Scala analysis: J_P_Mander
John Pike Mander's Adlington-Hall organ tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78.000 cents 78.000000 2: 192.000 cents 192.000000 3: 294.000 cents 294.000000 4: 384.000 cents 384.000000 5: 498.000 cents 498.000000 6: 578.000 cents 578.000000 7: 696.000 cents 696.000000 8: 775.000 cents 775.000000 9: 888.000 cents 888.000000 10: 996.000 cents 996.000000 11: 1080.000 cents 1080.000000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 120.0000 cents 120.0000 1: 78.0000 cents 78.0000 2: 114.0000 cents 114.0000 3: 102.0000 cents 102.0000 4: 90.0000 cents 90.0000 5: 114.0000 cents 114.0000 6: 80.0000 cents 80.0000 7: 118.0000 cents 118.0000 8: 79.0000 cents 79.0000 9: 113.0000 cents 113.0000 10: 108.0000 cents 108.0000 11: 84.0000 cents 84.0000 12: 120.0000 cents 120.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 78.00000 cents 1: 1 79.00000 cents 1: 1 80.00000 cents 1: 1 84.00000 cents 1: 1 90.00000 cents 1: 1 102.00000 cents 1: 1 108.00000 cents 1: 1 113.00000 cents 1: 2 114.00000 cents 1: 1 118.00000 cents 1: 1 120.00000 cents 2: 4 192.00000 cents 2: 1 194.00000 cents 2: 1 197.00000 cents 2: 2 198.00000 cents 2: 2 204.00000 cents 2: 1 216.00000 cents 2: 1 221.00000 cents 3: 1 277.00000 cents 3: 1 282.00000 cents 3: 1 284.00000 cents 3: 1 294.00000 cents 3: 1 300.00000 cents 3: 1 305.00000 cents 3: 2 306.00000 cents 3: 1 310.00000 cents 3: 3 312.00000 cents 4: 2 384.00000 cents 4: 1 386.00000 cents 4: 2 390.00000 cents 4: 1 391.00000 cents 4: 1 396.00000 cents 4: 1 402.00000 cents 4: 1 414.00000 cents 4: 1 418.00000 cents 4: 1 420.00000 cents 4: 1 425.00000 cents 5: 1 481.00000 cents 5: 3 498.00000 cents 5: 1 500.00000 cents 5: 1 502.00000 cents 5: 1 503.00000 cents 5: 5 504.00000 cents 6: 1 578.00000 cents 6: 2 582.00000 cents 6: 1 583.00000 cents 6: 1 588.00000 cents 6: 1 594.00000 cents 6: 1 606.00000 cents 6: 1 612.00000 cents 6: 1 617.00000 cents 6: 2 618.00000 cents 6: 1 622.00000 cents 7: 5 696.00000 cents 7: 1 697.00000 cents 7: 1 698.00000 cents 7: 1 700.00000 cents 7: 3 702.00000 cents 7: 1 719.00000 cents 8: 1 775.00000 cents 8: 1 780.00000 cents 8: 1 782.00000 cents 8: 1 786.00000 cents 8: 1 798.00000 cents 8: 1 804.00000 cents 8: 1 809.00000 cents 8: 2 810.00000 cents 8: 1 814.00000 cents 8: 2 816.00000 cents 9: 3 888.00000 cents 9: 1 890.00000 cents 9: 2 894.00000 cents 9: 1 895.00000 cents 9: 1 900.00000 cents 9: 1 906.00000 cents 9: 1 916.00000 cents 9: 1 918.00000 cents 9: 1 923.00000 cents 10: 1 979.00000 cents 10: 1 984.00000 cents 10: 2 996.00000 cents 10: 2 1002.00000 cents 10: 1 1003.00000 cents 10: 1 1006.00000 cents 10: 4 1008.00000 cents 11: 1 1080.00000 cents 11: 1 1082.00000 cents 11: 2 1086.00000 cents 11: 1 1087.00000 cents 11: 1 1092.00000 cents 11: 1 1098.00000 cents 11: 1 1110.00000 cents 11: 1 1116.00000 cents 11: 1 1120.00000 cents 11: 1 1121.00000 cents 11: 1 1122.00000 cents Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 8.72727 = 96/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 78.0 192.0 294.0 384.0 498.0 578.0 696.0 775.0 888.0 996.0 1080.0 1200.0 78.0 : 114.0 216.0 306.0 420.0 500.0 618.0 697.0 810.0 918.0 1002.0 1122.0 1200.0 192.0 : 102.0 192.0 306.0 386.0 504.0 583.0 696.0 804.0 888.0 1008.0 1086.0 1200.0 294.0 : 90.0 204.0 284.0 402.0 481.0 594.0 702.0 786.0 906.0 984.0 1098.0 1200.0 384.0 : 114.0 194.0 312.0 391.0 504.0 612.0 696.0 816.0 894.0 1008.0 1110.0 1200.0 498.0 : 80.0 198.0 277.0 390.0 498.0 582.0 702.0 780.0 894.0 996.0 1086.0 1200.0 578.0 : 118.0 197.0 310.0 418.0 502.0 622.0 700.0 814.0 916.0 1006.0 1120.0 1200.0 696.0 : 79.0 192.0 300.0 384.0 504.0 582.0 696.0 798.0 888.0 1002.0 1082.0 1200.0 775.0 : 113.0 221.0 305.0 425.0 503.0 617.0 719.0 809.0 923.0 1003.0 1121.0 1200.0 888.0 : 108.0 192.0 312.0 390.0 504.0 606.0 696.0 810.0 890.0 1008.0 1087.0 1200.0 996.0 : 84.0 204.0 282.0 396.0 498.0 588.0 702.0 782.0 900.0 979.0 1092.0 1200.0 1080.0: 120.0 198.0 312.0 414.0 504.0 618.0 698.0 816.0 895.0 1008.0 1116.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.0000 .. 120.0000 cents 42.00000 cents 78.00000 cents 2: 192.0000 .. 221.0000 cents 29.00000 cents 72.00000 cents 3: 277.0000 .. 312.0000 cents 35.00000 cents 56.00000 cents 4: 384.0000 .. 425.0000 cents 41.00000 cents 72.00000 cents 5: 481.0000 .. 504.0000 cents 23.00000 cents 56.00000 cents 6: 578.0000 .. 622.0000 cents 44.00000 cents 74.00000 cents 7: 696.0000 .. 719.0000 cents 23.00000 cents 74.00000 cents 8: 775.0000 .. 816.0000 cents 41.00000 cents 56.00000 cents 9: 888.0000 .. 923.0000 cents 35.00000 cents 72.00000 cents 10: 979.0000 .. 1008.0000 cents 29.00000 cents 56.00000 cents 11: 1080.0000 .. 1122.0000 cents 42.00000 cents 72.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 78.00000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 120.00000 cents Average / Smallest step : 1.282051 Largest / Average step : 1.200000 Largest / Smallest step : 1.538462 Median interval of one step : 105.00000 cents, amount: 0 Most common interval of one step : 114.00000 cents, amount: 2 Least squares average step : 98.68000 cents, oct.: 1184.16000 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 2/1 degrees: 78 192 294 384 498 578 696 775 888 996 1080 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1129 of 1129.000 cents and inv. generated superset size: 505 = 493 more = 4208.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDBEFGHIJK Step pattern size order : AIFEICJBHGDK Scale is a Constant Structure, by a margin of 56.00000 cents Scale diversity : 1.283937 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.680000 Rothenberg efficiency : 0.211827 redundancy: 0.788173 Efficiency x scale size : 2.541919 Number of different interval sizes : 96 = 8.72727 / class Number of one step interval sizes : 11 Highest interval variety : 11 Mean interval variety : 8.72727 = 96/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 1.00000 cents Most common intervals : 504.00000 cents & inv., amount: 5 Most common triad is 0.0 504.000 696.000 cents, amount: 4 Number of recognisable fifths : 12, average 700.0000 cents Number of appreciable fifths : 11, average 698.2727 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited inverse transpositions with margin 41.0000 cents: 1 6 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: 14.5172 c. M:-25.0000 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 10.9199 c. M:-21.7895 c. Meantone Chromatic (1/3-comma) 28: 2 2 3 2 3 1 3 2 3 2 2 3 SP D3 SD: 11.7746 c. M: 20.8571 c. 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 8.9925 c. M: 19.0345 c. Schismic-12 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 5.9391 c. M:-15.6774 c. Meantone Chromatic (53/220-comma) 37: 2 4 3 3 3 3 3 3 3 4 2 4 SP D3 SD: 8.8772 c. M: 14.9189 c. 40: 3 3 4 3 4 2 4 3 4 3 3 4 SP D3 SD: 8.2108 c. M:-12.0000 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 7.7066 c. M:-15.2439 c. Schismic-12 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 6.7978 c. M:-12.9767 c. Meantone Chromatic (1/5-comma) 46: 3 4 4 4 4 3 5 3 4 4 3 5 SP D3 S SD: 6.2786 c. M: 10.4348 c. 48: 3 5 4 3 5 3 5 3 5 4 3 5 SP T3 SD: 5.8023 c. M:-12.0000 c. 49: 3 5 4 4 4 4 4 4 4 5 3 5 SP D3 SD: 6.7864 c. M: 10.2857 c. 50: 3 5 4 4 5 3 5 3 5 4 4 5 SP D3 SD: 5.0415 c. M: 12.0000 c. 57: 4 5 5 4 6 3 6 4 5 5 4 6 SP SD: 5.2405 c. M: 9.5789 c. 58: 4 5 5 5 5 4 6 3 6 5 4 6 SP SD: 5.2869 c. M: 9.4828 c. 60: 4 6 5 4 6 4 6 4 5 6 4 6 SP D3 SD: 4.5552 c. M: 8.0000 c. 62: 4 6 5 5 6 4 6 4 6 5 5 6 SP D3 SD: 3.6634 c. M: 8.9032 c. 67: 4 7 5 5 7 4 7 4 7 6 4 7 SP SD: 5.6485 c. M: 7.8806 c. 68: 4 7 6 5 6 5 6 5 6 6 5 7 SP SD: 5.1191 c. M: 7.7647 c. 70: 5 6 6 5 7 5 7 4 7 6 5 7 SP SD: 4.3175 c. M:-7.7143 c. 73: 5 7 6 5 7 5 7 5 7 7 5 7 SP SD: 4.2939 c. M:-6.7397 c. 74: 5 7 6 6 7 5 7 5 7 7 5 7 SP D3 S SD: 4.6721 c. M:-9.4054 c. 77: 5 7 7 6 7 5 8 5 7 7 5 8 SP SD: 3.3289 c. M:-5.6104 c. 81: 5 8 7 6 8 5 8 5 8 7 6 8 SP SD: 2.7559 c. M:-5.7037 c. 90: 6 8 8 7 8 6 9 6 9 8 6 9 SP SD: 3.3898 c. M: 5.3333 c. 93: 6 9 8 7 9 6 9 6 9 8 7 9 SP SD: 2.6135 c. M:-5.2258 c. 101: 7 9 9 7 10 7 10 6 10 9 7 10 SP SD: 3.1594 c. M:-5.1683 c. 106: 7 10 9 8 10 7 10 7 10 10 7 11 SP SD: 2.9571 c. M: 5.4340 c. 107: 7 10 9 8 10 7 11 7 10 10 7 11 SP SD: 2.7982 c. M: 6.0374 c. 110: 7 11 9 8 11 7 11 7 10 10 8 11 SP SD: 2.5184 c. M: 4.3636 c. 118: 8 11 10 9 11 8 11 8 11 11 8 12 SP SD: 2.2732 c. M: 4.4746 c. 119: 8 11 10 9 11 8 12 8 11 11 8 12 SP SD: 1.9309 c. M: 3.8824 c. 138: 9 13 12 10 13 9 14 9 13 12 10 14 SP SD: 2.1389 c. M: 4.6957 c. 142: 9 14 12 10 14 9 14 10 13 13 10 14 SP SD: 2.1981 c. M: 3.7183 c. 143: 9 14 12 11 13 10 14 9 14 13 10 14 SP SD: 1.9404 c. M: 2.9720 c. 150: 10 14 13 11 14 10 15 10 14 13 11 15 SP SD: 1.6583 c. M: 4.0000 c. 169: 11 16 14 13 16 11 17 11 16 15 12 17 SP SD: 1.3902 c. M: 2.8757 c. 173: 11 17 14 13 17 11 17 12 16 16 12 17 SP SD: 2.0396 c. M:-2.8439 c. 176: 11 17 15 13 17 12 17 12 16 16 12 18 SP SD: 1.6822 c. M: 3.0000 c. 180: 12 17 15 14 17 12 17 12 17 16 13 18 SP SD: 1.8283 c. M:-2.6667 c. 181: 12 17 15 14 17 12 18 12 17 16 13 18 SP SD: 1.0591 c. M: 2.2873 c. 200: 13 19 17 15 19 13 20 13 19 18 14 20 SP SD: 0.6455 c. M: 2.0000 c. 212: 14 20 18 16 20 14 21 14 20 19 15 21 SP SD: 0.6572 c. M:-1.2453 c. 369: 24 35 31 28 35 25 36 24 35 33 26 37 SP SD: 0.6264 c. M: 1.3171 c. 388: 25 37 33 29 37 26 38 26 36 35 27 39 SP SD: 0.5117 c. M:-1.2887 c. 396: 26 37 34 30 37 27 39 26 37 36 27 40 SP SD: 0.8244 c. M: 1.2121 c. 399: 26 38 34 30 38 26 39 27 37 36 28 40 SP SD: 0.7664 c. M: 1.2632 c. 400: 26 38 34 30 38 27 39 26 38 36 28 40 SP SD: 0.4082 c. M:-1.0000 c. 457: 30 43 39 34 44 30 45 30 43 41 32 46 SP SD: 0.5557 c. M:-0.9059 c. 469: 30 45 40 35 45 31 46 31 44 42 33 47 SP SD: 0.5186 c. M: 1.2409 c. 477: 31 45 41 36 45 32 47 31 45 43 33 48 SP SD: 0.5289 c. M:-0.9057 c. 519: 34 49 44 39 49 35 51 34 49 47 36 52 SP SD: 0.3964 c. M: 0.8902 c. 523: 34 50 44 39 50 35 51 35 49 47 37 52 SP SD: 0.4807 c. M: 0.8260 c. 531: 35 50 45 40 50 36 52 35 50 48 37 53 SP SD: 0.4756 c. M:-1.0960 c. 550: 36 52 47 41 52 37 54 36 52 50 38 55 SP SD: 0.4399 c. M:-1.0909 c. 569: 37 54 48 43 54 38 56 37 54 51 40 57 SP SD: 0.4355 c. M: 1.0105 c. 581: 38 55 49 44 55 39 57 38 55 52 41 58 SP SD: 0.3466 c. M: 0.7126 c. 588: 38 56 50 44 56 39 58 39 55 53 41 59 SP SD: 0.2963 c. M:-0.5102 c. 600: 39 57 51 45 57 40 59 40 56 54 42 60 SP SD: 0.2887 c. M:-1.0000 c. 612: 40 58 52 46 58 41 60 40 58 55 43 61 SP SD: 0.2847 c. M: 0.4902 c. 788: 51 75 67 59 75 52 78 52 74 71 55 79 SP SD: 0.2966 c. M: 0.8426 c. 800: 52 76 68 60 76 53 79 53 75 72 56 80 SP SD: 0.2041 c. M: 0.5000 c. 943: 61 90 80 71 89 63 93 62 89 85 66 94 SP SD: 0.2716 c. M: 0.4390 c. 957: 62 91 81 72 91 64 94 63 90 86 67 96 SP SD: 0.2762 c. M: 0.5831 c. 969: 63 92 82 73 92 65 95 64 91 87 68 97 SP SD: 0.2212 c. M: 0.5015 c. 988: 64 94 84 74 94 66 97 65 93 89 69 99 SP SD: 0.1410 c. M: 0.2672 c. 1000: 65 95 85 75 95 67 98 66 94 90 70 100 SP SD: 0.1291 c. M:-0.4000 c. 1188: 77 113 101 89 113 79 117 78 112 107 83 119 SP SD: 0.1466 c. M: 0.2525 c. 1200: 78 114 102 90 114 80 118 79 113 108 84 120 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: 2.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 1.2139 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9787 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.9030 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.9189 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.6693 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 7.8611 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.1838 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.3937 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.6775 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.2552 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 9.0546 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 8.4131 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 6.2714 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 4.9343 cents 18:19:20:21:22:24:25:27:28:30:32:34:36 SD: 4.6323 cents 21:22:23:25:26:28:29:31:33:35:37:39:42 SD: 4.3141 cents 23:24:26:27:29:31:32:34:36:38:41:43:46 SD: 3.8621 cents 25:26:28:30:31:33:35:37:39:42:44:47:50 SD: 3.6682 cents 27:28:30:32:34:36:38:40:42:45:48:50:54 SD: 2.9631 cents 28:29:31:33:35:37:39:42:44:47:50:52:56 SD: 2.8852 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.3331 cents 42:44:47:50:52:56:59:63:66:70:75:78:84 SD: 2.0769 cents 43:45:48:51:54:57:60:64:67:72:76:80:86 SD: 1.8056 cents 45:47:50:53:56:60:63:67:70:75:80:84:90 SD: 1.7220 cents 48:50:54:57:60:64:67:72:75:80:85:90:96 SD: 1.6268 cents 59:62:66:70:74:79:82:88:92:99:105:110:118 SD: 1.6192 cents 60:63:67:71:75:80:84:90:94:100:107:112:120 SD: 1.0517 cents 69:72:77:82:86:92:96:103:108:115:123:129:138 SD: 1.0072 cents 85:89:95:101:106:113:119:127:133:142:151:159:170 SD: 0.8028 cents 103:108:115:122:129:137:144:154:161:172:183:192:206 SD: 0.7463 cents 109:114:122:129:136:145:152:163:171:182:194:203:218 SD: 0.7186 cents 113:118:126:134:141:151:158:169:177:189:201:211:226 SD: 0.6253 cents 129:135:144:153:161:172:180:193:202:215:229:241:258 SD: 0.4845 cents 172:180:192:204:215:229:240:257:269:287:306:321:344 SD: 0.4048 cents 194:203:217:230:242:259:271:290:304:324:345:362:388 SD: 0.3643 cents 216:226:241:256:270:288:302:323:338:361:384:403:432 SD: 0.3538 cents 222:232:248:263:277:296:310:332:347:371:395:414:444 SD: 0.2932 cents 237:248:265:281:296:316:331:354:371:396:421:442:474 SD: 0.2546 cents 282:295:315:334:352:376:394:422:441:471:501:526:564 SD: 0.2385 cents 330:345:369:391:412:440:461:493:516:551:587:616:660 SD: 0.2331 cents 342:358:382:405:427:456:478:511:535:571:608:638:684 SD: 0.2265 cents 351:367:392:416:438:468:490:525:549:586:624:655:702 SD: 0.1608 cents 459:480:513:544:573:612:641:686:718:767:816:857:918 SD: 0.1361 cents 519:543:580:615:648:692:725:776:812:867:923:968:1038 SD: 0.1288 cents 540:565:603:640:674:720:754:807:845:902:960:1008:1080 SD: 0.1103 cents 588:615:657:697:734:784:821:879:920:982:1045:1097:1176 SD: 0.0674 cents