Scala analysis: peprmint
Peppermint 24: Wilson/Pepper apotome/limma=Phi, 2 chains spaced for pure 7:6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.680 cents 58.679693 2: 128.669 cents 128.669246 3: 187.349 cents 187.348938 4: 208.191 cents 208.191213 5: 7/6 266.870906 septimal minor third 6: 287.713 cents 287.713180 7: 346.393 cents 346.392873 8: 416.382 cents 416.382426 9: 475.062 cents 475.062119 10: 495.904 cents 495.904393 11: 554.584 cents 554.584086 12: 624.574 cents 624.573639 13: 683.253 cents 683.253332 14: 704.096 cents 704.095607 15: 762.775 cents 762.775299 16: 832.765 cents 832.764852 17: 891.445 cents 891.444545 18: 912.287 cents 912.286820 19: 970.967 cents 970.966512 20: 991.809 cents 991.808787 21: 1050.488 cents 1050.488479 22: 1120.478 cents 1120.478033 23: 1179.158 cents 1179.157725 24: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 20.8423 cents 20.8423 1: 58.6797 cents 58.6797 2: 69.9896 cents 69.9896 3: 58.6797 cents 58.6797 4: 20.8423 cents 20.8423 5: 58.6797 cents 58.6797 6: 20.8423 cents 20.8423 7: 58.6797 cents 58.6797 8: 69.9896 cents 69.9896 9: 58.6797 cents 58.6797 10: 20.8423 cents 20.8423 11: 58.6797 cents 58.6797 12: 69.9896 cents 69.9896 13: 58.6797 cents 58.6797 14: 20.8423 cents 20.8423 15: 58.6797 cents 58.6797 16: 69.9896 cents 69.9896 17: 58.6797 cents 58.6797 18: 20.8423 cents 20.8423 19: 58.6797 cents 58.6797 20: 20.8423 cents 20.8423 21: 58.6797 cents 58.6797 22: 69.9896 cents 69.9896 23: 58.6797 cents 58.6797 24: 20.8423 cents 20.8423
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 20.84227 cents 1: 12 58.67969 cents 1: 5 69.98955 cents 2: 14 79.52197 cents 2: 10 128.66925 cents 3: 2 100.36424 cents 3: 7 138.20166 cents 3: 10 149.51152 cents 3: 5 187.34894 cents 4: 4 159.04393 cents 4: 20 208.19121 cents 5: 2 217.72363 cents 5: 9 229.03349 cents 5: 10 7/6 266.871 cents septimal minor third 5: 3 278.18077 cents 6: 18 287.71318 cents 6: 6 336.86046 cents 7: 4 308.55545 cents 7: 9 346.39287 cents 7: 8 357.70273 cents 7: 3 395.54015 cents 8: 8 367.23515 cents 8: 16 416.38243 cents 9: 4 425.91484 cents 9: 11 437.22470 cents 9: 8 475.06212 cents 9: 1 486.37198 cents 10: 22 495.90439 cents 10: 2 545.05167 cents 11: 6 516.74667 cents 11: 11 554.58409 cents 11: 6 565.89395 cents 11: 1 603.73136 cents 12: 12 575.42636 cents 12: 12 624.57364 cents 13: 1 596.26864 cents 13: 6 634.10605 cents 13: 11 645.41591 cents 13: 6 683.25333 cents 14: 2 654.94833 cents 14: 22 704.09561 cents 15: 1 713.62802 cents 15: 8 724.93788 cents 15: 11 762.77530 cents 15: 4 774.08516 cents 16: 16 783.61757 cents 16: 8 832.76485 cents 17: 3 804.45985 cents 17: 8 842.29727 cents 17: 9 853.60713 cents 17: 4 891.44454 cents 18: 6 863.13954 cents 18: 18 912.28682 cents 19: 3 921.81923 cents 19: 10 933.12909 cents 19: 9 970.96651 cents 19: 2 982.27637 cents 20: 20 991.80879 cents 20: 4 1040.95607 cents 21: 5 1012.65106 cents 21: 10 1050.48848 cents 21: 7 1061.79834 cents 21: 2 1099.63576 cents 22: 10 1071.33075 cents 22: 14 1120.47803 cents 23: 5 1130.01045 cents 23: 12 1141.32031 cents 23: 7 1179.15772 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.95652 = 68/23
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 24 0.0 : 58.7 128.7 187.3 208.2 266.9 287.7 346.4 416.4 475.1 495.9 554.6 624.6 683.3 704.1 762.8 832.8 891.4 912.3 971.0 991.8 1050.5 1120.5 1179.2 1200.0 58.7 : 70.0 128.7 149.5 208.2 229.0 287.7 357.7 416.4 437.2 495.9 565.9 624.6 645.4 704.1 774.1 832.8 853.6 912.3 933.1 991.8 1061.8 1120.5 1141.3 1200.0 128.7 : 58.7 79.5 138.2 159.0 217.7 287.7 346.4 367.2 425.9 495.9 554.6 575.4 634.1 704.1 762.8 783.6 842.3 863.1 921.8 991.8 1050.5 1071.3 1130.0 1200.0 187.3 : 20.8 79.5 100.4 159.0 229.0 287.7 308.6 367.2 437.2 495.9 516.7 575.4 645.4 704.1 724.9 783.6 804.5 863.1 933.1 991.8 1012.7 1071.3 1141.3 1200.0 208.2 : 58.7 79.5 138.2 208.2 266.9 287.7 346.4 416.4 475.1 495.9 554.6 624.6 683.3 704.1 762.8 783.6 842.3 912.3 971.0 991.8 1050.5 1120.5 1179.2 1200.0 266.9 : 20.8 79.5 149.5 208.2 229.0 287.7 357.7 416.4 437.2 495.9 565.9 624.6 645.4 704.1 724.9 783.6 853.6 912.3 933.1 991.8 1061.8 1120.5 1141.3 1200.0 287.7 : 58.7 128.7 187.3 208.2 266.9 336.9 395.5 416.4 475.1 545.1 603.7 624.6 683.3 704.1 762.8 832.8 891.4 912.3 971.0 1041.0 1099.6 1120.5 1179.2 1200.0 346.4 : 70.0 128.7 149.5 208.2 278.2 336.9 357.7 416.4 486.4 545.1 565.9 624.6 645.4 704.1 774.1 832.8 853.6 912.3 982.3 1041.0 1061.8 1120.5 1141.3 1200.0 416.4 : 58.7 79.5 138.2 208.2 266.9 287.7 346.4 416.4 475.1 495.9 554.6 575.4 634.1 704.1 762.8 783.6 842.3 912.3 971.0 991.8 1050.5 1071.3 1130.0 1200.0 475.1 : 20.8 79.5 149.5 208.2 229.0 287.7 357.7 416.4 437.2 495.9 516.7 575.4 645.4 704.1 724.9 783.6 853.6 912.3 933.1 991.8 1012.7 1071.3 1141.3 1200.0 495.9 : 58.7 128.7 187.3 208.2 266.9 336.9 395.5 416.4 475.1 495.9 554.6 624.6 683.3 704.1 762.8 832.8 891.4 912.3 971.0 991.8 1050.5 1120.5 1179.2 1200.0 554.6 : 70.0 128.7 149.5 208.2 278.2 336.9 357.7 416.4 437.2 495.9 565.9 624.6 645.4 704.1 774.1 832.8 853.6 912.3 933.1 991.8 1061.8 1120.5 1141.3 1200.0 624.6 : 58.7 79.5 138.2 208.2 266.9 287.7 346.4 367.2 425.9 495.9 554.6 575.4 634.1 704.1 762.8 783.6 842.3 863.1 921.8 991.8 1050.5 1071.3 1130.0 1200.0 683.3 : 20.8 79.5 149.5 208.2 229.0 287.7 308.6 367.2 437.2 495.9 516.7 575.4 645.4 704.1 724.9 783.6 804.5 863.1 933.1 991.8 1012.7 1071.3 1141.3 1200.0 704.1 : 58.7 128.7 187.3 208.2 266.9 287.7 346.4 416.4 475.1 495.9 554.6 624.6 683.3 704.1 762.8 783.6 842.3 912.3 971.0 991.8 1050.5 1120.5 1179.2 1200.0 762.8 : 70.0 128.7 149.5 208.2 229.0 287.7 357.7 416.4 437.2 495.9 565.9 624.6 645.4 704.1 724.9 783.6 853.6 912.3 933.1 991.8 1061.8 1120.5 1141.3 1200.0 832.8 : 58.7 79.5 138.2 159.0 217.7 287.7 346.4 367.2 425.9 495.9 554.6 575.4 634.1 654.9 713.6 783.6 842.3 863.1 921.8 991.8 1050.5 1071.3 1130.0 1200.0 891.4 : 20.8 79.5 100.4 159.0 229.0 287.7 308.6 367.2 437.2 495.9 516.7 575.4 596.3 654.9 724.9 783.6 804.5 863.1 933.1 991.8 1012.7 1071.3 1141.3 1200.0 912.3 : 58.7 79.5 138.2 208.2 266.9 287.7 346.4 416.4 475.1 495.9 554.6 575.4 634.1 704.1 762.8 783.6 842.3 912.3 971.0 991.8 1050.5 1120.5 1179.2 1200.0 971.0 : 20.8 79.5 149.5 208.2 229.0 287.7 357.7 416.4 437.2 495.9 516.7 575.4 645.4 704.1 724.9 783.6 853.6 912.3 933.1 991.8 1061.8 1120.5 1141.3 1200.0 991.8 : 58.7 128.7 187.3 208.2 266.9 336.9 395.5 416.4 475.1 495.9 554.6 624.6 683.3 704.1 762.8 832.8 891.4 912.3 971.0 1041.0 1099.6 1120.5 1179.2 1200.0 1050.5: 70.0 128.7 149.5 208.2 278.2 336.9 357.7 416.4 437.2 495.9 565.9 624.6 645.4 704.1 774.1 832.8 853.6 912.3 982.3 1041.0 1061.8 1120.5 1141.3 1200.0 1120.5: 58.7 79.5 138.2 208.2 266.9 287.7 346.4 367.2 425.9 495.9 554.6 575.4 634.1 704.1 762.8 783.6 842.3 912.3 971.0 991.8 1050.5 1071.3 1130.0 1200.0 1179.2: 20.8 79.5 149.5 208.2 229.0 287.7 308.6 367.2 437.2 495.9 516.7 575.4 645.4 704.1 724.9 783.6 853.6 912.3 933.1 991.8 1012.7 1071.3 1141.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.8423 .. 69.9896 cents 49.14728 cents 20.84227 cents 2: 79.5220 .. 128.6692 cents 49.14728 cents 9.53241 cents 3: 100.3642 .. 187.3489 cents 86.98470 cents -28.30500 cents 4: 159.0439 .. 208.1912 cents 49.14728 cents -28.30500 cents 5: 217.7236 .. 278.1808 cents 60.45714 cents 9.53241 cents 6: 287.7132 .. 336.8605 cents 49.14728 cents 9.53241 cents 7: 308.5555 .. 395.5402 cents 86.98470 cents -28.30500 cents 8: 367.2351 .. 416.3824 cents 49.14728 cents -28.30500 cents 9: 425.9148 .. 486.3720 cents 60.45714 cents 9.53241 cents 10: 495.9044 .. 545.0517 cents 49.14728 cents 9.53241 cents 11: 516.7467 .. 603.7314 cents 86.98470 cents -28.30500 cents 12: 575.4264 .. 624.5736 cents 49.14728 cents -28.30500 cents 13: 596.2686 .. 683.2533 cents 86.98470 cents -28.30500 cents 14: 654.9483 .. 704.0956 cents 49.14728 cents -28.30500 cents 15: 713.6280 .. 774.0852 cents 60.45714 cents 9.53241 cents 16: 783.6176 .. 832.7649 cents 49.14728 cents 9.53241 cents 17: 804.4598 .. 891.4445 cents 86.98470 cents -28.30500 cents 18: 863.1395 .. 912.2868 cents 49.14728 cents -28.30500 cents 19: 921.8192 .. 982.2764 cents 60.45714 cents 9.53241 cents 20: 991.8088 .. 1040.9561 cents 49.14728 cents 9.53241 cents 21: 1012.6511 .. 1099.6358 cents 86.98470 cents -28.30500 cents 22: 1071.3308 .. 1120.4780 cents 49.14728 cents -28.30500 cents 23: 1130.0104 .. 1179.1577 cents 49.14728 cents 9.53241 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 20.84227 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 69.98955 cents Average / Smallest step : 2.398970 Largest / Average step : 1.399791 Largest / Smallest step : 3.358057 Median interval of one step : 58.67969 cents, amount: 12 Most common interval of one step : 58.67969 cents, amount: 12 Least squares average step : 50.88864 cents, oct.: 1221.32741 cents Scale is not proper Step pattern alph. order: ABACACABACABACABACACABAC Step pattern size order : MLMSMSMLMSMLMSMLMSMSMLMS Scale is a Constant Structure, by a margin of 7.46273 cents Scale diversity : 1.253776 Lumma stability : 0.114174 Lumma impropriety factor : 0.276831 Number of different interval sizes : 68 = 2.95652 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.95652 = 68/23 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 7.46273 cents Most common intervals : 495.90439 cents & inv., amount: 22 Most common triad is 0.0 495.904 704.096 cents, amount: 20 Number of recognisable fifths : 23, average 704.5101 cents Scale contains two identical disjunct "tetrachords" of 11 notes Formal octave complements present : 7 = 29.1667% Limited inverse transpositions : 23 Inversional symmetry on intervals : 11-12 23-24 -- Rational properties -- Prime limit : 7 (not all pitches rational)
FIT/MODE
24: 1 1 1 1 1 0 1 2 1 0 2 1 1 1 1 1 1 1 1 0 2 1 1 1 N T3 SD: 27.0280 c. M: 46.3929 c. 25: 1 2 1 0 2 0 1 2 1 0 2 1 1 1 1 1 2 0 1 1 1 1 2 0 N SD: 13.5353 c. M:-21.4159 c. 28: 1 2 1 1 1 1 1 2 1 1 1 2 1 0 2 1 2 0 2 0 2 1 2 0 N SD: 12.5663 c. M:-20.9401 c. 29: 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 P D3 SD: 13.6111 c. M: 22.4790 c. 30: 1 2 2 0 2 0 2 1 2 0 2 2 1 1 1 2 1 1 1 1 1 2 1 1 N SD: 11.2915 c. M: 19.1577 c. 32: 2 1 2 1 1 1 1 2 2 0 2 2 1 1 1 2 2 0 2 0 2 2 1 1 N SD: 10.6322 c. M:-16.8088 c. 38: 2 2 2 0 2 1 2 2 2 0 2 3 1 1 2 2 2 1 1 1 2 2 2 1 N SD: 11.8085 c. M: 23.5981 c. 39: 2 2 2 1 1 1 2 2 2 1 2 2 2 1 2 2 2 0 2 1 2 2 2 1 N SD: 9.9595 c. M: 20.7171 c. 40: 2 2 2 1 2 1 2 2 2 1 1 3 2 0 2 3 2 0 2 1 2 2 2 1 N SD: 9.0363 c. M: 14.5841 c. 41: 2 2 2 1 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2 1 P D3 SD: 7.1033 c. M: 13.3958 c. 46: 2 3 2 1 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 1 2 3 2 1 N SD: 4.2680 c. M: 7.2624 c. 58: 3 3 3 1 3 1 3 3 3 1 3 3 3 1 3 3 3 1 3 1 3 3 3 1 N D3 SD: 2.8056 c. M:-5.3313 c. 63: 3 4 3 1 3 1 3 4 3 1 3 4 3 1 3 4 3 1 3 1 3 4 3 1 N G SD: 2.5858 c. M:-5.3304 c. 96: 5 5 5 2 4 2 5 5 5 2 4 6 5 1 5 6 4 2 5 1 5 6 4 2 N SD: 3.4008 c. M:-4.7351 c. 104: 5 6 5 2 5 2 5 6 5 2 5 6 5 2 5 6 5 2 5 2 5 6 5 2 N SD: 1.4946 c. M: 2.9830 c. 121: 6 7 6 2 6 2 6 7 6 2 6 7 6 2 6 7 6 2 6 2 6 7 6 2 N SD: 0.6631 c. M:-1.1174 c. 225: 11 13 11 4 11 4 11 13 11 4 11 13 11 4 11 13 11 4 11 4 11 13 11 4 N SD: 0.4114 c. M: 0.7779 c. 288: 14 17 14 5 14 5 14 17 14 5 14 17 14 5 14 17 14 5 14 5 14 17 14 5 N SD: 0.3003 c. M:-0.5685 c. 346: 17 20 17 6 17 6 17 20 17 6 17 20 17 6 17 20 17 6 17 6 17 20 17 6 N SD: 0.2211 c. M:-0.4279 c. 409: 20 24 20 7 20 7 20 24 20 7 20 24 20 7 20 24 20 7 20 7 20 24 20 7 N SD: 0.2595 c. M:-0.4870 c. 513: 25 30 25 9 25 9 25 30 25 9 25 30 25 9 25 30 25 9 25 9 25 30 25 9 N SD: 0.1454 c. M: 0.2165 c. 634: 31 37 31 11 31 11 31 37 31 11 31 37 31 11 31 37 31 11 31 11 31 37 31 11 N SD: 0.0216 c. M:-0.0427 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.0703 cents 3 .. 6 match: 3 H SD: 2.4674 cents 4 .. 8 match: 4 H SD: 7.5552 cents 5 .. 10 match: 5 H SD: 10.1763 cents 6 .. 12 match: 6 H SD: 1.2979 cents 7 .. 14 match: 7 H SD: 6.7026 cents 8 .. 16 match: 8 H SD: 5.6458 cents 9 .. 18 match: 9 H SD: 2.7797 cents 10 .. 20 match: 10 H SD: 6.0448 cents 11 .. 22 match: 11 H SD: 4.7321 cents 12 .. 24 match: 12 H SD: 4.2831 cents 13 .. 26 match: 13 H SD: 3.4281 cents 14 .. 28 match: 14 H SD: 4.6275 cents 15 .. 30 match: 15 H SD: 5.0193 cents 16 .. 32 match: 15 SD: 3.5725 cents 17 .. 34 match: 15 S SD: 5.3276 cents 18 .. 36 match: 16 S SD: 2.9082 cents 19 .. 38 match: 18 S SD: 3.8517 cents 20 .. 40 match: 18 SD: 4.6212 cents 21 .. 42 match: 19 SD: 3.7801 cents 22 .. 44 match: 18 SD: 3.1016 cents 23 .. 46 match: 22 S SD: 2.7796 cents 24 .. 48 match: 20 SD: 2.7012 cents 25 .. 50 match: 20 S SD: 3.0447 cents 26 .. 52 match: 20 SD: 2.4216 cents 27 .. 54 match: 21 SD: 2.1704 cents 28 .. 56 match: 20 SD: 2.6861 cents 29 .. 58 match: 21 SD: 2.3937 cents 30 .. 60 match: 21 SD: 2.4289 cents 31 .. 62 match: 22 SD: 2.3252 cents 32 .. 64 match: 22 SD: 2.0931 cents 33 .. 66 match: 22 SD: 2.2879 cents 34 .. 68 match: 20 SD: 2.1103 cents 35 .. 70 match: 21 SD: 2.0284 cents 36 .. 72 match: 24 SD: 1.8135 cents 37 .. 74 match: 23 SD: 1.6733 cents 38 .. 76 match: 22 SD: 2.1532 cents 39 .. 78 match: 23 SD: 1.8607 cents 40 .. 80 match: 21 SD: 1.5233 cents 41 .. 82 match: 21 SD: 1.7979 cents 42 .. 84 match: 22 SD: 1.7039 cents 43 .. 86 match: 22 SD: 1.7919 cents 44 .. 88 match: 24 SD: 1.6678 cents 45 .. 90 match: 23 SD: 1.5600 cents 46 .. 92 match: 22 SD: 1.8007 cents 47 .. 94 match: 23 SD: 1.6573 cents 48 .. 96 match: 24 SD: 1.3880 cents 49 .. 98 match: 23 SD: 1.4124 cents 50 .. 100 match: 23 SD: 1.3717 cents 51 .. 102 match: 23 SD: 1.4607 cents 52 .. 104 match: 23 SD: 1.3186 cents 53 .. 106 match: 24 SD: 1.2345 cents 54 .. 108 match: 24 SD: 1.0775 cents 57 .. 114 match: 22 SD: 1.4745 cents 58 .. 116 match: 22 SD: 1.1703 cents 60 .. 120 match: 24 SD: 1.0171 cents 63 .. 126 match: 23 SD: 1.0695 cents 66 .. 132 match: 23 SD: 0.9549 cents 69 .. 138 match: 23 SD: 1.0769 cents 72 .. 144 match: 24 SD: 1.0031 cents 76 .. 152 match: 24 SD: 0.8236 cents 78 .. 156 match: 24 SD: 0.7228 cents 85 .. 170 match: 24 SD: 0.6993 cents 88 .. 176 match: 24 SD: 0.6947 cents 89 .. 178 match: 24 SD: 0.6650 cents 108 .. 216 match: 24 SD: 0.6265 cents 114 .. 228 match: 24 SD: 0.5155 cents 132 .. 264 match: 24 SD: 0.4520 cents 143 .. 286 match: 24 SD: 0.4364 cents 150 .. 300 match: 24 SD: 0.4222 cents 157 .. 314 match: 24 SD: 0.3826 cents 166 .. 332 match: 24 SD: 0.3757 cents 172 .. 344 match: 24 SD: 0.3540 cents 180 .. 360 match: 24 SD: 0.3341 cents 181 .. 362 match: 24 SD: 0.3191 cents 193 .. 386 match: 24 SD: 0.3027 cents 199 .. 398 match: 24 SD: 0.2811 cents 209 .. 418 match: 24 SD: 0.2530 cents 235 .. 470 match: 24 SD: 0.2106 cents 283 .. 566 match: 24 SD: 0.2027 cents 313 .. 626 match: 24 SD: 0.1949 cents 320 .. 640 match: 24 SD: 0.1948 cents 323 .. 646 match: 24 SD: 0.1935 cents 343 .. 686 match: 24 SD: 0.1658 cents 376 .. 752 match: 24 SD: 0.1338 cents 437 .. 874 match: 24 SD: 0.1160 cents 492 .. 984 match: 24 SD: 0.1086 cents 516 .. 1032 match: 24 SD: 0.1082 cents 548 .. 1096 match: 24 SD: 0.1069 cents 570 .. 1140 match: 24 SD: 0.0958 cents