Scala analysis: michael7
Michael's 7-note, more or less 7-limit scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 119.558 cents 119.558000 2: 221.670 cents 221.669500 3: 498.000 cents 498.000000 4: 616.795 cents 616.795000 5: 710.000 cents 710.000000 6: 933.123 cents 933.123000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 266.8770 cents 266.8770 1: 119.5580 cents 119.5580 2: 102.1115 cents 102.1115 3: 276.3305 cents 276.3305 4: 118.7950 cents 118.7950 5: 93.2050 cents 93.2050 6: 223.1230 cents 223.1230 7: 266.8770 cents 266.8770
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 93.20500 cents 1: 1 102.11150 cents 1: 1 118.79500 cents 1: 1 119.55800 cents 1: 1 223.12300 cents 1: 1 266.87700 cents 1: 1 276.33050 cents 2: 1 212.00000 cents 2: 1 221.66950 cents 2: 1 316.32800 cents 2: 1 378.44200 cents 2: 1 386.43500 cents 2: 1 395.12550 cents 2: 1 490.00000 cents 3: 1 435.12300 cents 3: 1 488.33050 cents 3: 1 488.54650 cents 3: 1 497.23700 cents 3: 1 498.00000 cents 3: 1 583.20500 cents 3: 1 609.55800 cents 4: 1 590.44200 cents 4: 1 616.79500 cents 4: 1 702.00000 cents 4: 1 702.76300 cents 4: 1 711.45350 cents 4: 1 711.66950 cents 4: 1 764.87700 cents 5: 1 710.00000 cents 5: 1 804.87450 cents 5: 1 813.56500 cents 5: 1 821.55800 cents 5: 1 883.67200 cents 5: 1 978.33050 cents 5: 1 988.00000 cents 6: 1 923.66950 cents 6: 1 933.12300 cents 6: 1 976.87700 cents 6: 1 1080.44200 cents 6: 1 1081.20500 cents 6: 1 1097.88850 cents 6: 1 1106.79500 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 : 119.6 221.7 498.0 616.8 710.0 933.1 1200.0 119.6 : 102.1 378.4 497.2 590.4 813.6 1080.4 1200.0 221.7 : 276.3 395.1 488.3 711.5 978.3 1097.9 1200.0 498.0 : 118.8 212.0 435.1 702.0 821.6 923.7 1200.0 616.8 : 93.2 316.3 583.2 702.8 804.9 1081.2 1200.0 710.0 : 223.1 490.0 609.6 711.7 988.0 1106.8 1200.0 933.1 : 266.9 386.4 488.5 764.9 883.7 976.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.2050 .. 276.3305 cents 183.12550 cents 93.20500 cents 2: 212.0000 .. 490.0000 cents 278.00000 cents -64.33050 cents 3: 435.1230 .. 609.5580 cents 174.43500 cents -54.87700 cents 4: 590.4420 .. 764.8770 cents 174.43500 cents -19.11600 cents 5: 710.0000 .. 988.0000 cents 278.00000 cents -54.87700 cents 6: 923.6695 .. 1106.7950 cents 183.12550 cents -64.33050 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 93.20500 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 276.33050 cents Average / Smallest step : 1.839264 Largest / Average step : 1.611928 Largest / Smallest step : 2.964760 Median interval of one step : 119.55800 cents, amount: 1 Least squares average step : 157.66296 cents, oct.: 1103.64075 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : DBGCAEF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 1.45350 cents Scale diversity : 1.521704 Lumma stability : 0.155342 Lumma impropriety factor : 0.214609 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 : 0.21600 cents Number of recognisable fifths : 5, average 707.5772 cents Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 0 1 2 0 1 1 2 N T3 SD: 69.6465 c. M: 119.5580 c. 8: 1 0 2 1 1 1 2 N D3 SD: 40.2606 c. M: 71.6695 c. 9: 1 1 2 1 0 2 2 N SD: 33.4407 c. M:-49.8717 c. 10: 1 1 2 1 1 2 2 P D3 S SD: 15.8774 c. M:-26.8770 c. 12: 1 1 3 1 1 2 3 N SD: 18.2651 c. M: 33.1230 c. Chromatic Hypophrygian inverse 17: 2 1 4 2 1 3 4 N SD: 12.9792 c. M:-21.6185 c. 22: 2 2 5 2 2 4 5 N SD: 8.3592 c. M: 16.7950 c. 27: 3 2 6 3 2 5 6 N SD: 6.5880 c. M:-13.7753 c. 31: 3 3 7 3 2 6 7 N SD: 7.0649 c. M: 13.2258 c. 37: 4 3 8 4 3 7 8 N SD: 6.8913 c. M: 11.5135 c. 39: 4 3 9 4 3 7 9 N SD: 5.2444 c. M: 10.0461 c. 48: 5 4 11 5 3 9 11 N SD: 6.3021 c. M: 10.0000 c. 49: 5 4 11 5 4 9 11 N SD: 3.8601 c. M: 8.2041 c. 53: 5 5 12 5 4 10 12 N SD: 5.0976 c. M: 8.1132 c. 58: 6 5 13 6 4 11 13 N SD: 4.1496 c. M: 6.5517 c. 68: 7 6 15 7 5 13 15 N SD: 4.0211 c. M:-7.7423 c. 70: 7 6 16 7 5 13 16 N SD: 3.9347 c. M: 7.4087 c. 72: 7 6 17 7 6 13 16 N SD: 3.4204 c. M:-6.6667 c. 78: 8 6 18 8 6 15 17 N SD: 4.1421 c. M: 6.2849 c. 80: 8 7 18 8 6 15 18 N SD: 2.8850 c. M: 5.0000 c. 81: 8 7 19 8 6 15 18 N SD: 3.0391 c. M:-5.7037 c. 91: 9 8 21 9 7 17 20 N SD: 2.3841 c. M:-3.1407 c. 103: 10 9 24 10 8 19 23 N SD: 1.7048 c. M: 3.0531 c. 113: 11 10 26 11 9 21 25 N SD: 1.4886 c. M: 2.7438 c. 130: 13 11 30 13 10 24 29 N SD: 0.7982 c. M:-1.6665 c. 140: 14 12 32 14 11 26 31 N SD: 0.9145 c. M:-1.4286 c. 152: 15 13 35 15 12 28 34 N SD: 0.9059 c. M: 1.5441 c. 243: 24 21 56 24 19 45 54 N SD: 0.7061 c. M:-1.1111 c. 270: 27 23 62 27 21 50 60 N SD: 0.6319 c. M:-1.1111 c. 282: 28 24 65 28 22 52 63 N SD: 0.5677 c. M: 1.2081 c. 292: 29 25 67 29 23 54 65 N SD: 0.5155 c. M:-0.9589 c. 374: 37 32 86 37 29 70 83 N SD: 0.6496 c. M: 0.9091 c. 383: 38 33 88 38 30 71 85 N SD: 0.6439 c. M:-1.2272 c. 391: 39 33 90 39 30 73 87 N SD: 0.5720 c. M: 1.0486 c. 395: 39 34 91 39 31 73 88 N SD: 0.5645 c. M: 1.0770 c. 412: 41 35 95 41 32 76 92 N SD: 0.5632 c. M: 1.0842 c. 422: 42 36 97 42 33 78 94 N SD: 0.4191 c. M:-0.9005 c. 444: 44 38 102 44 35 82 99 N SD: 0.5823 c. M:-0.8108 c. 450: 45 38 104 44 35 84 100 N SD: 0.5173 c. M: 0.7950 c. 453: 45 39 104 45 35 84 101 N SD: 0.4596 c. M:-0.8471 c. 482: 48 41 111 48 37 90 107 N SD: 0.3511 c. M:-0.6324 c. 504: 50 43 116 50 39 94 112 N SD: 0.3276 c. M: 0.5104 c. 634: 63 54 146 63 49 118 141 N SD: 0.2058 c. M: 0.3151 c. 774: 77 66 178 77 60 144 172 N SD: 0.1914 c. M: 0.3256 c. 850: 85 72 196 84 66 158 189 N SD: 0.2263 c. M:-0.4420 c. 872: 87 74 201 86 68 162 194 N SD: 0.1530 c. M: 0.2812 c. 1002: 100 85 231 99 78 186 223 N SD: 0.1530 c. M:-0.2036 c. 1142: 114 97 263 113 89 212 254 N SD: 0.1572 c. M:-0.3327 c. 1224: 122 104 282 121 95 228 272 N SD: 0.1273 c. M:-0.2103 c. 1354: 135 115 312 134 105 252 301 N SD: 0.0845 c. M:-0.1119 c. 1494: 149 127 344 148 116 278 332 N SD: 0.0971 c. M:-0.2103 c. 1506: 150 128 347 149 117 280 335 N SD: 0.0697 c. M: 0.1556 c. 1646: 164 140 379 163 128 306 366 N SD: 0.0483 c. M:-0.0851 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 4.0225 cents 3 x x 4 x x 5:6 S SD: 16.2548 cents 4 x x 5 x 6:7:8 S SD: 29.3824 cents 5 x 6 x 7:8:9:10 S SD: 33.4021 cents 6 x 7:8 x 9:10:12 S SD: 13.3953 cents 7 x 8:9:10:11:12:14 S SD: 16.0765 cents 8 x 9:11 x 12:14:16 SD: 13.4129 cents 9 x 10:12:13:14:15:18 S SD: 14.2677 cents 10:11 x 13:14:15:17:20 SD: 12.2840 cents 12:13:14:16:17:18:21:24 S SD: 8.9607 cents 14:15:16:19:20:21:24:28 SD: 4.7321 cents 24:26:27:32:34:36:41:48 SD: 4.4450 cents 28:30:32:37:40:42:48:56 SD: 2.8401 cents 39:42:44:52:56:59:67:78 SD: 2.8238 cents 42:45:48:56:60:63:72:84 S SD: 1.7817 cents 57:61:65:76:81:86:98:114 SD: 1.6795 cents 59:63:67:79:84:89:101:118 SD: 1.6181 cents 67:72:76:89:96:101:115:134 SD: 1.5516 cents 73:78:83:97:104:110:125:146 SD: 1.2707 cents 81:87:92:108:116:122:139:162 SD: 0.9838 cents 87:93:99:116:124:131:149:174 SD: 0.8632 cents 124:133:141:165:177:187:213:248 SD: 0.7791 cents 126:135:143:168:180:190:216:252 SD: 0.4100 cents 168:180:191:224:240:253:288:336 SD: 0.2082 cents 294:315:334:392:420:443:504:588 SD: 0.1585 cents 462:495:525:616:660:696:792:924 SD: 0.1389 cents 519:556:590:692:741:782:890:1038 SD: 0.1194 cents 570:611:648:760:814:859:977:1140 SD: 0.1187 cents