Scala analysis: Zimbabwe_Mbira_02
Mbira 2 (Mbira), Zimbabwe
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 196.000 cents 196.000000 2: 377.000 cents 377.000000 3: 506.000 cents 506.000000 4: 676.000 cents 676.000000 5: 877.000 cents 877.000000 6: 1050.000 cents 1050.000000 7: 1148.000 cents 1148.000000
SHOW/INTERVAL
0: 98.0000 cents 98.0000 1: 196.0000 cents 196.0000 2: 181.0000 cents 181.0000 3: 129.0000 cents 129.0000 4: 170.0000 cents 170.0000 5: 201.0000 cents 201.0000 6: 173.0000 cents 173.0000 7: 98.0000 cents 98.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 98.00000 cents 1: 1 129.00000 cents 1: 1 170.00000 cents 1: 1 173.00000 cents 1: 1 181.00000 cents 1: 1 196.00000 cents 1: 1 201.00000 cents 2: 1 271.00000 cents 2: 1 294.00000 cents 2: 1 299.00000 cents 2: 1 310.00000 cents 2: 1 371.00000 cents 2: 1 374.00000 cents 2: 1 377.00000 cents 3: 1 467.00000 cents 3: 1 472.00000 cents 3: 1 475.00000 cents 3: 1 480.00000 cents 3: 1 500.00000 cents 3: 1 506.00000 cents 3: 1 544.00000 cents 4: 1 604.00000 cents 4: 1 642.00000 cents 4: 1 648.00000 cents 4: 1 668.00000 cents 4: 1 673.00000 cents 4: 1 676.00000 cents 4: 1 681.00000 cents 5: 1 771.00000 cents 5: 1 774.00000 cents 5: 1 777.00000 cents 5: 1 838.00000 cents 5: 1 849.00000 cents 5: 1 854.00000 cents 5: 1 877.00000 cents 6: 1 947.00000 cents 6: 1 952.00000 cents 6: 1 967.00000 cents 6: 1 975.00000 cents 6: 1 978.00000 cents 6: 1 1019.00000 cents 6: 1 1050.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 196.0 377.0 506.0 676.0 877.0 1050.0 1148.0 196.0 : 181.0 310.0 480.0 681.0 854.0 952.0 1148.0 377.0 : 129.0 299.0 500.0 673.0 771.0 967.0 1148.0 506.0 : 170.0 371.0 544.0 642.0 838.0 1019.0 1148.0 676.0 : 201.0 374.0 472.0 668.0 849.0 978.0 1148.0 877.0 : 173.0 271.0 467.0 648.0 777.0 947.0 1148.0 1050.0: 98.0 294.0 475.0 604.0 774.0 975.0 1148.0 1148.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.0000 .. 201.0000 cents 103.00000 cents 98.00000 cents 2: 271.0000 .. 377.0000 cents 106.00000 cents 70.00000 cents 3: 467.0000 .. 544.0000 cents 77.00000 cents 90.00000 cents 4: 604.0000 .. 681.0000 cents 77.00000 cents 60.00000 cents 5: 771.0000 .. 877.0000 cents 106.00000 cents 90.00000 cents 6: 947.0000 .. 1050.0000 cents 103.00000 cents 70.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 98.00000 cents, class 1 Average step (divided formal octave): 164.0000 cents Largest one step interval : 201.00000 cents Average / Smallest step : 1.673469 Largest / Average step : 1.225610 Largest / Smallest step : 2.051020 Median interval of one step : 173.00000 cents, amount: 1 Least squares average step : 170.66429 cents, oct.: 1194.65000 cents Scale is strictly proper Scale is a mode of a 1148-tone equal temperament with octave 1148.000 cents degrees: 196 377 506 676 877 1050 1148 Least number of segments generator : 575 of 575.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 663 of 663.000 cents and inv. generated superset size: 218 = 211 more = 3114.286% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : FEBCGDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 60.00000 cents Scale diversity : 1.586225 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.501742 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 3.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 503.0000 cents Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 40.7536 c. M: 66.0000 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 29.5949 c. M:-59.1111 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 30.5708 c. M: 46.8000 c. Pseudo Rast 11: 2 2 1 1 2 2 1 P D3 S SD: 30.1016 c. M: 49.8182 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 12.6541 c. M: 27.6667 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 20: 3 4 2 3 3 3 2 SP D3 SD: 16.8858 c. M:-24.8000 c. 21: 3 4 2 3 4 3 2 SP T3 SD: 15.9732 c. M: 32.0000 c. 22: 4 3 3 3 4 3 2 SP D3 SD: 9.9831 c. M:-15.8182 c. Chameleon Porcupine 25: 4 4 3 4 4 4 2 SP T3 SD: 8.1740 c. M:-12.8000 c. 34: 6 5 4 5 6 5 3 SP SD: 3.5251 c. M:-6.5882 c. 46: 8 7 5 7 8 7 4 SP SD: 3.5462 c. M: 6.8696 c. 59: 10 9 7 9 10 9 5 SP SD: 3.4446 c. M: 7.3051 c. 70: 12 11 8 10 12 11 6 SP SD: 3.3891 c. M: 7.8000 c. 71: 12 11 8 11 12 11 6 SP SD: 3.3438 c. M: 5.1127 c. 81: 14 13 9 12 14 12 7 SP SD: 3.3522 c. M:-5.6667 c. 82: 14 13 9 12 15 12 7 SP SD: 2.5635 c. M:-5.0000 c. 86: 15 13 10 13 15 13 7 SP SD: 3.5828 c. M:-4.7907 c. 88: 15 14 10 13 15 13 8 SP SD: 3.0317 c. M: 6.3636 c. 89: 15 14 10 13 16 13 8 SP SD: 3.3427 c. M: 5.2584 c. 93: 16 15 10 14 16 14 8 SP SD: 2.5024 c. M:-5.6667 c. 98: 17 15 11 15 17 15 8 SP SD: 2.7330 c. M:-4.2857 c. 104: 18 16 12 15 18 16 9 SP SD: 2.5833 c. M: 4.9615 c. 106: 18 17 12 15 19 16 9 SP SD: 2.2458 c. M: 4.5283 c. 107: 18 17 12 16 19 16 9 SP SD: 1.8243 c. M: 2.8785 c. 127: 22 20 14 19 22 19 11 SP SD: 1.7402 c. M:-2.8661 c. 131: 22 21 15 19 23 20 11 SP SD: 1.6898 c. M: 3.2061 c. 140: 24 22 16 20 25 21 12 SP SD: 1.6784 c. M: 3.6000 c. 141: 24 22 16 21 25 21 12 SP SD: 1.3863 c. M: 2.4752 c. 153: 26 24 17 23 27 23 13 SP SD: 1.5335 c. M: 3.2810 c. 165: 28 26 19 24 29 25 14 SP SD: 1.0964 c. M:-1.9030 c. 177: 30 28 20 26 31 27 15 SP SD: 1.0248 c. M: 1.4689 c. 211: 36 33 24 31 37 32 18 SP SD: 0.8809 c. M: 1.5877 c. 234: 40 37 26 35 41 35 20 SP SD: 0.7112 c. M:-1.1709 c. 258: 44 41 29 38 45 39 22 SP SD: 0.6985 c. M:-1.2558 c. 268: 46 42 30 40 47 40 23 SP SD: 0.7163 c. M:-1.1343 c. 270: 46 43 30 40 47 41 23 SP SD: 0.7041 c. M:-1.4148 c. 292: 50 46 33 43 51 44 25 SP SD: 0.5442 c. M:-1.1644 c. 304: 52 48 34 45 53 46 26 SP SD: 0.4426 c. M: 0.8947 c. 374: 64 59 42 55 66 56 32 SP SD: 0.5417 c. M:-0.8824 c. 386: 66 61 43 57 68 58 33 SP SD: 0.4893 c. M: 0.8808 c. 399: 68 63 45 59 70 60 34 SP SD: 0.2991 c. M:-0.5439 c. 411: 70 65 46 61 72 62 35 SP SD: 0.2630 c. M: 0.4769 c. 445: 76 70 50 66 78 67 38 SP SD: 0.2025 c. M: 0.3640 c. 703: 120 111 79 104 123 106 60 SP SD: 0.1282 c. M:-0.2304 c. 1114: 190 176 125 165 195 168 95 SP SD: 0.1076 c. M: 0.2011 c. 1148: 196 181 129 170 201 173 98 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 52.0000 cents 2 x x x 3 x x 4 S SD: 29.0588 cents 3 x x 4 x 5 x 6 S SD: 17.7057 cents 4 x 5 x 6 x 7:8 S SD: 25.0670 cents 5 x 6:7 x 8:9:10 S SD: 26.3679 cents 6:7 x 8:9:10:11:12 S SD: 15.3823 cents 7:8:9 x 10:12:13:14 S SD: 19.9723 cents 8:9:10:11:12:13:15:16 SD: 13.0739 cents 9:10:11:12:13:15 x 17 SD: 11.7067 cents 12:13:15:16:18:20:22:23 SD: 9.7376 cents 15:17:19:20:22:25:28:29 SD: 7.4660 cents 17:19:21:23:25:28:31:33 SD: 3.9819 cents 32:36:40:43:47:53:59:62 SD: 2.8392 cents 33:37:41:44:49:55:61:64 SD: 2.7859 cents 41:46:51:55:61:68:75:80 SD: 2.3224 cents 50:56:62:67:74:83:92:97 SD: 1.1209 cents 65:73:81:87:96:108:119:126 SD: 1.1130 cents 82:92:102:110:121:136:150:159 SD: 0.9834 cents 100:112:124:134:148:166:183:194 SD: 0.9479 cents 103:115:128:138:152:171:189:200 SD: 0.8463 cents 115:129:143:154:170:191:211:223 SD: 0.5272 cents 132:148:164:177:195:219:242:256 SD: 0.4891 cents 168:188:209:225:248:279:308:326 SD: 0.3961 cents 209:234:260:280:309:347:383:406 SD: 0.3793 cents 218:244:271:292:322:362:400:423 SD: 0.2578 cents 300:336:373:402:443:498:550:582 SD: 0.2487 cents 333:373:414:446:492:553:611:646 SD: 0.2345 cents 350:392:435:469:517:581:642:679 SD: 0.2044 cents 391:438:486:524:578:649:717:759 SD: 0.1984 cents 427:478:531:572:631:709:783:829 SD: 0.1885 cents 477:534:593:639:705:792:875:926 SD: 0.1746 cents 542:607:674:726:801:900:994:1052 SD: 0.1505 cents 559:626:695:749:826:928:1025:1085 SD: 0.1213 cents