 5 3 4 5 3 5 SP D3 SD: 6.9086 c. M: 10.3673 c. 51: 4 4 4 4 5 4 5 4 4 4 4 5 SP D3 SD: 6.5414 c. M: 11.6471 c. 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 3.5405 c. M: 8.9811 c. Schismic-12 61: 5 5 5 5 5 5 6 4 5 6 4 6 SP D3 SD: 5.5203 c. M:-8.3607 c. 62: 5 5 5 5 6 4 6 5 5 5 5 6 SP D3 SD: 4.5303 c. M: 8.9032 c. 63: 5 5 5 5 6 5 6 5 5 5 5 6 SP D3 SD: 5.0290 c. M: 8.2857 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.1235 c. M:-7.0769 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.3543 c. M:-6.5974 c. 82: 6 7 7 6 8 6 8 6 7 7 6 8 SP D3 SD: 2.9951 c. M: 6.4122 c. 84: 6 8 7 6 8 6 8 6 7 8 6 8 SP D3 SD: 3.8308 c. M: 6.2857 c. 86: 6 8 7 7 8 6 8 7 7 7 7 8 SP D3 S SD: 3.2808 c. M: 6.2791 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 3.7548 c. M:-6.2472 c. 91: 7 8 7 7 9 7 8 7 8 8 6 9 SP SD: 3.7296 c. M:-6.1978 c. 92: 7 8 8 7 8 7 9 7 7 8 7 9 SP SD: 3.5946 c. M:-6.0000 c. 93: 7 8 8 7 9 7 8 7 8 8 7 9 SP SD: 3.1589 c. M:-5.5484 c. 94: 7 8 8 7 9 7 9 7 8 8 7 9 SP D3 SD: 1.9396 c. M: 4.5106 c. 106: 8 9 9 8 10 8 10 8 9 9 8 10 SP D3 SD: 1.5107 c. M: 3.5472 c. 118: 9 10 10 9 11 9 11 9 10 10 9 11 SP D3 SD: 1.6416 c. M:-2.9153 c. 147: 11 13 12 11 14 11 14 11 12 13 11 14 SP SD: 1.2804 c. M: 3.2265 c. 151: 11 14 12 12 14 11 14 12 12 13 12 14 SP SD: 2.1029 c. M:-2.7417 c. 158: 12 14 13 12 15 11 15 12 13 14 12 15 SP SD: 2.0023 c. M: 3.3924 c. 159: 12 14 13 12 15 12 15 12 13 14 12 15 SP SD: 0.9764 c. M: 1.9943 c. 171: 13 15 14 13 16 13 16 13 14 15 13 16 SP SD: 1.0502 c. M:-1.7544 c. 241: 18 21 20 19 22 18 23 18 20 21 18 23 SP SD: 0.9602 c. M:-2.0747 c. 253: 19 22 21 20 23 19 24 19 21 22 19 24 SP SD: 0.9380 c. M:-2.0328 c. 282: 21 25 23 22 26 21 27 21 24 24 21 27 SP SD: 0.8944 c. M:-2.1277 c. 294: 22 26 24 23 27 22 28 22 25 25 22 28 SP SD: 0.8496 c. M:-2.0408 c. 306: 23 27 25 24 28 23 29 23 26 26 23 29 SP SD: 0.9280 c. M:-2.1176 c. 307: 23 27 25 24 28 23 29 24 25 27 23 29 SP SD: 0.9254 c. M: 1.6808 c. 311: 23 28 25 24 29 23 29 24 26 27 23 30 SP SD: 1.0634 c. M: 1.7556 c. 316: 24 28 25 25 29 24 29 25 26 27 24 30 SP SD: 1.0222 c. M:-1.6709 c. 317: 24 28 26 24 30 23 30 24 27 27 24 30 SP SD: 0.9619 c. M:-1.6845 c. 319: 24 28 26 25 29 24 30 25 26 28 24 30 SP SD: 0.8998 c. M:-1.7304 c. 320: 24 28 26 25 30 24 30 24 27 28 24 30 SP SD: 0.9863 c. M:-1.5000 c. 323: 24 29 26 25 30 24 30 25 27 28 24 31 SP SD: 0.7921 c. M: 1.5480 c. 335: 25 30 27 26 31 25 31 26 28 29 25 32 SP SD: 0.6045 c. M: 1.4925 c. 343: 26 30 28 27 31 26 32 26 29 30 25 33 SP SD: 0.8984 c. M: 1.4519 c. 347: 26 31 28 27 32 26 32 27 29 30 26 33 SP SD: 0.5472 c. M: 1.4409 c. 351: 26 31 29 27 33 26 33 27 29 30 27 33 SP SD: 0.8656 c. M:-1.1795 c. 355: 27 31 29 27 33 27 33 27 30 31 26 34 SP SD: 0.8552 c. M: 1.5479 c. 359: 27 32 29 28 33 27 33 28 30 31 27 34 SP SD: 0.6264 c. M: 1.3928 c. 388: 29 34 32 30 36 29 36 30 32 34 29 37 SP SD: 0.6230 c. M: 1.2784 c. 400: 30 35 33 31 37 30 37 31 33 35 30 38 SP SD: 0.5008 c. M: 1.0000 c. 412: 31 36 34 32 38 31 38 32 34 36 31 39 SP SD: 0.4934 c. M: 0.9709 c. 424: 32 37 35 33 39 32 39 33 35 37 32 40 SP SD: 0.5872 c. M: 0.9434 c. 429: 32 38 35 33 40 32 40 33 36 37 32 41 SP SD: 0.4786 c. M: 0.8860 c. 441: 33 39 36 34 41 33 41 34 37 38 33 42 SP SD: 0.3196 c. M: 0.6803 c. 453: 34 40 37 35 42 34 42 35 38 39 34 43 SP SD: 0.2882 c. M:-0.7152 c. 576: 43 51 47 45 53 43 54 44 48 50 43 55 SP SD: 0.3501 c. M:-0.6000 c. 588: 44 52 48 46 54 44 55 45 49 51 44 56 SP SD: 0.2884 c. M:-0.8551 c. 600: 45 53 49 46 56 45 56 46 50 52 45 57 SP SD: 0.2598 c. M: 0.9000 c. 612: 46 54 50 47 57 46 57 47 51 53 46 58 SP SD: 0.2305 c. M: 0.6255 c. 624: 47 55 51 48 58 47 58 48 52 54 47 59 SP SD: 0.2996 c. M:-0.5385 c. 682: 51 60 56 53 63 51 64 52 57 59 51 65 SP SD: 0.2888 c. M: 0.6921 c. 694: 52 61 57 54 64 52 65 53 58 60 52 66 SP SD: 0.2454 c. M: 0.6110 c. 735: 55 65 60 57 68 55 69 56 61 64 55 70 SP SD: 0.2474 c. M: 0.5714 c. 747: 56 66 61 58 69 56 70 57 62 65 56 71 SP SD: 0.1872 c. M: 0.4337 c. 759: 57 67 62 59 70 57 71 58 63 66 57 72 SP SD: 0.2105 c. M:-0.4518 c. 1012: 76 89 83 78 94 76 94 78 84 88 76 96 SP SD: 0.2162 c. M: 0.3953 c. 1017: 76 90 83 79 94 76 95 78 85 88 76 97 SP SD: 0.2431 c. M: 0.4543 c. 1024: 77 90 84 79 95 77 95 79 85 89 77 97 SP SD: 0.2278 c. M: 0.3906 c. 1029: 77 91 84 80 95 77 96 79 86 89 77 98 SP SD: 0.1860 c. M: 0.2915 c. 1041: 78 92 85 81 96 78 97 80 87 90 78 99 SP SD: 0.1709 c. M:-0.4199 c. 1094: 82 97 89 85 101 82 102 84 91 95 82 104 SP SD: 0.1611 c. M:-0.3437 c. 1176: 88 104 96 91 109 88 110 90 98 102 88 112 SP SD: 0.1565 c. M: 0.2857 c. 1188: 89 105 97 92 110 89 111 91 99 103 89 113 SP SD: 0.0743 c. M: 0.1414 c. 1200: 90 106 98 93 111 90 112 92 100 104 90 114 SP SD: 0.0289 c. M:-0.1000 c. 2388: 179 211 195 185 221 179 223 183 199 207 179 227 SP SD: 0.0380 c. M: 0.0704 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: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.5471 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.8127 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.5767 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.7109 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.4419 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.3953 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.9555 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.5244 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.3285 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.7274 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.2846 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.0928 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.4569 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.0692 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.9837 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.1603 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.3967 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.3655 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.5306 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.5229 cents 36:38:40:43:45:48:51:54:57:60:64:67:72 SD: 2.3506 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.3097 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.8776 cents 52:55:58:62:65:69:73:78:82:87:92:97:104 SD: 1.6830 cents 55:58:62:65:69:73:77:82:87:92:98:103:110 SD: 1.6158 cents 59:62:66:70:74:79:83:88:93:99:105:110:118 SD: 1.3720 cents 60:63:67:71:75:80:84:90:95:100:107:112:120 SD: 1.2554 cents 72:76:81:85:90:96:101:108:114:121:128:135:144 SD: 1.1520 cents 76:80:85:90:95:101:107:114:120:127:135:142:152 SD: 0.7898 cents 92:97:103:109:115:123:129:138:145:154:164:172:184 SD: 0.7787 cents 108:114:121:128:135:144:152:162:171:181:192:202:216 SD: 0.5985 cents 135:142:151:160:169:180:190:202:213:226:240:253:270 SD: 0.5373 cents 150:158:168:178:188:200:211:225:237:251:267:281:300 SD: 0.5203 cents 151:159:169:179:189:201:212:226:239:253:268:283:302 SD: 0.5096 cents 167:176:187:198:209:223:235:250:264:280:297:313:334 SD: 0.4943 cents 168:177:188:199:210:224:236:252:265:281:299:315:336 SD: 0.4324 cents 183:193:205:217:229:244:257:274:289:306:325:343:366 SD: 0.3653 cents 227:239:254:269:284:303:319:340:359:380:404:425:454 SD: 0.3261 cents 243:256:272:288:304:324:341:364:384:407:432:455:486 SD: 0.1764 cents 319:336:357:378:399:425:448:478:504:534:567:597:638 SD: 0.1761 cents 432:455:484:512:540:576:607:647:683:723:768:809:864 SD: 0.1542 cents 450:474:504:533:563:600:632:674:711:753:800:843:900 SD: 0.1514 cents 507:534:568:601:634:676:712:760:801:849:901:949:1014 SD: 0.1323 cents 540:569:605:640:675:720:758:809:853:904:960:1011:1080 SD: 0.1315 cents 567:597:635:672:709:756:796:850:896:949:1008:1062:1134 SD: 0.1258 cents