Creates a scale table for equal divisions of a specified period.
Usage
et_scale_table(
note_names = c("C", "C#|Db", "D", "D#|Eb", "E", "F", "F#|Gb", "G", "G#|Ab", "A",
"A#|Bb", "B"),
period = 2
)Value
a data.table with six columns:
note_name: the note name (character)ratio: the ratio that defines the note, as a number between 1 andperiodratio_frac: the ratio as a vulgar fraction (character). The ratios for most EDOs are irrational, so this is an approximation.ratio_cents: the ratio in cents (hundredths of a semitone)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
#> note_name ratio ratio_frac ratio_cents interval_cents degree
#> <char> <num> <charFrac> <num> <num> <num>
#> 1: C 1.000000 1 0 NA 0
#> 2: C#|Db 1.059463 1461/1379 100 100 1
#> 3: D 1.122462 1714/1527 200 100 2
#> 4: D#|Eb 1.189207 1785/1501 300 100 3
#> 5: E 1.259921 635/504 400 100 4
#> 6: F 1.334840 3249/2434 500 100 5
#> 7: F#|Gb 1.414214 1393/985 600 100 6
#> 8: G 1.498307 2213/1477 700 100 7
#> 9: G#|Ab 1.587401 1008/635 800 100 8
#> 10: A 1.681793 3002/1785 900 100 9
#> 11: A#|Bb 1.781797 1527/857 1000 100 10
#> 12: B 1.887749 2943/1559 1100 100 11
#> 13: C' 2.000000 2 1200 100 12
# 19-EDO
print(edo19 <- et_scale_table(edo19_names))
#> note_name ratio ratio_frac ratio_cents interval_cents degree
#> <char> <num> <charFrac> <num> <num> <num>
#> 1: C 1.000000 1 0.00000 NA 0
#> 2: C# 1.037155 977/942 63.15789 63.15789 1
#> 3: Db 1.075691 739/687 126.31579 63.15789 2
#> 4: D 1.115658 627/562 189.47368 63.15789 3
#> 5: D# 1.157110 1009/872 252.63158 63.15789 4
#> 6: Eb 1.200103 2333/1944 315.78947 63.15789 5
#> 7: E 1.244693 1114/895 378.94737 63.15789 6
#> 8: E#|Fb 1.290939 1553/1203 442.10526 63.15789 7
#> 9: F 1.338904 1442/1077 505.26316 63.15789 8
#> 10: F# 1.388651 1297/934 568.42105 63.15789 9
#> 11: Gb 1.440247 1639/1138 631.57895 63.15789 10
#> 12: G 1.493759 1077/721 694.73684 63.15789 11
#> 13: G# 1.549260 2406/1553 757.89474 63.15789 12
#> 14: Ab 1.606822 895/557 821.05263 63.15789 13
#> 15: A 1.666524 3893/2336 884.21053 63.15789 14
#> 16: A# 1.728444 1744/1009 947.36842 63.15789 15
#> 17: Bb 1.792664 1124/627 1010.52632 63.15789 16
#> 18: B 1.859271 1123/604 1073.68421 63.15789 17
#> 19: B#|Cb 1.928352 1884/977 1136.84211 63.15789 18
#> 20: C' 2.000000 2 1200.00000 63.15789 19
#> note_name ratio ratio_frac ratio_cents interval_cents degree
# 31-EDO
print(edo31 <- et_scale_table(edo31_names))
#> note_name ratio ratio_frac ratio_cents interval_cents degree
#> <char> <num> <charFrac> <num> <num> <num>
#> 1: C 1.000000 1 0.00000 NA 0
#> 2: C/# 1.022611 1402/1371 38.70968 38.70968 1
#> 3: C# 1.045734 1189/1137 77.41935 38.70968 2
#> 4: Db 1.069380 1156/1081 116.12903 38.70968 3
#> 5: D/b 1.093560 900/823 154.83871 38.70968 4
#> 6: D 1.118287 1645/1471 193.54839 38.70968 5
#> 7: D/# 1.143573 685/599 232.25806 38.70968 6
#> 8: D# 1.169431 987/844 270.96774 38.70968 7
#> 9: Eb 1.195873 3999/3344 309.67742 38.70968 8
#> 10: E/b 1.222914 982/803 348.38710 38.70968 9
#> 11: E 1.250566 2211/1768 387.09677 38.70968 10
#> 12: Fb 1.278843 3403/2661 425.80645 38.70968 11
#> 13: E# 1.307759 1500/1147 464.51613 38.70968 12
#> 14: F 1.337329 781/584 503.22581 38.70968 13
#> 15: F/# 1.367568 253/185 541.93548 38.70968 14
#> 16: F# 1.398491 1853/1325 580.64516 38.70968 15
#> 17: Gb 1.430113 2783/1946 619.35484 38.70968 16
#> 18: G/b 1.462450 370/253 658.06452 38.70968 17
#> 19: G 1.495518 1168/781 696.77419 38.70968 18
#> 20: G/# 1.529334 1147/750 735.48387 38.70968 19
#> 21: G# 1.563914 2557/1635 774.19355 38.70968 20
#> 22: Ab 1.599276 3536/2211 812.90323 38.70968 21
#> 23: A/b 1.635438 803/491 851.61290 38.70968 22
#> 24: A 1.672418 6785/4057 890.32258 38.70968 23
#> 25: A/# 1.710234 1387/811 929.03226 38.70968 24
#> 26: A# 1.748905 1198/685 967.74194 38.70968 25
#> 27: Bb 1.788450 2942/1645 1006.45161 38.70968 26
#> 28: B/b 1.828889 823/450 1045.16129 38.70968 27
#> 29: B 1.870243 1081/578 1083.87097 38.70968 28
#> 30: Cb 1.912532 1465/766 1122.58065 38.70968 29
#> 31: B# 1.955777 1371/701 1161.29032 38.70968 30
#> 32: C' 2.000000 2 1200.00000 38.70968 31
#> note_name ratio ratio_frac ratio_cents interval_cents degree
# equal-tempered Bohlen-Pierce
print(bohlen_pierce_et <- et_scale_table(bohlen_pierce_et_names, period = 3))
#> note_name ratio ratio_frac ratio_cents interval_cents degree
#> <char> <num> <charFrac> <num> <num> <num>
#> 1: C 1.000000 1 0.0000 NA 0
#> 2: C#|Db 1.088182 1197/1100 146.3042 146.3042 1
#> 3: D 1.184141 881/744 292.6085 146.3042 2
#> 4: E 1.288561 1746/1355 438.9127 146.3042 3
#> 5: F 1.402189 1025/731 585.2169 146.3042 4
#> 6: F#|Gb 1.525837 3691/2419 731.5212 146.3042 5
#> 7: G 1.660389 2645/1593 877.8254 146.3042 6
#> 8: H 1.806806 1646/911 1024.1296 146.3042 7
#> 9: H#|Jb 1.966134 2090/1063 1170.4338 146.3042 8
#> 10: J 2.139512 2101/982 1316.7381 146.3042 9
#> 11: A 2.328179 1355/582 1463.0423 146.3042 10
#> 12: A#|Bb 2.533483 1135/448 1609.3465 146.3042 11
#> 13: B 2.756891 6101/2213 1755.6508 146.3042 12
#> 14: C' 3.000000 3 1901.9550 146.3042 13