Scala analysis: org1373a
English organ tuning (1373) with 18:17:16 ficta semitones (Eb-G#)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 9/8 203.910002 major whole tone 3: 81/68 302.864594 Persian wosta 4: 81/64 407.820003 Pythagorean major third 5: 4/3 498.044999 perfect fourth 6: 24/17 596.999591 1st septendecimal tritone 7: 3/2 701.955001 perfect fifth 8: 27/17 800.909593 septendecimal minor sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 243/128 1109.775004 Pythagorean major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 18/17 98.9546 Arabic lute index finger 2: 17/16 104.9554 17th harmonic 3: 18/17 98.9546 Arabic lute index finger 4: 17/16 104.9554 17th harmonic 5: 256/243 90.2250 limma, Pythagorean minor second 6: 18/17 98.9546 Arabic lute index finger 7: 17/16 104.9554 17th harmonic 8: 18/17 98.9546 Arabic lute index finger 9: 17/16 104.9554 17th harmonic 10: 256/243 90.2250 limma, Pythagorean minor second 11: 2187/2048 113.6850 apotome 12: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 256/243 90.225 cents limma, Pythagorean minor second 1: 4 18/17 98.955 cents Arabic lute index finger 1: 4 17/16 104.955 cents 17th harmonic 1: 1 2187/2048 113.685 cents apotome 2: 2 512/459 189.180 cents 2: 2 272/243 195.180 cents Persian whole tone 2: 8 9/8 203.910 cents major whole tone 3: 6 32/27 294.135 cents Pythagorean minor third 3: 3 81/68 302.865 cents Persian wosta 3: 3 153/128 308.865 cents 4: 4 64/51 393.090 cents 4: 4 34/27 399.090 cents septendecimal major third 4: 4 81/64 407.820 cents Pythagorean major third 5: 10 4/3 498.045 cents perfect fourth 5: 1 729/544 506.775 cents 5: 1 1377/1024 512.775 cents 6: 2 1024/729 588.270 cents Pythagorean diminished fifth 6: 4 24/17 597.000 cents 1st septendecimal tritone 6: 4 17/12 603.000 cents 2nd septendecimal tritone 6: 2 729/512 611.730 cents Pythagorean tritone 7: 1 2048/1377 687.225 cents 7: 1 1088/729 693.225 cents 7: 10 3/2 701.955 cents perfect fifth 8: 4 128/81 792.180 cents Pythagorean minor sixth 8: 4 27/17 800.910 cents septendecimal minor sixth 8: 4 51/32 806.910 cents 9: 3 256/153 891.135 cents 9: 3 136/81 897.135 cents 9: 6 27/16 905.865 cents Pythagorean major sixth 10: 8 16/9 996.090 cents Pythagorean minor seventh 10: 2 243/136 1004.820 cents 10: 2 459/256 1010.820 cents 11: 1 4096/2187 1086.315 cents Pythagorean diminished octave 11: 4 32/17 1095.045 cents 17th subharmonic 11: 4 17/9 1101.045 cents septendecimal major seventh 11: 3 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 99.0 203.9 302.9 407.8 498.0 597.0 702.0 800.9 905.9 996.1 1109.8 1200.0 99.0 : 105.0 203.9 308.9 399.1 498.0 603.0 702.0 806.9 897.1 1010.8 1101.0 1200.0 203.9 : 99.0 203.9 294.1 393.1 498.0 597.0 702.0 792.2 905.9 996.1 1095.0 1200.0 302.9 : 105.0 195.2 294.1 399.1 498.0 603.0 693.2 806.9 897.1 996.1 1101.0 1200.0 407.8 : 90.2 189.2 294.1 393.1 498.0 588.3 702.0 792.2 891.1 996.1 1095.0 1200.0 498.0 : 99.0 203.9 302.9 407.8 498.0 611.7 702.0 800.9 905.9 1004.8 1109.8 1200.0 597.0 : 105.0 203.9 308.9 399.1 512.8 603.0 702.0 806.9 905.9 1010.8 1101.0 1200.0 702.0 : 99.0 203.9 294.1 407.8 498.0 597.0 702.0 800.9 905.9 996.1 1095.0 1200.0 800.9 : 105.0 195.2 308.9 399.1 498.0 603.0 702.0 806.9 897.1 996.1 1101.0 1200.0 905.9 : 90.2 203.9 294.1 393.1 498.0 597.0 702.0 792.2 891.1 996.1 1095.0 1200.0 996.1 : 113.7 203.9 302.9 407.8 506.8 611.7 702.0 800.9 905.9 1004.8 1109.8 1200.0 1109.8: 90.2 189.2 294.1 393.1 498.0 588.3 687.2 792.2 891.1 996.1 1086.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 113.6850 cents 531441/524288, 23.4600 cents 256/243, 90.2250 cents 2: 189.1796 .. 203.9100 cents 4131/4096, 14.7304 cents 1048576/1003833, 75.4946 cents 3: 294.1350 .. 308.8654 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 4: 393.0896 .. 407.8200 cents 4131/4096, 14.7304 cents 8192/7803, 84.2242 cents 5: 498.0450 .. 512.7754 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 6: 588.2700 .. 611.7300 cents 531441/524288, 23.4600 cents 1048576/1003833, 75.4946 cents 7: 687.2246 .. 701.9550 cents 4131/4096, 14.7304 cents 1048576/1003833, 75.4946 cents 8: 792.1800 .. 806.9104 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 9: 891.1346 .. 905.8650 cents 4131/4096, 14.7304 cents 8192/7803, 84.2242 cents 10: 996.0900 .. 1010.8204 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 11: 1086.3150 .. 1109.7750 cents 531441/524288, 23.4600 cents 1048576/1003833, 75.4946 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 2187/2048, 113.6850 cents Average / Smallest step : 1.108340 Largest / Average step : 1.136850 Largest / Smallest step : 1.260017 Median interval of one step : 18/17, 98.9546 cents, amount: 4 Least squares average step : 100.24776 cents, oct.: 1202.97310 cents Scale is strictly proper Step pattern alph. order: ABABCABABCDC Step pattern size order : BCBCABCBCADA Scale is a Constant Structure, by a margin of 75.49458 cents Scale diversity : 1.128069 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.843147 Rothenberg efficiency : 0.507744 redundancy: 0.492256 Efficiency x scale size : 6.092929 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 289/288, 6.0008 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Most common triad is 0.0 498.045 701.955 cents, amount: 8 Number of recognisable fifths : 12, average 700.0000 cents Number of appreciable fifths : 11, average 701.1614 cents Scale contains two identical conjunct hexachords Scale is a well-temperament. It has 3 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 5 = 41.6667% Limited transpositions with margin 23.4600 cents: 1 2 3 4 5 6 7 8 9 10 Limited inverse transpositions with margin 23.4600 cents: 1 2 3 4 5 6 7 8 9 11 -- Rational properties -- Prime limit : 17 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.016727 Average absolute harmonicity : 0.167638 Specific harmonicity : 0.088501 Fundamental : 1/19584, -14.2574 octaves, 0.0134 Hz. Guide tone : 3888, 11.9248 octaves, 1017200.198 Hz. Exponens Consonantiae : 7.614259E+07, 26.18220 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 442.5, average 36.87500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.38893, average 1.19908 Sum of Tenney's harmonic distance : 28.51621, average 2.37635 Vogel's harmonic complexity : 28.83333 Wille's k value : 18589 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 8 Triangular lattice diameter : 7 Lattice compactness : 384.37657, average 4.92790 Lattice compactness (without 2's) : 205.64874, average 2.63652 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 4 -1.00000 34 1 3: -2 .. 5 1.83333 28 7 17: -1 .. 0 -0.33333 4 4 Average exponent except 2's : 18 / 12 = 1.50000 Average absolute exponent except 2's: 32 / 12 = 2.66667 Scale is weakly epimorphic with val: <12 17 47| Scale is JI-epimorphic with val: <12 19 49| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 4.5502 c. M: 9.7750 c. Twelve-tone Chromatic (1/11-comma) 49: 4 4 4 5 3 4 5 4 4 4 4 4 SP D3 SD: 7.1642 c. M: 9.2445 c. 52: 4 5 4 5 4 4 4 5 4 4 5 4 SP D3 SD: 5.9027 c. M:-9.6473 c. 53: 4 5 4 5 4 4 5 4 5 4 5 4 SP M ME SD: 4.8654 c. M: 8.5250 c. 57: 5 5 4 5 5 4 5 5 5 4 6 4 SP D3 SD: 6.1425 c. M: 8.1278 c. 58: 5 5 5 5 4 5 5 5 5 4 6 4 SP D3 SD: 4.6078 c. M:-7.4802 c. 65: 5 6 5 6 5 5 6 5 6 5 6 5 SP M ME SD: 4.0748 c. M: 7.4800 c. 70: 6 6 6 6 5 6 6 6 6 5 7 5 SP D3 SD: 3.2751 c. M:-5.7068 c. 82: 7 7 7 7 6 7 7 7 7 6 8 6 SP D3 SD: 2.4285 c. M:-4.4525 c. 94: 8 8 8 8 7 8 8 8 8 7 9 7 SP D3 SD: 1.9242 c. M:-3.5184 c. 106: 9 9 9 9 8 9 9 9 9 8 10 8 SP D3 SD: 1.6807 c. M:-3.0004 c. 118: 10 10 10 10 9 10 10 10 10 9 11 9 SP D3 SD: 1.6241 c. M:-3.0004 c. 123: 10 11 10 11 9 10 11 10 11 9 12 9 SP SD: 1.3081 c. M:-2.4201 c. 135: 11 12 11 12 10 11 12 11 12 10 13 10 SP SD: 0.8658 c. M: 1.4440 c. 147: 12 13 12 13 11 12 13 12 13 11 14 11 SP SD: 0.5851 c. M: 1.0812 c. 159: 13 14 13 14 12 13 14 13 14 12 15 12 SP SD: 0.5298 c. M: 0.9778 c. 241: 20 21 20 21 18 20 21 20 21 18 23 18 SP SD: 0.4863 c. M:-0.8698 c. 253: 21 22 21 22 19 21 22 21 22 19 24 19 SP SD: 0.3847 c. M:-0.6927 c. 388: 32 34 32 34 29 32 34 32 34 29 37 29 SP SD: 0.2518 c. M:-0.5343 c. 400: 33 35 33 35 30 33 35 33 35 30 38 30 SP SD: 0.1118 c. M:-0.2250 c. 412: 34 36 34 36 31 34 36 34 36 31 39 31 SP SD: 0.0499 c. M:-0.0878 c. 812: 67 71 67 71 61 67 71 67 71 61 77 61 SP SD: 0.0532 c. M:-0.0911 c. 971: 80 85 80 85 73 80 85 80 85 73 92 73 SP SD: 0.0501 c. M: 0.0892 c. 1224: 101 107 101 107 92 101 107 101 107 92 116 92 SP SD: 0.0415 c. M:-0.0766 c. 1371: 113 120 113 120 103 113 120 113 120 103 130 103 SP SD: 0.0411 c. M:-0.0718 c. 1383: 114 121 114 121 104 114 121 114 121 104 131 104 SP SD: 0.0243 c. M: 0.0446 c. 1783: 147 156 147 156 134 147 156 147 156 134 169 134 SP SD: 0.0208 c. M:-0.0399 c. 1795: 148 157 148 157 135 148 157 148 157 135 170 135 SP SD: 0.0150 c. M: 0.0257 c. 2195: 181 192 181 192 165 181 192 181 192 165 208 165 SP SD: 0.0093 c. M:-0.0200 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: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.6813 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.3211 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.2991 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.5175 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.1214 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.4987 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.7816 cents 11:12 x 13:14:15:16 x 17:19:20:21:22 SD: 11.2271 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3453 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.4276 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.5918 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.3304 cents 18:19:20:21:23:24:25:27:29:30:32:34:36 SD: 5.2783 cents 19:20:21:23:24:25:27:29:30:32:34:36:38 SD: 5.0330 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.3643 cents 30:32:34:36:38:40:42:45:48:51:53:57:60 SD: 2.8235 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.7350 cents 32:34:36:38:41:43:45:48:51:54:57:61:64 SD: 2.4171 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 2.4038 cents 41:43:46:49:52:55:58:62:65:69:73:78:82 SD: 2.2238 cents 42:44:47:50:53:56:59:63:67:71:75:80:84 SD: 2.1804 cents 46:49:52:55:58:61:65:69:73:78:82:87:92 SD: 1.8455 cents 48:51:54:57:61:64:68:72:76:81:85:91:96 SD: 1.2677 cents 68:72:77:81:86:91:96:102:108:115:121:129:136 SD: 1.1409 cents 78:83:88:93:99:104:110:117:124:132:139:148:156 SD: 1.0988 cents 80:85:90:95:101:107:113:120:127:135:142:152:160 SD: 0.9241 cents 90:95:101:107:114:120:127:135:143:152:160:171:180 SD: 0.6732 cents 120:127:135:143:152:160:169:180:191:203:213:228:240 SD: 0.6587 cents 121:128:136:144:153:161:171:182:192:204:215:230:242 SD: 0.6424 cents 135:143:152:161:171:180:191:203:214:228:240:256:270 SD: 0.6341 cents 136:144:153:162:172:181:192:204:216:230:242:258:272 SD: 0.4567 cents 168:178:189:200:213:224:237:252:267:284:299:319:336 SD: 0.4392 cents 184:195:207:219:233:245:260:276:292:311:327:349:368 SD: 0.4226 cents 192:203:216:229:243:256:271:288:305:324:341:365:384 SD: 0.3725 cents 226:239:254:269:286:301:319:339:359:381:402:429:452 SD: 0.3429 cents 234:248:263:279:296:312:330:351:372:395:416:444:468 SD: 0.3354 cents 240:254:270:286:304:320:339:360:381:405:427:456:480 SD: 0.2428 cents 272:288:306:324:344:363:384:408:432:459:484:516:544 SD: 0.2390 cents 294:311:331:350:372:392:415:441:467:496:523:558:588 SD: 0.2255 cents 304:322:342:362:385:405:429:456:483:513:540:577:608 SD: 0.2218 cents 320:339:360:381:405:427:452:480:508:540:569:608:640 SD: 0.2186 cents 342:362:385:407:433:456:483:513:543:577:608:649:684 SD: 0.2037 cents 391:414:440:466:495:521:552:587:621:660:695:742:782 SD: 0.1958 cents 408:432:459:486:516:544:576:612:648:689:725:775:816 SD: 0.1816 cents 423:448:476:504:535:564:597:635:672:714:752:803:846 SD: 0.1770 cents 440:466:495:524:557:587:621:660:699:743:782:835:880 SD: 0.1648 cents 456:483:513:543:577:608:644:684:724:770:811:866:912 SD: 0.1611 cents 464:491:522:553:587:619:655:696:737:783:825:881:928 SD: 0.1558 cents 474:502:533:565:600:632:669:711:753:800:843:900:948 SD: 0.1504 cents 496:525:558:591:628:661:700:744:788:837:882:942:992 SD: 0.1471 cents 512:542:576:610:648:683:723:768:813:864:910:972:1024 SD: 0.1009 cents 576:610:648:686:729:768:813:864:915:972:1024:1094:1152 SD: 0.0865 cents