Mathematical Diagrams of Equal-Tempered Guitar Fingerboards (c)1998 by Joe Monzo

Mathematical Diagrams of Equal-Tempered Guitar Fingerboards
© 1998 by Joe Monzo

with letter-name, absolute power of 2, and absolute Semitones

19-Equal

"standard" guitar tuning

open
string
E
n^{0

0.00}

A
2^(8/19)
5.05

D
2^(16/19)
10.11

G
2^1+(5/19)
12+3.16

B
2^1+(11/19)
12+6.95

E
2^2

24+0.00

==========
==========
==========
==========
==========
==========
1st fret
E#/Fb
2^(1/19)
0.63

A#
2^(9/19)
5.68

D#
2^(17/19)
10.74

G#
2^1+(6/19)
12+3.79

B#/Cb
2^1+(12/19)
12+7.58

E#/Fb
2^2+(1/19)
24+0.63
2nd fret
F
2^(2/19)
1.26

Bb
2^(10/19)
6.32

Eb
2^(18/19)
11.37

Ab
2^1+(7/19)
12+4.42

C
2^1+(13/19)
12+8.21

F
2^2+(2/19)
24+1.26
3rd fret
F#
2^(3/19)
1.89

B
2^(11/19)
6.95

E
2^1

12+0.00

A
2^1+(8/19)
12+5.05

C#
2^1+(14/19)
12+8.84

F#
2^2+(3/19)
24+1.89
4th fret
Gb
2^(4/19)
2.53

B#/Cb
2^(12/19)
7.58

E#/Fb
2^1+(1/19)
12+0.63

A#
2^1+(9/19)
12+5.68

Db
2^1+(15/19)
12+9.47

Gb
2^2+(4/19)
24+2.53
5th fret
G
2^(5/19)
3.16

C
2^(13/19)
8.21

F
2^1+(2/19)
12+1.26

Bb
2^1+(10/19)
12+6.32

D
2^1+(16/19)
12+10.11

G
2^2+(5/19)
24+3.16
6th fret
G#
2^(6/19)
3.79

C#
2^(14/19)
8.84

F#
2^1+(3/19)
12+1.89

B
2^1+(11/19)
12+6.95

D#
2^1+(17/19)
12+10.74

G#
2^2+(6/19)
24+3.79
7th fret
Ab
2^(7/19)
4.42

Db
2^(15/19)
9.47

Gb
2^1+(4/19)
12+2.53

B#/Cb
2^1+(12/19)
12+7.58

Eb
2^1+(18/19)
12+11.37

Ab
2^2+(7/19)
24+4.42
8th fret
A
2^(8/19)
5.05

D
2^(16/19)
10.11

G
2^1+(5/19)
12+3.16

C
2^1+(13/19)
12+8.21

E
2^{2

24+0.00}

A
2^2+(8/19)
24+5.05
9th fret
A#
2^(9/19)
5.68

D#
2^(17/19)
10.74

G#
2^1+(6/19)
12+3.79

C#
2^1+(14/19)
12+8.84

E#/Fb
2^2+(1/19)
24+0.63

A#
2^2+(9/19)
24+5.68
10th fret
Bb
2^(10/19)
6.32

Eb
2^(18/19)
11.37

Ab
2^1+(7/19)
12+4.42

Db
2^1+(15/19)
12+9.47

F
2^2+(2/19)
24+1.26

Bb
2^2+(10/19)
24+6.32
11th fret
B
2^(11/19)
6.95

E
2^{1

12+0.00}

A
22^1+(8/19)
12+5.05

D
2^1+(16/19)
12+10.11

F#
2^2+(3/19)
24+1.89

B
2^2+(11/19)
24+6.95
12th fret
B#/Cb
2^(12/19)
7.58

E#/Fb
2^1+(1/19)
12+0.63

A#
2^1+(9/19)
12+5.68

D#
2^1+(17/19)
12+10.74

Gb
2^2+(4/19)
24+2.53

B#/Cb
2^2+(12/19)
24+7.58
13th fret
C
2^(13/19)
8.21

F
2^1+(2/19)
12+1.26

Bb
2^1+(10/19)
12+6.32

Eb
2^1+(18/19)
12+11.37

G
2^2+(5/19)
24+3.16

C
2^2+(13/19)
24+8.21
14th fret
C#
2^(14/19)
8.84

F#
2^1+(3/19)
12+1.89

B
2^1+(11/19)
12+6.95

E
2^{2

24+0.00}

G#
2^2+(6/19)
24+3.79

C#
2^2+(14/19)
24+8.84
15th fret
Db
2^(15/19)
9.47

Gb
2^1+(4/19)
12+2.53

B#/Cb
2^1+(12/19)
12+7.58

E#/Fb
2^2+(1/19)
24+0.63

Ab
2^2+(7/19)
24+4.42

Db
2^2+(15/19)
24+9.47
16th fret
D
2^(16/19)
10.11

G
2^1+(5/19)
12+3.16

C
2^1+(13/19)
12+8.21

F
2^2+(2/19)
24+1.26

A
2^2+(8/19)
24+5.05

D
2^2+(16/19)
24+10.11
17th fret
D#
2^(17/19)
10.74

G#
2^1+(6/19)
12+3.79

C#
2^1+(14/19)
12+8.84

F#
2^2+(3/19)
24+1.89

A#
2^2+(9/19)
24+5.68

D#
2^2+(17/19)
24+10.74
18th fret
Eb
2^(18/19)
11.37

Ab
2^1+(7/19)
12+4.42

Db
2^1+(15/19)
12+9.47

Gb
2^2+(4/19)
24+2.53

Bb
2^2+(10/19)
24+6.32

Eb
2^2+(18/19)
24+11.37
19th fret
E
2^{1

12+0.00}

A
2^1+(8/19)
12+5.05

D
2^1+(16/19)
12+10.11

G
2^2+(5/19)
24+3.16

B
2^2+(11/19)
24+6.95

E
2^{3

36+0.00}

Last updated: 1998 November 6

Mailing address: PO Box 620027, San Diego, CA 92102

Telephone: 619 231 3673

email: sonicarts@ixpres.com

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open string	E n^{0 0.00}	A 2^(8/19) 5.05	D 2^(16/19) 10.11	G 2^1+(5/19) 12+3.16	B 2^1+(11/19) 12+6.95	E 2^2 24+0.00
	==========	==========	==========	==========	==========	==========
1st fret	E#/Fb 2^(1/19) 0.63	A# 2^(9/19) 5.68	D# 2^(17/19) 10.74	G# 2^1+(6/19) 12+3.79	B#/Cb 2^1+(12/19) 12+7.58	E#/Fb 2^2+(1/19) 24+0.63
2nd fret	F 2^(2/19) 1.26	Bb 2^(10/19) 6.32	Eb 2^(18/19) 11.37	Ab 2^1+(7/19) 12+4.42	C 2^1+(13/19) 12+8.21	F 2^2+(2/19) 24+1.26
3rd fret	F# 2^(3/19) 1.89	B 2^(11/19) 6.95	E 2^1 12+0.00	A 2^1+(8/19) 12+5.05	C# 2^1+(14/19) 12+8.84	F# 2^2+(3/19) 24+1.89
4th fret	Gb 2^(4/19) 2.53	B#/Cb 2^(12/19) 7.58	E#/Fb 2^1+(1/19) 12+0.63	A# 2^1+(9/19) 12+5.68	Db 2^1+(15/19) 12+9.47	Gb 2^2+(4/19) 24+2.53
5th fret	G 2^(5/19) 3.16	C 2^(13/19) 8.21	F 2^1+(2/19) 12+1.26	Bb 2^1+(10/19) 12+6.32	D 2^1+(16/19) 12+10.11	G 2^2+(5/19) 24+3.16
6th fret	G# 2^(6/19) 3.79	C# 2^(14/19) 8.84	F# 2^1+(3/19) 12+1.89	B 2^1+(11/19) 12+6.95	D# 2^1+(17/19) 12+10.74	G# 2^2+(6/19) 24+3.79
7th fret	Ab 2^(7/19) 4.42	Db 2^(15/19) 9.47	Gb 2^1+(4/19) 12+2.53	B#/Cb 2^1+(12/19) 12+7.58	Eb 2^1+(18/19) 12+11.37	Ab 2^2+(7/19) 24+4.42
8th fret	A 2^(8/19) 5.05	D 2^(16/19) 10.11	G 2^1+(5/19) 12+3.16	C 2^1+(13/19) 12+8.21	E 2^{2 24+0.00}	A 2^2+(8/19) 24+5.05
9th fret	A# 2^(9/19) 5.68	D# 2^(17/19) 10.74	G# 2^1+(6/19) 12+3.79	C# 2^1+(14/19) 12+8.84	E#/Fb 2^2+(1/19) 24+0.63	A# 2^2+(9/19) 24+5.68
10th fret	Bb 2^(10/19) 6.32	Eb 2^(18/19) 11.37	Ab 2^1+(7/19) 12+4.42	Db 2^1+(15/19) 12+9.47	F 2^2+(2/19) 24+1.26	Bb 2^2+(10/19) 24+6.32
11th fret	B 2^(11/19) 6.95	E 2^{1 12+0.00}	A 22^1+(8/19) 12+5.05	D 2^1+(16/19) 12+10.11	F# 2^2+(3/19) 24+1.89	B 2^2+(11/19) 24+6.95
12th fret	B#/Cb 2^(12/19) 7.58	E#/Fb 2^1+(1/19) 12+0.63	A# 2^1+(9/19) 12+5.68	D# 2^1+(17/19) 12+10.74	Gb 2^2+(4/19) 24+2.53	B#/Cb 2^2+(12/19) 24+7.58
13th fret	C 2^(13/19) 8.21	F 2^1+(2/19) 12+1.26	Bb 2^1+(10/19) 12+6.32	Eb 2^1+(18/19) 12+11.37	G 2^2+(5/19) 24+3.16	C 2^2+(13/19) 24+8.21
14th fret	C# 2^(14/19) 8.84	F# 2^1+(3/19) 12+1.89	B 2^1+(11/19) 12+6.95	E 2^{2 24+0.00}	G# 2^2+(6/19) 24+3.79	C# 2^2+(14/19) 24+8.84
15th fret	Db 2^(15/19) 9.47	Gb 2^1+(4/19) 12+2.53	B#/Cb 2^1+(12/19) 12+7.58	E#/Fb 2^2+(1/19) 24+0.63	Ab 2^2+(7/19) 24+4.42	Db 2^2+(15/19) 24+9.47
16th fret	D 2^(16/19) 10.11	G 2^1+(5/19) 12+3.16	C 2^1+(13/19) 12+8.21	F 2^2+(2/19) 24+1.26	A 2^2+(8/19) 24+5.05	D 2^2+(16/19) 24+10.11
17th fret	D# 2^(17/19) 10.74	G# 2^1+(6/19) 12+3.79	C# 2^1+(14/19) 12+8.84	F# 2^2+(3/19) 24+1.89	A# 2^2+(9/19) 24+5.68	D# 2^2+(17/19) 24+10.74
18th fret	Eb 2^(18/19) 11.37	Ab 2^1+(7/19) 12+4.42	Db 2^1+(15/19) 12+9.47	Gb 2^2+(4/19) 24+2.53	Bb 2^2+(10/19) 24+6.32	Eb 2^2+(18/19) 24+11.37
19th fret	E 2^{1 12+0.00}	A 2^1+(8/19) 12+5.05	D 2^1+(16/19) 12+10.11	G 2^2+(5/19) 24+3.16	B 2^2+(11/19) 24+6.95	E 2^{3 36+0.00}

Mathematical Diagrams of Equal-Tempered Guitar Fingerboards © 1998 by Joe Monzo

Mathematical Diagrams of Equal-Tempered Guitar Fingerboards
© 1998 by Joe Monzo