Scala analysis: shur17
Peppermint 17-note thirdtone set for Persian dastgah-ha
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69.990 cents 69.989550 2: 128.669 cents 128.669240 3: 208.191 cents 208.191210 4: 287.713 cents 287.713180 5: 357.703 cents 357.702730 6: 416.382 cents 416.382430 7: 495.904 cents 495.904390 8: 565.894 cents 565.893950 9: 624.574 cents 624.573640 10: 704.096 cents 704.095610 11: 774.085 cents 774.085160 12: 832.765 cents 832.764850 13: 912.287 cents 912.286820 14: 991.809 cents 991.808790 15: 1061.798 cents 1061.798340 16: 1120.478 cents 1120.478030 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 79.5220 cents 79.5220 1: 69.9895 cents 69.9895 2: 58.6797 cents 58.6797 3: 79.5220 cents 79.5220 4: 79.5220 cents 79.5220 5: 69.9895 cents 69.9895 6: 58.6797 cents 58.6797 7: 79.5220 cents 79.5220 8: 69.9896 cents 69.9896 9: 58.6797 cents 58.6797 10: 79.5220 cents 79.5220 11: 69.9895 cents 69.9895 12: 58.6797 cents 58.6797 13: 79.5220 cents 79.5220 14: 79.5220 cents 79.5220 15: 69.9895 cents 69.9895 16: 58.6797 cents 58.6797 17: 79.5220 cents 79.5220
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 58.67969 cents 1: 5 69.98955 cents 1: 7 79.52197 cents 2: 5 128.66924 cents 2: 5 138.20166 cents 2: 5 149.51152 cents 2: 2 159.04394 cents 3: 13 208.19121 cents 3: 2 217.72363 cents 3: 2 229.03349 cents 4: 3 266.87091 cents 4: 3 278.18077 cents 4: 11 287.71318 cents 5: 3 336.86046 cents 5: 5 346.39288 cents 5: 5 357.70273 cents 5: 4 367.23515 cents 6: 9 416.38243 cents 6: 4 425.91484 cents 6: 4 437.22471 cents 7: 1 475.06212 cents 7: 1 486.37198 cents 7: 15 495.90439 cents 8: 1 545.05167 cents 8: 5 554.58409 cents 8: 5 565.89395 cents 8: 6 575.42637 cents 9: 6 624.57364 cents 9: 5 634.10606 cents 9: 5 645.41592 cents 9: 1 654.94833 cents 10: 15 704.09561 cents 10: 1 713.62802 cents 10: 1 724.93788 cents 11: 4 762.77530 cents 11: 4 774.08516 cents 11: 9 783.61758 cents 12: 4 832.76485 cents 12: 5 842.29727 cents 12: 5 853.60713 cents 12: 3 863.13955 cents 13: 11 912.28682 cents 13: 3 921.81924 cents 13: 3 933.12910 cents 14: 2 970.96651 cents 14: 2 982.27637 cents 14: 13 991.80879 cents 15: 2 1040.95606 cents 15: 5 1050.48848 cents 15: 5 1061.79834 cents 15: 5 1071.33076 cents 16: 7 1120.47803 cents 16: 5 1130.01045 cents 16: 5 1141.32031 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.37500 = 27/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 70.0 128.7 208.2 287.7 357.7 416.4 495.9 565.9 624.6 704.1 774.1 832.8 912.3 991.8 1061.8 1120.5 1200.0 70.0 : 58.7 138.2 217.7 287.7 346.4 425.9 495.9 554.6 634.1 704.1 762.8 842.3 921.8 991.8 1050.5 1130.0 1200.0 128.7 : 79.5 159.0 229.0 287.7 367.2 437.2 495.9 575.4 645.4 704.1 783.6 863.1 933.1 991.8 1071.3 1141.3 1200.0 208.2 : 79.5 149.5 208.2 287.7 357.7 416.4 495.9 565.9 624.6 704.1 783.6 853.6 912.3 991.8 1061.8 1120.5 1200.0 287.7 : 70.0 128.7 208.2 278.2 336.9 416.4 486.4 545.1 624.6 704.1 774.1 832.8 912.3 982.3 1041.0 1120.5 1200.0 357.7 : 58.7 138.2 208.2 266.9 346.4 416.4 475.1 554.6 634.1 704.1 762.8 842.3 912.3 971.0 1050.5 1130.0 1200.0 416.4 : 79.5 149.5 208.2 287.7 357.7 416.4 495.9 575.4 645.4 704.1 783.6 853.6 912.3 991.8 1071.3 1141.3 1200.0 495.9 : 70.0 128.7 208.2 278.2 336.9 416.4 495.9 565.9 624.6 704.1 774.1 832.8 912.3 991.8 1061.8 1120.5 1200.0 565.9 : 58.7 138.2 208.2 266.9 346.4 425.9 495.9 554.6 634.1 704.1 762.8 842.3 921.8 991.8 1050.5 1130.0 1200.0 624.6 : 79.5 149.5 208.2 287.7 367.2 437.2 495.9 575.4 645.4 704.1 783.6 863.1 933.1 991.8 1071.3 1141.3 1200.0 704.1 : 70.0 128.7 208.2 287.7 357.7 416.4 495.9 565.9 624.6 704.1 783.6 853.6 912.3 991.8 1061.8 1120.5 1200.0 774.1 : 58.7 138.2 217.7 287.7 346.4 425.9 495.9 554.6 634.1 713.6 783.6 842.3 921.8 991.8 1050.5 1130.0 1200.0 832.8 : 79.5 159.0 229.0 287.7 367.2 437.2 495.9 575.4 654.9 724.9 783.6 863.1 933.1 991.8 1071.3 1141.3 1200.0 912.3 : 79.5 149.5 208.2 287.7 357.7 416.4 495.9 575.4 645.4 704.1 783.6 853.6 912.3 991.8 1061.8 1120.5 1200.0 991.8 : 70.0 128.7 208.2 278.2 336.9 416.4 495.9 565.9 624.6 704.1 774.1 832.8 912.3 982.3 1041.0 1120.5 1200.0 1061.8: 58.7 138.2 208.2 266.9 346.4 425.9 495.9 554.6 634.1 704.1 762.8 842.3 912.3 971.0 1050.5 1130.0 1200.0 1120.5: 79.5 149.5 208.2 287.7 367.2 437.2 495.9 575.4 645.4 704.1 783.6 853.6 912.3 991.8 1071.3 1141.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6797 .. 79.5220 cents 20.84228 cents 58.67969 cents 2: 128.6692 .. 159.0439 cents 30.37470 cents 49.14727 cents 3: 208.1912 .. 229.0335 cents 20.84228 cents 49.14727 cents 4: 266.8709 .. 287.7132 cents 20.84227 cents 37.83742 cents 5: 336.8605 .. 367.2351 cents 30.37469 cents 49.14728 cents 6: 416.3824 .. 437.2247 cents 20.84228 cents 49.14728 cents 7: 475.0621 .. 495.9044 cents 20.84227 cents 37.83741 cents 8: 545.0517 .. 575.4264 cents 30.37470 cents 49.14728 cents 9: 624.5736 .. 654.9483 cents 30.37469 cents 49.14727 cents 10: 704.0956 .. 724.9379 cents 20.84227 cents 49.14728 cents 11: 762.7753 .. 783.6176 cents 20.84228 cents 37.83742 cents 12: 832.7649 .. 863.1396 cents 30.37470 cents 49.14727 cents 13: 912.2868 .. 933.1291 cents 20.84228 cents 49.14727 cents 14: 970.9665 .. 991.8088 cents 20.84228 cents 37.83741 cents 15: 1040.9561 .. 1071.3308 cents 30.37470 cents 49.14727 cents 16: 1120.4780 .. 1141.3203 cents 20.84228 cents 49.14727 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 58.67969 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 79.52197 cents Average / Smallest step : 1.202942 Largest / Average step : 1.126561 Largest / Smallest step : 1.355187 Median interval of one step : 69.98955 cents, amount: 5 Most common interval of one step : 79.52197 cents, amount: 7 Least squares average step : 70.34059 cents, oct.: 1195.79004 cents Scale is strictly proper Step pattern alph. order: ABCCABCABCABCCABC Step pattern size order : MSLLMSLMSLMSLLMSL Scale is a Constant Structure, by a margin of 37.83741 cents Scale diversity : 1.237424 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.674441 Number of different interval sizes : 54 = 3.37500 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.37500 = 27/8 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 9.53241 cents Most common intervals : 495.90439 cents & inv., amount: 15 Most common triad is 0.0 495.904 704.096 cents, amount: 13 Number of recognisable fifths : 16, average 704.6914 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 7 = 41.1765% Limited transpositions with margin 30.3747 cents: 1 11 Limited inverse transpositions with margin 30.3747 cents: 3 6 10 13 16 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.5751 c. M:-14.2940 c. 40: 2 2 3 3 2 2 3 2 2 2 3 2 2 3 2 2 3 P D3 SD: 8.6833 c. M:-14.0956 c. 41: 2 2 3 3 2 2 3 2 2 3 2 2 3 3 2 2 3 SP D3 S SD: 8.0642 c. M: 13.2527 c. 45: 3 2 3 3 2 3 3 2 2 3 3 2 3 3 3 2 3 SP D3 SD: 7.3565 c. M: 11.2403 c. 46: 3 2 3 3 3 2 3 3 2 3 3 2 3 3 3 2 3 SP M ME I SD: 4.4460 c. M:-8.5235 c. 58: 3 3 4 4 3 3 4 3 3 4 3 3 4 4 3 3 4 SP D3 S SD: 4.6021 c. M: 8.5679 c. 63: 4 3 4 4 4 3 4 4 3 4 4 3 4 4 4 3 4 SP M ME I SD: 3.8683 c. M:-6.8672 c. 75: 4 4 5 5 4 4 5 4 4 5 4 4 5 5 4 4 5 SP D3 S SD: 3.2156 c. M: 6.0852 c. 87: 5 4 6 6 5 4 6 5 4 6 5 4 6 6 5 4 6 SP SD: 2.3794 c. M: 5.1786 c. 96: 6 4 7 6 6 4 7 5 5 6 6 5 6 6 6 5 6 SP SD: 3.4584 c. M:-5.0105 c. 101: 6 5 7 6 6 5 7 6 5 6 6 5 7 6 6 5 7 SP SD: 3.3164 c. M: 5.6702 c. 102: 6 5 7 6 6 5 7 6 5 7 6 5 6 7 6 5 7 SP T3 SD: 3.2361 c. M: 6.4045 c. 104: 6 5 7 7 6 5 7 6 5 7 6 5 7 7 6 5 7 SP SD: 0.9544 c. M: 1.9956 c. 121: 7 6 8 8 7 6 8 7 6 8 7 6 8 8 7 6 8 SP SD: 0.3543 c. M: 0.6779 c. 346: 20 17 23 23 20 17 23 20 17 23 20 17 23 23 20 17 23 SP SD: 0.3609 c. M: 0.6748 c. 392: 23 19 26 26 23 19 26 23 19 26 23 19 26 26 23 19 26 SP SD: 0.2401 c. M:-0.4605 c. 513: 30 25 34 34 30 25 34 30 25 34 30 25 34 34 30 25 34 SP SD: 0.1022 c. M:-0.1920 c. 634: 37 31 42 42 37 31 42 37 31 42 37 31 42 42 37 31 42 SP SD: 0.0279 c. M:-0.0473 c. 2023: 118 99 134 134 118 99 134 118 99 134 118 99 134 134 118 99 134 SP SD: 0.0264 c. M:-0.0577 c. 2127: 124 104 141 141 124 104 141 124 104 141 124 104 141 141 124 104 141 SP SD: 0.0243 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: 9.3367 cents 4 .. 8 match: 4 H SD: 9.1903 cents 5 .. 10 match: 5 H SD: 9.1326 cents 6 .. 12 match: 6 H SD: 6.1873 cents 7 .. 14 match: 7 H SD: 5.5903 cents 8 .. 16 match: 8 H SD: 6.0507 cents 9 .. 18 match: 9 H SD: 5.1886 cents 10 .. 20 match: 10 H SD: 7.0482 cents 11 .. 22 match: 11 H SD: 6.1560 cents 12 .. 24 match: 12 H SD: 5.1260 cents 13 .. 26 match: 13 H SD: 5.2036 cents 14 .. 28 match: 14 H SD: 4.6791 cents 15 .. 30 match: 14 SD: 5.8499 cents 16 .. 32 match: 15 S SD: 4.3680 cents 17 .. 34 match: 15 S SD: 5.8200 cents 18 .. 36 match: 16 S SD: 3.6731 cents 19 .. 38 match: 16 SD: 5.0946 cents 20 .. 40 match: 16 SD: 5.1247 cents 21 .. 42 match: 17 SD: 3.5574 cents 22 .. 44 match: 17 SD: 3.5320 cents 23 .. 46 match: 17 SD: 2.9100 cents 26 .. 52 match: 17 SD: 2.3572 cents 39 .. 78 match: 17 SD: 1.6688 cents 44 .. 88 match: 17 SD: 1.6573 cents 48 .. 96 match: 17 SD: 1.3972 cents 52 .. 104 match: 17 SD: 1.3418 cents 55 .. 110 match: 17 SD: 1.3036 cents 62 .. 124 match: 17 SD: 1.2455 cents 65 .. 130 match: 17 SD: 1.1968 cents 66 .. 132 match: 17 SD: 1.0835 cents 76 .. 152 match: 17 SD: 0.9939 cents 78 .. 156 match: 17 SD: 0.5460 cents 117 .. 234 match: 17 SD: 0.5260 cents 143 .. 286 match: 17 SD: 0.4882 cents 144 .. 288 match: 17 SD: 0.4674 cents 165 .. 330 match: 17 SD: 0.4111 cents 166 .. 332 match: 17 SD: 0.4093 cents 170 .. 340 match: 17 SD: 0.3950 cents 193 .. 386 match: 17 SD: 0.3860 cents 195 .. 390 match: 17 SD: 0.3585 cents 209 .. 418 match: 17 SD: 0.3237 cents 217 .. 434 match: 17 SD: 0.3143 cents 235 .. 470 match: 17 SD: 0.2861 cents 243 .. 486 match: 17 SD: 0.2586 cents 283 .. 566 match: 17 SD: 0.2551 cents 287 .. 574 match: 17 SD: 0.1886 cents 389 .. 778 match: 17 SD: 0.1766 cents 392 .. 784 match: 17 SD: 0.1679 cents 414 .. 828 match: 17 SD: 0.1633 cents 415 .. 830 match: 17 SD: 0.1590 cents 431 .. 862 match: 17 SD: 0.1417 cents 437 .. 874 match: 17 SD: 0.1309 cents 530 .. 1060 match: 17 SD: 0.1282 cents 548 .. 1096 match: 17 SD: 0.1201 cents 580 .. 1160 match: 17 SD: 0.1119 cents