Scala analysis: 12_prism
225:224 scale by Carl Lumma.
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: 28/25 196.198479 middle second 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 112/75 694.243478 marvelous 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: 28/15 1080.557192 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 21/20 84.4672 minor semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 16/15 111.7313 minor diatonic semitone 8: 15/14 119.4428 major diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 21/20 84.4672 minor semitone 11: 16/15 111.7313 minor diatonic semitone 12: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 1: 3 15/14 119.443 cents major diatonic semitone 2: 2 35/32 155.140 cents septimal neutral second 2: 2 125/112 190.115 cents classic augmented semitone 2: 4 28/25 196.198 cents middle second 2: 4 8/7 231.174 cents septimal whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 2 75/64 274.582 cents classic augmented second 3: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 1 448/375 307.930 cents 3: 4 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 4: 8 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 5: 2 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 2 75/56 505.757 cents marvelous fourth 5: 1 168/125 511.840 cents 5: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 6 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 6 10/7 617.488 cents Euler's tritone 7: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 1 125/84 688.160 cents 7: 2 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 8: 4 25/16 772.627 cents classic augmented fifth 8: 8 8/5 813.686 cents minor sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 375/224 892.070 cents 9: 2 42/25 898.153 cents quasi-equal major sixth 9: 2 128/75 925.418 cents diminished seventh 9: 2 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 4 25/14 1003.802 cents middle minor seventh 10: 2 224/125 1009.885 cents 10: 2 64/35 1044.860 cents septimal neutral seventh 11: 3 28/15 1080.557 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 3 40/21 1115.533 cents acute major seventh 11: 2 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: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 196.2 266.9 386.3 498.0 582.5 694.2 813.7 884.4 968.8 1080.6 1200.0 111.7 : 84.5 155.1 274.6 386.3 470.8 582.5 702.0 772.6 857.1 968.8 1088.3 1200.0 196.2 : 70.7 190.1 301.8 386.3 498.0 617.5 688.2 772.6 884.4 1003.8 1115.5 1200.0 266.9 : 119.4 231.2 315.6 427.4 546.8 617.5 702.0 813.7 933.1 1044.9 1129.3 1200.0 386.3 : 111.7 196.2 307.9 427.4 498.0 582.5 694.2 813.7 925.4 1009.9 1080.6 1200.0 498.0 : 84.5 196.2 315.6 386.3 470.8 582.5 702.0 813.7 898.2 968.8 1088.3 1200.0 582.5 : 111.7 231.2 301.8 386.3 498.0 617.5 729.2 813.7 884.4 1003.8 1115.5 1200.0 694.2 : 119.4 190.1 274.6 386.3 505.8 617.5 702.0 772.6 892.1 1003.8 1088.3 1200.0 813.7 : 70.7 155.1 266.9 386.3 498.0 582.5 653.2 772.6 884.4 968.8 1080.6 1200.0 884.4 : 84.5 196.2 315.6 427.4 511.8 582.5 702.0 813.7 898.2 1009.9 1129.3 1200.0 968.8 : 111.7 231.2 342.9 427.4 498.0 617.5 729.2 813.7 925.4 1044.9 1115.5 1200.0 1080.6: 119.4 231.2 315.6 386.3 505.8 617.5 702.0 813.7 933.1 1003.8 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 119.4428 cents 36/35, 48.7704 cents 25/24, 70.6724 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 3: 266.8709 .. 342.9054 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 5: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 525/512, 43.4083 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 9: 857.0946 .. 933.1291 cents 256/245, 76.0345 cents 525/512, 43.4083 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1129.3276 cents 36/35, 48.7704 cents 49/48, 35.6968 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 : 15/14, 119.4428 cents Average / Smallest step : 1.414979 Largest / Average step : 1.194428 Largest / Smallest step : 1.690091 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 : 98.67401 cents, oct.: 1184.08810 cents Scale is strictly proper Step pattern alph. order: ABCDABADCBAD Step pattern size order : CBADCBCDABCD Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.402556 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.440966 Rothenberg efficiency : 0.356421 redundancy: 0.643579 Efficiency x scale size : 4.277056 Number of different interval sizes : 44 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.00000 = 4 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 3136/3125, 6.0832 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 8 Most common triad is 0.0 386.314 813.686 cents, amount: 4 Number of recognisable fifths : 9, average 698.7086 cents Number of appreciable fifths : 8, average 700.0271 cents Best fifths form a closed circle Scale contains a complete diamond : 1 5 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval class 1 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 Scale is n-1 differentially coherent in interval classes 5 and 6 combined Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 7 Odd number limit : 375 (O: 375 U: 375) Highest odd numerator or denominator: 75 Scale harmonicity : 0.026211 Average absolute harmonicity : 0.163320 Specific harmonicity : 0.131784 Fundamental : 1/300, -8.2288 octaves, 0.8721 Hz. Guide tone : 560, 9.1293 octaves, 146510.317 Hz. Exponens Consonantiae : 1.680000E+05, 17.35810 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 195.0, average 16.25000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.73451, average 0.89454 Sum of Tenney's harmonic distance : 21.84671, average 1.82056 Vogel's harmonic complexity : 15.58333 Wille's k value : 262 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 237.96117, average 3.05078 Lattice compactness (without 2's) : 124.85945, average 1.60076 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.08333 23 1 3: -1 .. 0 -0.50000 6 1 5: -2 .. 1 -0.50000 10 4 7: 0 .. 1 0.50000 6 6 Average exponent except 2's :-6 / 12 =-0.50000 Average absolute exponent except 2's: 22 / 12 = 1.83333 Scale is weakly epimorphic with val: <12 17 26 32| Scale is weakly epimorphic with val: <12 17 28 34| Scale is weakly epimorphic with val: <12 18 25 34| Scale is weakly epimorphic with val: <12 18 26 31| Scale is weakly epimorphic with val: <12 18 26 33| Scale is weakly epimorphic with val: <12 18 26 35| Scale is weakly epimorphic with val: <12 18 26 37| Scale is weakly epimorphic with val: <12 18 28 31| Scale is weakly epimorphic with val: <12 18 28 33| Scale is weakly epimorphic with val: <12 18 28 35| Scale is weakly epimorphic with val: <12 18 28 37| Scale is weakly epimorphic with val: <12 18 29 32| Scale is weakly epimorphic with val: <12 18 31 34| Scale is weakly epimorphic with val: <12 19 26 32| Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 21 25 31| Scale is weakly epimorphic with val: <12 21 26 32| Scale is weakly epimorphic with val: <12 21 28 34| Scale is weakly epimorphic with val: <12 21 29 35| Scale is weakly epimorphic with val: <12 21 31 37|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.2277 c. M:-33.1291 c. Twelve-tone Chromatic (1/11-comma) 18: 2 1 1 2 1 2 1 2 1 2 1 2 P D3 SD: 19.1147 c. M: 31.3783 c. 19: 2 1 1 2 2 1 2 2 1 1 2 2 P D3 SD: 10.5190 c. M: 21.4575 c. 24: 2 2 1 3 2 2 2 2 2 1 3 2 P T3 SD: 13.3267 c. M:-19.4428 c. 25: 2 2 1 3 2 2 2 3 1 2 2 3 P D3 SD: 15.6952 c. M: 26.8709 c. 26: 2 2 2 2 3 2 2 3 1 2 2 3 P T3 SD: 12.9613 c. M: 19.4236 c. 27: 3 1 2 3 2 2 3 2 2 2 2 3 P SD: 12.4667 c. M:-21.6020 c. 29: 3 2 1 3 3 2 3 3 1 2 3 3 P SD: 11.7233 c. M: 18.5950 c. 31: 3 2 2 3 3 2 3 3 2 2 3 3 SP D3 SD: 3.2765 c. M:-5.9639 c. Fokker 12-tone 68: 6 5 4 7 6 5 6 7 4 5 6 7 SP SD: 3.2402 c. M: 6.0082 c. 72: 7 5 4 7 7 5 7 7 4 5 7 7 SP SD: 2.9954 c. M:-5.7565 c. Smith's Prism 84: 8 6 5 8 8 6 8 8 5 6 8 8 SP SD: 3.2260 c. M:-5.7565 c. 87: 8 6 5 9 8 6 8 9 5 6 8 9 SP SD: 2.9392 c. M: 4.8019 c. 99: 9 7 6 10 9 7 9 10 6 7 9 10 SP SD: 1.6808 c. M: 3.3344 c. 118: 11 8 7 12 11 8 11 12 7 8 11 12 SP SD: 1.9335 c. M: 2.9781 c. 121: 11 9 7 12 11 9 11 12 7 9 11 12 SP SD: 1.7552 c. M:-3.0749 c. 130: 12 9 8 13 12 9 12 13 8 9 12 13 SP SD: 1.2748 c. M: 2.3523 c. 140: 13 10 8 14 13 10 13 14 8 10 13 14 SP SD: 0.7419 c. M: 1.5016 c. 171: 16 12 10 17 16 12 16 17 10 12 16 17 SP SD: 0.3117 c. M:-0.5494 c. 410: 38 29 24 41 38 29 38 41 24 29 38 41 SP SD: 0.3715 c. M: 0.5849 c. 441: 41 31 26 44 41 31 41 44 26 31 41 44 SP SD: 0.1909 c. M: 0.3659 c. 612: 57 43 36 61 57 43 57 61 36 43 57 61 SP SD: 0.1191 c. M: 0.2042 c. 935: 87 66 55 93 87 66 87 93 55 66 87 93 SP SD: 0.0990 c. M:-0.1652 c. 966: 90 68 57 96 90 68 90 96 57 68 90 96 SP SD: 0.1166 c. M:-0.2098 c. 1106: 103 78 65 110 103 78 103 110 65 78 103 110 SP SD: 0.0935 c. M:-0.1849 c. 1236: 115 87 73 123 115 87 115 123 73 87 115 123 SP SD: 0.0783 c. M:-0.1194 c. 1376: 128 97 81 137 128 97 128 137 81 97 128 137 SP SD: 0.0527 c. M: 0.1034 c. 1407: 131 99 83 140 131 99 131 140 83 99 131 140 SP SD: 0.0425 c. M:-0.0801 c. 1547: 144 109 91 154 144 109 144 154 91 109 144 154 SP SD: 0.0340 c. M: 0.0665 c. 1578: 147 111 93 157 147 111 147 157 93 111 147 157 SP SD: 0.0372 c. M:-0.0558 c. 2019: 188 142 119 201 188 142 188 201 119 142 188 201 SP SD: 0.0309 c. M: 0.0618 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: 3.8558 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: 1.9279 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.7943 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 5.3555 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.0804 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.4082 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 10.0450 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.9122 cents 11:12 x 13:14:15 x 16 x 18:19:21:22 SD: 10.8924 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 4.5467 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 7.0078 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 8.5175 cents 15:16:17:18:19:20:21:22:24:25:26:28:30 S SD: 5.6345 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.3116 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.8331 cents 23:25:26:27:29:31:32:34:37:38:40:43:46 SD: 4.4697 cents 24:26:27:28:30:32:34:36:38:40:42:45:48 S SD: 3.3822 cents 28:30:31:33:35:37:39:42:45:47:49:52:56 SD: 3.1586 cents 30:32:34:35:38:40:42:45:48:50:53:56:60 SD: 2.9748 cents 32:34:36:37:40:43:45:48:51:53:56:60:64 SD: 2.4581 cents 40:43:45:47:50:53:56:60:64:67:70:75:80 SD: 2.2113 cents 42:45:47:49:53:56:59:63:67:70:74:78:84 SD: 2.1534 cents 43:46:48:50:54:57:60:64:69:72:75:80:86 SD: 1.8269 cents 48:51:54:56:60:64:67:72:77:80:84:90:96 SD: 1.3724 cents 60:64:67:70:75:80:84:90:96:100:105:112:120 SD: 0.7732 cents 107:114:120:125:134:143:150:160:171:178:187:200:214 SD: 0.7335 cents 108:115:121:126:135:144:151:161:173:180:189:202:216 SD: 0.5235 cents 120:128:134:140:150:160:168:179:192:200:210:224:240 SD: 0.4592 cents 132:141:148:154:165:176:185:197:211:220:231:246:264 SD: 0.4147 cents 168:179:188:196:210:224:235:251:269:280:294:314:336 SD: 0.3258 cents 180:192:202:210:225:240:252:269:288:300:315:336:360 SD: 0.3054 cents 192:205:215:224:240:256:269:287:307:320:336:358:384 SD: 0.2944 cents 240:256:269:280:300:320:336:358:384:400:420:448:480 SD: 0.1936 cents 300:320:336:350:375:400:420:448:480:500:525:560:600 S SD: 0.0000 cents