Scala analysis: pep_dudon_ibina_E
Peppermint tempering of Dudon's Ibina: 72:78:88:96:108:117:128:144
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 138.202 cents 138.201660 2: 346.393 cents 346.392870 3: 495.904 cents 495.904390 4: 704.096 cents 704.095610 5: 842.297 cents 842.297270 6: 991.809 cents 991.808790 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 208.1912 cents 208.1912 1: 138.2017 cents 138.2017 2: 208.1912 cents 208.1912 3: 149.5115 cents 149.5115 4: 208.1912 cents 208.1912 5: 138.2017 cents 138.2017 6: 149.5115 cents 149.5115 7: 208.1912 cents 208.1912
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 138.20166 cents 1: 2 149.51152 cents 1: 3 208.19121 cents 2: 1 287.71318 cents 2: 3 346.39287 cents 2: 3 357.70273 cents 3: 5 495.90439 cents 3: 1 554.58408 cents 3: 1 565.89395 cents 4: 1 634.10605 cents 4: 1 645.41592 cents 4: 5 704.09561 cents 5: 3 842.29727 cents 5: 3 853.60713 cents 5: 1 912.28682 cents 6: 3 991.80879 cents 6: 2 1050.48848 cents 6: 2 1061.79834 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 138.2 346.4 495.9 704.1 842.3 991.8 1200.0 138.2 : 208.2 357.7 565.9 704.1 853.6 1061.8 1200.0 346.4 : 149.5 357.7 495.9 645.4 853.6 991.8 1200.0 495.9 : 208.2 346.4 495.9 704.1 842.3 1050.5 1200.0 704.1 : 138.2 287.7 495.9 634.1 842.3 991.8 1200.0 842.3 : 149.5 357.7 495.9 704.1 853.6 1061.8 1200.0 991.8 : 208.2 346.4 554.6 704.1 912.3 1050.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.2017 .. 208.1912 cents 69.98955 cents 138.20166 cents 2: 287.7132 .. 357.7027 cents 69.98955 cents 79.52197 cents 3: 495.9044 .. 565.8939 cents 69.98956 cents 138.20166 cents 4: 634.1061 .. 704.0956 cents 69.98956 cents 68.21210 cents 5: 842.2973 .. 912.2868 cents 69.98955 cents 138.20166 cents 6: 991.8088 .. 1061.7983 cents 69.98955 cents 79.52197 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 138.20166 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 208.19121 cents Average / Smallest step : 1.240423 Largest / Average step : 1.214449 Largest / Smallest step : 1.506431 Median interval of one step : 149.51152 cents, amount: 2 Most common interval of one step : 208.19121 cents, amount: 3 Least squares average step : 169.26730 cents, oct.: 1184.87110 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : SLMLSML Scale is a Constant Structure, by a margin of 68.21210 cents Scale diversity : 1.298296 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.650052 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 11.30986 cents Most common intervals : 495.90439 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 346.393 704.096 cents Most common triad is 0.0 495.904 704.096 cents, amount: 3 Number of recognisable fifths : 5, average 704.0956 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 69.9896 cents: 3 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.9225 c. M:-36.7626 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 17.0689 c. M: 31.8088 c. 17: 2 3 2 3 2 2 3 SP M ME S SD: 3.6559 c. M:-6.5483 c. 58: 7 10 7 10 7 7 10 SP M DE S SD: 3.9746 c. M:-6.6259 c. 63: 7 11 8 11 7 8 11 SP T3 SD: 2.8416 c. M: 4.8683 c. 70: 8 12 9 12 8 9 12 SP T3 SD: 2.0037 c. M: 3.5357 c. 80: 9 14 10 14 9 10 14 SP T3 SD: 1.7879 c. M: 3.2017 c. 87: 10 15 11 15 10 11 15 SP T3 SD: 0.9165 c. M: 1.5653 c. 104: 12 18 13 18 12 13 18 SP T3 SD: 0.2668 c. M:-0.4989 c. 225: 26 39 28 39 26 28 39 SP T3 SD: 0.2625 c. M:-0.4650 c. 329: 38 57 41 57 38 41 57 SP T3 SD: 0.2277 c. M:-0.4002 c. 409: 47 71 51 71 47 51 71 SP T3 SD: 0.1722 c. M: 0.3043 c. 426: 49 74 53 74 49 53 74 SP T3 SD: 0.1416 c. M: 0.2595 c. 513: 59 89 64 89 59 64 89 SP T3 SD: 0.1257 c. M: 0.1940 c. 530: 61 92 66 92 61 66 92 SP T3 SD: 0.0630 c. M: 0.1107 c. 634: 73 110 79 110 73 79 110 SP T3 SD: 0.0179 c. M: 0.0313 c. 2006: 231 348 250 348 231 250 348 SP T3 SD: 0.0179 c. M: 0.0320 c. 2023: 233 351 252 351 233 252 351 SP T3 SD: 0.0131 c. M:-0.0233 c. 2127: 245 369 265 369 245 265 369 SP T3 SD: 0.0118 c. M:-0.0212 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 1.0703 cents 3 x x 4 x 5 x 6 S SD: 14.0386 cents 4 x 5 x 6 x 7:8 S SD: 11.5284 cents 5 x 6:7 x 8:9:10 S SD: 19.9300 cents 6 x 7:8:9:10:11:12 S SD: 17.8065 cents 7:8 x 9 x 11:12:14 SD: 27.8302 cents 8:9:10:11:12:13:14:16 S SD: 13.9371 cents 9:10:11:12:14:15:16:18 S SD: 12.3272 cents 10:11:12:13:15:16:18:20 SD: 9.9901 cents 12:13:15:16:18:20:21:24 SD: 8.9218 cents 13:14:16:17:20:21:23:26 SD: 8.0300 cents 14:15:17:19:21:23:25:28 SD: 6.3479 cents 21:23:26:28:32:34:37:42 SD: 5.9690 cents 22:24:27:29:33:36:39:44 SD: 3.6238 cents 27:29:33:36:41:44:48:54 SD: 3.5246 cents 35:38:43:47:53:57:62:70 SD: 3.3125 cents 36:39:44:48:54:59:64:72 SD: 2.0038 cents 48:52:59:64:72:78:85:96 SD: 1.6648 cents 58:63:71:77:87:94:103:116 SD: 1.5513 cents 72:78:88:96:108:117:128:144 SD: 0.8055 cents 118:128:144:157:177:192:209:236 SD: 0.6612 cents 132:143:161:176:198:215:234:264 SD: 0.6610 cents 144:156:176:192:216:234:255:288 SD: 0.6339 cents 145:157:177:193:218:236:257:290 SD: 0.3936 cents 193:209:236:257:290:314:342:386 SD: 0.3514 cents 217:235:265:289:326:353:385:434 SD: 0.1540 cents 410:444:501:546:616:667:727:820 SD: 0.1432 cents 482:522:589:642:724:784:855:964 SD: 0.1366 cents 506:548:618:674:760:823:897:1012 SD: 0.1222 cents 552:598:674:735:829:898:979:1104 SD: 0.1214 cents 578:626:706:770:868:940:1025:1156 SD: 0.1105 cents 600:650:733:799:901:976:1064:1200 SD: 0.0701 cents