Scala analysis: semipor7
Seventh 16/15&250/243 = 648/625&250/243 scale = inverse semipor8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 27/20 519.551289 acute fourth 5: 3/2 701.955001 perfect fifth 6: 5/3 884.358713 major sixth, BP sixth 7: 9/5 1017.596288 just minor seventh, BP seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.4037 minor whole tone 4: 81/80 21.5063 syntonic comma, Didymus comma 5: 10/9 182.4037 minor whole tone 6: 10/9 182.4037 minor whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 5 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 4 6/5 315.641 cents minor third 2: 2 100/81 364.807 cents grave major third 3: 1 243/200 337.148 cents acute minor third 3: 2 5/4 386.314 cents major third 3: 5 4/3 498.045 cents perfect fourth 4: 3 27/20 519.551 cents acute fourth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 3 40/27 680.449 cents grave fifth 5: 5 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 400/243 862.852 cents grave major sixth 6: 2 81/50 835.193 cents acute minor sixth 6: 4 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 7: 5 9/5 1017.596 cents just minor seventh, BP seventh 7: 2 50/27 1066.762 cents grave major seventh 7: 1 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.14286 = 22/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 182.4 315.6 498.0 519.6 702.0 884.4 1017.6 1200.0 182.4 : 133.2 315.6 337.1 519.6 702.0 835.2 1017.6 1200.0 315.6 : 182.4 203.9 386.3 568.7 702.0 884.4 1066.8 1200.0 498.0 : 21.5 203.9 386.3 519.6 702.0 884.4 1017.6 1200.0 519.6 : 182.4 364.8 498.0 680.4 862.9 996.1 1178.5 1200.0 702.0 : 182.4 315.6 498.0 680.4 813.7 996.1 1017.6 1200.0 884.4 : 133.2 315.6 498.0 631.3 813.7 835.2 1017.6 1200.0 1017.6: 182.4 364.8 498.0 680.4 702.0 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 182.4037 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 2: 203.9100 .. 364.8074 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 3: 337.1476 .. 498.0450 cents 800/729, 160.8974 cents 19683/20000,-27.6598 cents 4: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 5: 701.9550 .. 862.8524 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 6: 835.1926 .. 996.0900 cents 800/729, 160.8974 cents 19683/20000,-27.6598 cents 7: 1017.5963 .. 1178.4937 cents 800/729, 160.8974 cents 81/80, 21.5063 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 6.974704 Largest / Average step : 1.216025 Largest / Smallest step : 8.481412 Median interval of one step : 10/9, 182.4037 cents, amount: 5 Most common interval of one step : 10/9, 182.4037 cents, amount: 5 Least squares average step : 146.69180 cents, oct.: 1173.53442 cents Scale is not proper Step pattern alph. order: ABACAABA Step pattern size order : LMLSLLML Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.309147 Lumma stability : 0.107531 Lumma impropriety factor : 0.046100 Rothenberg efficiency : 0.478125 redundancy: 0.521875 Efficiency x scale size : 3.825000 Number of different interval sizes : 22 = 3.14286 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.14286 = 22/7 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common triad is 0.0 182.404 498.045 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 3 5 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 87.5000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.033186 Average absolute harmonicity : 0.240172 Specific harmonicity : 0.185723 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 9.720000E+04, 16.56867 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 57.0, average 7.12500 Mersenne's string divisions : 8251320 Sum of van Prooijen's expressibility: 5.69203, average 0.71150 Sum of Tenney's harmonic distance : 11.15142, average 1.39393 Vogel's harmonic complexity : 13.75000 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 98.71002, average 2.74194 Lattice compactness (without 2's) : 78.27894, average 2.17441 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.25000 8 1 3: -2 .. 3 0.37500 11 2 5: -1 .. 1 -0.12500 5 5 Average exponent except 2's : 2 / 8 = 0.25000 Average absolute exponent except 2's: 16 / 8 = 2.00000 Scale is JI-epimorphic with val: <8 13 19| = patent
FIT/MODE
8: 1 1 1 0 2 1 1 1 N T3 SD: 38.7997 c. M: 69.5513 c. 10: 1 1 2 0 2 1 1 2 P D3 SD: 46.2553 c. M: 75.6413 c. 11: 2 1 2 0 1 2 1 2 N SD: 31.6169 c. M:-47.4095 c. 12: 2 1 2 0 2 2 1 2 N T3 SD: 13.6860 c. M: 19.5513 c. 19: 3 2 3 0 3 3 2 3 N SD: 7.1446 c. M: 14.2881 c. 26: 4 3 4 0 4 4 3 4 N SD: 7.4761 c. M: 11.8590 c. 27: 4 3 4 1 4 4 3 4 P SD: 7.4285 c. M:-13.7820 c. 33: 5 4 5 0 5 5 4 5 N SD: 8.8368 c. M:-11.6314 c. 34: 5 4 5 1 5 5 4 5 P SD: 5.0809 c. M:-9.8605 c. 39: 6 4 6 1 6 6 4 6 N SD: 5.1771 c. M: 7.9490 c. 41: 6 5 6 1 6 6 5 6 P SD: 5.3078 c. M:-7.2780 c. 46: 7 5 7 1 7 7 5 7 N SD: 1.9306 c. M: 2.5978 c. 53: 8 6 8 1 8 8 6 8 N SD: 1.0175 c. M: 1.3398 c. 99: 15 11 15 2 15 15 11 15 N SD: 0.8829 c. M:-1.6608 c. 118: 18 13 18 2 18 18 13 18 N SD: 0.5118 c. M: 0.9072 c. 171: 26 19 26 3 26 26 19 26 N SD: 0.1557 c. M: 0.2530 c. 388: 59 43 59 7 59 59 43 59 N SD: 0.1101 c. M: 0.1774 c. 441: 67 49 67 8 67 67 49 67 N SD: 0.0884 c. M:-0.1766 c. 559: 85 62 85 10 85 85 62 85 N SD: 0.0543 c. M:-0.0778 c. 612: 93 68 93 11 93 93 68 93 N SD: 0.0395 c. M:-0.0566 c. 1000: 152 111 152 18 152 152 111 152 N SD: 0.0351 c. M:-0.0487 c. 1171: 178 130 178 21 178 178 130 178 N SD: 0.0087 c. M: 0.0136 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5 x 6 S SD: 0.0000 cents 4 x 5 x x 6 x 7:8 S SD: 21.4668 cents 5 x 6 x 7 x 8:9:10 S SD: 18.9300 cents 6 x 7:8 x 9:10:11:12 S SD: 9.7006 cents 7:8 x 9 x 11:12:13:14 SD: 22.4442 cents 8:9:10 x 11:12:13:14:16 S SD: 14.8227 cents 9:10:11:12 x 14:15:16:18 S SD: 10.5325 cents 11:12:13 x 15:17:18:20:22 SD: 11.0596 cents 12:13:14:16 x 18:20:22:24 S SD: 10.4088 cents 14:16:17 x 19:21:23:25:28 SD: 8.6810 cents 15:17:18:20 x 23:25:27:30 SD: 7.3167 cents 16:18:19:21:22:24:27:29:32 SD: 7.0152 cents 17:19:20 x 23:26:28:31:34 SD: 8.2660 cents 18:20:22:24 x 27:30:32:36 S SD: 5.4803 cents 20:22:24 x 27:30:33:36:40 S SD: 3.5152 cents 21:23:25:28 x 32:35:38:42 SD: 5.7811 cents 23:26:28 x 31:35:38:41:46 SD: 7.3554 cents 24:27:29:32 x 36:40:43:48 SD: 3.6994 cents 26:29:31 x 35:39:43:47:52 SD: 2.9476 cents 27:30:32:36 x 41:45:49:54 SD: 4.7705 cents 28:31:34:37:38:42:47:50:56 SD: 4.1923 cents 29:32:35 x 39:44:48:52:58 SD: 4.2023 cents 30:33:36:40:41:45:50:54:60 SD: 3.4323 cents 32:36:38 x 43:48:53:58:64 SD: 4.7746 cents 33:37:40:44:45:50:55:59:66 SD: 4.4905 cents 34:38:41:45:46:51:57:61:68 SD: 2.7597 cents 35:39:42 x 47:53:58:63:70 SD: 3.1183 cents 36:40:43:48:49:54:60:65:72 SD: 2.1447 cents 38:42:46 x 51:57:63:68:76 SD: 3.5044 cents 39:43:47:52:53:59:65:70:78 SD: 3.0779 cents 40:44:48:53:54:60:67:72:80 SD: 2.7814 cents 41:46:49:55 x 62:68:74:82 SD: 3.8681 cents 42:47:50:56:57:63:70:76:84 SD: 2.8203 cents 44:49:53:59 x 66:73:79:88 SD: 2.1940 cents 45:50:54:60:61:68:75:81:90 SD: 1.8277 cents 47:52:56:63 x 71:78:85:94 SD: 3.3854 cents 48:53:58:64:65:72:80:86:96 SD: 2.3530 cents 51:57:61:68:69:77:85:92:102 SD: 2.1316 cents 54:60:65:72:73:81:90:97:108 SD: 0.8552 cents 100:111:120:133:135:150:167:180:200 SD: 0.7261 cents 114:127:137:152:154:171:190:205:228 SD: 0.6984 cents 120:133:144:160:162:180:200:216:240 SD: 0.5417 cents 126:140:151:168:170:189:210:227:252 SD: 0.3669 cents 180:200:216:240:243:270:300:324:360 SD: 0.0000 cents