Scala analysis: keen1
Keenanismic tempering of [5/4, 11/8, 3/2, 12/7, 2], 284et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 384.507 cents 384.507040 2: 549.296 cents 549.295770 3: 701.408 cents 701.408450 4: 933.803 cents 933.802820 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 266.1972 cents 266.1972 1: 384.5070 cents 384.5070 2: 164.7887 cents 164.7887 3: 152.1127 cents 152.1127 4: 232.3944 cents 232.3944 5: 266.1972 cents 266.1972
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 152.11268 cents 1: 1 164.78873 cents 1: 1 232.39437 cents 1: 1 266.19718 cents 1: 1 384.50704 cents 2: 1 316.90141 cents 2: 1 384.50705 cents 2: 1 498.59155 cents 2: 1 549.29577 cents 2: 1 650.70422 cents 3: 1 549.29578 cents 3: 1 650.70423 cents 3: 1 701.40845 cents 3: 1 815.49295 cents 3: 1 883.09859 cents 4: 1 815.49296 cents 4: 1 933.80282 cents 4: 1 967.60563 cents 4: 1 1035.21127 cents 4: 1 1047.88732 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 384.5 549.3 701.4 933.8 1200.0 384.5 : 164.8 316.9 549.3 815.5 1200.0 549.3 : 152.1 384.5 650.7 1035.2 1200.0 701.4 : 232.4 498.6 883.1 1047.9 1200.0 933.8 : 266.2 650.7 815.5 967.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 152.1127 .. 384.5070 cents 232.39436 cents 152.11268 cents 2: 316.9014 .. 650.7042 cents 333.80281 cents -67.60563 cents 3: 549.2958 .. 883.0986 cents 333.80281 cents -101.40844 cents 4: 815.4930 .. 1047.8873 cents 232.39436 cents -67.60563 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 152.11268 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 384.50704 cents Average / Smallest step : 1.577778 Largest / Average step : 1.602113 Largest / Smallest step : 2.527778 Median interval of one step : 232.39437 cents, amount: 1 Least squares average step : 242.22791 cents, oct.: 1211.13956 cents Scale is not proper Scale is a mode of a 284-tone equal temperament with octave 2/1 degrees: 91 130 166 221 284 Least number of segments generator : 143 of 604.225 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 193 of 815.493 cents and inv. generated superset size: 59 = 54 more = 1180.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : EBACD Scale is not a Constant Structure Scale diversity : 1.577122 Lumma stability : 0.253521 Lumma impropriety factor : 0.197183 Rothenberg efficiency : 0.480000 redundancy: 0.520000 Efficiency x scale size : 2.400000 Number of different interval sizes : 16 = 4.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 12.67605 cents Number of recognisable fifths : 1, average 701.4084 cents Formal octave complements present : 1 = 20.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
5: 2 0 1 1 1 N T3 SD: 54.6859 c. M:-95.4930 c. 6: 2 1 1 1 1 P M ME S SD: 58.1607 c. M:-98.5916 c. 7: 2 1 1 1 2 N D3 I SD: 42.6227 c. M: 76.6600 c. 9: 3 1 1 2 2 N SD: 18.4502 c. M: 34.7418 c. 15: 5 2 2 3 3 N SD: 16.6526 c. M:-26.1972 c. 19: 6 3 2 4 4 N SD: 11.1823 c. M:-19.1253 c. 22: 7 3 3 4 5 N SD: 4.9729 c. M:-7.6825 c. 31: 10 4 4 6 7 N SD: 4.5851 c. M: 7.3603 c. 41: 13 6 5 8 9 N SD: 3.7742 c. M:-6.8018 c. 46: 15 6 6 9 10 N SD: 4.1325 c. M:-6.7973 c. 50: 16 7 6 10 11 N SD: 2.8861 c. M: 5.4084 c. 63: 20 9 8 12 14 N SD: 2.5931 c. M: 3.5547 c. 68: 22 9 9 13 15 N SD: 2.8686 c. M:-4.4739 c. 72: 23 10 9 14 16 N SD: 0.9031 c. M: 1.4084 c. 166: 53 23 21 32 37 N SD: 0.8439 c. M: 1.3745 c. 181: 58 25 23 35 40 N SD: 0.8721 c. M:-1.3540 c. 190: 61 26 24 37 42 N SD: 0.5661 c. M:-0.9340 c. 212: 68 29 27 41 47 N SD: 0.3067 c. M:-0.4783 c. 284: 91 39 36 55 63 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.2733 cents 3 x 4 x 5:6 S SD: 23.7378 cents 4:5 x 6:7:8 S SD: 8.7685 cents 6 x 8:9:10:12 S SD: 17.8039 cents 8:10:11:12:14:16 S SD: 7.0264 cents 16:20:22:24:27:32 SD: 5.6149 cents 24:30:33:36:41:48 SD: 1.4489 cents 32:40:44:48:55:64 SD: 0.9447 cents 56:70:77:84:96:112 S SD: 0.5694 cents 144:180:198:216:247:288 SD: 0.5571 cents 158:197:217:237:271:316 SD: 0.5300 cents 172:215:236:258:295:344 SD: 0.5014 cents 182:227:250:273:312:364 SD: 0.4403 cents 190:237:261:285:326:380 SD: 0.4260 cents 214:267:294:321:367:428 SD: 0.3258 cents 238:297:327:357:408:476 SD: 0.3139 cents 246:307:338:369:422:492 SD: 0.2912 cents 270:337:371:405:463:540 SD: 0.2552 cents 302:377:415:453:518:604 SD: 0.2510 cents 326:407:448:489:559:652 SD: 0.2506 cents 330:412:453:495:566:660 SD: 0.2129 cents 354:442:486:531:607:708 SD: 0.1802 cents 386:482:530:579:662:772 SD: 0.1394 cents 442:552:607:663:758:884 SD: 0.1216 cents