Scala analysis: met24-ptolemy_hom_Bup
Tempering of Ptolemy's Homalon or Equable Diatonic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150.000 cents 150.000000 2: 312.891 cents 312.890630 3: 495.703 cents 495.703130 4: 703.125 cents 703.125000 5: 853.125 cents 853.125000 6: 1016.016 cents 1016.015630 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 183.9844 cents 183.9844 1: 150.0000 cents 150.0000 2: 162.8906 cents 162.8906 3: 182.8125 cents 182.8125 4: 207.4219 cents 207.4219 5: 150.0000 cents 150.0000 6: 162.8906 cents 162.8906 7: 183.9844 cents 183.9844
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 150.00000 cents 1: 2 162.89063 cents 1: 1 182.81250 cents 1: 1 183.98437 cents 1: 1 207.42187 cents 2: 2 312.89063 cents 2: 1 333.98437 cents 2: 1 345.70313 cents 2: 1 346.87500 cents 2: 1 357.42187 cents 2: 1 390.23437 cents 3: 1 495.70313 cents 3: 3 496.87500 cents 3: 1 520.31250 cents 3: 1 540.23437 cents 3: 1 553.12500 cents 4: 1 646.87500 cents 4: 1 659.76563 cents 4: 1 679.68750 cents 4: 3 703.12500 cents 4: 1 704.29687 cents 5: 1 809.76563 cents 5: 1 842.57813 cents 5: 1 853.12500 cents 5: 1 854.29687 cents 5: 1 866.01563 cents 5: 2 887.10937 cents 6: 1 992.57813 cents 6: 1 1016.01563 cents 6: 1 1017.18750 cents 6: 2 1037.10937 cents 6: 2 1050.00000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.33333 = 16/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 150.0 312.9 495.7 703.1 853.1 1016.0 1200.0 150.0 : 162.9 345.7 553.1 703.1 866.0 1050.0 1200.0 312.9 : 182.8 390.2 540.2 703.1 887.1 1037.1 1200.0 495.7 : 207.4 357.4 520.3 704.3 854.3 1017.2 1200.0 703.1 : 150.0 312.9 496.9 646.9 809.8 992.6 1200.0 853.1 : 162.9 346.9 496.9 659.8 842.6 1050.0 1200.0 1016.0: 184.0 334.0 496.9 679.7 887.1 1037.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.0000 .. 207.4219 cents 57.42187 cents 150.00000 cents 2: 312.8906 .. 390.2344 cents 77.34374 cents 105.46876 cents 3: 495.7031 .. 553.1250 cents 57.42187 cents 105.46876 cents 4: 646.8750 .. 704.2969 cents 57.42187 cents 93.75000 cents 5: 809.7656 .. 887.1094 cents 77.34374 cents 105.46876 cents 6: 992.5781 .. 1050.0000 cents 57.42187 cents 105.46876 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 150.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 207.42187 cents Average / Smallest step : 1.142857 Largest / Average step : 1.209961 Largest / Smallest step : 1.382812 Median interval of one step : 162.89063 cents, amount: 2 Least squares average step : 170.26507 cents, oct.: 1191.85547 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 128 267 423 600 728 867 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 655 of 767.578 cents and inv. generated superset size: 192 = 185 more = 2742.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDABE Step pattern size order : ABCEABD Scale is a Constant Structure, by a margin of 93.75000 cents Scale diversity : 1.339376 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.679688 Rothenberg efficiency : 0.355102 redundancy: 0.644898 Efficiency x scale size : 2.485714 Number of different interval sizes : 32 = 5.33333 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.33333 = 16/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 1.17187 cents Most common intervals : 496.87500 cents & inv., amount: 3 Most common triad is 0.0 703.125 1050.000 cents, amount: 1 Number of recognisable fifths : 4, average 703.4180 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 = 14.2857% Limited inverse transpositions with margin 77.3437 cents: 6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 17.6450 c. M:-29.9665 c. Lebeng 15: 2 2 2 3 2 2 2 SP M ME I SD: 16.8159 c. M:-26.8750 c. Miller's Porcupine-7 17: 2 2 3 3 2 2 3 SP D3 S SD: 16.1646 c. M: 30.5377 c. 19: 2 3 3 3 3 2 3 SP D3 S SD: 15.7096 c. M:-31.0855 c. 22: 3 3 3 4 3 3 3 SP M ME I SD: 13.3612 c. M:-20.3480 c. Minor quasi-equal Heptatonic, Miller's Porcupine-7 24: 3 3 4 4 3 3 4 SP D3 S SD: 8.1123 c. M: 16.0156 c. Maqam Hussaini, Ushaq, Neutral Diatonic Dorian 31: 4 4 5 5 4 4 5 SP D3 S SD: 5.6621 c. M: 9.5640 c. Neutral Diatonic Dorian 34: 4 5 5 6 4 5 5 SP T3 SD: 5.3964 c. M: 8.8235 c. 39: 5 5 6 7 5 5 6 SP SD: 4.5574 c. M:-8.4135 c. 46: 6 6 7 8 6 6 7 SP SD: 3.8900 c. M:-7.7446 c. 58: 7 8 9 10 7 8 9 SP SD: 2.9884 c. M: 5.1724 c. 65: 8 9 10 11 8 9 10 SP SD: 2.1357 c. M: 3.8942 c. 73: 9 10 11 13 9 10 11 SP SD: 2.3211 c. M:-3.7243 c. 80: 10 11 12 14 10 11 12 SP SD: 1.9946 c. M:-3.9844 c. 97: 12 13 15 17 12 13 15 SP SD: 1.8140 c. M: 3.6123 c. 104: 13 14 16 18 13 14 16 SP SD: 0.7041 c. M: 1.3522 c. 169: 21 23 26 29 21 23 26 SP SD: 0.7866 c. M:-1.3383 c. 184: 23 25 28 32 23 25 28 SP SD: 0.8374 c. M:-1.3757 c. 215: 27 29 33 37 27 29 33 SP SD: 0.5886 c. M:-1.0411 c. 249: 31 34 38 43 31 34 38 SP SD: 0.5262 c. M:-0.8518 c. 319: 40 43 49 55 40 43 49 SP SD: 0.5650 c. M:-0.8486 c. 353: 44 48 54 61 44 48 54 SP SD: 0.3926 c. M:-0.6142 c. 457: 57 62 70 79 57 62 70 SP SD: 0.3913 c. M:-0.5949 c. 464: 58 63 71 80 58 63 71 SP SD: 0.3897 c. M:-0.8486 c. 560: 70 76 85 97 70 76 86 SP SD: 0.3229 c. M: 0.7031 c. 567: 71 77 86 98 71 77 87 SP SD: 0.3154 c. M: 0.4795 c. 640: 80 87 97 111 80 87 98 SP SD: 0.2938 c. M: 0.7031 c. 664: 83 90 101 115 83 90 102 SP SD: 0.2620 c. M: 0.5224 c. 671: 84 91 102 116 84 91 103 SP SD: 0.2065 c. M: 0.3231 c. 775: 97 105 118 134 97 105 119 SP SD: 0.1691 c. M: 0.2737 c. 809: 101 110 123 140 101 110 124 SP SD: 0.1564 c. M: 0.2767 c. 855: 107 116 130 148 107 116 131 SP SD: 0.1555 c. M: 0.2645 c. 913: 114 124 139 158 114 124 140 SP SD: 0.1110 c. M: 0.1938 c. 920: 115 125 140 159 115 125 141 SP SD: 0.0796 c. M:-0.1528 c. 1024: 128 139 156 177 128 139 157 SP SD: 0.0000 c. M: 0.0000 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: 0.5850 cents 3 x x 4 x 5 x 6 S SD: 10.4405 cents 4 x 5 x 6 x 7:8 S SD: 21.8220 cents 5 x 6:7 x 8:9:10 S SD: 19.0801 cents 6 x 7:8:9:10:11:12 S SD: 10.8170 cents 7:8 x 9 x 11:13:14 SD: 27.0953 cents 8:9:10:11:12:13:14:16 S SD: 16.7680 cents 9:10:11:12:14:15:16:18 S SD: 12.3202 cents 10:11:12:13:15:16:18:20 SD: 8.4676 cents 14:15:17:19:21:23:25:28 SD: 7.4946 cents 19:21:23:25:29:31:34:38 SD: 6.7416 cents 20:22:24:27:30:33:36:40 S SD: 4.5100 cents 24:26:29:32:36:39:43:48 SD: 3.3649 cents 30:33:36:40:45:49:54:60 SD: 2.2859 cents 36:39:43:48:54:59:65:72 SD: 2.1080 cents 46:50:55:61:69:75:83:92 SD: 1.8934 cents 54:59:65:72:81:88:97:108 SD: 1.7260 cents 55:60:66:73:83:90:99:110 SD: 1.6151 cents 64:70:77:85:96:105:115:128 SD: 1.5508 cents 66:72:79:88:99:108:119:132 SD: 0.7873 cents 100:109:120:133:150:164:180:200 SD: 0.7424 cents 121:132:145:161:182:198:218:242 SD: 0.7187 cents 130:142:156:173:195:213:234:260 SD: 0.6911 cents 132:144:158:176:198:216:237:264 SD: 0.6063 cents 157:171:188:209:236:257:282:314 SD: 0.5752 cents 166:181:199:221:249:272:299:332 SD: 0.5190 cents 178:194:213:237:267:291:320:356 SD: 0.4911 cents 187:204:224:249:281:306:336:374 SD: 0.3709 cents 223:243:267:297:335:365:401:446 SD: 0.3254 cents 232:253:278:309:348:380:417:464 SD: 0.2768 cents 253:276:303:337:380:414:455:506 SD: 0.2380 cents 287:313:344:382:431:470:516:574 SD: 0.2288 cents 308:336:369:410:462:504:554:616 SD: 0.2210 cents 353:385:423:470:530:578:635:706 SD: 0.1369 cents 465:507:557:619:698:761:836:930 SD: 0.1252 cents 485:529:581:646:728:794:872:970 SD: 0.1201 cents 531:579:636:707:797:869:955:1062 SD: 0.0962 cents