Scala analysis: dentirrmean
Tom Dent's 7-limit irregular meantone
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 1875/1792 78.383950 2: 28/25 196.198479 middle second 3: 1875/1568 309.558043 4: 5/4 386.313714 major third 5: 75/56 505.756522 marvelous fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 196/125 778.710671 9: 375/224 892.070236 10: 224/125 1009.884765 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: 1875/1792 78.3839 2: 50176/46875 117.8145 3: 46875/43904 113.3596 4: 392/375 76.7557 5: 15/14 119.4428 major diatonic semitone 6: 392/375 76.7557 7: 15/14 119.4428 major diatonic semitone 8: 392/375 76.7557 9: 46875/43904 113.3596 10: 50176/46875 117.8145 11: 1875/1792 78.3839 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 392/375 76.756 cents 1: 2 1875/1792 78.384 cents 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 46875/43904 113.360 cents 1: 2 50176/46875 117.815 cents 1: 2 15/14 119.443 cents major diatonic semitone 2: 4 125/112 190.115 cents classic augmented semitone 2: 6 28/25 196.198 cents middle second 2: 2 8/7 231.174 cents septimal whole tone 3: 1 234375/200704 268.499 cents 3: 2 10976/9375 272.954 cents 3: 4 448/375 307.930 cents 3: 4 1875/1568 309.558 cents 3: 1 6/5 315.641 cents minor third 4: 6 5/4 386.314 cents major third 4: 2 784/625 392.397 cents two (middle second) 4: 2 125/98 421.289 cents 4: 2 32/25 427.373 cents classic diminished fourth 5: 1 307328/234375 469.153 cents 5: 2 4/3 498.045 cents perfect fourth 5: 2 234375/175616 499.673 cents 5: 3 12544/9375 504.128 cents 5: 4 75/56 505.757 cents marvelous fourth 6: 2 625/448 576.429 cents 6: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 4 10/7 617.488 cents Euler's tritone 6: 2 896/625 623.571 cents 7: 4 112/75 694.243 cents marvelous fifth 7: 3 9375/6272 695.872 cents 7: 2 351232/234375 700.327 cents 7: 2 3/2 701.955 cents perfect fifth 7: 1 234375/153664 730.847 cents 8: 2 25/16 772.627 cents classic augmented fifth 8: 2 196/125 778.711 cents 8: 2 625/392 807.603 cents 8: 6 8/5 813.686 cents minor sixth 9: 1 5/3 884.359 cents major sixth, BP sixth 9: 4 3136/1875 890.442 cents 9: 4 375/224 892.070 cents 9: 2 9375/5488 927.046 cents 9: 1 401408/234375 931.501 cents 10: 2 7/4 968.826 cents harmonic seventh 10: 6 25/14 1003.802 cents middle minor seventh 10: 4 224/125 1009.885 cents 11: 2 28/15 1080.557 cents grave major seventh 11: 2 46875/25088 1082.185 cents 11: 2 87808/46875 1086.640 cents 11: 1 15/8 1088.269 cents classic major seventh 11: 2 3584/1875 1121.616 cents 11: 3 375/196 1123.244 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.54545 = 50/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 78.4 196.2 309.6 386.3 505.8 582.5 702.0 778.7 892.1 1009.9 1088.3 1200.0 78.4 : 117.8 231.2 307.9 427.4 504.1 623.6 700.3 813.7 931.5 1009.9 1121.6 1200.0 196.2 : 113.4 190.1 309.6 386.3 505.8 582.5 695.9 813.7 892.1 1003.8 1082.2 1200.0 309.6 : 76.8 196.2 273.0 392.4 469.2 582.5 700.3 778.7 890.4 968.8 1086.6 1200.0 386.3 : 119.4 196.2 315.6 392.4 505.8 623.6 702.0 813.7 892.1 1009.9 1123.2 1200.0 505.8 : 76.8 196.2 273.0 386.3 504.1 582.5 694.2 772.6 890.4 1003.8 1080.6 1200.0 582.5 : 119.4 196.2 309.6 427.4 505.8 617.5 695.9 813.7 927.0 1003.8 1123.2 1200.0 702.0 : 76.8 190.1 307.9 386.3 498.0 576.4 694.2 807.6 884.4 1003.8 1080.6 1200.0 778.7 : 113.4 231.2 309.6 421.3 499.7 617.5 730.8 807.6 927.0 1003.8 1123.2 1200.0 892.1 : 117.8 196.2 307.9 386.3 504.1 617.5 694.2 813.7 890.4 1009.9 1086.6 1200.0 1009.9: 78.4 190.1 268.5 386.3 499.7 576.4 695.9 772.6 892.1 968.8 1082.2 1200.0 1088.3: 111.7 190.1 307.9 421.3 498.0 617.5 694.2 813.7 890.4 1003.8 1121.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.7557 .. 119.4428 cents 5625/5488, 42.6871 cents 392/375, 76.7557 cents 2: 190.1152 .. 231.1741 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 3: 268.4992 .. 315.6413 cents 401408/390625, 47.1421 cents 234375/229376, 37.3251 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 469.1526 .. 505.7565 cents 17578125/17210368, 36.6039 cents 9604/9375, 41.7801 cents 6: 576.4289 .. 623.5711 cents 401408/390625, 47.1421 cents 25/24, 70.6724 cents 7: 694.2435 .. 730.8474 cents 17578125/17210368, 36.6039 cents 25/24, 70.6724 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 9604/9375, 41.7801 cents 9: 884.3587 .. 931.5008 cents 401408/390625, 47.1421 cents 25/24, 70.6724 cents 10: 968.8259 .. 1009.8848 cents 128/125, 41.0589 cents 234375/229376, 37.3251 cents 11: 1080.5572 .. 1123.2443 cents 5625/5488, 42.6871 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 392/375, 76.7557 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 1.302835 Largest / Average step : 1.194428 Largest / Smallest step : 1.556143 Median interval of one step : 112.54542 cents, amount: 0 Most common interval of one step : 392/375, 76.7557 cents, amount: 3 Least squares average step : 99.40057 cents, oct.: 1192.80686 cents Scale is strictly proper Step pattern alph. order: ABCDEDEDCBAF Step pattern size order : BEDAFAFADEBC Scale is a Constant Structure, by a margin of 37.32509 cents Scale diversity : 1.277413 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.613130 Rothenberg efficiency : 0.297499 redundancy: 0.702501 Efficiency x scale size : 3.569986 Number of different interval sizes : 50 = 4.54545 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.54545 = 50/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 703125/702464, 1.6283 cents Number of recognisable fifths : 11, average 697.1957 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 7 Odd number limit : 234375 (O: 234375 U: 234375) Highest odd numerator or denominator: 1875 Scale harmonicity : 0.009842 Average absolute harmonicity : 0.144094 Specific harmonicity : 0.060000 Fundamental : 1/1568000, -20.5805 octaves, 0.0002 Hz. Guide tone : 2940000, 21.4874 octaves, 769179161.985 Hz. Exponens Consonantiae : 4.609920E+12, 42.06788 octaves Euler's gradus suavitatis : 68 Sum of Mann's harmonic distance : 4307.5, average 358.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 19.78414, average 1.64868 Sum of Tenney's harmonic distance : 39.22710, average 3.26892 Vogel's harmonic complexity : 39.58333 Wille's k value : 820312 Wilson's harmonic complexity : 66 Rectangular lattice diameter : 12 Triangular lattice diameter : 8 Lattice compactness : 417.85112, average 5.35707 Lattice compactness (without 2's) : 251.41470, average 3.22327 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -8 .. 5 -1.41667 37 1 3: 0 .. 1 0.50000 6 1 5: -3 .. 4 0.50000 24 2 7: -2 .. 2 0.00000 10 8 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 40 / 12 = 3.33333 Scale is weakly epimorphic with val: <12 17 28 34| Scale is weakly epimorphic with val: <12 18 27 34| Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 20 29 33| Scale is weakly epimorphic with val: <12 21 28 34|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.4318 c. M:-21.6161 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 10.5248 c. M: 20.8159 c. Meantone Chromatic (1/3-comma) 26: 2 2 3 1 3 2 2 2 2 3 2 2 SP D3 SD: 12.5070 c. M:-19.4236 c. 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 12.4019 c. M: 23.1047 c. Schismic-12 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 2.8853 c. M: 5.1808 c. Meantone Chromatic (53/220-comma) 74: 5 7 7 5 7 5 7 5 7 7 5 7 SP M DE SD: 2.5205 c. M: 4.6577 c. Meantone Chromatic (3/14-comma), Grosstone-12 97: 6 10 9 6 10 6 10 6 9 10 6 9 SP SD: 2.3255 c. M:-4.5482 c. 109: 7 11 10 7 11 7 11 7 10 11 7 10 SP SD: 1.7514 c. M:-2.9593 c. 128: 8 13 12 8 13 8 13 8 12 13 8 12 SP SD: 1.5483 c. M: 3.3839 c. 140: 9 14 13 9 14 9 14 9 13 14 9 13 SP SD: 0.8779 c. M:-1.5438 c. 171: 11 17 16 11 17 11 17 11 16 17 11 16 SP SD: 0.5780 c. M: 1.1910 c. 202: 13 20 19 13 20 13 20 13 19 20 13 19 SP SD: 0.7076 c. M: 1.1562 c. 214: 14 21 20 14 21 14 21 14 20 21 14 20 SP SD: 0.6821 c. M: 1.1468 c. 311: 20 31 29 20 31 20 31 20 29 31 20 29 SP SD: 0.6570 c. M: 1.2135 c. 354: 23 35 33 23 35 23 35 23 33 35 23 33 SP SD: 0.5509 c. M: 1.0835 c. 367: 24 36 35 23 37 23 37 23 35 36 24 34 SP SD: 0.6423 c. M:-1.0687 c. 373: 24 37 35 24 37 24 37 24 35 37 24 35 SP SD: 0.6137 c. M: 1.1722 c. 379: 25 37 36 24 38 24 38 24 36 37 25 35 SP SD: 0.5978 c. M:-0.9474 c. 385: 25 38 36 25 38 25 38 25 36 38 25 36 SP SD: 0.5299 c. M: 0.9866 c. 398: 26 39 38 25 40 25 40 25 38 39 26 37 SP SD: 0.5281 c. M:-0.9947 c. 410: 27 40 39 26 41 26 41 26 39 40 27 38 SP SD: 0.4240 c. M:-0.6859 c. 441: 29 43 42 28 44 28 44 28 42 43 29 41 SP SD: 0.3593 c. M:-0.6460 c. 550: 36 54 52 35 55 35 55 35 52 54 36 51 SP SD: 0.3018 c. M:-0.5905 c. 569: 37 56 54 36 57 36 57 36 54 56 37 53 SP SD: 0.3274 c. M: 0.5033 c. 581: 38 57 55 37 58 37 58 37 55 57 38 54 SP SD: 0.1642 c. M:-0.2825 c. 612: 40 60 58 39 61 39 61 39 58 60 40 57 SP SD: 0.1332 c. M: 0.2793 c. 752: 49 74 71 48 75 48 75 48 71 74 49 70 SP SD: 0.1153 c. M:-0.2216 c. 783: 51 77 74 50 78 50 78 50 74 77 51 73 SP SD: 0.1123 c. M: 0.2230 c. 795: 52 78 75 51 79 51 79 51 75 78 52 74 SP SD: 0.0911 c. M:-0.1573 c. 1364: 89 134 129 87 136 87 136 87 129 134 89 127 SP SD: 0.0843 c. M:-0.1194 c. 1376: 90 135 130 88 137 88 137 88 130 135 90 128 SP SD: 0.0625 c. M:-0.1044 c. 1407: 92 138 133 90 140 90 140 90 133 138 92 131 SP SD: 0.0416 c. M:-0.0809 c. 1578: 103 155 149 101 157 101 157 101 149 155 103 147 SP SD: 0.0386 c. M: 0.0570 c. 2159: 141 212 204 138 215 138 215 138 204 212 141 201 SP SD: 0.0220 c. M:-0.0367 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: 3.6352 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.2647 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.2657 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.7962 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.7801 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.1643 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.0224 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.8621 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 10.0780 cents 12 x 13:14:15:16:17:18:19:20 x 23:24 SD: 8.6101 cents 13:14:15 x 16:17:18 x 20:22:23:24:26 S SD: 10.2896 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.9638 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.8947 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.0841 cents 20:21:22:24:25:27:28:30:31:33:36:38:40 SD: 4.4510 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 2.9673 cents 32:33:36:38:40:43:45:48:50:54:57:60:64 SD: 2.9622 cents 35:37:39:42:44:47:49:53:55:59:63:66:70 SD: 2.8075 cents 39:41:44:47:49:52:55:59:61:65:70:73:78 SD: 2.6580 cents 40:42:45:48:50:54:56:60:63:67:72:75:80 SD: 1.7551 cents 56:59:63:67:70:75:78:84:88:94:100:105:112 SD: 1.5688 cents 60:63:67:72:75:80:84:90:94:100:108:113:120 SD: 1.5369 cents 62:65:69:74:78:83:87:93:97:104:111:116:124 SD: 1.5065 cents 65:68:73:78:81:87:91:98:102:109:116:122:130 SD: 1.2699 cents 67:70:75:80:84:90:94:101:105:112:120:126:134 SD: 1.1468 cents 68:71:76:81:85:91:95:102:107:114:122:128:136 SD: 1.1169 cents 82:86:92:98:103:110:115:123:129:137:147:154:164 SD: 1.0788 cents 83:87:93:99:104:111:116:125:130:139:149:156:166 SD: 0.9890 cents 88:92:99:105:110:118:123:132:138:147:158:165:176 SD: 0.8881 cents 92:96:103:110:115:123:129:138:144:154:165:173:184 SD: 0.7243 cents 127:133:142:152:159:170:178:191:199:213:228:238:254 SD: 0.6876 cents 128:134:143:153:160:171:179:192:201:214:229:240:256 SD: 0.6599 cents 132:138:148:158:165:177:185:198:207:221:237:248:264 SD: 0.5254 cents 148:155:166:177:185:198:207:222:232:248:265:278:296 SD: 0.4550 cents 168:176:188:201:210:225:235:252:263:281:301:315:336 SD: 0.3734 cents 192:201:215:230:240:257:269:288:301:321:344:360:384 SD: 0.3588 cents 200:209:224:239:250:268:280:300:314:335:358:375:400 SD: 0.3372 cents 215:225:241:257:269:288:301:323:337:360:385:403:430 SD: 0.3208 cents 240:251:269:287:300:321:336:360:376:402:430:450:480 SD: 0.2734 cents 260:272:291:311:325:348:364:390:408:435:466:488:520 SD: 0.2516 cents 280:293:314:335:350:375:392:420:439:469:502:525:560 SD: 0.2254 cents 368:385:412:440:460:493:515:552:577:616:659:690:736 SD: 0.1373 cents 500:523:560:598:625:670:700:750:784:837:896:938:1000 SD: 0.1203 cents 592:619:663:708:740:793:829:888:928:991:1061:1110:1184 SD: 0.1179 cents