Creates a keyboard map
Value
the keyboard map. This is a data.table with eight columns:
note_number: the MIDI note number from.NN_MINthrough.NN_MAXname_12edo: note name of the key in 12EDO. This is the key you'd normally press to play this note numberoctave_12edo: the octave the key normally playsnote_name: the note name from the scale tableratio_frac: ratio for the note as a vulgar fraction. Note that for equal tempered scales this is usually an approximation to an irrational number. The algorithm used appears to give six decimal places of accuracy.degree: the scale degree of the noteoctave: the octave number of the notefreq: the frequency in Hzcents: cents above lowest MIDI note.NN_MIN, which has frequency.FREQ_MIN.ref_keyname: some synthesizers, including the Korg Minilogue XD, let you retune a key as an offset in cents from another reference key. This column is the name of that reference key.ref_octave: the octave number of the reference keyref_offset: the offset in cents from the reference key
Details
The function is currently hard-coded to compute the map so that
middle C with frequency .FREQ_MIDDLE_Cis mapped to MIDI note number
.NN_MIDDLE_C and scale degree 0. With the current constants this is the
same as it is on 12EDO with A440 on note 69. This note is 6000 cents above
MIDI note number 0 in 12EDO.
Normally you would only use this to remap a keyboard to a scale with more than 12 notes per octave. For scales with 12 or fewer notes to the octave, it's easier to remap all octaves using the offsets computed with offset_matrix!
Examples
# make sure we can print a whole keyboard map
options(max.print = 2000)
eikosany <- cps_scale_table(root_divisor = 33)
print(eikosany_keyboard_map <- keyboard_map(eikosany), nrows = 128)
#> Key: <note_number>
#> note_number name_12edo octave_12edo note_name ratio_frac degree
#> <num> <char> <num> <char> <char> <num>
#> 1: 0 C -1 1x3x11 1 0
#> 2: 1 C# -1 3x5x9 45/44 1
#> 3: 2 D -1 1x5x7 35/33 2
#> 4: 3 D# -1 3x9x11 9/8 3
#> 5: 4 E -1 1x7x11 7/6 4
#> 6: 5 F -1 5x7x9 105/88 5
#> 7: 6 F# -1 3x5x11 5/4 6
#> 8: 7 G -1 1x3x7 14/11 7
#> 9: 8 G# -1 7x9x11 21/16 8
#> 10: 9 A -1 1x5x9 15/11 9
#> 11: 10 A# -1 3x7x9 63/44 10
#> 12: 11 B -1 5x7x11 35/24 11
#> 13: 12 C 0 1x9x11 3/2 12
#> 14: 13 C# 0 3x5x7 35/22 13
#> 15: 14 D 0 1x3x9 18/11 14
#> 16: 15 D# 0 1x5x11 5/3 15
#> 17: 16 E 0 3x7x11 7/4 16
#> 18: 17 F 0 1x3x5 20/11 17
#> 19: 18 F# 0 5x9x11 15/8 18
#> 20: 19 G 0 1x7x9 21/11 19
#> 21: 20 G# 0 1x3x11 1 0
#> 22: 21 A 0 3x5x9 45/44 1
#> 23: 22 A# 0 1x5x7 35/33 2
#> 24: 23 B 0 3x9x11 9/8 3
#> 25: 24 C 1 1x7x11 7/6 4
#> 26: 25 C# 1 5x7x9 105/88 5
#> 27: 26 D 1 3x5x11 5/4 6
#> 28: 27 D# 1 1x3x7 14/11 7
#> 29: 28 E 1 7x9x11 21/16 8
#> 30: 29 F 1 1x5x9 15/11 9
#> 31: 30 F# 1 3x7x9 63/44 10
#> 32: 31 G 1 5x7x11 35/24 11
#> 33: 32 G# 1 1x9x11 3/2 12
#> 34: 33 A 1 3x5x7 35/22 13
#> 35: 34 A# 1 1x3x9 18/11 14
#> 36: 35 B 1 1x5x11 5/3 15
#> 37: 36 C 2 3x7x11 7/4 16
#> 38: 37 C# 2 1x3x5 20/11 17
#> 39: 38 D 2 5x9x11 15/8 18
#> 40: 39 D# 2 1x7x9 21/11 19
#> 41: 40 E 2 1x3x11 1 0
#> 42: 41 F 2 3x5x9 45/44 1
#> 43: 42 F# 2 1x5x7 35/33 2
#> 44: 43 G 2 3x9x11 9/8 3
#> 45: 44 G# 2 1x7x11 7/6 4
#> 46: 45 A 2 5x7x9 105/88 5
#> 47: 46 A# 2 3x5x11 5/4 6
#> 48: 47 B 2 1x3x7 14/11 7
#> 49: 48 C 3 7x9x11 21/16 8
#> 50: 49 C# 3 1x5x9 15/11 9
#> 51: 50 D 3 3x7x9 63/44 10
#> 52: 51 D# 3 5x7x11 35/24 11
#> 53: 52 E 3 1x9x11 3/2 12
#> 54: 53 F 3 3x5x7 35/22 13
#> 55: 54 F# 3 1x3x9 18/11 14
#> 56: 55 G 3 1x5x11 5/3 15
#> 57: 56 G# 3 3x7x11 7/4 16
#> 58: 57 A 3 1x3x5 20/11 17
#> 59: 58 A# 3 5x9x11 15/8 18
#> 60: 59 B 3 1x7x9 21/11 19
#> 61: 60 C 4 1x3x11 1 0
#> 62: 61 C# 4 3x5x9 45/44 1
#> 63: 62 D 4 1x5x7 35/33 2
#> 64: 63 D# 4 3x9x11 9/8 3
#> 65: 64 E 4 1x7x11 7/6 4
#> 66: 65 F 4 5x7x9 105/88 5
#> 67: 66 F# 4 3x5x11 5/4 6
#> 68: 67 G 4 1x3x7 14/11 7
#> 69: 68 G# 4 7x9x11 21/16 8
#> 70: 69 A 4 1x5x9 15/11 9
#> 71: 70 A# 4 3x7x9 63/44 10
#> 72: 71 B 4 5x7x11 35/24 11
#> 73: 72 C 5 1x9x11 3/2 12
#> 74: 73 C# 5 3x5x7 35/22 13
#> 75: 74 D 5 1x3x9 18/11 14
#> 76: 75 D# 5 1x5x11 5/3 15
#> 77: 76 E 5 3x7x11 7/4 16
#> 78: 77 F 5 1x3x5 20/11 17
#> 79: 78 F# 5 5x9x11 15/8 18
#> 80: 79 G 5 1x7x9 21/11 19
#> 81: 80 G# 5 1x3x11 1 0
#> 82: 81 A 5 3x5x9 45/44 1
#> 83: 82 A# 5 1x5x7 35/33 2
#> 84: 83 B 5 3x9x11 9/8 3
#> 85: 84 C 6 1x7x11 7/6 4
#> 86: 85 C# 6 5x7x9 105/88 5
#> 87: 86 D 6 3x5x11 5/4 6
#> 88: 87 D# 6 1x3x7 14/11 7
#> 89: 88 E 6 7x9x11 21/16 8
#> 90: 89 F 6 1x5x9 15/11 9
#> 91: 90 F# 6 3x7x9 63/44 10
#> 92: 91 G 6 5x7x11 35/24 11
#> 93: 92 G# 6 1x9x11 3/2 12
#> 94: 93 A 6 3x5x7 35/22 13
#> 95: 94 A# 6 1x3x9 18/11 14
#> 96: 95 B 6 1x5x11 5/3 15
#> 97: 96 C 7 3x7x11 7/4 16
#> 98: 97 C# 7 1x3x5 20/11 17
#> 99: 98 D 7 5x9x11 15/8 18
#> 100: 99 D# 7 1x7x9 21/11 19
#> 101: 100 E 7 1x3x11 1 0
#> 102: 101 F 7 3x5x9 45/44 1
#> 103: 102 F# 7 1x5x7 35/33 2
#> 104: 103 G 7 3x9x11 9/8 3
#> 105: 104 G# 7 1x7x11 7/6 4
#> 106: 105 A 7 5x7x9 105/88 5
#> 107: 106 A# 7 3x5x11 5/4 6
#> 108: 107 B 7 1x3x7 14/11 7
#> 109: 108 C 8 7x9x11 21/16 8
#> 110: 109 C# 8 1x5x9 15/11 9
#> 111: 110 D 8 3x7x9 63/44 10
#> 112: 111 D# 8 5x7x11 35/24 11
#> 113: 112 E 8 1x9x11 3/2 12
#> 114: 113 F 8 3x5x7 35/22 13
#> 115: 114 F# 8 1x3x9 18/11 14
#> 116: 115 G 8 1x5x11 5/3 15
#> 117: 116 G# 8 3x7x11 7/4 16
#> 118: 117 A 8 1x3x5 20/11 17
#> 119: 118 A# 8 5x9x11 15/8 18
#> 120: 119 B 8 1x7x9 21/11 19
#> 121: 120 C 9 1x3x11 1 0
#> 122: 121 C# 9 3x5x9 45/44 1
#> 123: 122 D 9 1x5x7 35/33 2
#> 124: 123 D# 9 3x9x11 9/8 3
#> 125: 124 E 9 1x7x11 7/6 4
#> 126: 125 F 9 5x7x9 105/88 5
#> 127: 126 F# 9 3x5x11 5/4 6
#> 128: 127 G 9 1x3x7 14/11 7
#> note_number name_12edo octave_12edo note_name ratio_frac degree
#> period_number freq cents ref_keyname ref_octave ref_offset
#> <num> <num> <num> <char> <num> <num>
#> 1: -3 32.70320 2400.000 C 2 0
#> 2: -3 33.44645 2438.906 C 2 39
#> 3: -3 34.68521 2501.867 C# 2 2
#> 4: -3 36.79110 2603.910 D 2 4
#> 5: -3 38.15373 2666.871 D# 2 -33
#> 6: -3 39.02086 2705.777 D# 2 6
#> 7: -3 40.87899 2786.314 E 2 -14
#> 8: -3 41.62225 2817.508 E 2 18
#> 9: -3 42.92294 2870.781 F 2 -29
#> 10: -3 44.59527 2936.951 F 2 37
#> 11: -3 46.82503 3021.418 F# 2 21
#> 12: -3 47.69216 3053.185 G 2 -47
#> 13: -3 49.05479 3101.955 G 2 2
#> 14: -3 52.02781 3203.822 G# 2 4
#> 15: -3 53.51432 3252.592 A 2 -47
#> 16: -3 54.50533 3284.359 A 2 -16
#> 17: -3 57.23059 3368.826 A# 2 -31
#> 18: -3 59.46036 3434.996 A# 2 35
#> 19: -3 61.31849 3488.269 B 2 -12
#> 20: -3 62.43337 3519.463 B 2 19
#> 21: -2 65.40639 3600.000 C 3 0
#> 22: -2 66.89290 3638.906 C 3 39
#> 23: -2 69.37042 3701.867 C# 3 2
#> 24: -2 73.58219 3803.910 D 3 4
#> 25: -2 76.30746 3866.871 D# 3 -33
#> 26: -2 78.04172 3905.777 D# 3 6
#> 27: -2 81.75799 3986.314 E 3 -14
#> 28: -2 83.24450 4017.508 E 3 18
#> 29: -2 85.84589 4070.781 F 3 -29
#> 30: -2 89.19053 4136.951 F 3 37
#> 31: -2 93.65006 4221.418 F# 3 21
#> 32: -2 95.38432 4253.185 G 3 -47
#> 33: -2 98.10959 4301.955 G 3 2
#> 34: -2 104.05562 4403.822 G# 3 4
#> 35: -2 107.02864 4452.592 A 3 -47
#> 36: -2 109.01065 4484.359 A 3 -16
#> 37: -2 114.46118 4568.826 A# 3 -31
#> 38: -2 118.92071 4634.996 A# 3 35
#> 39: -2 122.63698 4688.269 B 3 -12
#> 40: -2 124.86675 4719.463 B 3 19
#> 41: -1 130.81278 4800.000 C 4 0
#> 42: -1 133.78580 4838.906 C 4 39
#> 43: -1 138.74083 4901.867 C# 4 2
#> 44: -1 147.16438 5003.910 D 4 4
#> 45: -1 152.61491 5066.871 D# 4 -33
#> 46: -1 156.08343 5105.777 D# 4 6
#> 47: -1 163.51598 5186.314 E 4 -14
#> 48: -1 166.48900 5217.508 E 4 18
#> 49: -1 171.69178 5270.781 F 4 -29
#> 50: -1 178.38107 5336.951 F 4 37
#> 51: -1 187.30012 5421.418 F# 4 21
#> 52: -1 190.76864 5453.185 G 4 -47
#> 53: -1 196.21917 5501.955 G 4 2
#> 54: -1 208.11125 5603.822 G# 4 4
#> 55: -1 214.05728 5652.592 A 4 -47
#> 56: -1 218.02130 5684.359 A 4 -16
#> 57: -1 228.92237 5768.826 A# 4 -31
#> 58: -1 237.84142 5834.996 A# 4 35
#> 59: -1 245.27397 5888.269 B 4 -12
#> 60: -1 249.73349 5919.463 B 4 19
#> 61: 0 261.62557 6000.000 C 5 0
#> 62: 0 267.57160 6038.906 C 5 39
#> 63: 0 277.48166 6101.867 C# 5 2
#> 64: 0 294.32876 6203.910 D 5 4
#> 65: 0 305.22983 6266.871 D# 5 -33
#> 66: 0 312.16687 6305.777 D# 5 6
#> 67: 0 327.03196 6386.314 E 5 -14
#> 68: 0 332.97799 6417.508 E 5 18
#> 69: 0 343.38355 6470.781 F 5 -29
#> 70: 0 356.76213 6536.951 F 5 37
#> 71: 0 374.60024 6621.418 F# 5 21
#> 72: 0 381.53728 6653.185 G 5 -47
#> 73: 0 392.43835 6701.955 G 5 2
#> 74: 0 416.22249 6803.822 G# 5 4
#> 75: 0 428.11456 6852.592 A 5 -47
#> 76: 0 436.04261 6884.359 A 5 -16
#> 77: 0 457.84474 6968.826 A# 5 -31
#> 78: 0 475.68285 7034.996 A# 5 35
#> 79: 0 490.54793 7088.269 B 5 -12
#> 80: 0 499.46699 7119.463 B 5 19
#> 81: 1 523.25113 7200.000 C 6 0
#> 82: 1 535.14320 7238.906 C 6 39
#> 83: 1 554.96332 7301.867 C# 6 2
#> 84: 1 588.65752 7403.910 D 6 4
#> 85: 1 610.45965 7466.871 D# 6 -33
#> 86: 1 624.33374 7505.777 D# 6 6
#> 87: 1 654.06391 7586.314 E 6 -14
#> 88: 1 665.95598 7617.508 E 6 18
#> 89: 1 686.76711 7670.781 F 6 -29
#> 90: 1 713.52427 7736.951 F 6 37
#> 91: 1 749.20048 7821.418 F# 6 21
#> 92: 1 763.07457 7853.185 G 6 -47
#> 93: 1 784.87670 7901.955 G 6 2
#> 94: 1 832.44498 8003.822 G# 6 4
#> 95: 1 856.22912 8052.592 A 6 -47
#> 96: 1 872.08522 8084.359 A 6 -16
#> 97: 1 915.68948 8168.826 A# 6 -31
#> 98: 1 951.36569 8234.996 A# 6 35
#> 99: 1 981.09587 8288.269 B 6 -12
#> 100: 1 998.93398 8319.463 B 6 19
#> 101: 2 1046.50226 8400.000 C 7 0
#> 102: 2 1070.28640 8438.906 C 7 39
#> 103: 2 1109.92664 8501.867 C# 7 2
#> 104: 2 1177.31504 8603.910 D 7 4
#> 105: 2 1220.91930 8666.871 D# 7 -33
#> 106: 2 1248.66747 8705.777 D# 7 6
#> 107: 2 1308.12783 8786.314 E 7 -14
#> 108: 2 1331.91197 8817.508 E 7 18
#> 109: 2 1373.53422 8870.781 F 7 -29
#> 110: 2 1427.04854 8936.951 F 7 37
#> 111: 2 1498.40096 9021.418 F# 7 21
#> 112: 2 1526.14913 9053.185 G 7 -47
#> 113: 2 1569.75339 9101.955 G 7 2
#> 114: 2 1664.88996 9203.822 G# 7 4
#> 115: 2 1712.45825 9252.592 A 7 -47
#> 116: 2 1744.17044 9284.359 A 7 -16
#> 117: 2 1831.37896 9368.826 A# 7 -31
#> 118: 2 1902.73138 9434.996 A# 7 35
#> 119: 2 1962.19174 9488.269 B 7 -12
#> 120: 2 1997.86795 9519.463 B 7 19
#> 121: 3 2093.00452 9600.000 C 8 0
#> 122: 3 2140.57281 9638.906 C 8 39
#> 123: 3 2219.85328 9701.867 C# 8 2
#> 124: 3 2354.63009 9803.910 D 8 4
#> 125: 3 2441.83861 9866.871 D# 8 -33
#> 126: 3 2497.33494 9905.777 D# 8 6
#> 127: 3 2616.25565 9986.314 E 8 -14
#> 128: 3 2663.82394 10017.508 E 8 18
#> period_number freq cents ref_keyname ref_octave ref_offset
# 12-EDO for sanity check
print(vanilla_keyboard_map <- keyboard_map(et_scale_table()), nrows = 128)
#> Key: <note_number>
#> note_number name_12edo octave_12edo note_name ratio_frac degree
#> <num> <char> <num> <char> <char> <num>
#> 1: 0 C -1 C 1 0
#> 2: 1 C# -1 C#|Db 1461/1379 1
#> 3: 2 D -1 D 1714/1527 2
#> 4: 3 D# -1 D#|Eb 1785/1501 3
#> 5: 4 E -1 E 635/504 4
#> 6: 5 F -1 F 3249/2434 5
#> 7: 6 F# -1 F#|Gb 1393/985 6
#> 8: 7 G -1 G 2213/1477 7
#> 9: 8 G# -1 G#|Ab 1008/635 8
#> 10: 9 A -1 A 3002/1785 9
#> 11: 10 A# -1 A#|Bb 1527/857 10
#> 12: 11 B -1 B 2943/1559 11
#> 13: 12 C 0 C 1 0
#> 14: 13 C# 0 C#|Db 1461/1379 1
#> 15: 14 D 0 D 1714/1527 2
#> 16: 15 D# 0 D#|Eb 1785/1501 3
#> 17: 16 E 0 E 635/504 4
#> 18: 17 F 0 F 3249/2434 5
#> 19: 18 F# 0 F#|Gb 1393/985 6
#> 20: 19 G 0 G 2213/1477 7
#> 21: 20 G# 0 G#|Ab 1008/635 8
#> 22: 21 A 0 A 3002/1785 9
#> 23: 22 A# 0 A#|Bb 1527/857 10
#> 24: 23 B 0 B 2943/1559 11
#> 25: 24 C 1 C 1 0
#> 26: 25 C# 1 C#|Db 1461/1379 1
#> 27: 26 D 1 D 1714/1527 2
#> 28: 27 D# 1 D#|Eb 1785/1501 3
#> 29: 28 E 1 E 635/504 4
#> 30: 29 F 1 F 3249/2434 5
#> 31: 30 F# 1 F#|Gb 1393/985 6
#> 32: 31 G 1 G 2213/1477 7
#> 33: 32 G# 1 G#|Ab 1008/635 8
#> 34: 33 A 1 A 3002/1785 9
#> 35: 34 A# 1 A#|Bb 1527/857 10
#> 36: 35 B 1 B 2943/1559 11
#> 37: 36 C 2 C 1 0
#> 38: 37 C# 2 C#|Db 1461/1379 1
#> 39: 38 D 2 D 1714/1527 2
#> 40: 39 D# 2 D#|Eb 1785/1501 3
#> 41: 40 E 2 E 635/504 4
#> 42: 41 F 2 F 3249/2434 5
#> 43: 42 F# 2 F#|Gb 1393/985 6
#> 44: 43 G 2 G 2213/1477 7
#> 45: 44 G# 2 G#|Ab 1008/635 8
#> 46: 45 A 2 A 3002/1785 9
#> 47: 46 A# 2 A#|Bb 1527/857 10
#> 48: 47 B 2 B 2943/1559 11
#> 49: 48 C 3 C 1 0
#> 50: 49 C# 3 C#|Db 1461/1379 1
#> 51: 50 D 3 D 1714/1527 2
#> 52: 51 D# 3 D#|Eb 1785/1501 3
#> 53: 52 E 3 E 635/504 4
#> 54: 53 F 3 F 3249/2434 5
#> 55: 54 F# 3 F#|Gb 1393/985 6
#> 56: 55 G 3 G 2213/1477 7
#> 57: 56 G# 3 G#|Ab 1008/635 8
#> 58: 57 A 3 A 3002/1785 9
#> 59: 58 A# 3 A#|Bb 1527/857 10
#> 60: 59 B 3 B 2943/1559 11
#> 61: 60 C 4 C 1 0
#> 62: 61 C# 4 C#|Db 1461/1379 1
#> 63: 62 D 4 D 1714/1527 2
#> 64: 63 D# 4 D#|Eb 1785/1501 3
#> 65: 64 E 4 E 635/504 4
#> 66: 65 F 4 F 3249/2434 5
#> 67: 66 F# 4 F#|Gb 1393/985 6
#> 68: 67 G 4 G 2213/1477 7
#> 69: 68 G# 4 G#|Ab 1008/635 8
#> 70: 69 A 4 A 3002/1785 9
#> 71: 70 A# 4 A#|Bb 1527/857 10
#> 72: 71 B 4 B 2943/1559 11
#> 73: 72 C 5 C 1 0
#> 74: 73 C# 5 C#|Db 1461/1379 1
#> 75: 74 D 5 D 1714/1527 2
#> 76: 75 D# 5 D#|Eb 1785/1501 3
#> 77: 76 E 5 E 635/504 4
#> 78: 77 F 5 F 3249/2434 5
#> 79: 78 F# 5 F#|Gb 1393/985 6
#> 80: 79 G 5 G 2213/1477 7
#> 81: 80 G# 5 G#|Ab 1008/635 8
#> 82: 81 A 5 A 3002/1785 9
#> 83: 82 A# 5 A#|Bb 1527/857 10
#> 84: 83 B 5 B 2943/1559 11
#> 85: 84 C 6 C 1 0
#> 86: 85 C# 6 C#|Db 1461/1379 1
#> 87: 86 D 6 D 1714/1527 2
#> 88: 87 D# 6 D#|Eb 1785/1501 3
#> 89: 88 E 6 E 635/504 4
#> 90: 89 F 6 F 3249/2434 5
#> 91: 90 F# 6 F#|Gb 1393/985 6
#> 92: 91 G 6 G 2213/1477 7
#> 93: 92 G# 6 G#|Ab 1008/635 8
#> 94: 93 A 6 A 3002/1785 9
#> 95: 94 A# 6 A#|Bb 1527/857 10
#> 96: 95 B 6 B 2943/1559 11
#> 97: 96 C 7 C 1 0
#> 98: 97 C# 7 C#|Db 1461/1379 1
#> 99: 98 D 7 D 1714/1527 2
#> 100: 99 D# 7 D#|Eb 1785/1501 3
#> 101: 100 E 7 E 635/504 4
#> 102: 101 F 7 F 3249/2434 5
#> 103: 102 F# 7 F#|Gb 1393/985 6
#> 104: 103 G 7 G 2213/1477 7
#> 105: 104 G# 7 G#|Ab 1008/635 8
#> 106: 105 A 7 A 3002/1785 9
#> 107: 106 A# 7 A#|Bb 1527/857 10
#> 108: 107 B 7 B 2943/1559 11
#> 109: 108 C 8 C 1 0
#> 110: 109 C# 8 C#|Db 1461/1379 1
#> 111: 110 D 8 D 1714/1527 2
#> 112: 111 D# 8 D#|Eb 1785/1501 3
#> 113: 112 E 8 E 635/504 4
#> 114: 113 F 8 F 3249/2434 5
#> 115: 114 F# 8 F#|Gb 1393/985 6
#> 116: 115 G 8 G 2213/1477 7
#> 117: 116 G# 8 G#|Ab 1008/635 8
#> 118: 117 A 8 A 3002/1785 9
#> 119: 118 A# 8 A#|Bb 1527/857 10
#> 120: 119 B 8 B 2943/1559 11
#> 121: 120 C 9 C 1 0
#> 122: 121 C# 9 C#|Db 1461/1379 1
#> 123: 122 D 9 D 1714/1527 2
#> 124: 123 D# 9 D#|Eb 1785/1501 3
#> 125: 124 E 9 E 635/504 4
#> 126: 125 F 9 F 3249/2434 5
#> 127: 126 F# 9 F#|Gb 1393/985 6
#> 128: 127 G 9 G 2213/1477 7
#> note_number name_12edo octave_12edo note_name ratio_frac degree
#> period_number freq cents ref_keyname ref_octave ref_offset
#> <num> <num> <num> <char> <num> <num>
#> 1: -5 8.175799 0 C 0 0
#> 2: -5 8.661957 100 C# 0 0
#> 3: -5 9.177024 200 D 0 0
#> 4: -5 9.722718 300 D# 0 0
#> 5: -5 10.300861 400 E 0 0
#> 6: -5 10.913382 500 F 0 0
#> 7: -5 11.562326 600 F# 0 0
#> 8: -5 12.249857 700 G 0 0
#> 9: -5 12.978272 800 G# 0 0
#> 10: -5 13.750000 900 A 0 0
#> 11: -5 14.567618 1000 A# 0 0
#> 12: -5 15.433853 1100 B 0 0
#> 13: -4 16.351598 1200 C 1 0
#> 14: -4 17.323914 1300 C# 1 0
#> 15: -4 18.354048 1400 D 1 0
#> 16: -4 19.445436 1500 D# 1 0
#> 17: -4 20.601722 1600 E 1 0
#> 18: -4 21.826764 1700 F 1 0
#> 19: -4 23.124651 1800 F# 1 0
#> 20: -4 24.499715 1900 G 1 0
#> 21: -4 25.956544 2000 G# 1 0
#> 22: -4 27.500000 2100 A 1 0
#> 23: -4 29.135235 2200 A# 1 0
#> 24: -4 30.867706 2300 B 1 0
#> 25: -3 32.703196 2400 C 2 0
#> 26: -3 34.647829 2500 C# 2 0
#> 27: -3 36.708096 2600 D 2 0
#> 28: -3 38.890873 2700 D# 2 0
#> 29: -3 41.203445 2800 E 2 0
#> 30: -3 43.653529 2900 F 2 0
#> 31: -3 46.249303 3000 F# 2 0
#> 32: -3 48.999429 3100 G 2 0
#> 33: -3 51.913087 3200 G# 2 0
#> 34: -3 55.000000 3300 A 2 0
#> 35: -3 58.270470 3400 A# 2 0
#> 36: -3 61.735413 3500 B 2 0
#> 37: -2 65.406391 3600 C 3 0
#> 38: -2 69.295658 3700 C# 3 0
#> 39: -2 73.416192 3800 D 3 0
#> 40: -2 77.781746 3900 D# 3 0
#> 41: -2 82.406889 4000 E 3 0
#> 42: -2 87.307058 4100 F 3 0
#> 43: -2 92.498606 4200 F# 3 0
#> 44: -2 97.998859 4300 G 3 0
#> 45: -2 103.826174 4400 G# 3 0
#> 46: -2 110.000000 4500 A 3 0
#> 47: -2 116.540940 4600 A# 3 0
#> 48: -2 123.470825 4700 B 3 0
#> 49: -1 130.812783 4800 C 4 0
#> 50: -1 138.591315 4900 C# 4 0
#> 51: -1 146.832384 5000 D 4 0
#> 52: -1 155.563492 5100 D# 4 0
#> 53: -1 164.813778 5200 E 4 0
#> 54: -1 174.614116 5300 F 4 0
#> 55: -1 184.997211 5400 F# 4 0
#> 56: -1 195.997718 5500 G 4 0
#> 57: -1 207.652349 5600 G# 4 0
#> 58: -1 220.000000 5700 A 4 0
#> 59: -1 233.081881 5800 A# 4 0
#> 60: -1 246.941651 5900 B 4 0
#> 61: 0 261.625565 6000 C 5 0
#> 62: 0 277.182631 6100 C# 5 0
#> 63: 0 293.664768 6200 D 5 0
#> 64: 0 311.126984 6300 D# 5 0
#> 65: 0 329.627557 6400 E 5 0
#> 66: 0 349.228231 6500 F 5 0
#> 67: 0 369.994423 6600 F# 5 0
#> 68: 0 391.995436 6700 G 5 0
#> 69: 0 415.304698 6800 G# 5 0
#> 70: 0 440.000000 6900 A 5 0
#> 71: 0 466.163762 7000 A# 5 0
#> 72: 0 493.883301 7100 B 5 0
#> 73: 1 523.251131 7200 C 6 0
#> 74: 1 554.365262 7300 C# 6 0
#> 75: 1 587.329536 7400 D 6 0
#> 76: 1 622.253967 7500 D# 6 0
#> 77: 1 659.255114 7600 E 6 0
#> 78: 1 698.456463 7700 F 6 0
#> 79: 1 739.988845 7800 F# 6 0
#> 80: 1 783.990872 7900 G 6 0
#> 81: 1 830.609395 8000 G# 6 0
#> 82: 1 880.000000 8100 A 6 0
#> 83: 1 932.327523 8200 A# 6 0
#> 84: 1 987.766603 8300 B 6 0
#> 85: 2 1046.502261 8400 C 7 0
#> 86: 2 1108.730524 8500 C# 7 0
#> 87: 2 1174.659072 8600 D 7 0
#> 88: 2 1244.507935 8700 D# 7 0
#> 89: 2 1318.510228 8800 E 7 0
#> 90: 2 1396.912926 8900 F 7 0
#> 91: 2 1479.977691 9000 F# 7 0
#> 92: 2 1567.981744 9100 G 7 0
#> 93: 2 1661.218790 9200 G# 7 0
#> 94: 2 1760.000000 9300 A 7 0
#> 95: 2 1864.655046 9400 A# 7 0
#> 96: 2 1975.533205 9500 B 7 0
#> 97: 3 2093.004522 9600 C 8 0
#> 98: 3 2217.461048 9700 C# 8 0
#> 99: 3 2349.318143 9800 D 8 0
#> 100: 3 2489.015870 9900 D# 8 0
#> 101: 3 2637.020455 10000 E 8 0
#> 102: 3 2793.825851 10100 F 8 0
#> 103: 3 2959.955382 10200 F# 8 0
#> 104: 3 3135.963488 10300 G 8 0
#> 105: 3 3322.437581 10400 G# 8 0
#> 106: 3 3520.000000 10500 A 8 0
#> 107: 3 3729.310092 10600 A# 8 0
#> 108: 3 3951.066410 10700 B 8 0
#> 109: 4 4186.009045 10800 C 9 0
#> 110: 4 4434.922096 10900 C# 9 0
#> 111: 4 4698.636287 11000 D 9 0
#> 112: 4 4978.031740 11100 D# 9 0
#> 113: 4 5274.040911 11200 E 9 0
#> 114: 4 5587.651703 11300 F 9 0
#> 115: 4 5919.910763 11400 F# 9 0
#> 116: 4 6271.926976 11500 G 9 0
#> 117: 4 6644.875161 11600 G# 9 0
#> 118: 4 7040.000000 11700 A 9 0
#> 119: 4 7458.620184 11800 A# 9 0
#> 120: 4 7902.132820 11900 B 9 0
#> 121: 5 8372.018090 12000 C 10 0
#> 122: 5 8869.844191 12100 C# 10 0
#> 123: 5 9397.272573 12200 D 10 0
#> 124: 5 9956.063479 12300 D# 10 0
#> 125: 5 10548.081821 12400 E 10 0
#> 126: 5 11175.303406 12500 F 10 0
#> 127: 5 11839.821527 12600 F# 10 0
#> 128: 5 12543.853951 12700 G 10 0
#> period_number freq cents ref_keyname ref_octave ref_offset
# check middle C setting
print(
eikosany_keyboard_map_c3 <-
keyboard_map(cps_scale_table(root_divisor = 33), middle_c_octave = 3), nrows = 128)
#> Key: <note_number>
#> note_number name_12edo octave_12edo note_name ratio_frac degree
#> <num> <char> <num> <char> <char> <num>
#> 1: 0 C -2 1x3x11 1 0
#> 2: 1 C# -2 3x5x9 45/44 1
#> 3: 2 D -2 1x5x7 35/33 2
#> 4: 3 D# -2 3x9x11 9/8 3
#> 5: 4 E -2 1x7x11 7/6 4
#> 6: 5 F -2 5x7x9 105/88 5
#> 7: 6 F# -2 3x5x11 5/4 6
#> 8: 7 G -2 1x3x7 14/11 7
#> 9: 8 G# -2 7x9x11 21/16 8
#> 10: 9 A -2 1x5x9 15/11 9
#> 11: 10 A# -2 3x7x9 63/44 10
#> 12: 11 B -2 5x7x11 35/24 11
#> 13: 12 C -1 1x9x11 3/2 12
#> 14: 13 C# -1 3x5x7 35/22 13
#> 15: 14 D -1 1x3x9 18/11 14
#> 16: 15 D# -1 1x5x11 5/3 15
#> 17: 16 E -1 3x7x11 7/4 16
#> 18: 17 F -1 1x3x5 20/11 17
#> 19: 18 F# -1 5x9x11 15/8 18
#> 20: 19 G -1 1x7x9 21/11 19
#> 21: 20 G# -1 1x3x11 1 0
#> 22: 21 A -1 3x5x9 45/44 1
#> 23: 22 A# -1 1x5x7 35/33 2
#> 24: 23 B -1 3x9x11 9/8 3
#> 25: 24 C 0 1x7x11 7/6 4
#> 26: 25 C# 0 5x7x9 105/88 5
#> 27: 26 D 0 3x5x11 5/4 6
#> 28: 27 D# 0 1x3x7 14/11 7
#> 29: 28 E 0 7x9x11 21/16 8
#> 30: 29 F 0 1x5x9 15/11 9
#> 31: 30 F# 0 3x7x9 63/44 10
#> 32: 31 G 0 5x7x11 35/24 11
#> 33: 32 G# 0 1x9x11 3/2 12
#> 34: 33 A 0 3x5x7 35/22 13
#> 35: 34 A# 0 1x3x9 18/11 14
#> 36: 35 B 0 1x5x11 5/3 15
#> 37: 36 C 1 3x7x11 7/4 16
#> 38: 37 C# 1 1x3x5 20/11 17
#> 39: 38 D 1 5x9x11 15/8 18
#> 40: 39 D# 1 1x7x9 21/11 19
#> 41: 40 E 1 1x3x11 1 0
#> 42: 41 F 1 3x5x9 45/44 1
#> 43: 42 F# 1 1x5x7 35/33 2
#> 44: 43 G 1 3x9x11 9/8 3
#> 45: 44 G# 1 1x7x11 7/6 4
#> 46: 45 A 1 5x7x9 105/88 5
#> 47: 46 A# 1 3x5x11 5/4 6
#> 48: 47 B 1 1x3x7 14/11 7
#> 49: 48 C 2 7x9x11 21/16 8
#> 50: 49 C# 2 1x5x9 15/11 9
#> 51: 50 D 2 3x7x9 63/44 10
#> 52: 51 D# 2 5x7x11 35/24 11
#> 53: 52 E 2 1x9x11 3/2 12
#> 54: 53 F 2 3x5x7 35/22 13
#> 55: 54 F# 2 1x3x9 18/11 14
#> 56: 55 G 2 1x5x11 5/3 15
#> 57: 56 G# 2 3x7x11 7/4 16
#> 58: 57 A 2 1x3x5 20/11 17
#> 59: 58 A# 2 5x9x11 15/8 18
#> 60: 59 B 2 1x7x9 21/11 19
#> 61: 60 C 3 1x3x11 1 0
#> 62: 61 C# 3 3x5x9 45/44 1
#> 63: 62 D 3 1x5x7 35/33 2
#> 64: 63 D# 3 3x9x11 9/8 3
#> 65: 64 E 3 1x7x11 7/6 4
#> 66: 65 F 3 5x7x9 105/88 5
#> 67: 66 F# 3 3x5x11 5/4 6
#> 68: 67 G 3 1x3x7 14/11 7
#> 69: 68 G# 3 7x9x11 21/16 8
#> 70: 69 A 3 1x5x9 15/11 9
#> 71: 70 A# 3 3x7x9 63/44 10
#> 72: 71 B 3 5x7x11 35/24 11
#> 73: 72 C 4 1x9x11 3/2 12
#> 74: 73 C# 4 3x5x7 35/22 13
#> 75: 74 D 4 1x3x9 18/11 14
#> 76: 75 D# 4 1x5x11 5/3 15
#> 77: 76 E 4 3x7x11 7/4 16
#> 78: 77 F 4 1x3x5 20/11 17
#> 79: 78 F# 4 5x9x11 15/8 18
#> 80: 79 G 4 1x7x9 21/11 19
#> 81: 80 G# 4 1x3x11 1 0
#> 82: 81 A 4 3x5x9 45/44 1
#> 83: 82 A# 4 1x5x7 35/33 2
#> 84: 83 B 4 3x9x11 9/8 3
#> 85: 84 C 5 1x7x11 7/6 4
#> 86: 85 C# 5 5x7x9 105/88 5
#> 87: 86 D 5 3x5x11 5/4 6
#> 88: 87 D# 5 1x3x7 14/11 7
#> 89: 88 E 5 7x9x11 21/16 8
#> 90: 89 F 5 1x5x9 15/11 9
#> 91: 90 F# 5 3x7x9 63/44 10
#> 92: 91 G 5 5x7x11 35/24 11
#> 93: 92 G# 5 1x9x11 3/2 12
#> 94: 93 A 5 3x5x7 35/22 13
#> 95: 94 A# 5 1x3x9 18/11 14
#> 96: 95 B 5 1x5x11 5/3 15
#> 97: 96 C 6 3x7x11 7/4 16
#> 98: 97 C# 6 1x3x5 20/11 17
#> 99: 98 D 6 5x9x11 15/8 18
#> 100: 99 D# 6 1x7x9 21/11 19
#> 101: 100 E 6 1x3x11 1 0
#> 102: 101 F 6 3x5x9 45/44 1
#> 103: 102 F# 6 1x5x7 35/33 2
#> 104: 103 G 6 3x9x11 9/8 3
#> 105: 104 G# 6 1x7x11 7/6 4
#> 106: 105 A 6 5x7x9 105/88 5
#> 107: 106 A# 6 3x5x11 5/4 6
#> 108: 107 B 6 1x3x7 14/11 7
#> 109: 108 C 7 7x9x11 21/16 8
#> 110: 109 C# 7 1x5x9 15/11 9
#> 111: 110 D 7 3x7x9 63/44 10
#> 112: 111 D# 7 5x7x11 35/24 11
#> 113: 112 E 7 1x9x11 3/2 12
#> 114: 113 F 7 3x5x7 35/22 13
#> 115: 114 F# 7 1x3x9 18/11 14
#> 116: 115 G 7 1x5x11 5/3 15
#> 117: 116 G# 7 3x7x11 7/4 16
#> 118: 117 A 7 1x3x5 20/11 17
#> 119: 118 A# 7 5x9x11 15/8 18
#> 120: 119 B 7 1x7x9 21/11 19
#> 121: 120 C 8 1x3x11 1 0
#> 122: 121 C# 8 3x5x9 45/44 1
#> 123: 122 D 8 1x5x7 35/33 2
#> 124: 123 D# 8 3x9x11 9/8 3
#> 125: 124 E 8 1x7x11 7/6 4
#> 126: 125 F 8 5x7x9 105/88 5
#> 127: 126 F# 8 3x5x11 5/4 6
#> 128: 127 G 8 1x3x7 14/11 7
#> note_number name_12edo octave_12edo note_name ratio_frac degree
#> period_number freq cents ref_keyname ref_octave ref_offset
#> <num> <num> <num> <char> <num> <num>
#> 1: -3 32.70320 2400.000 C 2 0
#> 2: -3 33.44645 2438.906 C 2 39
#> 3: -3 34.68521 2501.867 C# 2 2
#> 4: -3 36.79110 2603.910 D 2 4
#> 5: -3 38.15373 2666.871 D# 2 -33
#> 6: -3 39.02086 2705.777 D# 2 6
#> 7: -3 40.87899 2786.314 E 2 -14
#> 8: -3 41.62225 2817.508 E 2 18
#> 9: -3 42.92294 2870.781 F 2 -29
#> 10: -3 44.59527 2936.951 F 2 37
#> 11: -3 46.82503 3021.418 F# 2 21
#> 12: -3 47.69216 3053.185 G 2 -47
#> 13: -3 49.05479 3101.955 G 2 2
#> 14: -3 52.02781 3203.822 G# 2 4
#> 15: -3 53.51432 3252.592 A 2 -47
#> 16: -3 54.50533 3284.359 A 2 -16
#> 17: -3 57.23059 3368.826 A# 2 -31
#> 18: -3 59.46036 3434.996 A# 2 35
#> 19: -3 61.31849 3488.269 B 2 -12
#> 20: -3 62.43337 3519.463 B 2 19
#> 21: -2 65.40639 3600.000 C 3 0
#> 22: -2 66.89290 3638.906 C 3 39
#> 23: -2 69.37042 3701.867 C# 3 2
#> 24: -2 73.58219 3803.910 D 3 4
#> 25: -2 76.30746 3866.871 D# 3 -33
#> 26: -2 78.04172 3905.777 D# 3 6
#> 27: -2 81.75799 3986.314 E 3 -14
#> 28: -2 83.24450 4017.508 E 3 18
#> 29: -2 85.84589 4070.781 F 3 -29
#> 30: -2 89.19053 4136.951 F 3 37
#> 31: -2 93.65006 4221.418 F# 3 21
#> 32: -2 95.38432 4253.185 G 3 -47
#> 33: -2 98.10959 4301.955 G 3 2
#> 34: -2 104.05562 4403.822 G# 3 4
#> 35: -2 107.02864 4452.592 A 3 -47
#> 36: -2 109.01065 4484.359 A 3 -16
#> 37: -2 114.46118 4568.826 A# 3 -31
#> 38: -2 118.92071 4634.996 A# 3 35
#> 39: -2 122.63698 4688.269 B 3 -12
#> 40: -2 124.86675 4719.463 B 3 19
#> 41: -1 130.81278 4800.000 C 4 0
#> 42: -1 133.78580 4838.906 C 4 39
#> 43: -1 138.74083 4901.867 C# 4 2
#> 44: -1 147.16438 5003.910 D 4 4
#> 45: -1 152.61491 5066.871 D# 4 -33
#> 46: -1 156.08343 5105.777 D# 4 6
#> 47: -1 163.51598 5186.314 E 4 -14
#> 48: -1 166.48900 5217.508 E 4 18
#> 49: -1 171.69178 5270.781 F 4 -29
#> 50: -1 178.38107 5336.951 F 4 37
#> 51: -1 187.30012 5421.418 F# 4 21
#> 52: -1 190.76864 5453.185 G 4 -47
#> 53: -1 196.21917 5501.955 G 4 2
#> 54: -1 208.11125 5603.822 G# 4 4
#> 55: -1 214.05728 5652.592 A 4 -47
#> 56: -1 218.02130 5684.359 A 4 -16
#> 57: -1 228.92237 5768.826 A# 4 -31
#> 58: -1 237.84142 5834.996 A# 4 35
#> 59: -1 245.27397 5888.269 B 4 -12
#> 60: -1 249.73349 5919.463 B 4 19
#> 61: 0 261.62557 6000.000 C 5 0
#> 62: 0 267.57160 6038.906 C 5 39
#> 63: 0 277.48166 6101.867 C# 5 2
#> 64: 0 294.32876 6203.910 D 5 4
#> 65: 0 305.22983 6266.871 D# 5 -33
#> 66: 0 312.16687 6305.777 D# 5 6
#> 67: 0 327.03196 6386.314 E 5 -14
#> 68: 0 332.97799 6417.508 E 5 18
#> 69: 0 343.38355 6470.781 F 5 -29
#> 70: 0 356.76213 6536.951 F 5 37
#> 71: 0 374.60024 6621.418 F# 5 21
#> 72: 0 381.53728 6653.185 G 5 -47
#> 73: 0 392.43835 6701.955 G 5 2
#> 74: 0 416.22249 6803.822 G# 5 4
#> 75: 0 428.11456 6852.592 A 5 -47
#> 76: 0 436.04261 6884.359 A 5 -16
#> 77: 0 457.84474 6968.826 A# 5 -31
#> 78: 0 475.68285 7034.996 A# 5 35
#> 79: 0 490.54793 7088.269 B 5 -12
#> 80: 0 499.46699 7119.463 B 5 19
#> 81: 1 523.25113 7200.000 C 6 0
#> 82: 1 535.14320 7238.906 C 6 39
#> 83: 1 554.96332 7301.867 C# 6 2
#> 84: 1 588.65752 7403.910 D 6 4
#> 85: 1 610.45965 7466.871 D# 6 -33
#> 86: 1 624.33374 7505.777 D# 6 6
#> 87: 1 654.06391 7586.314 E 6 -14
#> 88: 1 665.95598 7617.508 E 6 18
#> 89: 1 686.76711 7670.781 F 6 -29
#> 90: 1 713.52427 7736.951 F 6 37
#> 91: 1 749.20048 7821.418 F# 6 21
#> 92: 1 763.07457 7853.185 G 6 -47
#> 93: 1 784.87670 7901.955 G 6 2
#> 94: 1 832.44498 8003.822 G# 6 4
#> 95: 1 856.22912 8052.592 A 6 -47
#> 96: 1 872.08522 8084.359 A 6 -16
#> 97: 1 915.68948 8168.826 A# 6 -31
#> 98: 1 951.36569 8234.996 A# 6 35
#> 99: 1 981.09587 8288.269 B 6 -12
#> 100: 1 998.93398 8319.463 B 6 19
#> 101: 2 1046.50226 8400.000 C 7 0
#> 102: 2 1070.28640 8438.906 C 7 39
#> 103: 2 1109.92664 8501.867 C# 7 2
#> 104: 2 1177.31504 8603.910 D 7 4
#> 105: 2 1220.91930 8666.871 D# 7 -33
#> 106: 2 1248.66747 8705.777 D# 7 6
#> 107: 2 1308.12783 8786.314 E 7 -14
#> 108: 2 1331.91197 8817.508 E 7 18
#> 109: 2 1373.53422 8870.781 F 7 -29
#> 110: 2 1427.04854 8936.951 F 7 37
#> 111: 2 1498.40096 9021.418 F# 7 21
#> 112: 2 1526.14913 9053.185 G 7 -47
#> 113: 2 1569.75339 9101.955 G 7 2
#> 114: 2 1664.88996 9203.822 G# 7 4
#> 115: 2 1712.45825 9252.592 A 7 -47
#> 116: 2 1744.17044 9284.359 A 7 -16
#> 117: 2 1831.37896 9368.826 A# 7 -31
#> 118: 2 1902.73138 9434.996 A# 7 35
#> 119: 2 1962.19174 9488.269 B 7 -12
#> 120: 2 1997.86795 9519.463 B 7 19
#> 121: 3 2093.00452 9600.000 C 8 0
#> 122: 3 2140.57281 9638.906 C 8 39
#> 123: 3 2219.85328 9701.867 C# 8 2
#> 124: 3 2354.63009 9803.910 D 8 4
#> 125: 3 2441.83861 9866.871 D# 8 -33
#> 126: 3 2497.33494 9905.777 D# 8 6
#> 127: 3 2616.25565 9986.314 E 8 -14
#> 128: 3 2663.82394 10017.508 E 8 18
#> period_number freq cents ref_keyname ref_octave ref_offset
# Bohlen-Pierce (13 equal divisions of a perfect twelfth aka "tritave")
bohlen_pierce_et_scale <- et_scale_table(bohlen_pierce_et_names, period = 3)
print(bohlen_pierce_et_map <-
keyboard_map(bohlen_pierce_et_scale), nrows = 128)
#> Key: <note_number>
#> note_number name_12edo octave_12edo note_name ratio_frac degree
#> <num> <char> <num> <char> <char> <num>
#> 1: 0 C -1 F#|Gb 3691/2419 5
#> 2: 1 C# -1 G 2645/1593 6
#> 3: 2 D -1 H 1646/911 7
#> 4: 3 D# -1 H#|Jb 2090/1063 8
#> 5: 4 E -1 J 2101/982 9
#> 6: 5 F -1 A 1355/582 10
#> 7: 6 F# -1 A#|Bb 1135/448 11
#> 8: 7 G -1 B 6101/2213 12
#> 9: 8 G# -1 C 1 0
#> 10: 9 A -1 C#|Db 1197/1100 1
#> 11: 10 A# -1 D 881/744 2
#> 12: 11 B -1 E 1746/1355 3
#> 13: 12 C 0 F 1025/731 4
#> 14: 13 C# 0 F#|Gb 3691/2419 5
#> 15: 14 D 0 G 2645/1593 6
#> 16: 15 D# 0 H 1646/911 7
#> 17: 16 E 0 H#|Jb 2090/1063 8
#> 18: 17 F 0 J 2101/982 9
#> 19: 18 F# 0 A 1355/582 10
#> 20: 19 G 0 A#|Bb 1135/448 11
#> 21: 20 G# 0 B 6101/2213 12
#> 22: 21 A 0 C 1 0
#> 23: 22 A# 0 C#|Db 1197/1100 1
#> 24: 23 B 0 D 881/744 2
#> 25: 24 C 1 E 1746/1355 3
#> 26: 25 C# 1 F 1025/731 4
#> 27: 26 D 1 F#|Gb 3691/2419 5
#> 28: 27 D# 1 G 2645/1593 6
#> 29: 28 E 1 H 1646/911 7
#> 30: 29 F 1 H#|Jb 2090/1063 8
#> 31: 30 F# 1 J 2101/982 9
#> 32: 31 G 1 A 1355/582 10
#> 33: 32 G# 1 A#|Bb 1135/448 11
#> 34: 33 A 1 B 6101/2213 12
#> 35: 34 A# 1 C 1 0
#> 36: 35 B 1 C#|Db 1197/1100 1
#> 37: 36 C 2 D 881/744 2
#> 38: 37 C# 2 E 1746/1355 3
#> 39: 38 D 2 F 1025/731 4
#> 40: 39 D# 2 F#|Gb 3691/2419 5
#> 41: 40 E 2 G 2645/1593 6
#> 42: 41 F 2 H 1646/911 7
#> 43: 42 F# 2 H#|Jb 2090/1063 8
#> 44: 43 G 2 J 2101/982 9
#> 45: 44 G# 2 A 1355/582 10
#> 46: 45 A 2 A#|Bb 1135/448 11
#> 47: 46 A# 2 B 6101/2213 12
#> 48: 47 B 2 C 1 0
#> 49: 48 C 3 C#|Db 1197/1100 1
#> 50: 49 C# 3 D 881/744 2
#> 51: 50 D 3 E 1746/1355 3
#> 52: 51 D# 3 F 1025/731 4
#> 53: 52 E 3 F#|Gb 3691/2419 5
#> 54: 53 F 3 G 2645/1593 6
#> 55: 54 F# 3 H 1646/911 7
#> 56: 55 G 3 H#|Jb 2090/1063 8
#> 57: 56 G# 3 J 2101/982 9
#> 58: 57 A 3 A 1355/582 10
#> 59: 58 A# 3 A#|Bb 1135/448 11
#> 60: 59 B 3 B 6101/2213 12
#> 61: 60 C 4 C 1 0
#> 62: 61 C# 4 C#|Db 1197/1100 1
#> 63: 62 D 4 D 881/744 2
#> 64: 63 D# 4 E 1746/1355 3
#> 65: 64 E 4 F 1025/731 4
#> 66: 65 F 4 F#|Gb 3691/2419 5
#> 67: 66 F# 4 G 2645/1593 6
#> 68: 67 G 4 H 1646/911 7
#> 69: 68 G# 4 H#|Jb 2090/1063 8
#> 70: 69 A 4 J 2101/982 9
#> 71: 70 A# 4 A 1355/582 10
#> 72: 71 B 4 A#|Bb 1135/448 11
#> 73: 72 C 5 B 6101/2213 12
#> 74: 73 C# 5 C 1 0
#> 75: 74 D 5 C#|Db 1197/1100 1
#> 76: 75 D# 5 D 881/744 2
#> 77: 76 E 5 E 1746/1355 3
#> 78: 77 F 5 F 1025/731 4
#> 79: 78 F# 5 F#|Gb 3691/2419 5
#> 80: 79 G 5 G 2645/1593 6
#> 81: 80 G# 5 H 1646/911 7
#> 82: 81 A 5 H#|Jb 2090/1063 8
#> 83: 82 A# 5 J 2101/982 9
#> 84: 83 B 5 A 1355/582 10
#> 85: 84 C 6 A#|Bb 1135/448 11
#> 86: 85 C# 6 B 6101/2213 12
#> 87: 86 D 6 C 1 0
#> 88: 87 D# 6 C#|Db 1197/1100 1
#> 89: 88 E 6 D 881/744 2
#> 90: 89 F 6 E 1746/1355 3
#> 91: 90 F# 6 F 1025/731 4
#> 92: 91 G 6 F#|Gb 3691/2419 5
#> 93: 92 G# 6 G 2645/1593 6
#> 94: 93 A 6 H 1646/911 7
#> 95: 94 A# 6 H#|Jb 2090/1063 8
#> 96: 95 B 6 J 2101/982 9
#> 97: 96 C 7 A 1355/582 10
#> 98: 97 C# 7 A#|Bb 1135/448 11
#> 99: 98 D 7 B 6101/2213 12
#> 100: 99 D# 7 C 1 0
#> 101: 100 E 7 C#|Db 1197/1100 1
#> 102: 101 F 7 D 881/744 2
#> 103: 102 F# 7 E 1746/1355 3
#> 104: 103 G 7 F 1025/731 4
#> 105: 104 G# 7 F#|Gb 3691/2419 5
#> 106: 105 A 7 G 2645/1593 6
#> 107: 106 A# 7 H 1646/911 7
#> 108: 107 B 7 H#|Jb 2090/1063 8
#> 109: 108 C 8 J 2101/982 9
#> 110: 109 C# 8 A 1355/582 10
#> 111: 110 D 8 A#|Bb 1135/448 11
#> 112: 111 D# 8 B 6101/2213 12
#> 113: 112 E 8 C 1 0
#> 114: 113 F 8 C#|Db 1197/1100 1
#> 115: 114 F# 8 D 881/744 2
#> 116: 115 G 8 E 1746/1355 3
#> 117: 116 G# 8 F 1025/731 4
#> 118: 117 A 8 F#|Gb 3691/2419 5
#> 119: 118 A# 8 G 2645/1593 6
#> 120: 119 B 8 H 1646/911 7
#> 121: 120 C 9 H#|Jb 2090/1063 8
#> 122: 121 C# 9 J 2101/982 9
#> 123: 122 D 9 A 1355/582 10
#> 124: 123 D# 9 A#|Bb 1135/448 11
#> 125: 124 E 9 B 6101/2213 12
#> 126: 125 F 9 C 1 0
#> 127: 126 F# 9 C#|Db 1197/1100 1
#> 128: 127 G 9 D 881/744 2
#> note_number name_12edo octave_12edo note_name ratio_frac degree
#> period_number freq cents ref_keyname ref_octave ref_offset
#> <num> <num> <num> <char> <num> <num>
#> 1: -5 8.175799 0.000000 G# -3 22
#> 2: -5 8.175799 0.000000 A# -3 -32
#> 3: -5 8.175799 0.000000 B -3 14
#> 4: -5 8.175799 0.000000 C# -2 -39
#> 5: -5 8.175799 0.000000 D -2 7
#> 6: -5 8.175799 0.000000 E -2 -47
#> 7: -5 8.175799 0.000000 F -2 0
#> 8: -5 8.175799 0.000000 F# -2 46
#> 9: -4 8.175799 0.000000 G# -2 -8
#> 10: -4 8.175799 0.000000 A -2 38
#> 11: -4 8.175799 0.000000 B -2 -15
#> 12: -4 8.175799 0.000000 C -1 31
#> 13: -4 8.175799 0.000000 D -1 -23
#> 14: -4 8.175799 0.000000 D# -1 24
#> 15: -4 8.175799 0.000000 F -1 -30
#> 16: -4 8.175799 0.000000 F# -1 16
#> 17: -4 8.175799 0.000000 G# -1 -37
#> 18: -4 8.175799 0.000000 A -1 9
#> 19: -4 8.175799 0.000000 B -1 -45
#> 20: -4 8.183011 1.526536 C 0 2
#> 21: -4 8.904607 147.830767 C# 0 48
#> 22: -3 9.689836 294.134997 D# 0 -6
#> 23: -3 10.544307 440.439228 E 0 40
#> 24: -3 11.474128 586.743459 F# 0 -13
#> 25: -3 12.485942 733.047690 G 0 33
#> 26: -3 13.586981 879.351921 A 0 -21
#> 27: -3 14.785111 1025.656152 A# 0 26
#> 28: -3 16.088895 1171.960382 C 1 -28
#> 29: -3 17.507650 1318.264613 C# 1 18
#> 30: -3 19.051514 1464.568844 D# 1 -35
#> 31: -3 20.731519 1610.873075 E 1 11
#> 32: -3 22.559671 1757.177306 F# 1 -43
#> 33: -3 24.549034 1903.481537 G 1 3
#> 34: -3 26.713822 2049.785767 G# 1 50
#> 35: -2 29.069507 2196.089998 A# 1 -4
#> 36: -2 31.632922 2342.394229 B 1 42
#> 37: -2 34.422384 2488.698460 C# 2 -11
#> 38: -2 37.457827 2635.002691 D 2 35
#> 39: -2 40.760942 2781.306922 E 2 -19
#> 40: -2 44.355333 2927.611152 F 2 28
#> 41: -2 48.266686 3073.915383 G 2 -26
#> 42: -2 52.522951 3220.219614 G# 2 20
#> 43: -2 57.154542 3366.523845 A# 2 -33
#> 44: -2 62.194558 3512.828076 B 2 13
#> 45: -2 67.679014 3659.132307 C# 3 -41
#> 46: -2 73.647101 3805.436537 D 3 5
#> 47: -2 80.141467 3951.740768 E 3 -48
#> 48: -1 87.208522 4098.044999 F 3 -2
#> 49: -1 94.898765 4244.349230 F# 3 44
#> 50: -1 103.267151 4390.653461 G# 3 -9
#> 51: -1 112.373480 4536.957692 A 3 37
#> 52: -1 122.282825 4683.261922 B 3 -17
#> 53: -1 133.065999 4829.566153 C 4 30
#> 54: -1 144.800058 4975.870384 D 4 -24
#> 55: -1 157.568852 5122.174615 D# 4 22
#> 56: -1 171.463626 5268.478846 F 4 -32
#> 57: -1 186.583674 5414.783077 F# 4 15
#> 58: -1 203.037041 5561.087307 G# 4 -39
#> 59: -1 220.941302 5707.391538 A 4 7
#> 60: -1 240.424402 5853.695769 B 4 -46
#> 61: 0 261.625565 6000.000000 C 5 0
#> 62: 0 284.696295 6146.304231 C# 5 46
#> 63: 0 309.801453 6292.608462 D# 5 -7
#> 64: 0 337.120440 6438.912693 E 5 39
#> 65: 0 366.848476 6585.216923 F# 5 -15
#> 66: 0 399.197998 6731.521154 G 5 32
#> 67: 0 434.400173 6877.825385 A 5 -22
#> 68: 0 472.706555 7024.129616 A# 5 24
#> 69: 0 514.390879 7170.433847 C 6 -30
#> 70: 0 559.751021 7316.738078 C# 6 17
#> 71: 0 609.111122 7463.042308 D# 6 -37
#> 72: 0 662.823907 7609.346539 E 6 9
#> 73: 0 721.273206 7755.650770 F# 6 -44
#> 74: 1 784.876696 7901.955001 G 6 2
#> 75: 1 854.088884 8048.259232 G# 6 48
#> 76: 1 929.404358 8194.563463 A# 6 -5
#> 77: 1 1011.361319 8340.867693 B 6 41
#> 78: 1 1100.545429 8487.171924 C# 7 -13
#> 79: 1 1197.593994 8633.476155 D 7 33
#> 80: 1 1303.200519 8779.780386 E 7 -20
#> 81: 1 1418.119665 8926.084617 F 7 26
#> 82: 1 1543.172638 9072.388848 G 7 -28
#> 83: 1 1679.253063 9218.693078 G# 7 19
#> 84: 1 1827.333366 9364.997309 A# 7 -35
#> 85: 1 1988.471722 9511.301540 B 7 11
#> 86: 1 2163.819619 9657.605771 C# 8 -42
#> 87: 2 2354.630088 9803.910002 D 8 4
#> 88: 2 2562.266651 9950.214233 D# 8 50
#> 89: 2 2788.213073 10096.518463 F 8 -3
#> 90: 2 3034.083957 10242.822694 F# 8 43
#> 91: 2 3301.636287 10389.126925 G# 8 -11
#> 92: 2 3592.781982 10535.431156 A 8 35
#> 93: 2 3909.601558 10681.735387 B 8 -18
#> 94: 2 4254.358994 10828.039618 C 9 28
#> 95: 2 4629.517915 10974.343848 D 9 -26
#> 96: 2 5037.759190 11120.648079 D# 9 21
#> 97: 2 5482.000098 11266.952310 F 9 -33
#> 98: 2 5965.415165 11413.256541 F# 9 13
#> 99: 2 6491.458858 11559.560772 G# 9 -40
#> 100: 3 7063.890263 11705.865003 A 9 6
#> 101: 3 7686.799954 11852.169233 B 9 -48
#> 102: 3 8364.639219 11998.473464 C 10 -2
#> 103: 3 9102.251871 12144.777695 C# 10 45
#> 104: 3 9904.908862 12291.081926 D# 10 -9
#> 105: 3 10778.345947 12437.386157 E 10 37
#> 106: 3 11728.804673 12583.690388 F# 10 -16
#> 107: 3 12543.853951 12700.000000 G 10 30
#> 108: 3 12543.853951 12700.000000 A 10 -24
#> 109: 3 12543.853951 12700.000000 A# 10 23
#> 110: 3 12543.853951 12700.000000 C 11 -31
#> 111: 3 12543.853951 12700.000000 C# 11 15
#> 112: 3 12543.853951 12700.000000 D# 11 -38
#> 113: 4 12543.853951 12700.000000 E 11 8
#> 114: 4 12543.853951 12700.000000 F# 11 -46
#> 115: 4 12543.853951 12700.000000 G 11 0
#> 116: 4 12543.853951 12700.000000 G# 11 47
#> 117: 4 12543.853951 12700.000000 A# 11 -7
#> 118: 4 12543.853951 12700.000000 B 11 39
#> 119: 4 12543.853951 12700.000000 C# 12 -14
#> 120: 4 12543.853951 12700.000000 D 12 32
#> 121: 4 12543.853951 12700.000000 E 12 -22
#> 122: 4 12543.853951 12700.000000 F 12 25
#> 123: 4 12543.853951 12700.000000 G 12 -29
#> 124: 4 12543.853951 12700.000000 G# 12 17
#> 125: 4 12543.853951 12700.000000 A# 12 -37
#> 126: 5 12543.853951 12700.000000 B 12 10
#> 127: 5 12543.853951 12700.000000 C# 13 -44
#> 128: 5 12543.853951 12700.000000 D 13 2
#> period_number freq cents ref_keyname ref_octave ref_offset