Scala analysis: org1373a_tuning_34979_36356
English organ tuning (1373) with 18:17:16 accidental 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: 243/136 1004.819595 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: 18/17 98.9546 Arabic lute index finger 11: 17/16 104.9554 17th harmonic 12: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 18/17 98.955 cents Arabic lute index finger 1: 5 17/16 104.955 cents 17th harmonic 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: 1 1024/729 588.270 cents Pythagorean diminished fifth 6: 5 24/17 597.000 cents 1st septendecimal tritone 6: 5 17/12 603.000 cents 2nd septendecimal tritone 6: 1 729/512 611.730 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: 5 32/17 1095.045 cents 17th subharmonic 11: 5 17/9 1101.045 cents septendecimal major seventh 11: 2 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
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 1004.8 1109.8 1200.0 99.0 : 105.0 203.9 308.9 399.1 498.0 603.0 702.0 806.9 905.9 1010.8 1101.0 1200.0 203.9 : 99.0 203.9 294.1 393.1 498.0 597.0 702.0 800.9 905.9 996.1 1095.0 1200.0 302.9 : 105.0 195.2 294.1 399.1 498.0 603.0 702.0 806.9 897.1 996.1 1101.0 1200.0 407.8 : 90.2 189.2 294.1 393.1 498.0 597.0 702.0 792.2 891.1 996.1 1095.0 1200.0 498.0 : 99.0 203.9 302.9 407.8 506.8 611.7 702.0 800.9 905.9 1004.8 1109.8 1200.0 597.0 : 105.0 203.9 308.9 407.8 512.8 603.0 702.0 806.9 905.9 1010.8 1101.0 1200.0 702.0 : 99.0 203.9 302.9 407.8 498.0 597.0 702.0 800.9 905.9 996.1 1095.0 1200.0 800.9 : 105.0 203.9 308.9 399.1 498.0 603.0 702.0 806.9 897.1 996.1 1101.0 1200.0 905.9 : 99.0 203.9 294.1 393.1 498.0 597.0 702.0 792.2 891.1 996.1 1095.0 1200.0 1004.8: 105.0 195.2 294.1 399.1 498.0 603.0 693.2 792.2 897.1 996.1 1101.0 1200.0 1109.8: 90.2 189.2 294.1 393.1 498.0 588.3 687.2 792.2 891.1 996.1 1095.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 104.9554 cents 4131/4096, 14.7304 cents 256/243, 90.2250 cents 2: 189.1796 .. 203.9100 cents 4131/4096, 14.7304 cents 8192/7803, 84.2242 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: 1095.0446 .. 1109.7750 cents 4131/4096, 14.7304 cents 8192/7803, 84.2242 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 : 17/16, 104.9554 cents Average / Smallest step : 1.108340 Largest / Average step : 1.049554 Largest / Smallest step : 1.163263 Median interval of one step : 18/17, 98.9546 cents, amount: 5 Least squares average step : 100.38206 cents, oct.: 1204.58471 cents Scale is strictly proper Step pattern alph. order: ABABCABABABC Step pattern size order : MLMLSMLMLMLS Scale is a Constant Structure, by a margin of 75.49458 cents Scale diversity : 1.116096 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.857697 Rothenberg efficiency : 0.508565 redundancy: 0.491435 Efficiency x scale size : 6.102778 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 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 disjunct hexachords Scale is a well-temperament. It has 3 different sizes of fifth Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 25.0000% Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited transpositions with margin 14.7304 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 14.7304 cents: 1 2 3 4 5 6 7 8 9 10 11 -- Rational properties -- Prime limit : 17 Odd number limit : 1377 (O: 1377 U: 1377) Highest odd numerator or denominator: 243 Scale harmonicity : 0.017820 Average absolute harmonicity : 0.160503 Specific harmonicity : 0.085785 Fundamental : 1/6528, -12.6724 octaves, 0.0401 Hz. Guide tone : 1944, 10.9248 octaves, 508600.099 Hz. Exponens Consonantiae : 1.269043E+07, 23.59724 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 619.5, average 51.62500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.82029, average 1.31836 Sum of Tenney's harmonic distance : 30.87699, average 2.57308 Vogel's harmonic complexity : 25.58333 Wille's k value : 6196 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 357.73070, average 4.58629 Lattice compactness (without 2's) : 195.39804, average 2.50510 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 3 -1.58333 33 1 3: -1 .. 5 2.41667 31 6 17: -1 .. 0 -0.41667 5 5 Average exponent except 2's : 24 / 12 = 2.00000 Average absolute exponent except 2's: 36 / 12 = 3.00000 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: 4.6223 c. M: 9.7750 c. Twelve-tone Chromatic (1/11-comma) 53: 4 5 4 5 4 4 5 4 5 4 5 4 SP M ME SD: 5.4612 c. M: 8.5932 c. 57: 5 5 4 5 5 4 5 5 5 5 5 4 SP D3 SD: 6.0660 c. M: 8.1278 c. 58: 5 5 5 5 4 5 5 5 5 5 5 4 SP D3 S SD: 5.2153 c. M:-8.9735 c. 62: 5 6 5 5 5 5 5 5 6 5 5 5 SP D3 S SD: 5.0899 c. M:-8.9932 c. 63: 5 6 5 5 5 5 6 5 6 5 5 5 SP D3 SD: 4.8938 c. M:-8.4207 c. 65: 5 6 5 6 5 5 6 5 6 5 6 5 SP M ME SD: 4.6629 c. M: 7.8965 c. 68: 6 6 5 6 5 6 6 5 6 6 6 5 SP D3 SD: 4.5380 c. M:-7.8547 c. 69: 6 6 5 6 6 5 6 6 6 6 6 5 SP D3 SD: 5.0488 c. M: 7.8200 c. 70: 6 6 6 6 5 6 6 6 6 6 6 5 SP D3 S SD: 3.7543 c. M:-6.6090 c. 80: 7 7 6 7 6 7 7 6 7 7 7 6 SP D3 SD: 3.9449 c. M:-6.0900 c. 82: 7 7 7 7 6 7 7 7 7 7 7 6 SP D3 S SD: 2.8019 c. M:-4.9365 c. 94: 8 8 8 8 7 8 8 8 8 8 8 7 SP D3 S SD: 2.1973 c. M:-3.6910 c. 106: 9 9 9 9 8 9 9 9 9 9 9 8 SP D3 S SD: 1.8556 c. M:-3.0004 c. 111: 9 10 9 10 8 9 10 9 10 9 10 8 SP SD: 1.8492 c. M:-3.7385 c. 118: 10 10 10 10 9 10 10 10 10 10 10 9 SP D3 S SD: 1.7132 c. M:-3.0004 c. 123: 10 11 10 11 9 10 11 10 11 10 11 9 SP SD: 1.2780 c. M:-2.4201 c. 135: 11 12 11 12 10 11 12 11 12 11 12 10 SP SD: 0.8588 c. M: 1.4440 c. 147: 12 13 12 13 11 12 13 12 13 12 13 11 SP SD: 0.6207 c. M: 1.0812 c. 159: 13 14 13 14 12 13 14 13 14 13 14 12 SP SD: 0.6085 c. M: 1.0460 c. 241: 20 21 20 21 18 20 21 20 21 20 21 18 SP SD: 0.5597 c. M:-0.9895 c. 253: 21 22 21 22 19 21 22 21 22 21 22 19 SP SD: 0.4363 c. M:-0.7140 c. 265: 22 23 22 23 20 22 23 22 23 22 23 20 SP SD: 0.4189 c. M:-0.7363 c. 376: 31 33 31 33 28 31 33 31 33 31 33 28 SP SD: 0.4170 c. M:-0.8633 c. 388: 32 34 32 34 29 32 34 32 34 32 34 29 SP SD: 0.2626 c. M:-0.5343 c. 400: 33 35 33 35 30 33 35 33 35 33 35 30 SP SD: 0.1206 c. M:-0.2250 c. 412: 34 36 34 36 31 34 36 34 36 34 36 31 SP SD: 0.0503 c. M:-0.0878 c. 1224: 101 107 101 107 92 101 107 101 107 101 107 92 SP SD: 0.0477 c. M:-0.0824 c. 1371: 113 120 113 120 103 113 120 113 120 113 120 103 SP SD: 0.0403 c. M:-0.0718 c. 1383: 114 121 114 121 104 114 121 114 121 114 121 104 SP SD: 0.0278 c. M: 0.0474 c. 1783: 147 156 147 156 134 147 156 147 156 147 156 134 SP SD: 0.0203 c. M:-0.0399 c. 1795: 148 157 148 157 135 148 157 148 157 148 157 135 SP SD: 0.0168 c. M: 0.0285 c. 2195: 181 192 181 192 165 181 192 181 192 181 192 165 SP SD: 0.0094 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: 10.4823 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.2901 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.1956 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: 9.5827 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.5539 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.5572 cents 11:12 x 13:14:15:16 x 17:19:20:21:22 SD: 10.9553 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.6953 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.5243 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.5609 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.1317 cents 19:20:21:23:24:25:27:29:30:32:34:36:38 SD: 4.9482 cents 20:21:23:24:25:27:28:30:32:34:36:38:40 SD: 4.8931 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.5278 cents 30:32:34:36:38:40:42:45:48:51:54:57:60 S SD: 2.8788 cents 32:34:36:38:41:43:45:48:51:54:57:61:64 SD: 2.4417 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 2.2206 cents 42:44:47:50:53:56:59:63:67:71:75:80:84 SD: 2.0853 cents 46:49:52:55:58:61:65:69:73:78:82:87:92 SD: 1.8345 cents 48:51:54:57:61:64:68:72:76:81:86:91:96 SD: 1.2018 cents 78:83:88:93:99:104:110:117:124:132:139:148:156 SD: 1.1102 cents 80:85:90:95:101:107:113:120:127:135:143:152:160 SD: 0.8981 cents 90:95:101:107:114:120:127:135:143:152:161:171:180 SD: 0.6947 cents 120:127:135:143:152:160:169:180:191:203:214:228:240 SD: 0.6781 cents 121:128:136:144:153:161:171:182:192:204:216:230:242 SD: 0.6516 cents 135:143:152:161:171:180:191:203:214:228:241:256:270 SD: 0.6468 cents 136:144:153:162:172:181:192:204:216:230:243:258:272 SD: 0.4370 cents 168:178:189:200:213:224:237:252:267:284:300:319:336 SD: 0.4173 cents 192:203:216:229:243:256:271:288:305:324:343:365:384 SD: 0.3457 cents 226:239:254:269:286:301:319:339:359:381:404:429:452 SD: 0.3404 cents 234:248:263:279:296:312:330:351:372:395:418:444:468 SD: 0.3373 cents 240:254:270:286:304:320:339:360:381:405:429:456:480 SD: 0.2231 cents 272:288:306:324:344:363:384:408:432:459:486:516:544 SD: 0.1988 cents 304:322:342:362:385:405:429:456:483:513:543:577:608 SD: 0.1932 cents 376:398:423:448:476:501:531:564:597:635:672:714:752 SD: 0.1839 cents 408:432:459:486:516:544:576:612:648:689:729:775:816 SD: 0.1691 cents 440:466:495:524:557:587:621:660:699:743:786:835:880 SD: 0.1629 cents 456:483:513:543:577:608:644:684:724:770:815:866:912 SD: 0.1554 cents 464:491:522:553:587:619:655:696:737:783:829:881:928 SD: 0.1549 cents 474:502:533:565:600:632:669:711:753:800:847:900:948 SD: 0.1398 cents 512:542:576:610:648:683:723:768:813:864:915:972:1024 SD: 0.0985 cents 576:610:648:686:729:768:813:864:915:972:1029:1094:1152 SD: 0.0900 cents