Scala analysis: variant-on-marcel_12
Expansion of Marcel de Velde's JI tuning, TL #90805 (9 July 2010)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 13/12 138.572661 tridecimal 2/3-tone 3: 7/6 266.870906 septimal minor third 4: 11/9 347.407941 undecimal neutral third 5: 4/3 498.044999 perfect fourth 6: 13/9 636.617660 tridecimal diminished fifth 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 13/8 840.527662 tridecimal neutral sixth 10: 7/4 968.825906 harmonic seventh 11: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 117/112 75.6118 3: 14/13 128.2982 2/3-tone 4: 22/21 80.5370 undecimal minor semitone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 13/12 138.5727 tridecimal 2/3-tone 7: 27/26 65.3373 tridecimal comma 8: 28/27 62.9609 Archytas' 1/3-tone 9: 117/112 75.6118 10: 14/13 128.2982 2/3-tone 11: 22/21 80.5370 undecimal minor semitone 12: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 27/26 65.337 cents tridecimal comma 1: 2 117/112 75.612 cents 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 14/13 128.298 cents 2/3-tone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 14/13 128.298 cents 2/3-tone 2: 2 13/12 138.573 cents tridecimal 2/3-tone 2: 3 9/8 203.910 cents major whole tone 2: 2 44/39 208.835 cents 2: 1 112/99 213.598 cents 2: 2 8/7 231.174 cents septimal whole tone 2: 1 13/11 289.210 cents tridecimal minor third 3: 1 9/8 203.910 cents major whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 2 33/28 284.447 cents undecimal minor third 3: 1 13/11 289.210 cents tridecimal minor third 3: 1 32/27 294.135 cents Pythagorean minor third 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 2 16/13 359.472 cents tridecimal neutral third 3: 1 26/21 369.747 cents 4: 1 63/52 332.208 cents 4: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 4: 2 11/9 347.408 cents undecimal neutral third 4: 1 26/21 369.747 cents 4: 2 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 448/351 422.433 cents 4: 3 9/7 435.084 cents septimal major third, BP third 4: 1 4/3 498.045 cents perfect fourth 5: 1 33/26 412.745 cents tridecimal major third 5: 1 21/16 470.781 cents narrow fourth 5: 1 117/88 493.120 cents tridecimal gentle fourth 5: 7 4/3 498.045 cents perfect fourth 5: 1 18/13 563.382 cents tridecimal augmented fourth 5: 1 39/28 573.657 cents 6: 1 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 112/81 561.006 cents 6: 1 18/13 563.382 cents tridecimal augmented fourth 6: 2 39/28 573.657 cents 6: 1 88/63 578.582 cents 6: 1 63/44 621.418 cents 6: 2 56/39 626.343 cents 6: 1 13/9 636.618 cents tridecimal diminished fifth 6: 1 81/56 638.994 cents 6: 1 16/11 648.682 cents undecimal semi-diminished fifth 7: 1 56/39 626.343 cents 7: 1 13/9 636.618 cents tridecimal diminished fifth 7: 7 3/2 701.955 cents perfect fifth 7: 1 176/117 706.880 cents 7: 1 32/21 729.219 cents wide fifth 7: 1 52/33 787.255 cents tridecimal minor sixth 8: 1 3/2 701.955 cents perfect fifth 8: 3 14/9 764.916 cents septimal minor sixth 8: 1 351/224 777.567 cents 8: 2 11/7 782.492 cents undecimal augmented fifth 8: 1 21/13 830.253 cents 8: 2 18/11 852.592 cents undecimal neutral sixth 8: 1 64/39 857.517 cents 39th subharmonic 8: 1 104/63 867.792 cents 9: 1 21/13 830.253 cents 9: 2 13/8 840.528 cents tridecimal neutral sixth 9: 1 44/27 845.453 cents neutral sixth 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 1 22/13 910.790 cents tridecimal major sixth 9: 2 56/33 915.553 cents 9: 3 12/7 933.129 cents septimal major sixth 9: 1 16/9 996.090 cents Pythagorean minor seventh 10: 1 22/13 910.790 cents tridecimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 1 99/56 986.402 cents 10: 2 39/22 991.165 cents 10: 3 16/9 996.090 cents Pythagorean minor seventh 10: 2 24/13 1061.427 cents tridecimal neutral seventh 10: 1 13/7 1071.702 cents 16/3-tone 11: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 1 24/13 1061.427 cents tridecimal neutral seventh 11: 2 13/7 1071.702 cents 16/3-tone 11: 2 21/11 1119.463 cents undecimal major seventh 11: 2 224/117 1124.388 cents 11: 1 52/27 1134.663 cents 11: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 7.45455 = 82/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 63.0 138.6 266.9 347.4 498.0 636.6 702.0 764.9 840.5 968.8 1049.4 1200.0 63.0 : 75.6 203.9 284.4 435.1 573.7 639.0 702.0 777.6 905.9 986.4 1137.0 1200.0 138.6 : 128.3 208.8 359.5 498.0 563.4 626.3 702.0 830.3 910.8 1061.4 1124.4 1200.0 266.9 : 80.5 231.2 369.7 435.1 498.0 573.7 702.0 782.5 933.1 996.1 1071.7 1200.0 347.4 : 150.6 289.2 354.5 417.5 493.1 621.4 702.0 852.6 915.6 991.2 1119.5 1200.0 498.0 : 138.6 203.9 266.9 342.5 470.8 551.3 702.0 764.9 840.5 968.8 1049.4 1200.0 636.6 : 65.3 128.3 203.9 332.2 412.7 563.4 626.3 702.0 830.3 910.8 1061.4 1200.0 702.0 : 63.0 138.6 266.9 347.4 498.0 561.0 636.6 764.9 845.5 996.1 1134.7 1200.0 764.9 : 75.6 203.9 284.4 435.1 498.0 573.7 702.0 782.5 933.1 1071.7 1137.0 1200.0 840.5 : 128.3 208.8 359.5 422.4 498.0 626.3 706.9 857.5 996.1 1061.4 1124.4 1200.0 968.8 : 80.5 231.2 294.1 369.7 498.0 578.6 729.2 867.8 933.1 996.1 1071.7 1200.0 1049.4: 150.6 213.6 289.2 417.5 498.0 648.7 787.3 852.6 915.6 991.2 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 150.6371 cents 81/77, 87.6762 cents 28/27, 62.9609 cents 2: 128.2982 .. 289.2097 cents 169/154, 160.9115 cents 77/78,-22.3388 cents 3: 203.9100 .. 369.7468 cents 208/189, 165.8368 cents 99/104,-85.2997 cents 4: 332.2082 .. 498.0450 cents 208/189, 165.8368 cents 1323/1352,-37.5385 cents 5: 412.7453 .. 573.6568 cents 169/154, 160.9115 cents 99/104,-85.2997 cents 6: 551.3179 .. 648.6821 cents 128/121, 97.3641 cents 77/78,-22.3388 cents 7: 626.3432 .. 787.2547 cents 169/154, 160.9115 cents 77/78,-22.3388 cents 8: 701.9550 .. 867.7918 cents 208/189, 165.8368 cents 99/104,-85.2997 cents 9: 830.2532 .. 996.0900 cents 208/189, 165.8368 cents 1323/1352,-37.5385 cents 10: 910.7903 .. 1071.7018 cents 169/154, 160.9115 cents 99/104,-85.2997 cents 11: 1049.3629 .. 1137.0391 cents 81/77, 87.6762 cents 77/78,-22.3388 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 12/11, 150.6371 cents Average / Smallest step : 1.588287 Largest / Average step : 1.506371 Largest / Smallest step : 2.392549 Median interval of one step : 22/21, 80.5370 cents, amount: 2 Least squares average step : 97.02968 cents, oct.: 1164.35620 cents Scale is not proper Step pattern alph. order: ABCDEFGABCDE Step pattern size order : ACEDGFBACEDG Scale is not a Constant Structure Scale diversity : 1.421443 Lumma stability : 0.104935 Lumma impropriety factor : 0.421359 Rothenberg efficiency : 0.317508 redundancy: 0.682492 Efficiency x scale size : 3.810101 Number of different interval sizes : 66 = 6.00000 / class Number of one step interval sizes : 7 Highest interval variety : 10 Mean interval variety : 7.45455 = 82/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 729/728, 2.3764 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 9, average 702.5023 cents Scale contains two identical disjunct hexachords Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 7 and 8 combined -- Rational properties -- Prime limit : 13 Odd number limit : 351 (O: 351 U: 351) Highest odd numerator or denominator: 27 Scale harmonicity : 0.015086 Average absolute harmonicity : 0.162605 Specific harmonicity : 0.091670 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 12012, 13.5522 octaves, 3142646.290 Hz. Exponens Consonantiae : 2.594592E+06, 21.30708 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 111.0, average 9.25000 Mersenne's string divisions : 117417300 Sum of van Prooijen's expressibility: 10.45466, average 0.87122 Sum of Tenney's harmonic distance : 20.30119, average 1.69177 Vogel's harmonic complexity : 16.08333 Wille's k value : 175 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 211.12098, average 2.70668 Lattice compactness (without 2's) : 137.37762, average 1.76125 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.33333 16 1 3: -3 .. 1 -1.00000 14 2 7: 0 .. 1 0.33333 4 4 11: 0 .. 1 0.16667 2 2 13: 0 .. 1 0.25000 3 3 Average exponent except 2's :-3 / 12 =-0.25000 Average absolute exponent except 2's: 23 / 12 = 1.91667 Scale is weakly epimorphic with val: <12 19 34 40 42| Scale is weakly epimorphic with val: <12 19 35 41 44| Scale is weakly epimorphic with val: <12 19 35 44 46| Scale is weakly epimorphic with val: <12 19 37 40 46|
FIT/MODE
12: 0 1 1 1 2 1 1 0 1 1 1 2 N T3 SD: 47.0372 c. M: 68.8259 c. 14: 1 1 1 1 2 1 1 1 1 1 1 2 P D3 S SD: 20.4248 c. M: 36.6177 c. 16: 1 1 2 1 2 2 0 1 1 2 1 2 N SD: 21.5307 c. M:-38.3823 c. 17: 1 1 2 1 2 2 1 1 1 2 1 2 N D3 SD: 9.1754 c. M:-19.4094 c. 24: 1 2 2 2 3 3 1 1 2 2 2 3 N SD: 10.9684 c. M: 18.8259 c. 27: 1 2 3 2 3 3 2 1 2 3 2 3 N SD: 10.3849 c. M: 18.5165 c. 31: 2 2 3 2 4 4 1 2 2 3 2 4 N SD: 10.1358 c. M:-21.4469 c. 32: 2 2 3 2 4 4 2 1 2 4 2 4 N SD: 9.6527 c. M: 15.5277 c. 36: 2 2 4 2 5 4 2 2 2 4 2 5 N SD: 6.9173 c. M: 16.0296 c. 37: 2 2 4 3 4 5 2 2 2 4 2 5 N SD: 9.0126 c. M:-13.4625 c. 38: 2 2 4 3 5 4 2 2 3 4 2 5 N SD: 8.3344 c. M: 14.2393 c. 41: 2 3 4 3 5 5 2 2 3 4 3 5 N SD: 4.7510 c. M:-8.2528 c. 53: 3 3 6 3 7 6 3 3 3 6 3 7 N SD: 4.4639 c. M: 7.8535 c. 58: 3 4 6 4 7 7 3 3 4 6 4 7 N SD: 4.0527 c. M:-7.7482 c. 63: 3 4 7 4 8 7 4 3 4 7 4 8 N SD: 3.9513 c. M: 8.0462 c. 69: 4 4 7 5 9 8 3 4 4 8 4 9 N SD: 5.0020 c. M:-6.8606 c. 70: 4 4 8 4 9 8 4 4 4 8 4 9 N SD: 4.4857 c. M:-8.3170 c. 72: 4 4 8 5 9 8 4 4 4 8 5 9 N SD: 3.2438 c. M: 7.1943 c. 77: 4 5 8 5 10 9 4 4 5 8 5 10 N SD: 2.4252 c. M: 5.2071 c. 89: 5 5 10 6 11 10 5 5 5 10 6 11 N SD: 2.9539 c. M: 4.5726 c. 94: 5 6 10 6 12 11 5 5 6 10 6 12 N SD: 1.5710 c. M: 2.7271 c. 113: 6 7 12 8 14 13 6 6 7 12 8 14 N SD: 1.5019 c. M:-3.0345 c. 130: 7 8 14 9 16 15 7 7 8 14 9 16 N SD: 1.4666 c. M:-3.3613 c. 166: 9 10 18 11 21 19 9 9 10 18 11 21 N SD: 1.1141 c. M:-2.0993 c. 176: 9 11 19 12 22 20 10 9 11 19 12 22 N SD: 1.3254 c. M: 2.5268 c. 190: 10 12 20 13 24 22 10 10 12 20 13 24 N SD: 1.0797 c. M: 2.5101 c. 207: 11 13 22 14 26 24 11 11 13 22 14 26 N SD: 0.5344 c. M:-1.0635 c. 270: 14 17 29 18 34 31 15 14 17 29 18 34 N SD: 0.5604 c. M: 1.0621 c. 311: 16 20 33 21 39 36 17 16 20 33 21 39 N SD: 0.5481 c. M: 1.2246 c. 328: 17 21 35 22 41 38 18 17 21 35 22 41 N SD: 0.5129 c. M:-0.9358 c. 383: 20 24 41 26 48 44 21 20 24 41 26 48 N SD: 0.4855 c. M: 0.8410 c. 400: 21 25 43 27 50 46 22 21 25 43 27 50 N SD: 0.3877 c. M:-0.6371 c. 477: 25 30 51 32 60 55 26 25 30 51 32 60 N SD: 0.1910 c. M: 0.3063 c. 701: 37 44 75 47 88 81 38 37 44 75 47 88 N SD: 0.1652 c. M:-0.3772 c. 805: 42 51 86 54 101 93 44 42 51 86 54 101 N SD: 0.1580 c. M: 0.3522 c. 971: 51 61 104 65 122 112 53 51 61 104 65 122 N SD: 0.1049 c. M: 0.1604 c. 1012: 53 64 108 68 127 117 55 53 64 108 68 127 N SD: 0.0972 c. M:-0.1838 c. 1178: 62 74 126 79 148 136 64 62 74 126 79 148 N SD: 0.0944 c. M:-0.1970 c. 1282: 67 81 137 86 161 148 70 67 81 137 86 161 N SD: 0.1121 c. M: 0.2464 c. 1412: 74 89 151 95 177 163 77 74 89 151 95 177 N SD: 0.0893 c. M:-0.2121 c. 1489: 78 94 159 100 187 172 81 78 94 159 100 187 N SD: 0.0730 c. M: 0.1221 c. 1506: 79 95 161 101 189 174 82 79 95 161 101 189 N SD: 0.0556 c. M:-0.1098 c. 1889: 99 119 202 127 237 218 103 99 119 202 127 237 N SD: 0.0659 c. M: 0.0904 c. 1983: 104 125 212 133 249 229 108 104 125 212 133 249 N SD: 0.0234 c. M: 0.0554 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 14.6104 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.7264 cents 5 x x x 6 x 7 x x 8 x 9:10 S SD: 15.0547 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.3052 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 12.5247 cents 8 x x 9:10:11 x 12 x 13:14:15:16 S SD: 12.3929 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 9.4652 cents 10 x 11 x 12:13:14:15 x 16 x 18:20 S SD: 11.3784 cents 11 x 12:13 x 15:16 x 17:18:19:20:22 SD: 6.3781 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 6.7444 cents 13 x 14:15:16:17:19 x 20:21:23:24:26 SD: 5.6010 cents 14 x 15:16:17:19:20:21:22:23:25:26:28 SD: 6.7184 cents 15 x 16 x 18:20:22 x 23:24:26:28:30 S SD: 7.8699 cents 16 x 17:19:20:21:23:24:25:26:28:29:32 SD: 6.3289 cents 17:18 x 20:21:23:25 x 26:28:30:31:34 SD: 7.1762 cents 18:19:20:21:22:24:26:27:28:29:32:33:36 SD: 5.1534 cents 22:23:24:26:27:29:32:33:34:36:39:40:44 SD: 4.0881 cents 23:24:25:27:28:31:33:35:36:37:40:42:46 SD: 3.7260 cents 24:25:26:28:29:32:35:36:37:39:42:44:48 SD: 2.5907 cents 36:37:39:42:44:48:52:54:56:59:63:66:72 SD: 1.7838 cents 48:50:52:56:59:64:69:72:75:78:84:88:96 SD: 1.4062 cents 59:61:64:69:72:79:85:89:92:96:103:108:118 SD: 1.3789 cents 60:62:65:70:73:80:87:90:93:98:105:110:120 SD: 1.3476 cents 72:75:78:84:88:96:104:108:112:117:126:132:144 SD: 0.6426 cents 108:112:117:126:132:144:156:162:168:176:189:198:216 SD: 0.4104 cents 144:149:156:168:176:192:208:216:224:234:252:264:288 SD: 0.3224 cents 216:224:234:252:264:288:312:324:336:351:378:396:432 SD: 0.0000 cents