Scala analysis: xen05-harrison-cinna
Scale for 'Incidental Music for Corneille's "Cinna"'
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 10/9 182.403712 minor whole tone 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 25/18 568.717426 classic augmented fourth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 21/20 84.4672 minor semitone 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 21/20 84.4672 minor semitone 11: 15/14 119.4428 major diatonic semitone 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 2 35/32 155.140 cents septimal neutral second 2: 3 10/9 182.404 cents minor whole tone 2: 3 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 2 8/7 231.174 cents septimal whole tone 2: 1 144/125 244.969 cents classic diminished third 3: 2 7/6 266.871 cents septimal minor third 3: 2 75/64 274.582 cents classic augmented second 3: 1 32/27 294.135 cents Pythagorean minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 5 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 4: 1 56/45 378.602 cents septimal narrow major third 4: 6 5/4 386.314 cents major third 4: 1 63/50 400.108 cents quasi-equal major third 4: 1 80/63 413.578 cents wide major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 5: 1 125/96 456.986 cents classic augmented third 5: 1 21/16 470.781 cents narrow fourth 5: 7 4/3 498.045 cents perfect fourth 5: 2 27/20 519.551 cents acute fourth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 2 25/18 568.717 cents classic augmented fourth 6: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 45/32 590.224 cents diatonic tritone 6: 2 64/45 609.776 cents 2nd tritone 6: 2 10/7 617.488 cents Euler's tritone 6: 2 36/25 631.283 cents classic diminished fifth 7: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 2 40/27 680.449 cents grave fifth 7: 7 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 7: 1 192/125 743.014 cents classic diminished sixth 8: 1 14/9 764.916 cents septimal minor sixth 8: 2 25/16 772.627 cents classic augmented fifth 8: 1 63/40 786.422 cents narrow minor sixth 8: 1 100/63 799.892 cents quasi-equal minor sixth 8: 6 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 5 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 2 128/75 925.418 cents diminished seventh 9: 2 12/7 933.129 cents septimal major sixth 10: 1 125/72 955.031 cents classic augmented sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 1 225/128 976.537 cents augmented sixth 10: 3 16/9 996.090 cents Pythagorean minor seventh 10: 3 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 64/35 1044.860 cents septimal neutral seventh 11: 1 50/27 1066.762 cents grave major seventh 11: 2 28/15 1080.557 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 3 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.63636 = 62/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 182.4 266.9 386.3 498.0 568.7 702.0 813.7 884.4 968.8 1088.3 1200.0 111.7 : 70.7 155.1 274.6 386.3 457.0 590.2 702.0 772.6 857.1 976.5 1088.3 1200.0 182.4 : 84.5 203.9 315.6 386.3 519.6 631.3 702.0 786.4 905.9 1017.6 1129.3 1200.0 266.9 : 119.4 231.2 301.8 435.1 546.8 617.5 702.0 821.4 933.1 1044.9 1115.5 1200.0 386.3 : 111.7 182.4 315.6 427.4 498.0 582.5 702.0 813.7 925.4 996.1 1080.6 1200.0 498.0 : 70.7 203.9 315.6 386.3 470.8 590.2 702.0 813.7 884.4 968.8 1088.3 1200.0 568.7 : 133.2 245.0 315.6 400.1 519.6 631.3 743.0 813.7 898.2 1017.6 1129.3 1200.0 702.0 : 111.7 182.4 266.9 386.3 498.0 609.8 680.4 764.9 884.4 996.1 1066.8 1200.0 813.7 : 70.7 155.1 274.6 386.3 498.0 568.7 653.2 772.6 884.4 955.0 1088.3 1200.0 884.4 : 84.5 203.9 315.6 427.4 498.0 582.5 702.0 813.7 884.4 1017.6 1129.3 1200.0 968.8 : 119.4 231.2 342.9 413.6 498.0 617.5 729.2 799.9 933.1 1044.9 1115.5 1200.0 1088.3: 111.7 223.5 294.1 378.6 498.0 609.8 680.4 813.7 925.4 996.1 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 133.2376 cents 648/625, 62.5651 cents 25/24, 70.6724 cents 2: 155.1396 .. 244.9689 cents 4608/4375, 89.8292 cents 875/864, 21.9020 cents 3: 266.8709 .. 342.9054 cents 256/245, 76.0345 cents 875/864, 21.9020 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 5: 456.9861 .. 546.8154 cents 4608/4375, 89.8292 cents 875/864, 21.9020 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 875/864, 21.9020 cents 7: 653.1846 .. 743.0139 cents 4608/4375, 89.8292 cents 875/864, 21.9020 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 875/864, 21.9020 cents 9: 857.0946 .. 933.1291 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 10: 955.0311 .. 1044.8604 cents 4608/4375, 89.8292 cents 875/864, 21.9020 cents 11: 1066.7624 .. 1129.3276 cents 648/625, 62.5651 cents 875/864, 21.9020 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 27/25, 133.2376 cents Average / Smallest step : 1.414979 Largest / Average step : 1.332376 Largest / Smallest step : 1.885284 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 98.71778 cents, oct.: 1184.61331 cents Scale is strictly proper Step pattern alph. order: ABCDABEABCDA Step pattern size order : CABDCAECABDC Scale is a Constant Structure, by a margin of 21.90205 cents Scale diversity : 1.534306 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.323296 Rothenberg efficiency : 0.297108 redundancy: 0.702892 Efficiency x scale size : 3.565296 Number of different interval sizes : 62 = 5.63636 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.63636 = 62/11 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Number of recognisable fifths : 7, average 701.9550 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Scale contains a complete diamond : 1 3 15 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 58.3333% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 7 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 25 Scale harmonicity : 0.022479 Average absolute harmonicity : 0.188834 Specific harmonicity : 0.151268 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 8400, 13.0362 octaves, 2197654.749 Hz. Exponens Consonantiae : 3.024000E+06, 21.52803 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 92.5, average 7.70833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.44571, average 0.78714 Sum of Tenney's harmonic distance : 18.37480, average 1.53123 Vogel's harmonic complexity : 15.41667 Wille's k value : 337 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 246.75896, average 3.16358 Lattice compactness (without 2's) : 136.86951, average 1.75474 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.08333 21 1 3: -2 .. 1 -0.50000 10 2 5: -1 .. 2 0.33333 8 7 7: 0 .. 1 0.16667 2 2 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 20 / 12 = 1.66667 Scale is JI-epimorphic with val: <12 19 28 34| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.8409 c. M:-33.1291 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 1 2 2 1 2 2 1 1 2 2 P D3 SD: 10.6122 c. M: 21.4575 c. 24: 2 2 1 3 2 1 3 2 2 1 3 2 P T3 SD: 13.5437 c. M: 18.8259 c. 26: 2 2 2 2 3 1 3 3 1 2 3 2 P SD: 12.6059 c. M:-19.4236 c. 27: 3 1 2 3 2 2 3 2 2 2 3 2 P D3 SD: 12.0240 c. M:-22.8424 c. 29: 3 1 2 3 3 2 3 3 1 2 3 3 N SD: 12.8169 c. M: 18.5950 c. 31: 3 2 2 3 3 2 3 3 2 2 3 3 SP D3 SD: 5.8708 c. M:-11.9277 c. Fokker 12-tone 41: 4 2 3 4 4 2 5 4 2 3 4 4 P SD: 5.7114 c. M: 12.6199 c. 46: 4 3 3 5 4 3 5 4 3 3 5 4 SP SD: 4.5927 c. M:-7.3835 c. 53: 5 3 4 5 5 3 6 5 3 4 5 5 SP SD: 2.3252 c. M:-4.8272 c. 84: 8 5 6 8 8 5 9 8 5 6 8 8 SP SD: 2.3998 c. M:-4.5577 c. 87: 8 5 6 9 8 5 10 8 5 6 9 8 SP SD: 2.3221 c. M: 4.8019 c. 99: 9 6 7 10 9 6 11 9 6 7 10 9 SP SD: 1.3993 c. M:-2.6404 c. 118: 11 7 8 12 11 7 13 11 7 8 12 11 SP SD: 1.1130 c. M: 2.7242 c. 152: 14 9 11 15 14 9 17 14 9 11 15 14 SP SD: 1.0218 c. M:-2.2267 c. 171: 16 10 12 17 16 10 19 16 10 12 17 16 SP SD: 0.3222 c. M:-0.5494 c. 441: 41 26 31 44 41 26 49 41 26 31 44 41 SP SD: 0.1109 c. M: 0.2042 c. 612: 57 36 43 61 57 36 68 57 36 43 61 57 SP SD: 0.0909 c. M: 0.2042 c. 935: 87 55 66 93 87 55 104 87 55 66 93 87 SP SD: 0.0965 c. M: 0.1613 c. 1053: 98 62 74 105 98 62 117 98 62 74 105 98 SP SD: 0.0846 c. M: 0.2042 c. 1106: 103 65 78 110 103 65 123 103 65 78 110 103 SP SD: 0.0782 c. M: 0.1822 c. 1376: 128 81 97 137 128 81 153 128 81 97 137 128 SP SD: 0.0789 c. M: 0.1363 c. 1407: 131 83 99 140 131 83 156 131 83 99 140 131 SP SD: 0.0682 c. M:-0.1525 c. 1547: 144 91 109 154 144 91 172 144 91 109 154 144 SP SD: 0.0606 c. M: 0.1331 c. 1578: 147 93 111 157 147 93 175 147 93 111 157 147 SP SD: 0.0571 c. M:-0.1058 c. 1749: 163 103 123 174 163 103 194 163 103 123 174 163 SP SD: 0.0654 c. M:-0.1040 c. 1848: 172 109 130 184 172 109 205 172 109 130 184 172 SP SD: 0.0493 c. M:-0.1137 c. 2019: 188 119 142 201 188 119 224 188 119 142 201 188 SP SD: 0.0346 c. M:-0.0790 c. 2190: 204 129 154 218 204 129 243 204 129 154 218 204 SP SD: 0.0396 c. M:-0.0620 c. 2342: 218 138 165 233 218 138 260 218 138 165 233 218 SP SD: 0.0394 c. M:-0.0896 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: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 14.0675 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.4843 cents 7 x x 8:9 x 10 x 11 x 12:13:14 S SD: 13.2119 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 4.8181 cents 9 x 10 x 11:12 x x 14:15:16:17:18 S SD: 8.6592 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.4194 cents 11 x 12:13:14 x 15:17 x 18:19:21:22 SD: 10.3374 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.5090 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 7.3249 cents 14:15 x 16:18:19 x 21:22:23:25:26:28 SD: 8.7992 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 6.4828 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.0528 cents 18:19:20:21:23:24:25:27:29:30:32:34:36 SD: 4.4305 cents 24:26:27:28:30:32:33:36:38:40:42:45:48 S SD: 3.5496 cents 28:30:31:33:35:37:39:42:45:47:49:53:56 SD: 2.8294 cents 36:38:40:42:45:48:50:54:58:60:63:68:72 SD: 2.1006 cents 44:47:49:51:55:59:61:66:70:73:77:83:88 SD: 1.9072 cents 48:51:53:56:60:64:67:72:77:80:84:90:96 SD: 1.3400 cents 60:64:67:70:75:80:83:90:96:100:105:113:120 SD: 1.1231 cents 72:77:80:84:90:96:100:108:115:120:126:135:144 SD: 0.4513 cents 168:179:187:196:210:224:233:252:269:280:294:315:336 SD: 0.3824 cents 180:192:200:210:225:240:250:270:288:300:315:338:360 SD: 0.2136 cents 252:269:280:294:315:336:350:378:403:420:441:473:504 SD: 0.1998 cents 288:307:320:336:360:384:400:432:461:480:504:540:576 SD: 0.1129 cents 360:384:400:420:450:480:500:540:576:600:630:675:720 SD: 0.0000 cents