Scala analysis: porchrome3
Third 25/24&250/243 scale = inverse porchrome2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 5/4 386.313714 major third 3: 25/18 568.717426 classic augmented fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 125/108 253.0761 semi-augmented whole tone 3: 10/9 182.4037 minor whole tone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 1: 1 125/108 253.076 cents semi-augmented whole tone 2: 5 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 1 625/486 435.480 cents 3: 2 162/125 448.879 cents 3: 2 4/3 498.045 cents perfect fourth 3: 3 25/18 568.717 cents classic augmented fourth 4: 3 36/25 631.283 cents classic diminished fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 125/81 751.121 cents 5: 1 972/625 764.520 cents 5: 1 8/5 813.686 cents minor sixth 5: 5 5/3 884.359 cents major sixth, BP sixth 6: 1 216/125 946.924 cents semi-augmented sixth 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 50/27 1066.762 cents grave major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 133.2 386.3 568.7 702.0 884.4 1017.6 1200.0 133.2 : 253.1 435.5 568.7 751.1 884.4 1066.8 1200.0 386.3 : 182.4 315.6 498.0 631.3 813.7 946.9 1200.0 568.7 : 133.2 315.6 448.9 631.3 764.5 1017.6 1200.0 702.0 : 182.4 315.6 498.0 631.3 884.4 1066.8 1200.0 884.4 : 133.2 315.6 448.9 702.0 884.4 1017.6 1200.0 1017.6: 182.4 315.6 568.7 751.1 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 253.0761 cents 3125/2916, 119.8386 cents 27/25, 133.2376 cents 2: 315.6413 .. 435.4799 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents 3: 448.8789 .. 568.7174 cents 3125/2916, 119.8386 cents 78732/78125, 13.3990 cents 4: 631.2826 .. 751.1211 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents 5: 764.5201 .. 884.3587 cents 3125/2916, 119.8386 cents 78732/78125, 13.3990 cents 6: 946.9239 .. 1066.7624 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 125/108, 253.0761 cents Average / Smallest step : 1.286638 Largest / Average step : 1.476277 Largest / Smallest step : 1.899435 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 173.90863 cents, oct.: 1217.36043 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCACAC Step pattern size order : SLMSMSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.413097 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.400807 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 78732/78125, 13.3990 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 182.404 315.641 cents Most common triad is 0.0 315.641 884.359 cents, amount: 3 Number of recognisable fifths : 2, average 701.9550 cents Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 5 Odd number limit : 625 (O: 625 U: 625) Highest odd numerator or denominator: 27 Scale harmonicity : 0.023847 Average absolute harmonicity : 0.241091 Specific harmonicity : 0.147897 Fundamental : 1/900, -9.8138 octaves, 0.2907 Hz. Guide tone : 1350, 10.3987 octaves, 353194.513 Hz. Exponens Consonantiae : 1.215000E+06, 20.21252 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 67.0, average 9.57143 Mersenne's string divisions : 1408680 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 10.69203, average 1.52743 Vogel's harmonic complexity : 19.57143 Wille's k value : 562 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 80.38255, average 2.87081 Lattice compactness (without 2's) : 68.81123, average 2.45754 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.42857 5 1 3: -2 .. 3 0.42857 9 1 5: -2 .. 2 0.14286 7 5 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.5900 c. M: 54.4317 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 35.6941 c. M:-63.6863 c. 9: 1 2 1 1 2 1 1 P M ME S SD: 32.7131 c. M:-49.0704 c. Pelog Saptanada: Sunda 10: 1 2 2 1 1 1 2 N D3 SD: 32.6385 c. M: 57.5963 c. 11: 1 2 2 1 2 1 2 P M ME S SD: 34.3783 c. M: 59.0410 c. Orgone-7 12: 1 3 2 1 2 1 2 N T3 SD: 20.1024 c. M: 33.2376 c. Romanian Major, Mela Ramapriya, Raga Basant Bahar, Ramamanohari, Petrushka chord, Mixolydian flat 2 sharp 4 15: 2 3 2 2 2 2 2 SP M ME S SD: 16.1514 c. M:-26.7624 c. Miller's Porcupine-7 Major 19: 2 4 3 2 3 2 3 P T3 SD: 5.4033 c. M: 7.3663 c. 34: 4 7 5 4 5 4 5 SP T3 SD: 4.4314 c. M:-7.9389 c. 46: 5 10 7 5 7 5 7 P T3 SD: 3.2132 c. M:-5.1956 c. 53: 6 11 8 6 8 6 8 SP T3 SD: 1.6648 c. M: 2.6797 c. 72: 8 15 11 8 11 8 11 SP T3 SD: 1.6403 c. M: 2.9804 c. 99: 11 21 15 11 15 11 15 SP T3 SD: 0.8583 c. M:-1.5651 c. 118: 13 25 18 13 18 13 18 SP T3 SD: 0.5758 c. M: 1.0342 c. 152: 17 32 23 17 23 17 23 SP T3 SD: 0.5945 c. M:-0.9730 c. 171: 19 36 26 19 26 19 26 SP T3 SD: 0.2013 c. M: 0.3488 c. 270: 30 57 41 30 41 30 41 SP T3 SD: 0.1981 c. M:-0.3530 c. 441: 49 93 67 49 67 49 67 SP T3 SD: 0.0670 c. M:-0.0958 c. 612: 68 129 93 68 93 68 93 SP T3 SD: 0.0579 c. M:-0.0958 c. 730: 81 154 111 81 111 81 111 SP T3 SD: 0.0478 c. M: 0.0869 c. 901: 100 190 137 100 137 100 137 SP T3 SD: 0.0495 c. M: 0.0762 c. 1171: 130 247 178 130 178 130 178 SP T3 SD: 0.0164 c. M:-0.0272 c. 1342: 149 283 204 149 204 149 204 SP T3 SD: 0.0135 c. M: 0.0246 c. 1783: 198 376 271 198 271 198 271 SP T3 SD: 0.0115 c. M:-0.0210 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 12.1926 cents 5 x 6:7 x 8:9:10 S SD: 20.1787 cents 6 x x 8:9:10:11:12 S SD: 15.4967 cents 8:9:10:11:12:13:14:16 S SD: 13.9949 cents 9:10:11 x 14:15:16:18 SD: 15.2366 cents 10:11:13:14:15:17:18:20 SD: 11.9396 cents 11:12:14:15:17:18:20:22 SD: 11.3100 cents 12:13:15:17:18:20:22:24 SD: 6.7202 cents 16:17:20:22:24:27:29:32 SD: 5.9052 cents 20:22:25:28:30:33:36:40 SD: 5.5368 cents 23:25:29:32:35:38:41:46 SD: 5.5124 cents 24:26:30:33:36:40:43:48 SD: 2.8419 cents 36:39:45:50:54:60:65:72 SD: 1.0779 cents 64:69:80:89:96:107:115:128 SD: 1.0297 cents 88:95:110:122:132:147:158:176 SD: 0.9590 cents 100:108:125:139:150:167:180:200 SD: 0.5323 cents 136:147:170:189:204:227:245:272 SD: 0.4846 cents 164:177:205:228:246:273:295:328 SD: 0.4532 cents 188:203:235:261:282:313:338:376 SD: 0.4103 cents 200:216:250:278:300:333:360:400 SD: 0.3168 cents 224:242:280:311:336:373:403:448 SD: 0.2799 cents 252:272:315:350:378:420:454:504 SD: 0.2621 cents 276:298:345:383:414:460:497:552 SD: 0.2462 cents 288:311:360:400:432:480:518:576 SD: 0.1935 cents 324:350:405:450:486:540:583:648 SD: 0.1019 cents 540:583:675:750:810:900:972:1080 SD: 0.0848 cents 576:622:720:800:864:960:1037:1152 SD: 0.0573 cents