Scala analysis: xen07-morrison-decimal
Just approximation to ten tone equal temperament.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 8/7 231.174094 septimal whole tone 3: 16/13 359.472338 tridecimal neutral third 4: 4/3 498.044999 perfect fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 3/2 701.955001 perfect fifth 7: 13/8 840.527662 tridecimal neutral sixth 8: 7/4 968.825906 harmonic seventh 9: 28/15 1080.557192 grave major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 16/15 111.7313 minor diatonic semitone 3: 14/13 128.2982 2/3-tone 4: 13/12 138.5727 tridecimal 2/3-tone 5: 21/20 84.4672 minor semitone 6: 15/14 119.4428 major diatonic semitone 7: 13/12 138.5727 tridecimal 2/3-tone 8: 14/13 128.2982 2/3-tone 9: 16/15 111.7313 minor diatonic semitone 10: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 3 15/14 119.443 cents major diatonic semitone 1: 2 14/13 128.298 cents 2/3-tone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 2: 1 9/8 203.910 cents major whole tone 2: 1 91/80 223.040 cents 2: 2 8/7 231.174 cents septimal whole tone 2: 1 225/196 238.886 cents two (major diatonic semitone) 2: 2 224/195 240.030 cents 2: 1 65/56 258.015 cents 2: 2 7/6 266.871 cents septimal minor third 3: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 2 60/49 350.617 cents smaller approximation to neutral third 3: 1 49/40 351.338 cents larger approximation to neutral third 3: 2 16/13 359.472 cents tridecimal neutral third 3: 2 56/45 378.602 cents septimal narrow major third 3: 1 5/4 386.314 cents major third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 4: 1 98/75 463.069 cents 4: 2 21/16 470.781 cents narrow fourth 4: 2 120/91 478.915 cents 4: 1 169/128 481.055 cents 4: 3 4/3 498.045 cents perfect fourth 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 2 128/91 590.646 cents 5: 2 91/64 609.354 cents 5: 3 10/7 617.488 cents Euler's tritone 6: 3 3/2 701.955 cents perfect fifth 6: 1 256/169 718.945 cents two (tridecimal neutral third) 6: 2 91/60 721.085 cents 6: 2 32/21 729.219 cents wide fifth 6: 1 75/49 736.931 cents BP fifth 6: 1 49/32 737.652 cents 7: 1 8/5 813.686 cents minor sixth 7: 2 45/28 821.398 cents septimale wide minor sixth 7: 2 13/8 840.528 cents tridecimal neutral sixth 7: 1 80/49 848.662 cents smaller approximation to neutral sixth 7: 2 49/30 849.383 cents larger approximation to neutral sixth 7: 2 64/39 857.517 cents 39th subharmonic 8: 2 12/7 933.129 cents septimal major sixth 8: 1 112/65 941.985 cents 8: 2 195/112 959.970 cents 8: 1 392/225 961.114 cents 8: 2 7/4 968.826 cents harmonic seventh 8: 1 160/91 976.960 cents 8: 1 16/9 996.090 cents Pythagorean minor seventh 9: 2 24/13 1061.427 cents tridecimal neutral seventh 9: 2 13/7 1071.702 cents 16/3-tone 9: 3 28/15 1080.557 cents grave major seventh 9: 2 15/8 1088.269 cents classic major seventh 9: 1 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.77778 = 52/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 119.4 231.2 359.5 498.0 582.5 702.0 840.5 968.8 1080.6 1200.0 119.4 : 111.7 240.0 378.6 463.1 582.5 721.1 849.4 961.1 1080.6 1200.0 231.2 : 128.3 266.9 351.3 470.8 609.4 737.7 849.4 968.8 1088.3 1200.0 359.5 : 138.6 223.0 342.5 481.1 609.4 721.1 840.5 960.0 1071.7 1200.0 498.0 : 84.5 203.9 342.5 470.8 582.5 702.0 821.4 933.1 1061.4 1200.0 582.5 : 119.4 258.0 386.3 498.0 617.5 736.9 848.7 977.0 1115.5 1200.0 702.0 : 138.6 266.9 378.6 498.0 617.5 729.2 857.5 996.1 1080.6 1200.0 840.5 : 128.3 240.0 359.5 478.9 590.6 718.9 857.5 942.0 1061.4 1200.0 968.8 : 111.7 231.2 350.6 462.3 590.6 729.2 813.7 933.1 1071.7 1200.0 1080.6: 119.4 238.9 350.6 478.9 617.5 702.0 821.4 960.0 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 138.5727 cents 65/63, 54.1055 cents 21/20, 84.4672 cents 2: 203.9100 .. 266.8709 cents 28/27, 62.9609 cents 27/26, 65.3373 cents 3: 342.4827 .. 386.3137 cents 40/39, 43.8311 cents 117/112, 75.6118 cents 4: 462.3482 .. 498.0450 cents 49/48, 35.6968 cents 256/245, 76.0345 cents 5: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 21/20, 84.4672 cents 6: 701.9550 .. 737.6518 cents 49/48, 35.6968 cents 21/20, 84.4672 cents 7: 813.6863 .. 857.5173 cents 40/39, 43.8311 cents 256/245, 76.0345 cents 8: 933.1291 .. 996.0900 cents 28/27, 62.9609 cents 117/112, 75.6118 cents 9: 1061.4273 .. 1115.5328 cents 65/63, 54.1055 cents 27/26, 65.3373 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 13/12, 138.5727 cents Average / Smallest step : 1.420670 Largest / Average step : 1.154772 Largest / Smallest step : 1.640550 Median interval of one step : 15/14, 119.4428 cents, amount: 3 Most common interval of one step : 15/14, 119.4428 cents, amount: 3 Least squares average step : 119.83375 cents, oct.: 1198.33752 cents Scale is strictly proper Step pattern alph. order: ABCDEADCBA Step pattern size order : CBDEACEDBC Scale is a Constant Structure, by a margin of 65.33734 cents Scale diversity : 1.337017 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.643197 Rothenberg efficiency : 0.282778 redundancy: 0.717222 Efficiency x scale size : 2.827778 Number of different interval sizes : 52 = 5.77778 / class Number of one step interval sizes : 5 Highest interval variety : 7 Mean interval variety : 5.77778 = 52/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Number of recognisable fifths : 4, average 706.2024 cents Number of appreciable fifths : 3, average 701.9550 cents Best major thirds form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 9 = 90.0000% Scale is differentially coherent in interval class 1 Limited inverse transpositions with margin 35.6968 cents: 3 9 -- Rational properties -- Prime limit : 13 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.011110 Average absolute harmonicity : 0.187756 Specific harmonicity : 0.093633 Fundamental : 1/10920, -13.4147 octaves, 0.0240 Hz. Guide tone : 21840, 14.4147 octaves, 5713902.346 Hz. Exponens Consonantiae : 2.384928E+08, 27.82937 octaves Euler's gradus suavitatis : 56 Sum of Mann's harmonic distance : 87.5, average 8.75000 Mersenne's string divisions : 5761140 Sum of van Prooijen's expressibility: 8.06961, average 0.80696 Sum of Tenney's harmonic distance : 16.17834, average 1.61783 Vogel's harmonic complexity : 31.70000 Wille's k value : 8872 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 174.61597, average 3.17484 Lattice compactness (without 2's) : 85.81038, average 1.56019 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.50000 19 1 3: -1 .. 1 0.00000 4 2 5: -1 .. 1 -0.10000 3 7: -1 .. 1 0.10000 5 5 13: -1 .. 1 0.00000 2 2 Average exponent except 2's : 0 / 10 = 0.00000 Average absolute exponent except 2's: 14 / 10 = 1.40000 Scale is weakly epimorphic with val: <10 16 22 27 38| Scale is JI-epimorphic with val: <10 16 23 28 37| = patent Scale is weakly epimorphic with val: <10 17 21 26 39| Scale is weakly epimorphic with val: <10 17 24 29 34| Scale is weakly epimorphic with val: <10 17 24 29 36| Scale is weakly epimorphic with val: <10 18 21 26 39| Scale is weakly epimorphic with val: <10 18 24 29 34| Scale is weakly epimorphic with val: <10 18 24 29 36|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.5548 c. M:-18.0450 c. 21: 2 2 2 3 1 2 3 2 2 2 P D3 SD: 11.2660 c. M: 16.6152 c. 27: 3 2 3 3 2 3 3 3 2 3 SP M ME SD: 8.7575 c. M: 13.8905 c. 31: 3 3 3 4 2 3 4 3 3 3 SP D3 SD: 5.7205 c. M: 11.0852 c. 41: 4 4 4 5 3 4 5 4 4 4 SP D3 SD: 4.1681 c. M: 8.2528 c. 43: 4 4 5 5 3 4 5 5 4 4 SP SD: 5.6454 c. M:-7.9183 c. 50: 5 5 5 6 3 5 6 5 5 5 SP SD: 5.1991 c. M:-8.8259 c. 51: 5 5 5 6 4 5 6 5 5 5 SP D3 SD: 4.3510 c. M: 6.5312 c. 53: 5 5 6 6 4 5 6 6 5 5 SP SD: 4.2034 c. M:-6.2353 c. 60: 6 6 6 7 4 6 7 6 6 6 SP SD: 4.1343 c. M:-8.8259 c. 63: 6 6 7 7 5 6 7 7 6 6 SP SD: 3.9718 c. M:-7.9640 c. 68: 7 6 7 8 5 7 8 7 6 7 SP SD: 3.9471 c. M: 6.5312 c. 70: 7 6 8 8 5 7 8 8 6 7 SP SD: 3.7586 c. M:-8.3170 c. 72: 7 7 8 8 5 7 8 8 7 7 SP SD: 3.6956 c. M: 7.1943 c. 74: 7 7 8 9 5 7 9 8 7 7 SP SD: 4.0554 c. M:-5.9293 c. 77: 8 7 8 9 5 8 9 8 7 8 SP SD: 3.2536 c. M: 5.8888 c. 78: 8 7 8 9 6 8 9 8 7 8 SP SD: 4.0038 c. M:-5.7373 c. 79: 8 7 9 9 5 8 9 9 7 8 SP SD: 3.6230 c. M: 5.2970 c. 80: 8 7 9 9 6 8 9 9 7 8 SP SD: 3.1961 c. M:-6.1741 c. 84: 8 8 9 10 6 8 10 9 8 8 SP SD: 3.0901 c. M: 5.1571 c. 87: 9 8 9 10 6 9 10 9 8 9 SP SD: 2.8661 c. M:-4.6951 c. 89: 9 8 10 10 6 9 10 10 8 9 SP SD: 2.5620 c. M: 4.5726 c. 97: 10 9 10 11 7 10 11 10 9 10 SP SD: 2.9855 c. M:-4.2685 c. 99: 10 9 11 11 7 10 11 11 9 10 SP SD: 2.1272 c. M: 4.1640 c. 103: 10 10 11 12 7 10 12 11 10 10 SP SD: 2.1646 c. M: 2.9380 c. 113: 11 11 12 13 8 11 13 12 11 11 SP SD: 1.8878 c. M: 2.6286 c. 120: 12 11 13 14 8 12 14 13 11 12 SP SD: 1.3375 c. M: 2.5122 c. 130: 13 12 14 15 9 13 15 14 12 13 SP SD: 0.5292 c. M: 0.9737 c. 140: 14 13 15 16 10 14 16 15 13 14 SP SD: 0.5526 c. M:-0.9021 c. 270: 27 25 29 31 19 27 31 29 25 27 SP SD: 0.3758 c. M:-0.5572 c. 301: 30 28 32 35 21 30 35 32 28 30 SP SD: 0.3643 c. M: 0.6684 c. 311: 31 29 33 36 22 31 36 33 29 31 SP SD: 0.3564 c. M: 0.6299 c. 431: 43 40 46 50 30 43 50 46 40 43 SP SD: 0.3081 c. M: 0.6096 c. 441: 44 41 47 51 31 44 51 47 41 44 SP SD: 0.2029 c. M: 0.2887 c. 571: 57 53 61 66 40 57 66 61 53 57 SP SD: 0.2012 c. M: 0.3756 c. 764: 76 71 82 88 54 76 88 82 71 76 SP SD: 0.1859 c. M:-0.2840 c. 795: 79 74 85 92 56 79 92 85 74 79 SP SD: 0.1771 c. M:-0.2307 c. 925: 92 86 99 107 65 92 107 99 86 92 SP SD: 0.1430 c. M:-0.2552 c. 935: 93 87 100 108 66 93 108 100 87 93 SP SD: 0.1133 c. M:-0.1616 c. 1065: 106 99 114 123 75 106 123 114 99 106 SP SD: 0.0863 c. M:-0.1882 c. 1205: 120 112 129 139 85 120 139 129 112 120 SP SD: 0.0886 c. M:-0.1367 c. 1506: 150 140 161 174 106 150 174 161 140 150 SP SD: 0.0778 c. M: 0.1098 c. 1619: 161 151 173 187 114 161 187 173 151 161 SP SD: 0.0672 c. M:-0.1099 c. 1749: 174 163 187 202 123 174 202 187 163 174 SP SD: 0.0500 c. M:-0.0682 c. 1889: 188 176 202 218 133 188 218 202 176 188 SP SD: 0.0465 c. M:-0.0830 c. 2190: 218 204 234 253 154 218 253 234 204 218 SP SD: 0.0358 c. M:-0.0588 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 14.6104 cents 4 x x 5 x x 6 x 7 x 8 S SD: 6.7103 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 14.1706 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 10.7607 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 14.2200 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 6.2454 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 12.4225 cents 10:11 x 12:13:14:15:16:18:19:20 S SD: 11.0867 cents 11:12:13:14:15 x 17:18:19:21:22 SD: 13.1775 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 7.5330 cents 13:14:15:16:17:18:20:21:23:24:26 SD: 6.7821 cents 14:15:16:17:19:20:21:23:25:26:28 SD: 6.6082 cents 16:17:18:20:21:22:24:26:28:30:32 S SD: 5.8733 cents 21:23:24:26:28:29:32:34:37:39:42 SD: 5.5819 cents 22:24:25:27:29:31:33:36:39:41:44 SD: 4.7583 cents 26:28:30:32:35:36:39:42:46:49:52 SD: 4.1609 cents 27:29:31:33:36:38:41:44:47:50:54 SD: 3.2578 cents 30:32:34:37:40:42:45:49:53:56:60 SD: 2.5101 cents 40:43:46:49:53:56:60:65:70:75:80 SD: 1.9824 cents 48:51:55:59:64:67:72:78:84:90:96 SD: 1.7926 cents 56:60:64:69:75:78:84:91:98:105:112 SD: 1.4180 cents 69:74:79:85:92:97:104:112:121:129:138 SD: 1.2634 cents 70:75:80:86:93:98:105:114:123:131:140 SD: 1.1470 cents 82:88:94:101:109:115:123:133:144:153:164 SD: 1.1039 cents 83:89:95:102:111:116:125:135:145:155:166 SD: 1.0569 cents 96:103:110:118:128:134:144:156:168:179:192 SD: 0.7842 cents 112:120:128:138:149:157:168:182:196:209:224 SD: 0.4886 cents 168:180:192:207:224:235:252:273:294:314:336 SD: 0.3281 cents 240:257:274:295:320:336:360:390:420:448:480 SD: 0.3045 cents 252:270:288:310:336:353:378:410:441:470:504 SD: 0.2887 cents 264:283:302:325:352:370:396:429:462:493:528 SD: 0.2760 cents 280:300:320:345:373:392:420:455:490:523:560 SD: 0.2709 cents 308:330:352:379:411:431:462:501:539:575:616 SD: 0.2402 cents 320:343:366:394:427:448:480:520:560:597:640 SD: 0.2359 cents 352:377:402:433:469:493:528:572:616:657:704 SD: 0.2198 cents 378:405:432:465:504:529:567:614:662:706:756 SD: 0.2082 cents 390:418:446:480:520:546:585:634:683:728:780 SD: 0.1912 cents 408:437:466:502:544:571:612:663:714:762:816 SD: 0.1709 cents 420:450:480:517:560:588:630:683:735:784:840 SD: 0.1294 cents 560:600:640:689:747:784:840:910:980:1045:1120 SD: 0.1113 cents