Scala analysis: SpOldVienna
Sparschuh's 'old-Vienna' classics for abs.pitch A4=421.5Hz [2008]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 59/56 90.345753 2: 47/42 194.725715 3: 531/448 294.255754 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 59/42 588.390752 7: 3/2 701.955001 perfect fifth 8: 177/112 792.300754 9: 281/168 890.530677 10: 16/9 996.089998 Pythagorean minor 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: 59/56 90.3458 2: 188/177 104.3800 3: 1593/1504 99.5300 4: 560/531 92.0580 5: 16/15 111.7313 minor diatonic semitone 6: 59/56 90.3458 7: 63/59 113.5642 8: 59/56 90.3458 9: 562/531 98.2299 10: 896/843 105.5593 11: 135/128 92.1787 major chroma, major limma 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 59/56 90.346 cents 1: 1 560/531 92.058 cents 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 562/531 98.230 cents 1: 1 1593/1504 99.530 cents 1: 1 188/177 104.380 cents 1: 1 896/843 105.559 cents 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 63/59 113.564 cents 2: 1 281/252 188.576 cents 2: 1 105/94 191.588 cents 2: 1 47/42 194.726 cents 2: 1 315/281 197.738 cents 2: 2 118/105 202.077 cents 2: 2 1792/1593 203.789 cents 2: 4 9/8 203.910 cents major whole tone 3: 2 32/27 294.135 cents Pythagorean minor third 3: 3 531/448 294.256 cents 3: 2 70/59 295.968 cents 3: 1 281/236 302.140 cents 3: 1 56/47 303.319 cents 3: 1 376/315 306.457 cents 3: 1 336/281 309.469 cents 3: 1 6/5 315.641 cents minor third 4: 2 5/4 386.314 cents major third 4: 1 281/224 392.486 cents 4: 1 59/47 393.665 cents 4: 1 141/112 398.636 cents 4: 1 354/281 399.815 cents 4: 2 177/140 405.987 cents 4: 4 224/177 407.699 cents 5: 7 4/3 498.045 cents perfect fourth 5: 1 4779/3584 498.166 cents 5: 1 315/236 499.878 cents 5: 1 376/281 504.195 cents 5: 1 281/210 504.217 cents 5: 1 63/47 507.229 cents 6: 2 59/42 588.391 cents 6: 2 45/32 590.224 cents diatonic tritone 6: 1 2248/1593 596.275 cents 6: 1 531/376 597.575 cents 6: 1 752/531 602.425 cents 6: 1 1593/1124 603.725 cents 6: 2 64/45 609.776 cents 2nd tritone 6: 2 84/59 611.609 cents 7: 1 94/63 692.771 cents 7: 1 420/281 695.783 cents 7: 1 281/188 695.805 cents 7: 1 472/315 700.122 cents 7: 1 7168/4779 701.834 cents 7: 7 3/2 701.955 cents perfect fifth 8: 4 177/112 792.301 cents 8: 2 280/177 794.013 cents 8: 1 281/177 800.185 cents 8: 1 224/141 801.364 cents 8: 1 94/59 806.335 cents 8: 1 448/281 807.514 cents 8: 2 8/5 813.686 cents minor sixth 9: 1 5/3 884.359 cents major sixth, BP sixth 9: 1 281/168 890.531 cents 9: 1 315/188 893.543 cents 9: 1 47/28 896.681 cents 9: 1 472/281 897.860 cents 9: 2 59/35 904.032 cents 9: 3 896/531 905.744 cents 9: 2 27/16 905.865 cents Pythagorean major sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 1593/896 996.211 cents 10: 2 105/59 997.923 cents 10: 1 562/315 1002.262 cents 10: 1 84/47 1005.274 cents 10: 1 188/105 1008.412 cents 10: 1 504/281 1011.424 cents 11: 1 118/63 1086.436 cents 11: 2 15/8 1088.269 cents classic major seventh 11: 1 843/448 1094.441 cents 11: 1 177/94 1095.620 cents 11: 1 3008/1593 1100.470 cents 11: 1 531/281 1101.770 cents 11: 1 256/135 1107.821 cents octave - major chroma 11: 1 531/280 1107.942 cents 11: 3 112/59 1109.654 cents Highest number of different intervals for one interval class: 9 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 : 90.3 194.7 294.3 386.3 498.0 588.4 702.0 792.3 890.5 996.1 1088.3 1200.0 90.3 : 104.4 203.9 296.0 407.7 498.0 611.6 702.0 800.2 905.7 997.9 1109.7 1200.0 194.7 : 99.5 191.6 303.3 393.7 507.2 597.6 695.8 801.4 893.5 1005.3 1095.6 1200.0 294.3 : 92.1 203.8 294.1 407.7 498.0 596.3 701.8 794.0 905.7 996.1 1100.5 1200.0 386.3 : 111.7 202.1 315.6 406.0 504.2 609.8 702.0 813.7 904.0 1008.4 1107.9 1200.0 498.0 : 90.3 203.9 294.3 392.5 498.0 590.2 702.0 792.3 896.7 996.2 1088.3 1200.0 588.4 : 113.6 203.9 302.1 407.7 499.9 611.6 702.0 806.3 905.9 997.9 1109.7 1200.0 702.0 : 90.3 188.6 294.1 386.3 498.0 588.4 692.8 792.3 884.4 996.1 1086.4 1200.0 792.3 : 98.2 203.8 296.0 407.7 498.0 602.4 702.0 794.0 905.7 996.1 1109.7 1200.0 890.5 : 105.6 197.7 309.5 399.8 504.2 603.7 695.8 807.5 897.9 1011.4 1101.8 1200.0 996.1 : 92.2 203.9 294.3 398.6 498.2 590.2 702.0 792.3 905.9 996.2 1094.4 1200.0 1088.3: 111.7 202.1 306.5 406.0 498.0 609.8 700.1 813.7 904.0 1002.3 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.3458 .. 113.5642 cents 3528/3481, 23.2185 cents 59/56, 90.3458 cents 2: 188.5757 .. 203.9100 cents 567/562, 15.3343 cents 16579/15876, 75.0114 cents 3: 294.1350 .. 315.6413 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 4: 386.3137 .. 407.6992 cents 896/885, 21.3855 cents 25/24, 70.6724 cents 5: 498.0450 .. 507.2293 cents 189/188, 9.1843 cents 59/56, 90.3458 cents 6: 588.3908 .. 611.6092 cents 3528/3481, 23.2185 cents 2773/2646, 81.1615 cents 7: 692.7707 .. 701.9550 cents 189/188, 9.1843 cents 2773/2646, 81.1615 cents 8: 792.3008 .. 813.6863 cents 896/885, 21.3855 cents 59/56, 90.3458 cents 9: 884.3587 .. 905.8650 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 10: 996.0900 .. 1011.4243 cents 567/562, 15.3343 cents 256/243, 90.2250 cents 11: 1086.4358 .. 1109.6542 cents 3528/3481, 23.2185 cents 16579/15876, 75.0114 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 59/56, 90.3458 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 63/59, 113.5642 cents Average / Smallest step : 1.106859 Largest / Average step : 1.135642 Largest / Smallest step : 1.256996 Median interval of one step : 98.87998 cents, amount: 0 Most common interval of one step : 59/56, 90.3458 cents, amount: 3 Least squares average step : 99.27248 cents, oct.: 1191.26976 cents Scale is strictly proper Step pattern alph. order: ABCDEAFAGHIE Step pattern size order : AFEBHAIADGCH Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 1.142376 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.829603 Rothenberg efficiency : 0.260269 redundancy: 0.739731 Efficiency x scale size : 3.123232 Number of different interval sizes : 82 = 7.45455 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 7.45455 = 82/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 78961/78960, 0.0219 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 6 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 23.2185 cents: 2 5 7 9 10 Limited inverse transpositions with margin 23.2185 cents: 1 2 4 6 9 11 -- Rational properties -- Prime limit : 281 Odd number limit : 4779 (O: 4779 U: 4779) Highest odd numerator or denominator: 531 Scale harmonicity : 0.026772 Fundamental : 1/4032, -11.9773 octaves, 0.0649 Hz. Guide tone : 561033360, 29.0635 octaves, 146780669962.719 Hz. Exponens Consonantiae : 2.262087E+12, 41.04079 octaves Euler's gradus suavitatis : 413 Sum of Mann's harmonic distance : 1047.0, average 87.25000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.41912, average 1.36826 Sum of Tenney's harmonic distance : 32.25300, average 2.68775 Vogel's harmonic complexity : 61.66667 Wille's k value : 2389 Wilson's harmonic complexity : 411 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 283.64958, average 3.63653 Lattice compactness (without 2's) : 128.20909, average 1.64371 Number of different primes : 7 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -1.41667 31 1 3: -2 .. 2 -0.08333 11 3 5: 0 .. 1 0.16667 2 2 7: -1 .. 0 -0.50000 6 47: 0 .. 1 0.08333 1 1 59: 0 .. 1 0.33333 4 4 281: 0 .. 1 0.08333 1 1 Average exponent except 2's : 1 / 12 = 0.08333 Average absolute exponent except 2's: 25 / 12 = 2.08333 Scale is JI-epimorphic with val: <12 19 28 33 66 70 97| Scale is JI-epimorphic with val: <12 19 28 34 67 71 98| = patent Scale is JI-epimorphic with val: <12 19 28 35 68 72 99|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.0912 c. M:-13.6863 c. Twelve-tone Chromatic (1/11-comma) 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 5.3624 c. M: 12.4819 c. Schismic-12 49: 4 4 4 4 4 4 5 3 4 5 3 5 SP D3 SD: 6.8244 c. M: 10.7177 c. 51: 4 4 4 4 5 4 5 4 4 4 4 5 SP D3 SD: 6.4202 c. M: 11.9028 c. 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 3.4477 c. M:-9.0479 c. Schismic-12 61: 5 5 5 5 5 5 6 4 5 6 4 6 SP D3 SD: 5.3962 c. M:-8.0149 c. 62: 5 5 5 5 6 4 6 5 5 5 5 6 SP D3 SD: 4.7809 c. M: 8.9932 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 2.9712 c. M:-8.3512 c. 66: 5 6 5 5 6 5 7 5 5 6 5 6 SP D3 SD: 4.8842 c. M:-7.6992 c. 68: 5 6 6 5 6 5 7 5 5 6 6 6 SP D3 SD: 4.7863 c. M: 8.1777 c. 70: 5 6 6 5 7 5 7 5 6 6 5 7 SP D3 SD: 4.7435 c. M: 9.1709 c. 72: 5 7 6 5 7 5 7 6 5 7 5 7 SP T3 SD: 5.0234 c. M:-7.6992 c. 74: 6 6 6 6 7 5 7 6 6 6 6 7 SP D3 SD: 3.9235 c. M:-6.9515 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.1828 c. M:-7.8717 c. 80: 6 7 7 6 7 6 8 6 6 7 7 7 SP D3 SD: 4.0527 c. M:-6.7313 c. 82: 6 7 7 6 8 6 8 6 7 7 6 8 SP D3 SD: 3.0402 c. M: 5.8259 c. 90: 7 8 7 7 8 7 9 6 8 8 7 8 SP SD: 3.7151 c. M: 5.6341 c. 92: 7 8 8 7 8 7 9 7 7 8 7 9 SP SD: 3.5606 c. M:-5.7442 c. 94: 7 8 8 7 9 7 9 7 8 8 7 9 SP D3 SD: 1.9295 c. M: 3.3350 c. 106: 8 9 9 8 10 8 10 8 9 9 8 10 SP D3 SD: 1.4150 c. M:-3.8089 c. 118: 9 10 10 9 11 9 11 9 10 10 9 11 SP D3 SD: 1.4910 c. M:-4.3846 c. 142: 11 12 12 11 13 11 13 11 11 13 11 13 SP D3 S SD: 1.9350 c. M: 3.2067 c. 147: 11 13 12 11 14 11 14 11 12 13 11 14 SP SD: 1.1750 c. M: 2.6402 c. 159: 12 14 13 12 15 12 15 12 13 14 12 15 SP SD: 0.7419 c. M:-1.5007 c. 171: 13 15 14 13 16 13 16 13 14 15 13 16 SP SD: 0.7592 c. M:-1.7655 c. 265: 20 23 22 20 25 20 25 20 22 23 20 25 SP SD: 0.7493 c. M:-1.5448 c. 277: 21 24 23 21 26 21 26 21 23 24 21 26 SP SD: 0.7345 c. M:-1.8881 c. 282: 21 25 23 22 26 21 27 21 23 25 22 26 SP SD: 0.8164 c. M: 1.1690 c. 294: 22 26 24 23 27 22 28 22 24 26 23 27 SP SD: 0.7896 c. M:-1.5272 c. 330: 25 29 27 25 31 25 31 25 27 29 25 31 SP SD: 0.6917 c. M:-1.6379 c. 345: 26 30 29 26 32 26 33 26 28 30 27 32 SP SD: 0.6855 c. M:-1.3964 c. 364: 27 32 30 28 34 27 35 27 30 32 28 34 SP SD: 0.7773 c. M: 1.5776 c. 371: 28 32 31 28 35 28 35 28 30 33 28 35 SP SD: 0.6994 c. M: 1.4763 c. 376: 28 33 31 29 35 28 36 28 31 33 29 35 SP SD: 0.5467 c. M: 1.1567 c. 383: 29 33 32 29 36 29 36 29 31 34 29 36 SP SD: 0.5575 c. M: 1.0624 c. 388: 29 34 32 30 36 29 37 29 32 34 30 36 SP SD: 0.3935 c. M: 0.7619 c. 400: 30 35 33 31 37 30 38 30 33 35 31 37 SP SD: 0.3810 c. M:-0.7313 c. 518: 39 45 43 40 48 39 49 39 42 46 40 48 SP SD: 0.3576 c. M: 0.9554 c. 535: 40 47 44 41 50 40 51 40 44 47 41 50 SP SD: 0.4141 c. M: 0.7272 c. 547: 41 48 45 42 51 41 52 41 45 48 42 51 SP SD: 0.2812 c. M:-0.5211 c. 559: 42 49 46 43 52 42 53 42 46 49 43 52 SP SD: 0.2338 c. M:-0.6231 c. 612: 46 53 51 47 57 46 58 46 50 54 47 57 SP SD: 0.2181 c. M: 0.6081 c. 624: 47 54 52 48 58 47 59 47 51 55 48 58 SP SD: 0.1750 c. M: 0.4949 c. 636: 48 55 53 49 59 48 60 48 52 56 49 59 SP SD: 0.2480 c. M:-0.4787 c. 677: 51 59 56 52 63 51 64 51 55 60 52 63 SP SD: 0.2268 c. M: 0.7227 c. 771: 58 67 64 59 72 58 73 58 63 68 59 72 SP SD: 0.1671 c. M: 0.3310 c. 783: 59 68 65 60 73 59 74 59 64 69 60 73 SP SD: 0.0828 c. M: 0.1461 c. 1171: 88 102 97 90 109 88 111 88 96 103 90 109 SP SD: 0.0948 c. M: 0.1756 c. 1183: 89 103 98 91 110 89 112 89 97 104 91 110 SP SD: 0.0813 c. M:-0.1613 c. 1342: 101 117 111 103 125 101 127 101 110 118 103 125 SP SD: 0.0719 c. M:-0.2072 c. 1942: 146 169 161 149 181 146 184 146 159 171 149 181 SP SD: 0.0958 c. M: 0.1312 c. 1954: 147 170 162 150 182 147 185 147 160 172 150 182 SP SD: 0.0505 c. M: 0.0899 c. 1966: 148 171 163 151 183 148 186 148 161 173 151 183 SP SD: 0.0310 c. M:-0.0545 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: 2.0573 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.8160 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.5147 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.9960 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.7273 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.4112 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.8115 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4380 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 11.0425 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.7598 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 9.3782 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.1176 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.5419 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.1314 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 4.9314 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2998 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4003 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.5729 cents 33:35:37:39:41:44:46:50:52:55:59:62:66 SD: 2.5470 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.3066 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.9474 cents 48:51:54:57:60:64:67:72:76:80:85:90:96 SD: 1.9092 cents 52:55:58:62:65:69:73:78:82:87:92:98:104 SD: 1.7003 cents 57:60:64:68:71:76:80:86:90:95:101:107:114 SD: 1.6259 cents 59:62:66:70:74:79:83:89:93:99:105:111:118 SD: 1.4456 cents 60:63:67:71:75:80:84:90:95:100:107:113:120 SD: 1.2570 cents 72:76:81:85:90:96:101:108:114:120:128:135:144 SD: 1.1703 cents 76:80:85:90:95:101:107:114:120:127:135:143:152 SD: 0.8205 cents 108:114:121:128:135:144:152:162:171:181:192:203:216 SD: 0.6767 cents 126:133:141:149:158:168:177:189:199:211:224:236:252 SD: 0.6739 cents 128:135:143:152:160:171:180:192:202:214:228:240:256 SD: 0.6182 cents 136:143:152:161:170:181:191:204:215:227:242:255:272 SD: 0.5740 cents 144:152:161:171:180:192:202:216:228:241:256:270:288 SD: 0.5351 cents 150:158:168:178:188:200:211:225:237:251:267:281:300 SD: 0.5336 cents 152:160:170:180:190:203:214:228:240:254:270:285:304 SD: 0.4981 cents 168:177:188:199:210:224:236:252:266:281:299:315:336 SD: 0.3283 cents 244:257:273:289:305:325:343:366:386:408:434:458:488 SD: 0.3135 cents 260:274:291:308:325:347:365:390:411:435:462:488:520 SD: 0.2569 cents 296:312:331:351:370:395:416:444:468:495:526:555:592 SD: 0.2180 cents 312:329:349:370:390:416:438:468:493:522:555:585:624 SD: 0.2084 cents 336:354:376:398:420:448:472:504:531:562:597:630:672 SD: 0.1212 cents