Scala analysis: phillips_tuning_39746_39990
Pauline Phillips, organ manual scale, TL 7-10-2002
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 84.000 cents 84.000000 2: 200.000 cents 200.000000 3: 268.000 cents 268.000000 4: 384.000 cents 384.000000 5: 468.000 cents 468.000000 6: 584.000 cents 584.000000 7: 700.000 cents 700.000000 8: 768.000 cents 768.000000 9: 900.000 cents 900.000000 10: 968.000 cents 968.000000 11: 1084.000 cents 1084.000000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.0000 cents 116.0000 1: 84.0000 cents 84.0000 2: 116.0000 cents 116.0000 3: 68.0000 cents 68.0000 4: 116.0000 cents 116.0000 5: 84.0000 cents 84.0000 6: 116.0000 cents 116.0000 7: 116.0000 cents 116.0000 8: 68.0000 cents 68.0000 9: 132.0000 cents 132.0000 10: 68.0000 cents 68.0000 11: 116.0000 cents 116.0000 12: 116.0000 cents 116.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 68.00000 cents 1: 2 84.00000 cents 1: 6 116.00000 cents 1: 1 132.00000 cents 2: 4 184.00000 cents 2: 6 200.00000 cents 2: 2 232.00000 cents 3: 3 268.00000 cents 3: 3 300.00000 cents 3: 6 316.00000 cents 4: 8 384.00000 cents 4: 4 432.00000 cents 5: 1 468.00000 cents 5: 9 500.00000 cents 5: 2 516.00000 cents 6: 2 568.00000 cents 6: 4 584.00000 cents 6: 4 616.00000 cents 6: 2 632.00000 cents 7: 2 684.00000 cents 7: 9 700.00000 cents 7: 1 732.00000 cents 8: 4 768.00000 cents 8: 8 816.00000 cents 9: 6 884.00000 cents 9: 3 900.00000 cents 9: 3 932.00000 cents 10: 2 968.00000 cents 10: 6 1000.00000 cents 10: 4 1016.00000 cents 11: 1 1068.00000 cents 11: 6 1084.00000 cents 11: 2 1116.00000 cents 11: 3 1132.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.0 200.0 268.0 384.0 468.0 584.0 700.0 768.0 900.0 968.0 1084.0 1200.0 84.0 : 116.0 184.0 300.0 384.0 500.0 616.0 684.0 816.0 884.0 1000.0 1116.0 1200.0 200.0 : 68.0 184.0 268.0 384.0 500.0 568.0 700.0 768.0 884.0 1000.0 1084.0 1200.0 268.0 : 116.0 200.0 316.0 432.0 500.0 632.0 700.0 816.0 932.0 1016.0 1132.0 1200.0 384.0 : 84.0 200.0 316.0 384.0 516.0 584.0 700.0 816.0 900.0 1016.0 1084.0 1200.0 468.0 : 116.0 232.0 300.0 432.0 500.0 616.0 732.0 816.0 932.0 1000.0 1116.0 1200.0 584.0 : 116.0 184.0 316.0 384.0 500.0 616.0 700.0 816.0 884.0 1000.0 1084.0 1200.0 700.0 : 68.0 200.0 268.0 384.0 500.0 584.0 700.0 768.0 884.0 968.0 1084.0 1200.0 768.0 : 132.0 200.0 316.0 432.0 516.0 632.0 700.0 816.0 900.0 1016.0 1132.0 1200.0 900.0 : 68.0 184.0 300.0 384.0 500.0 568.0 684.0 768.0 884.0 1000.0 1068.0 1200.0 968.0 : 116.0 232.0 316.0 432.0 500.0 616.0 700.0 816.0 932.0 1000.0 1132.0 1200.0 1084.0: 116.0 200.0 316.0 384.0 500.0 584.0 700.0 816.0 884.0 1016.0 1084.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.0000 .. 132.0000 cents 64.00000 cents 68.00000 cents 2: 184.0000 .. 232.0000 cents 48.00000 cents 52.00000 cents 3: 268.0000 .. 316.0000 cents 48.00000 cents 36.00000 cents 4: 384.0000 .. 432.0000 cents 48.00000 cents 68.00000 cents 5: 468.0000 .. 516.0000 cents 48.00000 cents 36.00000 cents 6: 568.0000 .. 632.0000 cents 64.00000 cents 52.00000 cents 7: 684.0000 .. 732.0000 cents 48.00000 cents 52.00000 cents 8: 768.0000 .. 816.0000 cents 48.00000 cents 36.00000 cents 9: 884.0000 .. 932.0000 cents 48.00000 cents 68.00000 cents 10: 968.0000 .. 1016.0000 cents 48.00000 cents 36.00000 cents 11: 1068.0000 .. 1132.0000 cents 64.00000 cents 52.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 68.00000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 132.00000 cents Average / Smallest step : 1.470588 Largest / Average step : 1.320000 Largest / Smallest step : 1.941176 Median interval of one step : 116.00000 cents, amount: 6 Most common interval of one step : 116.00000 cents, amount: 6 Least squares average step : 98.17846 cents, oct.: 1178.14154 cents Scale is strictly proper Scale is a mode of a 300-tone equal temperament with octave 2/1 degrees: 21 50 67 96 117 146 175 192 225 242 271 300 Least number of segments generator : 151 of 604.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 233 of 932.000 cents and inv. generated superset size: 100 = 88 more = 833.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBABBCDCBB Step pattern size order : BCACBCCADACC Scale is a Constant Structure, by a margin of 36.00000 cents Scale diversity : 1.341264 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.520000 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.00000 cents Most common intervals : 500.00000 cents & inv., amount: 9 Most common triad is 0.0 500.000 700.000 cents, amount: 6 Number of recognisable fifths : 9, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- 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: 20.6559 c. M:-32.0000 c. Twelve-tone Chromatic (1/11-comma) 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 18.2675 c. M: 31.0588 c. 19: 1 2 1 2 1 2 2 1 2 1 2 2 P M ME SD: 14.8081 c. M: 25.8947 c. 23: 2 2 1 2 2 2 2 2 2 2 2 2 SP M ME SD: 14.5272 c. M:-23.3043 c. 25: 2 2 2 2 2 2 3 1 3 1 3 2 P D3 SD: 12.3288 c. M:-20.0000 c. 28: 2 3 1 3 2 3 2 2 3 2 2 3 SP D3 SD: 10.3411 c. M:-17.7143 c. 31: 2 3 2 3 2 3 3 2 3 2 3 3 SP M ME SD: 4.7366 c. M: 9.6774 c. 41: 3 4 2 4 3 4 4 2 5 2 4 4 SP SD: 3.9599 c. M:-7.3171 c. 53: 4 5 3 5 4 5 5 3 6 3 5 5 SP SD: 4.3535 c. M:-7.4717 c. 72: 5 7 4 7 5 7 7 4 8 4 7 7 SP SD: 0.8607 c. M: 1.3333 c. 156: 11 15 9 15 11 15 15 9 17 9 15 15 SP SD: 0.7945 c. M:-1.2308 c. 197: 14 19 11 19 14 19 19 11 22 11 19 19 SP SD: 0.7936 c. M:-1.5228 c. 228: 16 22 13 22 16 22 22 13 25 13 22 22 SP SD: 0.2718 c. M:-0.4211 c. 300: 21 29 17 29 21 29 29 17 33 17 29 29 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: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 11.2909 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.7849 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 16.5154 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.0832 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 9.7264 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.5224 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 9.0633 cents 10 x 11:12 x 13:14:15:16:17 x 19:20 SD: 9.2062 cents 11 x 12:13:14 x 15:16:17 x 19:21:22 SD: 11.5448 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 7.3050 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 7.4810 cents 14:15:16 x 17:18:20:21:22:24 x 26:28 S SD: 9.0483 cents 15:16:17:18:19:20:21:22:23:25:26:28:30 SD: 7.2230 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 4.1543 cents 23:24:26:27:29:30:32:34:36:39:40:43:46 SD: 3.5025 cents 25:26:28:29:31:33:35:37:39:42:44:47:50 SD: 3.0564 cents 32:34:36:37:40:42:45:48:50:54:56:60:64 SD: 2.4469 cents 40:42:45:47:50:52:56:60:62:67:70:75:80 SD: 1.8565 cents 48:50:54:56:60:63:67:72:75:81:84:90:96 SD: 1.5138 cents 60:63:67:70:75:79:84:90:94:101:105:112:120 SD: 1.3487 cents 64:67:72:75:80:84:90:96:100:108:112:120:128 SD: 1.2105 cents 72:76:81:84:90:94:101:108:112:121:126:135:144 SD: 1.1570 cents 80:84:90:93:100:105:112:120:125:135:140:150:160 SD: 1.0638 cents 84:88:94:98:105:110:118:126:131:141:147:157:168 SD: 0.7721 cents 97:102:109:113:121:127:136:145:151:163:170:181:194 SD: 0.7481 cents 100:105:112:117:125:131:140:150:156:168:175:187:200 SD: 0.5804 cents 138:145:155:161:172:181:193:207:215:232:241:258:276 SD: 0.5173 cents 145:152:163:169:181:190:203:217:226:244:254:271:290 SD: 0.4995 cents 161:169:181:188:201:211:226:241:251:271:282:301:322 SD: 0.4478 cents 197:207:221:230:246:258:276:295:307:331:345:368:394 SD: 0.3539 cents 222:233:249:259:277:291:311:333:346:373:388:415:444 SD: 0.3076 cents 245:257:275:286:306:321:343:367:382:412:429:458:490 SD: 0.2620 cents 287:301:322:335:358:376:402:430:447:483:502:537:574 SD: 0.2354 cents 299:314:336:349:373:392:419:448:466:503:523:559:598 SD: 0.2287 cents 342:359:384:399:427:448:479:512:533:575:598:640:684 SD: 0.2056 cents 383:402:430:447:478:502:537:574:597:644:670:716:766 SD: 0.1502 cents 399:419:448:466:498:523:559:598:622:671:698:746:798 SD: 0.1397 cents 548:575:615:640:684:718:768:821:854:922:959:1025:1096 SD: 0.1320 cents 580:609:651:677:724:760:813:869:904:975:1015:1085:1160 SD: 0.1237 cents