Scala analysis: perdeler23-symmetrical
Maqam/Dastgah tuning, mirror symmetry, two flavors of neutral 2nd-3rd-6th-7th
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.965 cents 76.965460 2: 132.248 cents 132.248350 3: 153.931 cents 153.930920 4: 209.214 cents 209.213810 5: 286.179 cents 286.179280 6: 341.462 cents 341.462170 7: 363.145 cents 363.144740 8: 418.428 cents 418.427630 9: 495.393 cents 495.393090 10: 550.676 cents 550.675980 11: 572.359 cents 572.358550 12: 627.641 cents 627.641450 13: 649.324 cents 649.324010 14: 704.607 cents 704.606910 15: 781.572 cents 781.572370 16: 836.855 cents 836.855260 17: 858.538 cents 858.537830 18: 913.821 cents 913.820720 19: 990.786 cents 990.786180 20: 1046.069 cents 1046.069080 21: 1067.752 cents 1067.751650 22: 1123.035 cents 1123.034540 23: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 76.9655 cents 76.9655 1: 76.9655 cents 76.9655 2: 55.2829 cents 55.2829 3: 21.6826 cents 21.6826 4: 55.2829 cents 55.2829 5: 76.9655 cents 76.9655 6: 55.2829 cents 55.2829 7: 21.6826 cents 21.6826 8: 55.2829 cents 55.2829 9: 76.9655 cents 76.9655 10: 55.2829 cents 55.2829 11: 21.6826 cents 21.6826 12: 55.2829 cents 55.2829 13: 21.6826 cents 21.6826 14: 55.2829 cents 55.2829 15: 76.9655 cents 76.9655 16: 55.2829 cents 55.2829 17: 21.6826 cents 21.6826 18: 55.2829 cents 55.2829 19: 76.9655 cents 76.9655 20: 55.2829 cents 55.2829 21: 21.6826 cents 21.6826 22: 55.2829 cents 55.2829 23: 76.9655 cents 76.9655
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 21.68257 cents 1: 11 55.28289 cents 1: 6 76.96546 cents 2: 12 76.96546 cents 2: 10 132.24835 cents 2: 1 153.93092 cents 3: 1 98.64803 cents 3: 6 132.24835 cents 3: 10 153.93092 cents 3: 4 187.53125 cents 3: 2 209.21381 cents 4: 2 153.93092 cents 4: 18 209.21381 cents 4: 2 230.89638 cents 4: 1 264.49670 cents 5: 1 209.21382 cents 5: 6 230.89639 cents 5: 8 264.49671 cents 5: 8 286.17928 cents 6: 12 286.17928 cents 6: 1 307.86184 cents 6: 8 341.46217 cents 6: 2 363.14474 cents 7: 2 307.86184 cents 7: 6 341.46217 cents 7: 9 363.14474 cents 7: 2 396.74506 cents 7: 4 418.42763 cents 8: 4 363.14473 cents 8: 13 418.42763 cents 8: 4 440.11020 cents 8: 2 473.71052 cents 9: 2 418.42763 cents 9: 6 440.11020 cents 9: 5 473.71052 cents 9: 10 495.39309 cents 10: 12 495.39309 cents 10: 2 517.07566 cents 10: 6 550.67598 cents 10: 3 572.35855 cents 11: 3 517.07566 cents 11: 6 550.67599 cents 11: 8 572.35855 cents 11: 6 627.64145 cents 12: 6 572.35855 cents 12: 8 627.64145 cents 12: 6 649.32401 cents 12: 3 682.92434 cents 13: 3 627.64145 cents 13: 6 649.32401 cents 13: 2 682.92434 cents 13: 12 704.60691 cents 14: 10 704.60691 cents 14: 5 726.28948 cents 14: 6 759.88980 cents 14: 2 781.57237 cents 15: 2 726.28948 cents 15: 4 759.88980 cents 15: 13 781.57237 cents 15: 4 836.85527 cents 16: 4 781.57237 cents 16: 2 803.25494 cents 16: 9 836.85526 cents 16: 6 858.53783 cents 16: 2 892.13816 cents 17: 2 836.85526 cents 17: 8 858.53783 cents 17: 1 892.13816 cents 17: 12 913.82072 cents 18: 8 913.82072 cents 18: 8 935.50329 cents 18: 6 969.10361 cents 18: 1 990.78618 cents 19: 1 935.50330 cents 19: 2 969.10362 cents 19: 18 990.78618 cents 19: 2 1046.06908 cents 20: 2 990.78619 cents 20: 4 1012.46875 cents 20: 10 1046.06908 cents 20: 6 1067.75165 cents 20: 1 1101.35197 cents 21: 1 1046.06908 cents 21: 10 1067.75165 cents 21: 12 1123.03454 cents 22: 6 1123.03454 cents 22: 11 1144.71711 cents 22: 6 1178.31743 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0.0 : 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1200.0 77.0 : 55.3 77.0 132.2 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1123.0 1200.0 132.2 : 21.7 77.0 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1067.8 1144.7 1200.0 153.9 : 55.3 132.2 187.5 209.2 264.5 341.5 396.7 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 836.9 892.1 913.8 969.1 1046.1 1123.0 1178.3 1200.0 209.2 : 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 990.8 1067.8 1123.0 1144.7 1200.0 286.2 : 55.3 77.0 132.2 209.2 264.5 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 913.8 990.8 1046.1 1067.8 1123.0 1200.0 341.5 : 21.7 77.0 153.9 209.2 230.9 286.2 307.9 363.1 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 858.5 935.5 990.8 1012.5 1067.8 1144.7 1200.0 363.1 : 55.3 132.2 187.5 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 836.9 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 418.4 : 77.0 132.2 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 781.6 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 495.4 : 55.3 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 704.6 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1200.0 550.7 : 21.7 77.0 98.6 153.9 230.9 286.2 307.9 363.1 440.1 495.4 517.1 572.4 649.3 726.3 781.6 803.3 858.5 935.5 990.8 1012.5 1067.8 1144.7 1200.0 572.4 : 55.3 77.0 132.2 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 627.6 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 627.6 : 21.7 77.0 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 572.4 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 649.3 : 55.3 132.2 187.5 209.2 264.5 341.5 396.7 418.4 473.7 550.7 627.6 682.9 704.6 759.9 836.9 892.1 913.8 969.1 1046.1 1101.4 1123.0 1178.3 1200.0 704.6 : 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 495.4 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1144.7 1200.0 781.6 : 55.3 77.0 132.2 209.2 264.5 286.2 341.5 418.4 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1067.8 1123.0 1200.0 836.9 : 21.7 77.0 153.9 209.2 230.9 286.2 363.1 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1012.5 1067.8 1144.7 1200.0 858.5 : 55.3 132.2 187.5 209.2 264.5 341.5 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 836.9 892.1 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 913.8 : 77.0 132.2 153.9 209.2 286.2 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 990.8 : 55.3 77.0 132.2 209.2 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1200.0 1046.1: 21.7 77.0 153.9 230.9 286.2 307.9 363.1 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 803.3 858.5 935.5 990.8 1012.5 1067.8 1144.7 1200.0 1067.8: 55.3 132.2 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 1123.0: 77.0 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.6826 .. 76.9655 cents 55.28289 cents 21.68257 cents 2: 76.9655 .. 153.9309 cents 76.96546 cents 1/1, 0.0000 cents 3: 98.6480 .. 209.2138 cents 110.56578 cents -55.28289 cents 4: 153.9309 .. 264.4967 cents 110.56578 cents -55.28289 cents 5: 209.2138 .. 286.1793 cents 76.96546 cents -55.28288 cents 6: 286.1793 .. 363.1447 cents 76.96546 cents 1/1, 0.0000 cents 7: 307.8618 .. 418.4276 cents 110.56579 cents -55.28290 cents 8: 363.1447 .. 473.7105 cents 110.56579 cents -55.28290 cents 9: 418.4276 .. 495.3931 cents 76.96546 cents -55.28289 cents 10: 495.3931 .. 572.3586 cents 76.96546 cents 1/1, 0.0000 cents 11: 517.0757 .. 627.6415 cents 110.56579 cents -55.28289 cents 12: 572.3585 .. 682.9243 cents 110.56579 cents -55.28290 cents 13: 627.6414 .. 704.6069 cents 76.96546 cents -55.28289 cents 14: 704.6069 .. 781.5724 cents 76.96546 cents 1/1, 0.0000 cents 15: 726.2895 .. 836.8553 cents 110.56579 cents -55.28289 cents 16: 781.5724 .. 892.1382 cents 110.56579 cents -55.28290 cents 17: 836.8553 .. 913.8207 cents 76.96546 cents -55.28290 cents 18: 913.8207 .. 990.7862 cents 76.96546 cents 1/1, 0.0000 cents 19: 935.5033 .. 1046.0691 cents 110.56578 cents -55.28288 cents 20: 990.7862 .. 1101.3520 cents 110.56578 cents -55.28289 cents 21: 1046.0691 .. 1123.0345 cents 76.96546 cents -55.28289 cents 22: 1123.0345 .. 1178.3174 cents 55.28289 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 23 -- Interval properties -- Smallest interval : 21.68256 cents, class 1 Average step (divided formal octave): 52.1739 cents Largest one step interval : 76.96546 cents Average / Smallest step : 2.406262 Largest / Average step : 1.475171 Largest / Smallest step : 3.549648 Median interval of one step : 55.28289 cents, amount: 11 Most common interval of one step : 55.28289 cents, amount: 11 Least squares average step : 51.74397 cents, oct.: 1190.11123 cents Scale is not proper Scale is a mode of a 1107-tone equal temperament with octave 2/1 degrees: 71 122 142 193 264 315 335 386 457 508 528 579 599 650 721 772 792 843 914 965 985 1036 1107 Least number of segments generator : 554 of 600.542 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 650 of 704.607 cents and inv. generated superset size: 23 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBABCBABCBCBABCBABCBA Step pattern size order : LMSMLMSMLMSMSMLMSMLMSML Scale is not a Constant Structure Scale diversity : 1.192070 Lumma stability : 0.036138 Lumma impropriety factor : 0.691036 Rothenberg efficiency : 0.695652 redundancy: 0.304348 Efficiency x scale size : 16.000000 Number of different interval sizes : 44 = 2.00000 / class Number of one step interval sizes : 3 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 21.68256 cents Most common intervals : 495.39309 cents & inv., amount: 22 Scale has Generated (pseudo-Myhill) property, generator: 704.607 cents and inv. Scale is a chain of 11 triads 0.0 495.393 990.786 cents Most common triad is 0.0 495.393 704.607 cents, amount: 21 Number of recognisable fifths : 22, average 704.6069 cents Scale contains two identical disjunct "tetrachords" of 10 notes Formal octave complements present : 23 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
23: 1 1 0 1 2 1 0 1 2 1 0 1 1 1 1 1 1 1 1 1 1 1 2 N T3 SD: 39.2625 c. M: 54.7647 c. 24: 2 1 0 1 2 1 0 1 2 1 0 2 0 1 2 1 0 1 2 1 0 1 2 N I SD: 13.9686 c. M: 23.0345 c. 26: 2 1 0 2 1 1 1 1 2 1 0 2 0 1 2 1 1 1 1 2 0 1 2 N I SD: 13.0282 c. M:-21.5554 c. 28: 2 1 1 1 2 1 0 2 2 1 0 2 0 1 2 2 0 1 2 1 1 1 2 N I SD: 12.3699 c. M: 20.2876 c. 29: 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 2 N D3 I SD: 7.6855 c. M:-12.7450 c. 42: 3 2 0 2 3 2 1 2 2 2 1 2 1 2 2 2 1 2 3 2 0 2 3 N I SD: 7.9453 c. M:-11.0738 c. 46: 3 2 1 2 3 2 1 2 3 2 1 2 1 2 3 2 1 2 3 2 1 2 3 N G I SD: 1.7186 c. M:-2.8499 c. 63: 4 3 1 3 4 3 1 3 4 3 1 3 1 3 4 3 1 3 4 3 1 3 4 N G I SD: 1.0281 c. M:-1.7050 c. 109: 7 5 2 5 7 5 2 5 7 5 2 5 2 5 7 5 2 5 7 5 2 5 7 N G I SD: 0.1310 c. M:-0.2173 c. 281: 18 13 5 13 18 13 5 13 18 13 5 13 5 13 18 13 5 13 18 13 5 13 18 N G I SD: 0.1289 c. M:-0.2137 c. 390: 25 18 7 18 25 18 7 18 25 18 7 18 7 18 25 18 7 18 25 18 7 18 25 N G I SD: 0.0562 c. M:-0.0933 c. 499: 32 23 9 23 32 23 9 23 32 23 9 23 9 23 32 23 9 23 32 23 9 23 32 N G I SD: 0.0153 c. M:-0.0254 c. 608: 39 28 11 28 39 28 11 28 39 28 11 28 11 28 39 28 11 28 39 28 11 28 39 N G I SD: 0.0109 c. M:-0.0181 c. 1107: 71 51 20 51 71 51 20 51 71 51 20 51 20 51 71 51 20 51 71 51 20 51 71 N G I SD: 0.0009 c. M:-0.0015 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.3260 cents 3 .. 6 match: 3 H SD: 8.6522 cents 4 .. 8 match: 4 H SD: 8.0082 cents 5 .. 10 match: 5 H SD: 9.0009 cents 6 .. 12 match: 6 H SD: 5.4376 cents 7 .. 14 match: 7 H SD: 5.0549 cents 8 .. 16 match: 8 H SD: 4.8236 cents 9 .. 18 match: 9 H SD: 5.3259 cents 10 .. 20 match: 10 H SD: 5.9992 cents 11 .. 22 match: 11 H SD: 4.2726 cents 12 .. 24 match: 12 H SD: 4.5162 cents 13 .. 26 match: 13 H SD: 4.9072 cents 14 .. 28 match: 14 H SD: 3.4266 cents 15 .. 30 match: 14 SD: 5.1506 cents 16 .. 32 match: 16 H SD: 3.8870 cents 17 .. 34 match: 17 H SD: 4.6384 cents 18 .. 36 match: 17 S SD: 3.6661 cents 19 .. 38 match: 17 S SD: 4.1323 cents 20 .. 40 match: 17 SD: 4.1462 cents 21 .. 42 match: 19 S SD: 3.0728 cents 22 .. 44 match: 19 SD: 2.4363 cents 23 .. 46 match: 19 SD: 2.4300 cents 24 .. 48 match: 19 SD: 2.9834 cents 25 .. 50 match: 19 SD: 3.1954 cents 26 .. 52 match: 19 SD: 2.4265 cents 27 .. 54 match: 19 SD: 2.9238 cents 28 .. 56 match: 23 SD: 2.7876 cents 29 .. 58 match: 21 SD: 2.7387 cents 30 .. 60 match: 21 SD: 2.3126 cents 31 .. 62 match: 19 SD: 2.9185 cents 32 .. 64 match: 20 SD: 2.3717 cents 33 .. 66 match: 21 SD: 2.1752 cents 34 .. 68 match: 20 SD: 2.2068 cents 35 .. 70 match: 20 SD: 2.3647 cents 36 .. 72 match: 20 SD: 2.1502 cents 37 .. 74 match: 21 SD: 1.8431 cents 38 .. 76 match: 20 SD: 2.1424 cents 39 .. 78 match: 21 SD: 1.5767 cents 40 .. 80 match: 22 SD: 1.5179 cents 42 .. 84 match: 22 SD: 1.6868 cents 44 .. 88 match: 22 SD: 1.7178 cents 45 .. 90 match: 21 SD: 1.5333 cents 46 .. 92 match: 22 SD: 1.3509 cents 47 .. 94 match: 20 SD: 1.5617 cents 48 .. 96 match: 22 SD: 1.2266 cents 49 .. 98 match: 22 SD: 1.6230 cents 50 .. 100 match: 23 SD: 1.5344 cents 51 .. 102 match: 23 SD: 1.3388 cents 53 .. 106 match: 22 SD: 1.4428 cents 54 .. 108 match: 23 SD: 1.3784 cents 55 .. 110 match: 23 SD: 1.3122 cents 57 .. 114 match: 22 SD: 1.4991 cents 58 .. 116 match: 22 SD: 1.4676 cents 59 .. 118 match: 22 SD: 1.2590 cents 61 .. 122 match: 23 SD: 1.0211 cents 62 .. 124 match: 22 SD: 1.0893 cents 64 .. 128 match: 23 SD: 1.0498 cents 66 .. 132 match: 23 SD: 0.9670 cents 72 .. 144 match: 23 SD: 0.9188 cents 77 .. 154 match: 23 SD: 0.9138 cents 84 .. 168 match: 23 SD: 0.7762 cents 87 .. 174 match: 23 SD: 0.7182 cents 101 .. 202 match: 23 SD: 0.7119 cents 105 .. 210 match: 23 SD: 0.6880 cents 106 .. 212 match: 23 SD: 0.6502 cents 109 .. 218 match: 23 SD: 0.6382 cents 110 .. 220 match: 23 SD: 0.5692 cents 115 .. 230 match: 23 SD: 0.5646 cents 117 .. 234 match: 23 SD: 0.5341 cents 128 .. 256 match: 23 SD: 0.4272 cents 150 .. 300 match: 23 SD: 0.4092 cents 151 .. 302 match: 23 SD: 0.3627 cents 171 .. 342 match: 23 SD: 0.3488 cents 179 .. 358 match: 23 SD: 0.3465 cents 193 .. 386 match: 23 SD: 0.2902 cents 217 .. 434 match: 23 SD: 0.2511 cents 257 .. 514 match: 23 SD: 0.2461 cents 265 .. 530 match: 23 SD: 0.2321 cents 266 .. 532 match: 23 SD: 0.2116 cents 288 .. 576 match: 23 SD: 0.1946 cents 312 .. 624 match: 23 SD: 0.1571 cents 352 .. 704 match: 23 SD: 0.1535 cents 380 .. 760 match: 23 SD: 0.1532 cents 416 .. 832 match: 23 SD: 0.1520 cents 417 .. 834 match: 23 SD: 0.1424 cents 428 .. 856 match: 23 SD: 0.1394 cents 444 .. 888 match: 23 SD: 0.1368 cents 462 .. 924 match: 23 SD: 0.1226 cents 483 .. 966 match: 23 SD: 0.1084 cents 505 .. 1010 match: 23 SD: 0.0858 cents