Scala analysis: met24-quasi_5-EDO_F
One of George Secor's alternatives for 5-EDO (blarney.txt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 264.844 cents 264.843750 2: 495.703 cents 495.703130 3: 703.125 cents 703.125000 4: 967.969 cents 967.968750 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 232.0312 cents 232.0312 1: 264.8438 cents 264.8438 2: 230.8594 cents 230.8594 3: 207.4219 cents 207.4219 4: 264.8437 cents 264.8437 5: 232.0312 cents 232.0312
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 207.42187 cents 1: 1 230.85938 cents 1: 1 232.03125 cents 1: 2 264.84375 cents 2: 1 438.28125 cents 2: 1 472.26562 cents 2: 1 495.70313 cents 2: 2 496.87500 cents 3: 2 703.12500 cents 3: 1 704.29687 cents 3: 1 727.73438 cents 3: 1 761.71875 cents 4: 2 935.15625 cents 4: 1 967.96875 cents 4: 1 969.14062 cents 4: 1 992.57813 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 264.8 495.7 703.1 968.0 1200.0 264.8 : 230.9 438.3 703.1 935.2 1200.0 495.7 : 207.4 472.3 704.3 969.1 1200.0 703.1 : 264.8 496.9 761.7 992.6 1200.0 968.0 : 232.0 496.9 727.7 935.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 207.4219 .. 264.8438 cents 57.42188 cents 207.42187 cents 2: 438.2813 .. 496.8750 cents 58.59375 cents 173.43750 cents 3: 703.1250 .. 761.7188 cents 58.59375 cents 206.25000 cents 4: 935.1562 .. 992.5781 cents 57.42188 cents 173.43750 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 207.42187 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 264.84375 cents Average / Smallest step : 1.157062 Largest / Average step : 1.103516 Largest / Smallest step : 1.276836 Median interval of one step : 232.03125 cents, amount: 1 Most common interval of one step : 264.84375 cents, amount: 2 Least squares average step : 240.68182 cents, oct.: 1203.40909 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 226 423 600 826 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 911 of 1067.578 cents and inv. generated superset size: 108 = 103 more = 2160.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCAD Step pattern size order : DBADC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 173.43750 cents Scale diversity : 1.240979 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.806641 Rothenberg efficiency : 0.480000 redundancy: 0.520000 Efficiency x scale size : 2.400000 Number of different interval sizes : 16 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17187 cents Number of recognisable fifths : 3, average 703.5156 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 20.0000% Limited transpositions with margin 58.5937 cents: 4 Limited inverse transpositions with margin 58.5938 cents: 2 4 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 15.5696 c. M: 24.8438 c. 17: 4 3 3 4 3 SP M ME S SD: 12.0617 c. M:-20.2665 c. Seventeen-tone Minor Pentatonic, Supra-5, Salendro Sejati: Sunda 22: 5 4 4 5 4 SP M ME S SD: 7.9061 c. M:-13.8494 c. Septimal Minor Pentatonic, Supra-5 26: 6 5 4 6 5 SP T3 SD: 9.0361 c. M:-12.0793 c. 27: 6 5 5 6 5 SP M ME S SD: 6.4769 c. M:-9.8090 c. Septimal Minor Pentatonic, Supra-5 31: 7 6 5 7 6 SP T3 SD: 5.1861 c. M:-7.5227 c. Septimal Minor Pentatonic 36: 8 7 6 8 7 SP T3 SD: 2.5786 c. M:-4.2969 c. 41: 9 8 7 9 8 SP T3 SD: 1.4449 c. M: 2.1151 c. 99: 22 19 17 22 19 SP T3 SD: 1.2588 c. M:-1.8229 c. 104: 23 20 18 23 20 SP T3 SD: 0.7223 c. M:-1.2620 c. 145: 32 28 25 32 28 SP T3 SD: 0.4288 c. M:-0.8486 c. 249: 55 48 43 55 48 SP T3 SD: 0.5001 c. M:-0.7059 c. 254: 56 49 44 56 49 SP T3 SD: 0.4800 c. M:-0.8120 c. 295: 65 57 51 65 57 SP T3 SD: 0.4257 c. M:-0.6038 c. 394: 87 76 68 87 76 SP T3 SD: 0.4618 c. M:-0.7436 c. 399: 88 77 69 88 77 SP T3 SD: 0.4311 c. M:-0.6344 c. 440: 97 85 76 97 85 SP T3 SD: 0.4080 c. M:-0.6605 c. 526: 116 101 91 116 102 SP SD: 0.4735 c. M: 0.6684 c. 538: 119 103 93 119 104 SP SD: 0.4254 c. M:-0.5838 c. 543: 120 104 94 120 105 SP SD: 0.3769 c. M: 0.6755 c. 579: 128 111 100 128 112 SP SD: 0.3530 c. M: 0.5343 c. 584: 129 112 101 129 113 SP SD: 0.3074 c. M: 0.4977 c. 589: 130 113 102 130 114 SP SD: 0.3167 c. M: 0.6267 c. 620: 137 119 107 137 120 SP SD: 0.3152 c. M: 0.5444 c. 625: 138 120 108 138 121 SP SD: 0.2752 c. M: 0.4050 c. 630: 139 121 109 139 122 SP SD: 0.2888 c. M: 0.4650 c. 666: 147 128 115 147 129 SP SD: 0.2767 c. M: 0.4223 c. 671: 148 129 116 148 130 SP SD: 0.2922 c. M: 0.4576 c. 683: 151 131 118 151 132 SP SD: 0.2819 c. M:-0.4564 c. 688: 152 132 119 152 133 SP SD: 0.2237 c. M: 0.3543 c. 693: 153 133 120 153 134 SP SD: 0.2161 c. M: 0.4650 c. 729: 161 140 126 161 141 SP SD: 0.1723 c. M: 0.2443 c. 734: 162 141 127 162 142 SP SD: 0.1694 c. M: 0.3353 c. 770: 170 148 133 170 149 SP SD: 0.1583 c. M: 0.2679 c. 775: 171 149 134 171 150 SP SD: 0.1607 c. M: 0.2268 c. 833: 184 160 144 184 161 SP SD: 0.1382 c. M:-0.2223 c. 838: 185 161 145 185 162 SP SD: 0.1139 c. M: 0.2377 c. 874: 193 168 151 193 169 SP SD: 0.0961 c. M: 0.1502 c. 879: 194 169 152 194 170 SP SD: 0.0707 c. M: 0.1400 c. 920: 203 177 159 203 178 SP SD: 0.0816 c. M: 0.1427 c. 983: 217 189 170 217 190 SP SD: 0.0603 c. M:-0.0882 c. 1024: 226 197 177 226 198 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.5850 cents 3 x 4 x 5:6 S SD: 27.8809 cents 4 x 5:6:7:8 S SD: 27.3498 cents 6:7:8:9:11:12 SD: 16.2923 cents 11:13:15:17:19:22 SD: 14.5886 cents 12:14:16:18:21:24 S SD: 0.6840 cents 139:162:185:209:243:278 SD: 0.6442 cents 151:176:201:227:264:302 SD: 0.5674 cents 163:190:217:245:285:326 SD: 0.5058 cents 175:204:233:263:306:350 SD: 0.4568 cents 187:218:249:281:327:374 SD: 0.4183 cents 199:232:265:299:348:398 SD: 0.3886 cents 211:246:281:317:369:422 SD: 0.3664 cents 223:260:297:335:390:446 SD: 0.3505 cents 235:274:313:353:411:470 SD: 0.3397 cents 247:288:329:371:432:494 SD: 0.3332 cents 259:302:345:389:453:518 SD: 0.3301 cents 271:316:361:407:474:542 SD: 0.3296 cents 284:331:378:426:497:568 SD: 0.3278 cents 290:338:386:435:507:580 SD: 0.3231 cents 296:345:394:444:518:592 SD: 0.3208 cents 302:352:402:453:528:604 SD: 0.3104 cents 314:366:418:471:549:628 SD: 0.3009 cents 326:380:434:489:570:652 SD: 0.2942 cents 338:394:450:507:591:676 SD: 0.2900 cents 350:408:466:525:612:700 SD: 0.2879 cents 362:422:482:543:633:724 SD: 0.2876 cents 363:423:483:545:635:726 SD: 0.2639 cents 375:437:499:563:656:750 SD: 0.2400 cents 387:451:515:581:677:774 SD: 0.2187 cents 399:465:531:599:698:798 SD: 0.1998 cents 411:479:547:617:719:822 SD: 0.1834 cents 423:493:563:635:740:846 SD: 0.1696 cents 435:507:579:653:761:870 SD: 0.1584 cents 447:521:595:671:782:894 SD: 0.1498 cents 459:535:611:689:803:918 SD: 0.1437 cents 471:549:627:707:824:942 SD: 0.1401 cents 483:563:643:725:845:966 SD: 0.1388 cents