Scala analysis: sheiman_michael-phi_section
Michael Sheiman's Phi Section scale, from Tuning List
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 149.464 cents 149.464000 2: 235.774 cents 235.774000 3: 273.024 cents 273.024000 4: 366.910 cents 366.910000 5: 466.181 cents 466.181000 6: 560.566 cents 560.566000 7: 597.316 cents 597.316000 8: 683.627 cents 683.627000 9: 833.090 cents 833.090000
SHOW/INTERVAL
0: 149.4630 cents 149.4630 1: 149.4640 cents 149.4640 2: 86.3100 cents 86.3100 3: 37.2500 cents 37.2500 4: 93.8860 cents 93.8860 5: 99.2710 cents 99.2710 6: 94.3850 cents 94.3850 7: 36.7500 cents 36.7500 8: 86.3110 cents 86.3110 9: 149.4630 cents 149.4630
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36.75000 cents 1: 1 37.25000 cents 1: 1 86.31000 cents 1: 1 86.31100 cents 1: 1 93.88600 cents 1: 1 94.38500 cents 1: 1 99.27100 cents 1: 1 149.46300 cents 1: 1 149.46400 cents 2: 1 123.06100 cents 2: 1 123.56000 cents 2: 1 131.13500 cents 2: 1 131.13600 cents 2: 1 193.15700 cents 2: 1 193.65600 cents 2: 2 235.77400 cents 2: 1 298.92700 cents 3: 2 217.44600 cents 3: 1 230.40600 cents 3: 1 230.40700 cents 3: 1 272.52400 cents 3: 1 273.02400 cents 3: 1 287.54200 cents 3: 1 385.23700 cents 3: 1 385.23800 cents 4: 2 316.71700 cents 4: 1 324.29200 cents 4: 1 324.79200 cents 4: 1 366.90900 cents 4: 1 366.91000 cents 4: 1 421.98800 cents 4: 1 422.48700 cents 4: 1 471.54800 cents 5: 1 361.54200 cents 5: 1 410.60300 cents 5: 1 411.10200 cents 5: 1 466.18000 cents 5: 1 466.18100 cents 5: 1 508.29800 cents 5: 1 508.79800 cents 5: 2 516.37300 cents 6: 1 447.85200 cents 6: 1 447.85300 cents 6: 1 545.54800 cents 6: 1 560.06600 cents 6: 1 560.56600 cents 6: 1 602.68300 cents 6: 1 602.68400 cents 6: 2 615.64400 cents 7: 1 534.16300 cents 7: 2 597.31600 cents 7: 1 639.43400 cents 7: 1 639.93300 cents 7: 1 701.95400 cents 7: 1 701.95500 cents 7: 1 709.53000 cents 7: 1 710.02900 cents 8: 1 683.62600 cents 8: 1 683.62700 cents 8: 1 733.81900 cents 8: 1 738.70500 cents 8: 1 739.20400 cents 8: 1 746.77900 cents 8: 1 746.78000 cents 8: 1 795.84000 cents 8: 1 796.34000 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 8.25000 = 33/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 149.5 235.8 273.0 366.9 466.2 560.6 597.3 683.6 833.1 149.5: 86.3 123.6 217.4 316.7 411.1 447.9 534.2 683.6 833.1 235.8: 37.3 131.1 230.4 324.8 361.5 447.9 597.3 746.8 833.1 273.0: 93.9 193.2 287.5 324.3 410.6 560.1 709.5 795.8 833.1 366.9: 99.3 193.7 230.4 316.7 466.2 615.6 702.0 739.2 833.1 466.2: 94.4 131.1 217.4 366.9 516.4 602.7 639.9 733.8 833.1 560.6: 36.8 123.1 272.5 422.0 508.3 545.5 639.4 738.7 833.1 597.3: 86.3 235.8 385.2 471.5 508.8 602.7 702.0 796.3 833.1 683.6: 149.5 298.9 385.2 422.5 516.4 615.6 710.0 746.8 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7500 .. 149.4640 cents 112.71400 cents 36.75000 cents 2: 123.0610 .. 298.9270 cents 175.86600 cents -26.40300 cents 3: 217.4460 .. 385.2380 cents 167.79200 cents -81.48100 cents 4: 316.7170 .. 471.5480 cents 154.83100 cents -68.52100 cents 5: 361.5420 .. 516.3730 cents 154.83100 cents -110.00600 cents 6: 447.8520 .. 615.6440 cents 167.79200 cents -68.52100 cents 7: 534.1630 .. 710.0290 cents 175.86600 cents -81.48100 cents 8: 683.6260 .. 796.3400 cents 112.71400 cents -26.40300 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 36.75000 cents, class 1 Average step (divided formal octave): 92.5656 cents Largest one step interval : 149.46400 cents Average / Smallest step : 2.518791 Largest / Average step : 1.614683 Largest / Smallest step : 4.067048 Median interval of one step : 93.88600 cents, amount: 1 Least squares average step : 90.35110 cents, oct.: 813.15988 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : ICBEGFADH Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 5.36700 cents Scale diversity : 1.043601 Lumma stability : 0.088226 Lumma impropriety factor : 0.498654 Rothenberg efficiency : 0.240741 redundancy: 0.759259 Efficiency x scale size : 2.166667 Number of different interval sizes : 66 = 8.25000 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 8.25000 = 33/4 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 0.00100 cents Number of recognisable fifths : 4, average 705.8670 cents Number of recognisable fourths : 2, average 508.5480 cents Formal octave complements present : 3 = 33.3333% 2/1 octave complements present : 1 = 11.1111% -- Rational properties --
FIT/MODE
9: 2 1 0 1 1 1 0 1 2 N I SD: 26.0991 c. M:-41.9227 c. 10: 2 1 0 1 2 1 0 1 2 N I SD: 21.8609 c. M: 33.6740 c. 11: 2 1 1 1 1 1 1 1 2 N D3 I SD: 15.8189 c. M: 30.4178 c. 12: 2 1 1 1 2 1 1 1 2 N D3 I SD: 16.8977 c. M:-27.5015 c. Houseini: Greece, Raga Rudra Manjiri, Modes of Major Pentatonic mixed 13: 2 2 0 2 1 2 0 2 2 N I SD: 17.9883 c. M: 21.2963 c. 15: 3 1 1 2 1 2 1 1 3 N I SD: 14.7731 c. M: 21.8663 c. 16: 3 1 1 2 2 2 0 2 3 N SD: 14.0312 c. M: 27.5015 c. 18: 3 2 1 2 2 2 1 2 3 N I SD: 6.0961 c. M: 10.6157 c. 21: 4 2 1 2 3 2 1 2 4 N I SD: 6.8608 c. M: 9.8714 c. 27: 5 3 1 3 3 3 1 3 5 N I SD: 6.3453 c. M:-11.0675 c. 28: 5 3 1 3 4 3 1 3 5 N I SD: 5.3334 c. M: 9.8714 c. 34: 6 4 1 4 4 4 1 4 6 N I SD: 4.7747 c. M:-9.2525 c. 39: 7 4 2 4 5 4 2 4 7 N I SD: 2.9490 c. M: 5.1727 c. 46: 8 5 2 5 6 5 2 5 8 N I SD: 3.1423 c. M: 4.6970 c. 57: 10 6 3 6 7 6 3 6 10 N I SD: 3.0274 c. M: 5.1727 c. 61: 11 6 3 7 7 7 3 6 11 N I SD: 1.9507 c. M:-3.6014 c. 68: 12 7 3 8 8 8 3 7 12 N I SD: 2.4024 c. M: 3.4949 c. 71: 13 7 3 8 9 8 3 7 13 N I SD: 2.5454 c. M: 3.1665 c. 73: 13 8 3 8 9 8 3 8 13 N I SD: 2.1376 c. M:-3.8820 c. 77: 14 8 3 9 9 9 3 8 14 N I SD: 1.8443 c. M: 2.5402 c. 88: 16 9 4 10 10 10 4 9 16 N I SD: 1.7203 c. M: 2.3013 c. 89: 16 9 4 10 11 10 4 9 16 N I SD: 1.3665 c. M: 1.8481 c. 95: 17 10 4 11 11 11 4 10 17 N I SD: 0.9466 c. M: 1.4045 c. 116: 21 12 5 13 14 13 5 12 21 N I SD: 0.9218 c. M: 1.3550 c. 134: 24 14 6 15 16 15 6 14 24 N I SD: 0.4638 c. M: 1.0279 c. 195: 35 20 9 22 23 22 9 20 35 N I SD: 0.5546 c. M: 0.9004 c. 223: 40 23 10 25 27 25 10 23 40 N I SD: 0.4416 c. M: 0.7987 c. 229: 41 24 10 26 27 26 10 24 41 N I SD: 0.4511 c. M:-0.6926 c. 272: 49 28 12 31 32 31 12 28 49 N I SD: 0.4411 c. M: 0.6307 c. 290: 52 30 13 33 34 33 13 30 52 N I SD: 0.4138 c. M: 0.7997 c. 311: 56 32 14 35 37 35 14 32 56 N I SD: 0.3587 c. M: 0.7081 c. 318: 57 33 14 36 38 36 14 33 57 N I SD: 0.2114 c. M: 0.5669 c. 357: 64 37 16 40 43 40 16 37 64 N I SD: 0.3111 c. M: 0.5371 c. 400: 72 41 18 45 48 45 18 41 72 N I SD: 0.3691 c. M: 0.4932 c. 406: 73 42 18 46 48 46 18 42 73 N I SD: 0.2905 c. M: 0.3893 c. 434: 78 45 19 49 52 49 19 45 78 N I SD: 0.2808 c. M: 0.4462 c. 452: 81 47 20 51 54 51 20 47 81 N I SD: 0.1696 c. M: 0.2577 c. 629: 113 65 28 71 75 71 28 65 113 N I SD: 0.1555 c. M: 0.3163 c. 820: 147 85 37 92 98 93 36 85 147 N SD: 0.1541 c. M:-0.2702 c. 897: 161 93 40 101 107 102 39 93 161 N SD: 0.1520 c. M:-0.3998 c. 908: 163 94 41 102 108 103 40 94 163 N SD: 0.1441 c. M:-0.3910 c. 915: 164 95 41 103 109 104 40 95 164 N SD: 0.1266 c. M:-0.2902 c. 936: 168 97 42 105 112 106 41 97 168 N SD: 0.1447 c. M:-0.2224 c. 947: 170 98 42 107 113 107 42 98 170 N I SD: 0.1324 c. M: 0.3124 c. 997: 179 103 45 112 119 113 44 103 179 N SD: 0.1224 c. M:-0.2162 c. 1031: 185 107 46 116 123 117 45 107 185 N SD: 0.1170 c. M:-0.2143 c. 1049: 188 109 47 118 125 119 46 109 188 N SD: 0.1122 c. M:-0.1723 c. 1092: 196 113 49 123 130 124 48 113 196 N SD: 0.0766 c. M:-0.1677 c. 1226: 220 127 55 138 146 139 54 127 220 N SD: 0.0539 c. M:-0.1425 c. 1272: 228 132 57 143 152 144 56 132 228 N SD: 0.0993 c. M: 0.1408 c. 1315: 236 136 59 148 157 149 58 136 236 N SD: 0.0790 c. M:-0.1067 c. 1360: 244 141 61 153 162 154 60 141 244 N SD: 0.0715 c. M:-0.1805 c. 1410: 253 146 63 159 168 160 62 146 253 N SD: 0.0540 c. M:-0.1449 c. 1449: 260 150 65 163 173 164 64 150 260 N SD: 0.0574 c. M: 0.0974 c. 1544: 277 160 69 174 184 175 68 160 277 N SD: 0.0166 c. M:-0.0431 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 366.9100 cents 2 x x x x x x x 3 x S SD: 18.3280 cents 3 x x x x 4 x x x 5 S SD: 30.1819 cents 4 x x x 5 x x x 6 x S SD: 13.3456 cents 5 x x 6 x x x 7 x 8 S SD: 16.3703 cents 6 x x 7 x 8 x x 9:10 S SD: 15.8461 cents 7 x 8 x x 9 x 10 x 11 S SD: 15.7227 cents 8 x 9 x 10 x 11 x 12:13 S SD: 8.6454 cents 9:10 x x 11:12 x 13 x 15 SD: 16.3141 cents 10:11 x 12 x 13 x 14:15:16 S SD: 9.3281 cents 11:12 x 13 x 14:15 x 16:18 S SD: 11.5369 cents 12:13 x 14:15:16 x 17:18:19 S SD: 8.2378 cents 13:14:15 x 16:17:18 x 19:21 SD: 5.2980 cents 14:15:16 x 17:18:19:20:21:23 SD: 9.0922 cents 15:16:17:18:19:20 x 21:22:24 S SD: 10.7754 cents 16:17:18:19:20:21:22:23:24:26 S SD: 8.1868 cents 17:19 x 20:21:22 x 24:25:28 SD: 8.4787 cents 18:20 x 21:22:24:25 x 27:29 SD: 7.7932 cents 19:21:22 x 23:25:26:27:28:31 SD: 6.9237 cents 20:22:23 x 25:26 x 28:30:32 SD: 5.9437 cents 21:23:24:25:26:27:29:30:31:34 SD: 5.4325 cents 22:24:25:26:27:29:30:31:33:36 SD: 5.0408 cents 23:25:26:27:28:30:32 x 34:37 SD: 5.0100 cents 24:26 x 28:30:31:33:34:36:39 SD: 4.9619 cents 25:27 x 29:31:33 x 35:37:40 SD: 5.3086 cents 26:28:30 x 32:34:36:37:39:42 SD: 4.3007 cents 29:32:33:34:36:38:40:41:43:47 SD: 2.8956 cents 31:34 x 36:38:41:43:44:46:50 SD: 3.9173 cents 32:35:37 x 40:42:44:45:47:52 SD: 4.3153 cents 33:36:38:39:41:43:46:47:49:53 SD: 3.6408 cents 34:37:39:40:42:45:47:48:50:55 SD: 2.9446 cents 38:41:44 x 47:50:53:54:56:61 SD: 4.7213 cents 39:43:45:46:48:51:54:55:58:63 SD: 3.1038 cents 41:45:47:48:51:54:57:58:61:66 SD: 2.6603 cents 42:46:48:49:52:55:58:59:62:68 SD: 1.9366 cents 55:60:63:64:68:72:76:78:82:89 SD: 1.6986 cents 68:74:78:80:84:89:94:96:101:110 SD: 1.0251 cents 97:106:111:114:120:127:134:137:144:157 SD: 0.9291 cents 110:120:126:129:136:144:152:155:163:178 SD: 0.6200 cents 123:134:141:144:152:161:170:174:183:199 SD: 0.6084 cents 136:148:156:159:168:178:188:192:202:220 SD: 0.5213 cents 165:180:189:193:204:216:228:233:245:267 SD: 0.2686 cents 233:254:267:273:288:305:322:329:346:377 SD: 0.1810 cents 398:434:456:466:492:521:550:562:591:644 SD: 0.1282 cents 521:568:597:610:644:682:720:736:773:843 SD: 0.1246 cents