Scala analysis: 001_H1
Hyperenharmonic tetrachord 80/79 * 79/78 * 13/10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80/79 21.776816 2: 40/39 43.831051 tridecimal minor diesis 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/10 454.2139 tridecimal semi-diminished fourth 1: 80/79 21.7768 2: 79/78 22.0542 3: 13/10 454.2139 tridecimal semi-diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 80/79 21.777 cents 1: 1 79/78 22.054 cents 1: 1 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 40/39 43.831 cents tridecimal minor diesis 2: 1 104/79 475.991 cents 2: 1 79/60 476.268 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 21.8 43.8 498.0 21.8 : 22.1 476.3 498.0 43.8 : 454.2 476.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.7768 .. 454.2139 cents 1027/800, 432.4371 cents 80/79, 21.7768 cents 2: 43.8311 .. 476.2682 cents 1027/800, 432.4371 cents 400/507,-410.3829 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 80/79, 21.7768 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/10, 454.2139 cents Average / Smallest step : 7.623474 Largest / Average step : 2.735981 Largest / Smallest step : 20.857684 Median interval of one step : 79/78, 22.0542 cents, amount: 1 Least squares average step : 114.54099 cents, oct.: 343.62298 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1761-tone equal temperament with octave 4/3 degrees: 77 155 1761 Least number of segments generator : 881 of 249.164 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1225 of 346.454 cents and inv. generated superset size: 44 = 41 more = 1466.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 21.77682 cents Scale diversity : 0.020593 Lumma stability : 0.087449 Lumma impropriety factor : 0.823988 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 6241/6240, 0.2774 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 432.1597 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 79 Odd number limit : 79 (O: 79 U: 79) Highest odd numerator or denominator: 79 Scale harmonicity : 0.028393 Fundamental : 1/3081, -11.5892 octaves, 0.0849 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 2.464800E+05, 17.91111 octaves Euler's gradus suavitatis : 101 Sum of Mann's harmonic distance : 122.5, average 40.83333 Mersenne's string divisions : 87927 Sum of van Prooijen's expressibility: 3.96581, average 1.32194 Sum of Tenney's harmonic distance : 8.07302, average 2.69101 Vogel's harmonic complexity : 68.66667 Wille's k value : 513 Wilson's harmonic complexity : 100 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 15.73687, average 2.62281 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 79: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 17 25 46| Scale is weakly epimorphic with val: <7 10 18 26 47| Scale is weakly epimorphic with val: <7 10 19 27 45| Scale is weakly epimorphic with val: <7 11 15 26 45| Scale is weakly epimorphic with val: <7 11 15 27 47| Scale is weakly epimorphic with val: <7 11 15 29 45| Scale is weakly epimorphic with val: <7 11 15 30 47| Scale is weakly epimorphic with val: <7 11 16 25 45| Scale is weakly epimorphic with val: <7 11 16 27 46| Scale is weakly epimorphic with val: <7 11 16 28 45| Scale is weakly epimorphic with val: <7 11 16 30 46| Scale is weakly epimorphic with val: <7 11 17 25 47| Scale is weakly epimorphic with val: <7 11 17 26 46| Scale is weakly epimorphic with val: <7 11 17 28 47| Scale is weakly epimorphic with val: <7 11 17 29 46| Scale is JI-epimorphic with val: <7 11 18 26 45| Scale is weakly epimorphic with val: <7 11 18 27 47| Scale is weakly epimorphic with val: <7 11 18 29 45| Scale is weakly epimorphic with val: <7 11 18 30 47| Scale is weakly epimorphic with val: <7 11 19 25 45| Scale is JI-epimorphic with val: <7 11 19 27 46| Scale is weakly epimorphic with val: <7 11 19 28 45| Scale is weakly epimorphic with val: <7 11 19 30 46| Scale is weakly epimorphic with val: <7 12 19 25 46| Scale is weakly epimorphic with val: <8 11 15 25 46| Scale is weakly epimorphic with val: <8 11 16 25 45| Scale is weakly epimorphic with val: <8 11 16 26 47| Scale is weakly epimorphic with val: <8 11 16 28 45| Scale is weakly epimorphic with val: <8 11 17 26 46| Scale is weakly epimorphic with val: <8 11 17 27 45| Scale is weakly epimorphic with val: <8 11 17 29 46| Scale is weakly epimorphic with val: <8 11 18 27 47| Scale is weakly epimorphic with val: <8 11 18 28 46| Scale is weakly epimorphic with val: <8 11 18 30 47| Scale is weakly epimorphic with val: <8 11 19 29 47| Scale is weakly epimorphic with val: <8 12 16 25 46| Scale is weakly epimorphic with val: <8 12 16 26 45| Scale is weakly epimorphic with val: <8 12 16 29 45| Scale is weakly epimorphic with val: <8 12 17 26 47| Scale is weakly epimorphic with val: <8 12 17 27 46| Scale is weakly epimorphic with val: <8 12 17 30 46| Scale is weakly epimorphic with val: <8 12 18 25 47| Scale is weakly epimorphic with val: <8 12 18 27 45| Scale is weakly epimorphic with val: <8 12 18 28 47| Scale is weakly epimorphic with val: <8 12 19 28 46|
FIT/MODE
3: 0 0 3 N M DE S SD: 28.2571 c. M: 43.8311 c. 8: 0 1 7 N G T3 SD: 16.4691 c. M: 21.7768 c. 9: 0 1 8 N G T3 SD: 14.2203 c. M: 21.7768 c. 10: 0 1 9 N G T3 SD: 13.0373 c. M: 21.7768 c. 11: 0 1 10 N G T3 SD: 12.6005 c. M: 21.7768 c. 12: 0 1 11 N G T3 SD: 12.6444 c. M: 21.7768 c. 13: 0 1 12 N G T3 SD: 12.9705 c. M: 21.7768 c. 14: 0 1 13 N G T3 SD: 13.4462 c. M: 21.7768 c. 15: 0 1 14 N G T3 SD: 13.9903 c. M: 21.7768 c. 16: 1 0 15 N G T3 SD: 9.1070 c. M: 12.7032 c. 17: 1 1 15 N M DE S SD: 9.5652 c. M:-14.7625 c. 18: 1 1 16 N M DE S SD: 7.4641 c. M:-11.5073 c. 19: 1 1 17 N M DE S SD: 5.5842 c. M:-8.5947 c. 20: 1 1 18 N M DE S SD: 3.8923 c. M:-5.9734 c. 21: 1 1 19 N M DE S SD: 2.3619 c. M:-3.6018 c. 22: 1 1 20 N M DE S SD: 0.9717 c. M:-1.4458 c. 23: 1 1 21 N M DE S SD: 0.3100 c. M: 0.5228 c. 45: 2 2 41 N M DE S SD: 0.3275 c. M:-0.4396 c. 68: 3 3 62 N M DE S SD: 0.1308 c. M:-0.1958 c. 91: 4 4 83 N M DE S SD: 0.0718 c. M:-0.1153 c. 205: 9 9 187 N M DE S SD: 0.0772 c. M: 0.1003 c. 250: 11 11 228 N M DE S SD: 0.0792 c. M:-0.1372 c. 296: 13 13 270 N M DE S SD: 0.0739 c. M:-0.0968 c. 387: 17 17 353 N M DE S SD: 0.0727 c. M:-0.1011 c. 478: 21 21 436 N M DE S SD: 0.0722 c. M:-0.1038 c. 501: 22 22 457 N M DE S SD: 0.0751 c. M:-0.0934 c. 523: 23 23 477 N M DE S SD: 0.0741 c. M:-0.1257 c. 569: 25 25 519 N M DE S SD: 0.0720 c. M:-0.1057 c. 659: 29 29 601 N M DE S SD: 0.0810 c. M:-0.1402 c. 660: 29 29 602 N M DE S SD: 0.0718 c. M:-0.1070 c. 706: 31 31 644 N M DE S SD: 0.0757 c. M: 0.0934 c. 751: 33 33 685 N M DE S SD: 0.0717 c. M:-0.1080 c. 842: 37 37 768 N M DE S SD: 0.0717 c. M:-0.1088 c. 909: 40 40 829 N M DE S SD: 0.0805 c. M:-0.1394 c. 911: 40 40 831 N M DE S SD: 0.0760 c. M: 0.0949 c. 919: 40 41 838 N T3 SD: 0.0688 c. M: 0.0991 c. 920: 40 41 839 N T3 SD: 0.0716 c. M: 0.1227 c. 942: 41 42 859 N T3 SD: 0.0649 c. M: 0.0997 c. 943: 41 42 860 N T3 SD: 0.0709 c. M: 0.1227 c. 964: 42 43 879 N T3 SD: 0.0660 c. M:-0.0837 c. 965: 42 43 880 N T3 SD: 0.0619 c. M: 0.1002 c. 966: 42 43 881 N T3 SD: 0.0710 c. M: 0.1227 c. 987: 43 44 900 N T3 SD: 0.0607 c. M: 0.0788 c. 988: 43 44 901 N T3 SD: 0.0600 c. M: 0.1008 c. 989: 43 44 902 N T3 SD: 0.0717 c. M: 0.1227 c. 1009: 44 45 920 N T3 SD: 0.0666 c. M:-0.0996 c. 1010: 44 45 921 N T3 SD: 0.0563 c. M: 0.0798 c. 1011: 44 45 922 N T3 SD: 0.0589 c. M: 0.1013 c. 1033: 45 46 942 N T3 SD: 0.0529 c. M: 0.0808 c. 1034: 45 46 943 N T3 SD: 0.0587 c. M: 0.1017 c. 1055: 46 47 962 N T3 SD: 0.0547 c. M:-0.0724 c. 1056: 46 47 963 N T3 SD: 0.0504 c. M: 0.0817 c. 1057: 46 47 964 N T3 SD: 0.0593 c. M: 0.1022 c. 1078: 47 48 983 N T3 SD: 0.0499 c. M: 0.0624 c. 1079: 47 48 984 N T3 SD: 0.0489 c. M: 0.0825 c. 1101: 48 49 1004 N T3 SD: 0.0459 c. M: 0.0637 c. 1102: 48 49 1005 N T3 SD: 0.0484 c. M: 0.0834 c. 1124: 49 50 1025 N T3 SD: 0.0428 c. M: 0.0649 c. 1125: 49 50 1026 N T3 SD: 0.0486 c. M: 0.0842 c. 1146: 50 51 1045 N T3 SD: 0.0454 c. M:-0.0630 c. 1147: 50 51 1046 N T3 SD: 0.0407 c. M: 0.0660 c. 1169: 51 52 1066 N T3 SD: 0.0409 c. M:-0.0514 c. 1170: 51 52 1067 N T3 SD: 0.0396 c. M: 0.0672 c. 1192: 52 53 1087 N T3 SD: 0.0371 c. M: 0.0500 c. 1193: 52 53 1088 N T3 SD: 0.0394 c. M: 0.0682 c. 1215: 53 54 1108 N T3 SD: 0.0343 c. M: 0.0514 c. 1216: 53 54 1109 N T3 SD: 0.0402 c. M: 0.0693 c. 1237: 54 55 1128 N T3 SD: 0.0376 c. M:-0.0549 c. 1238: 54 55 1129 N T3 SD: 0.0324 c. M: 0.0527 c. 1260: 55 56 1149 N T3 SD: 0.0333 c. M:-0.0443 c. 1261: 55 56 1150 N T3 SD: 0.0317 c. M: 0.0540 c. 1283: 56 57 1170 N T3 SD: 0.0296 c. M: 0.0383 c. 1284: 56 57 1171 N T3 SD: 0.0319 c. M: 0.0552 c. 1306: 57 58 1191 N T3 SD: 0.0269 c. M: 0.0398 c. 1329: 58 59 1212 N T3 SD: 0.0253 c. M: 0.0412 c. 1351: 59 60 1232 N T3 SD: 0.0268 c. M:-0.0382 c. 1352: 59 60 1233 N T3 SD: 0.0248 c. M: 0.0426 c. 1374: 60 61 1253 N T3 SD: 0.0232 c. M:-0.0288 c. 1375: 60 61 1254 N T3 SD: 0.0254 c. M: 0.0439 c. 1397: 61 62 1274 N T3 SD: 0.0206 c. M: 0.0297 c. 1420: 62 63 1295 N T3 SD: 0.0191 c. M: 0.0312 c. 1443: 63 64 1316 N T3 SD: 0.0189 c. M: 0.0326 c. 1465: 64 65 1336 N T3 SD: 0.0178 c. M:-0.0241 c. 1466: 64 65 1337 N T3 SD: 0.0199 c. M: 0.0341 c. 1488: 65 66 1357 N T3 SD: 0.0150 c. M: 0.0208 c. 1511: 66 67 1378 N T3 SD: 0.0136 c. M: 0.0224 c. 1534: 67 68 1399 N T3 SD: 0.0138 c. M: 0.0239 c. 1556: 68 69 1419 N T3 SD: 0.0133 c. M:-0.0200 c. 1557: 68 69 1420 N T3 SD: 0.0154 c. M: 0.0253 c. 1579: 69 70 1440 N T3 SD: 0.0102 c. M: 0.0130 c. 1602: 70 71 1461 N T3 SD: 0.0088 c. M: 0.0146 c. 1625: 71 72 1482 N T3 SD: 0.0095 c. M: 0.0161 c. 1670: 73 74 1523 N T3 SD: 0.0062 c. M:-0.0088 c. 1693: 74 75 1544 N T3 SD: 0.0045 c. M: 0.0076 c. 1761: 77 78 1606 N T3 SD: 0.0034 c. M:-0.0060 c. 1784: 78 79 1627 N T3 SD: 0.0009 c. M: 0.0013 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 111.5199 cents 7 x 8:9 S SD: 98.8199 cents 8 x 9:11 SD: 84.3553 cents 9 x 10:12 S SD: 69.2863 cents 10 x 11:13 SD: 64.4284 cents 11 x 12:15 S SD: 56.8357 cents 12 x 13:16 SD: 47.3708 cents 13 x 14:17 SD: 45.4555 cents 14 x 15:19 SD: 40.7924 cents 15 x 16:20 S SD: 33.9501 cents 16 x 17:21 SD: 33.4646 cents 17 x 18:23 SD: 30.3207 cents 18 x 19:24 SD: 24.8860 cents 19 x 20:25 S SD: 25.2393 cents 20 x 21:27 SD: 22.9881 cents 21 x 22:28 SD: 18.3530 cents 22 x 23:29 SD: 19.2923 cents 23 x 24:31 SD: 17.6160 cents 24 x 25:32 SD: 13.4207 cents 25 x 26:33 SD: 14.8498 cents 26 x 27:35 SD: 13.5737 cents 27 x 28:36 SD: 9.5649 cents 28 x 29:37 SD: 11.4824 cents 29 x 30:39 SD: 10.5079 cents 30 x 31:40 SD: 6.4679 cents 31 x 32:41 SD: 8.9507 cents 32 x 33:43 SD: 8.2259 cents 33 x 34:44 SD: 3.9257 cents 34 x 35:45 SD: 7.1345 cents 35 x 36:47 SD: 6.6376 cents 36 x 37:48 SD: 1.8015 cents 37 x 38:49 SD: 5.9839 cents 38 x 39:51 SD: 5.7047 cents 39 x 40:52 SD: 0.0000 cents 40 x 41:53 SD: 5.4540 cents 41 x 42:55 SD: 5.3671 cents 42 x 43:56 SD: 1.5471 cents 43 x 44:57 SD: 5.4348 cents 44 x 45:59 SD: 5.4879 cents 45 x 46:60 SD: 2.8902 cents 46 x 47:61 SD: 5.7566 cents 47 x 48:63 SD: 5.8918 cents 48 x 49:64 SD: 4.0671 cents 49 x 50:65 SD: 6.2617 cents 50 x 51:67 SD: 6.4367 cents 51 x 52:68 SD: 5.1069 cents 52 x 53:69 SD: 6.8451 cents 53:54 x 71 SD: 6.6781 cents 54:55 x 72 SD: 4.9949 cents 55:56 x 73 SD: 6.1420 cents 56:57 x 75 SD: 5.8750 cents 57:58 x 76 SD: 4.1662 cents 58:59 x 77 SD: 5.4093 cents 60:61:62:80 SD: 4.8775 cents 62:63:64:83 SD: 4.8025 cents 63:64:65:84 SD: 3.8826 cents 66:67:68:88 SD: 2.9771 cents 69:70:71:92 SD: 2.1495 cents 72:73:74:96 SD: 1.3905 cents 75:76:77:100 SD: 0.6933 cents 78:79:80:104 SD: 0.0925 cents