Creates a scale table for equal divisions of a specified period.
Value
a data.table with seven columns:
ratio: the ratio that defines the note, as a number between 1 andperiodratio_frac: the ratio as a vulgar fraction (character). The ratios for this type of scale are usually irrational, so this is an approximation, computed byfractional::fractional.ratio_cents: the ratio in cents (hundredths of a semitone)frequency: frequency of the note given thetonic_note_numberparameterbent_midi: the MIDI note number as an integer plus a fraction. For example, middle C is MIDI note number 60 and middle C sharp is 61. The quarter-tone half-way between C and C sharp would have abent_midivalue of 60.5. The namebent_midicomes from the fact that a MIDI sequencer can convert the value to a regular integer MIDI note number message and a pitch bend message.interval_cents: interval between this note and the previous notedegree: scale degree from zero to (number of notes) - 1
Examples
print(vanilla <- et_scale_table()) # default is 12EDO, of course
#> Key: <ratio>
#> ratio ratio_frac ratio_cents frequency bent_midi interval_cents degree
#> <num> <charFrac> <num> <num> <num> <num> <num>
#> 1: 1.000000 1 0 261.6256 60 NA 0
#> 2: 1.059463 1461/1379 100 277.1826 61 100 1
#> 3: 1.122462 1714/1527 200 293.6648 62 100 2
#> 4: 1.189207 1785/1501 300 311.1270 63 100 3
#> 5: 1.259921 635/504 400 329.6276 64 100 4
#> 6: 1.334840 3249/2434 500 349.2282 65 100 5
#> 7: 1.414214 1393/985 600 369.9944 66 100 6
#> 8: 1.498307 2213/1477 700 391.9954 67 100 7
#> 9: 1.587401 1008/635 800 415.3047 68 100 8
#> 10: 1.681793 3002/1785 900 440.0000 69 100 9
#> 11: 1.781797 1527/857 1000 466.1638 70 100 10
#> 12: 1.887749 2943/1559 1100 493.8833 71 100 11
#> 13: 2.000000 2 1200 523.2511 72 100 0
# 19-EDO
print(edo19 <- et_scale_table(2.0, 19))
#> Key: <ratio>
#> ratio ratio_frac ratio_cents frequency bent_midi interval_cents degree
#> <num> <charFrac> <num> <num> <num> <num> <num>
#> 1: 1.000000 1 0.00000 261.6256 60.00000 NA 0
#> 2: 1.037155 977/942 63.15789 271.3463 60.63158 63.15789 1
#> 3: 1.075691 739/687 126.31579 281.4282 61.26316 63.15789 2
#> 4: 1.115658 627/562 189.47368 291.8846 61.89474 63.15789 3
#> 5: 1.157110 1009/872 252.63158 302.7296 62.52632 63.15789 4
#> 6: 1.200103 2333/1944 315.78947 313.9776 63.15789 63.15789 5
#> 7: 1.244693 1114/895 378.94737 325.6434 63.78947 63.15789 6
#> 8: 1.290939 1553/1203 442.10526 337.7427 64.42105 63.15789 7
#> 9: 1.338904 1442/1077 505.26316 350.2915 65.05263 63.15789 8
#> 10: 1.388651 1297/934 568.42105 363.3066 65.68421 63.15789 9
#> 11: 1.440247 1639/1138 631.57895 376.8053 66.31579 63.15789 10
#> 12: 1.493759 1077/721 694.73684 390.8055 66.94737 63.15789 11
#> 13: 1.549260 2406/1553 757.89474 405.3259 67.57895 63.15789 12
#> 14: 1.606822 895/557 821.05263 420.3858 68.21053 63.15789 13
#> 15: 1.666524 3893/2336 884.21053 436.0053 68.84211 63.15789 14
#> 16: 1.728444 1744/1009 947.36842 452.2051 69.47368 63.15789 15
#> 17: 1.792664 1124/627 1010.52632 469.0068 70.10526 63.15789 16
#> 18: 1.859271 1123/604 1073.68421 486.4328 70.73684 63.15789 17
#> 19: 1.928352 1884/977 1136.84211 504.5062 71.36842 63.15789 18
#> 20: 2.000000 2 1200.00000 523.2511 72.00000 63.15789 0
#> ratio ratio_frac ratio_cents frequency bent_midi interval_cents degree
# 31-EDO
print(edo31 <- et_scale_table(2.0, 31))
#> Key: <ratio>
#> ratio ratio_frac ratio_cents frequency bent_midi interval_cents degree
#> <num> <charFrac> <num> <num> <num> <num> <num>
#> 1: 1.000000 1 0.00000 261.6256 60.00000 NA 0
#> 2: 1.022611 1402/1371 38.70968 267.5413 60.38710 38.70968 1
#> 3: 1.045734 1189/1137 77.41935 273.5908 60.77419 38.70968 2
#> 4: 1.069380 1156/1081 116.12903 279.7771 61.16129 38.70968 3
#> 5: 1.093560 900/823 154.83871 286.1032 61.54839 38.70968 4
#> 6: 1.118287 1645/1471 193.54839 292.5724 61.93548 38.70968 5
#> 7: 1.143573 685/599 232.25806 299.1879 62.32258 38.70968 6
#> 8: 1.169431 987/844 270.96774 305.9530 62.70968 38.70968 7
#> 9: 1.195873 3999/3344 309.67742 312.8710 63.09677 38.70968 8
#> 10: 1.222914 982/803 348.38710 319.9455 63.48387 38.70968 9
#> 11: 1.250566 2211/1768 387.09677 327.1799 63.87097 38.70968 10
#> 12: 1.278843 3403/2661 425.80645 334.5779 64.25806 38.70968 11
#> 13: 1.307759 1500/1147 464.51613 342.1432 64.64516 38.70968 12
#> 14: 1.337329 781/584 503.22581 349.8796 65.03226 38.70968 13
#> 15: 1.367568 253/185 541.93548 357.7908 65.41935 38.70968 14
#> 16: 1.398491 1853/1325 580.64516 365.8810 65.80645 38.70968 15
#> 17: 1.430113 2783/1946 619.35484 374.1541 66.19355 38.70968 16
#> 18: 1.462450 370/253 658.06452 382.6143 66.58065 38.70968 17
#> 19: 1.495518 1168/781 696.77419 391.2657 66.96774 38.70968 18
#> 20: 1.529334 1147/750 735.48387 400.1128 67.35484 38.70968 19
#> 21: 1.563914 2557/1635 774.19355 409.1599 67.74194 38.70968 20
#> 22: 1.599276 3536/2211 812.90323 418.4116 68.12903 38.70968 21
#> 23: 1.635438 803/491 851.61290 427.8725 68.51613 38.70968 22
#> 24: 1.672418 6785/4057 890.32258 437.5473 68.90323 38.70968 23
#> 25: 1.710234 1387/811 929.03226 447.4409 69.29032 38.70968 24
#> 26: 1.748905 1198/685 967.74194 457.5582 69.67742 38.70968 25
#> 27: 1.788450 2942/1645 1006.45161 467.9042 70.06452 38.70968 26
#> 28: 1.828889 823/450 1045.16129 478.4842 70.45161 38.70968 27
#> 29: 1.870243 1081/578 1083.87097 489.3034 70.83871 38.70968 28
#> 30: 1.912532 1465/766 1122.58065 500.3673 71.22581 38.70968 29
#> 31: 1.955777 1371/701 1161.29032 511.6813 71.61290 38.70968 30
#> 32: 2.000000 2 1200.00000 523.2511 72.00000 38.70968 0
#> ratio ratio_frac ratio_cents frequency bent_midi interval_cents degree
# equal-tempered Bohlen-Pierce
print(bohlen_pierce_et <- et_scale_table(3.0, 13))
#> Key: <ratio>
#> ratio ratio_frac ratio_cents frequency bent_midi interval_cents degree
#> <num> <charFrac> <num> <num> <num> <num> <num>
#> 1: 1.000000 1 0.0000 261.6256 60.00000 NA 0
#> 2: 1.088182 1197/1100 146.3042 284.6963 61.46304 146.3042 1
#> 3: 1.184141 881/744 292.6085 309.8015 62.92608 146.3042 2
#> 4: 1.288561 1746/1355 438.9127 337.1204 64.38913 146.3042 3
#> 5: 1.402189 1025/731 585.2169 366.8485 65.85217 146.3042 4
#> 6: 1.525837 3691/2419 731.5212 399.1980 67.31521 146.3042 5
#> 7: 1.660389 2645/1593 877.8254 434.4002 68.77825 146.3042 6
#> 8: 1.806806 1646/911 1024.1296 472.7066 70.24130 146.3042 7
#> 9: 1.966134 2090/1063 1170.4338 514.3909 71.70434 146.3042 8
#> 10: 2.139512 2101/982 1316.7381 559.7510 73.16738 146.3042 9
#> 11: 2.328179 1355/582 1463.0423 609.1111 74.63042 146.3042 10
#> 12: 2.533483 1135/448 1609.3465 662.8239 76.09347 146.3042 11
#> 13: 2.756891 6101/2213 1755.6508 721.2732 77.55651 146.3042 12
#> 14: 3.000000 3 1901.9550 784.8767 79.01955 146.3042 0
# Carlos Alpha
print(carlos_alpha <- et_scale_table(1.5, 9))
#> Key: <ratio>
#> ratio ratio_frac ratio_cents frequency bent_midi interval_cents degree
#> <num> <charFrac> <num> <num> <num> <num> <num>
#> 1: 1.000000 1 0.000 261.6256 60.00000 NA 0
#> 2: 1.046082 4472/4275 77.995 273.6818 60.77995 77.995 1
#> 3: 1.094287 1590/1453 155.990 286.2936 61.55990 77.995 2
#> 4: 1.144714 1321/1154 233.985 299.4865 62.33985 77.995 3
#> 5: 1.197465 1795/1499 311.980 313.2874 63.11980 77.995 4
#> 6: 1.252646 947/756 389.975 327.7243 63.89975 77.995 5
#> 7: 1.310371 1731/1321 467.970 342.8265 64.67970 77.995 6
#> 8: 1.370755 1453/1060 545.965 358.6246 65.45965 77.995 7
#> 9: 1.433922 2029/1415 623.960 375.1507 66.23960 77.995 8
#> 10: 1.500000 3/2 701.955 392.4383 67.01955 77.995 0