Scala analysis: pship
Pauline (225/224) tempered 10 note scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 268.146 cents 268.145800 2: 384.152 cents 384.152140 3: 500.158 cents 500.158479 4: 583.835 cents 583.835182 5: 699.842 cents 699.841521 6: 768.304 cents 768.304279 7: 884.311 cents 884.310618 8: 967.987 cents 967.987322 9: 1083.994 cents 1083.993661 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.0063 cents 116.0063 1: 268.1458 cents 268.1458 2: 116.0063 cents 116.0063 3: 116.0063 cents 116.0063 4: 83.6767 cents 83.6767 5: 116.0063 cents 116.0063 6: 68.4628 cents 68.4628 7: 116.0063 cents 116.0063 8: 83.6767 cents 83.6767 9: 116.0063 cents 116.0063 10: 116.0063 cents 116.0063
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68.46276 cents 1: 2 83.67670 cents 1: 6 116.00634 cents 1: 1 268.14580 cents 2: 2 184.46910 cents 2: 4 199.68304 cents 2: 2 232.01268 cents 2: 2 384.15214 cents 3: 2 268.14580 cents 3: 1 300.47544 cents 3: 4 315.68938 cents 3: 3 500.15848 cents 4: 4 384.15214 cents 4: 2 431.69572 cents 4: 2 583.83518 cents 4: 2 616.16482 cents 5: 1 467.82884 cents 5: 4 500.15848 cents 5: 4 699.84152 cents 5: 1 732.17116 cents 6: 2 583.83518 cents 6: 2 616.16482 cents 6: 2 768.30428 cents 6: 4 815.84786 cents 7: 3 699.84152 cents 7: 4 884.31062 cents 7: 1 899.52456 cents 7: 2 931.85420 cents 8: 2 815.84786 cents 8: 2 967.98732 cents 8: 4 1000.31696 cents 8: 2 1015.53090 cents 9: 1 931.85420 cents 9: 6 1083.99366 cents 9: 2 1116.32330 cents 9: 1 1131.53724 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 268.1 384.2 500.2 583.8 699.8 768.3 884.3 968.0 1084.0 1200.0 268.1 : 116.0 232.0 315.7 431.7 500.2 616.2 699.8 815.8 931.9 1200.0 384.2 : 116.0 199.7 315.7 384.2 500.2 583.8 699.8 815.8 1084.0 1200.0 500.2 : 83.7 199.7 268.1 384.2 467.8 583.8 699.8 968.0 1084.0 1200.0 583.8 : 116.0 184.5 300.5 384.2 500.2 616.2 884.3 1000.3 1116.3 1200.0 699.8 : 68.5 184.5 268.1 384.2 500.2 768.3 884.3 1000.3 1084.0 1200.0 768.3 : 116.0 199.7 315.7 431.7 699.8 815.8 931.9 1015.5 1131.5 1200.0 884.3 : 83.7 199.7 315.7 583.8 699.8 815.8 899.5 1015.5 1084.0 1200.0 968.0 : 116.0 232.0 500.2 616.2 732.2 815.8 931.9 1000.3 1116.3 1200.0 1084.0: 116.0 384.2 500.2 616.2 699.8 815.8 884.3 1000.3 1084.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.4628 .. 268.1458 cents 199.68304 cents 68.46276 cents 2: 184.4691 .. 384.1521 cents 199.68304 cents -83.67670 cents 3: 268.1458 .. 500.1585 cents 232.01268 cents -116.00634 cents 4: 384.1521 .. 616.1648 cents 232.01268 cents -116.00634 cents 5: 467.8288 .. 732.1712 cents 264.34231 cents -148.33598 cents 6: 583.8352 .. 815.8479 cents 232.01268 cents -148.33598 cents 7: 699.8415 .. 931.8542 cents 232.01268 cents -116.00634 cents 8: 815.8479 .. 1015.5309 cents 199.68304 cents -116.00634 cents 9: 931.8542 .. 1131.5372 cents 199.68304 cents -83.67670 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 68.46276 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 268.14580 cents Average / Smallest step : 1.752778 Largest / Average step : 2.234548 Largest / Smallest step : 3.916667 Median interval of one step : 116.00634 cents, amount: 6 Most common interval of one step : 116.00634 cents, amount: 6 Least squares average step : 126.41900 cents, oct.: 1264.19001 cents Scale is not proper Scale is a mode of a 631-tone equal temperament with octave 2/1 degrees: 141 202 263 307 368 404 465 509 570 631 Least number of segments generator : 316 of 600.951 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 482 of 916.640 cents and inv. generated superset size: 69 = 59 more = 690.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBCBDBCBB Step pattern size order : DCCBCACBCC Scale is not a Constant Structure Scale diversity : 1.361335 Lumma stability : 0.114105 Lumma impropriety factor : 0.692552 Rothenberg efficiency : 0.447857 redundancy: 0.552143 Efficiency x scale size : 4.478571 Number of different interval sizes : 28 = 3.11111 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 15.21394 cents Most common intervals : 500.15848 cents & inv., amount: 7 Number of recognisable fifths : 7, average 699.8415 cents Formal octave complements present : 3 = 30.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 5-6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
10: 2 1 1 1 1 0 1 1 1 1 N D3 SD: 26.1267 c. M: 48.3043 c. 12: 3 1 1 1 1 1 1 1 1 1 N M DE SD: 20.1469 c. M:-32.0127 c. 17: 4 1 2 1 2 1 2 1 1 2 N SD: 19.5867 c. M:-33.3364 c. 19: 4 2 2 1 2 1 2 1 2 2 N SD: 10.9420 c. M: 20.6189 c. 22: 5 2 2 2 2 1 2 2 2 2 N D3 SD: 9.2408 c. M:-16.1648 c. 31: 7 3 3 2 3 2 3 2 3 3 N SD: 3.4136 c. M:-6.0120 c. 41: 9 4 4 3 4 2 4 3 4 4 N SD: 3.8763 c. M: 7.3287 c. 53: 12 5 5 4 5 3 5 4 5 5 N SD: 2.9686 c. M:-5.5976 c. 72: 16 7 7 5 7 4 7 5 7 7 N SD: 0.9475 c. M: 1.6376 c. 103: 23 10 10 7 10 6 10 7 10 10 N SD: 0.7795 c. M: 1.3109 c. 156: 35 15 15 11 15 9 15 11 15 15 N SD: 0.7025 c. M:-1.2434 c. 175: 39 17 17 12 17 10 17 12 17 17 N SD: 0.5994 c. M: 1.1302 c. 197: 44 19 19 14 19 11 19 14 19 19 N SD: 0.6369 c. M: 1.0619 c. 228: 51 22 22 16 22 13 22 16 22 22 N SD: 0.2300 c. M:-0.4337 c. 300: 67 29 29 21 29 17 29 21 29 29 N SD: 0.1764 c. M: 0.3106 c. 331: 74 32 32 23 32 19 32 23 32 32 N SD: 0.1599 c. M:-0.2815 c. 403: 90 39 39 28 39 23 39 28 39 39 N SD: 0.1301 c. M: 0.2454 c. 559: 125 54 54 39 54 32 54 39 54 54 N SD: 0.1220 c. M:-0.2109 c. 631: 141 61 61 44 61 36 61 44 61 61 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x x 4 S SD: 1.0567 cents 3 x x 4 x x x 5 x x 6 S SD: 0.7047 cents 4 x 5 x x 6 x x 7 x 8 S SD: 0.7843 cents 5:6 x x 7 x 8 x 9 x 10 S SD: 16.4659 cents 6:7 x 8 x 9 x 10 x 11:12 S SD: 5.7971 cents 7:8:9 x 10 x 11 x 12:13:14 S SD: 11.6592 cents 8:9:10 x 11:12 x 13:14:15:16 S SD: 10.5539 cents 9 x 11:12:13 x 14:15:16:17:18 SD: 9.0421 cents 10:12 x 13:14:15:16:17 x 19:20 SD: 11.4231 cents 11:13:14:15 x 16:17:18:19:21:22 SD: 10.2327 cents 12:14:15:16:17:18:19:20:21:22:24 S SD: 4.8221 cents 20:23:25:27:28:30:31:33:35:37:40 SD: 4.2730 cents 23:27:29:31:32:34:36:38:40:43:46 SD: 4.1503 cents 24:28:30:32:34:36:37:40:42:45:48 SD: 2.7555 cents 32:37:40:43:45:48:50:53:56:60:64 SD: 2.4814 cents 36:42:45:48:50:54:56:60:63:67:72 SD: 1.8162 cents 48:56:60:64:67:72:75:80:84:90:96 SD: 0.9743 cents 72:84:90:96:101:108:112:120:126:135:144 SD: 0.7081 cents 84:98:105:112:118:126:131:140:147:157:168 SD: 0.6265 cents 120:140:150:160:168:180:187:200:210:224:240 SD: 0.5439 cents 132:154:165:176:185:198:206:220:231:247:264 SD: 0.4667 cents 177:207:221:236:248:265:276:295:310:331:354 SD: 0.4476 cents 185:216:231:247:259:277:288:308:324:346:370 SD: 0.3897 cents 197:230:246:263:276:295:307:328:345:368:394 SD: 0.3602 cents 209:244:261:279:293:313:326:348:366:391:418 SD: 0.3226 cents 245:286:306:327:343:367:382:408:429:458:490 SD: 0.3015 cents 269:314:336:359:377:403:419:448:471:503:538 SD: 0.2726 cents 287:335:358:383:402:430:447:478:502:537:574 SD: 0.2488 cents 299:349:373:399:419:448:466:498:523:559:598 SD: 0.2079 cents 347:405:433:463:486:520:541:578:607:649:694 SD: 0.1881 cents 387:452:483:517:542:580:603:645:677:724:774 SD: 0.1881 cents 394:460:492:526:552:590:614:657:689:737:788 SD: 0.1403 cents 471:550:588:629:660:706:734:785:824:881:942 SD: 0.1234 cents 591:690:738:789:828:885:921:985:1034:1105:1182 SD: 0.1210 cents