BEADGCF: Tuning a guitar in fourths

This is just a preview of the tables for some of my friends to look at, and not (yet) a tutorial of any significant value... but do come back later!

Why the standard tuning is wrong.

A standard guitar is tuned E2, A2, D3, G3, B3, E4. I feel that this common tuning is a disaster, as one has to memorize multiple variants of the same chord if it happens to cross the B3 string, with an extra shape introduced every time one moves the root string. I find this gratuitous memorization to be stupid and annoying, but very traditional.

As an alternative, one can tune the guitar uniformly in fourths, and only have one chord shape to memorize. Stanley Jordan is the only "famous" musician that I can think of who tunes his guitars in fourths.

Why you should consider tuning in fourths.

If you tune in fourths, replace B3 with C4 and E4 with F4, i.e., tune as
E2 A2 D3 G3 C4 F4. The notes on the guitar neck will make the following pattern (I hope that I numbered the notes correctly---if not, PLEASE correct me! I expect that C4 is "middle C" on a piano):

E2	A2	D3	G3	C4	F4
F2
	B2	E3	A3	D4	G4
G2	C3	F3
			B3	E4	A4
A2	D3	G3	C4	F4
					B4
B2	E3	A3	D4	G4	C5
C3	F3
		B3	E4	A4	D5
D3	G3	C4	F4
				B4	E5
E3	A3	D4	G4	C5	F5
F3
	B3	E4	A4	D5	G5
G3	C4	F4
			B4	E5	A5
A3	D4	G4	C5	F5
					B5
B3	E4	A4	D5	G5	C6
C4	F4
		B4	E5	A5	D6
D4	G4	C5	F5
				B5	E6
E4	A4	D5	G5	C6	F6

The advantage of tuning in fourths is that chords look the same. If you pick an arbitrary root, on any string, then observe where the following intervals (components of a chord) fall:

.	.	.	.	.	.
.	.	.	7	o3	oo6
.	2	5	o1	o4	.
.	.	.	.	.	oo7
.	3	6	o2	o5	oo1
1	4	.	.	.	.
.	.	7	o3	o6	oo2
.	5	o1	o4	.	.
.	.	.	.	o7	oo3
.	6	o2	o5	oo1	oo4
.	.	.	.	.	.
.	.	o3	.	.	oo5
.	.	.	.	.	.
.	.	.	.	.	.
.	.	.	.	.	.

(Note that BEADGC suggests 7362514 [more on this later].)

Looking at the notes across a fret.

If you look really hard at the pattern across the frets, it can also be thought of as
BEADG(BEADG(BEADG(BEADG(...)#)#)#)#,
i.e., think of C==B# and F==E#. Note that if you look at this as a series,
BEADG(BEADG(BEADG(BEAD(...)#)#)#)#
= B E A D G B# E# A# D# G# B## E## A## D## G## ...
= B E A D G C F A# D# G# C# F# B E A D G C F A# D# ....

So, the entire pattern is B E A D G C F A# D# G# C# F#, over and over again.

Semitones

Western music is only made up of twelve notes, and these notes (arbitrarily) doubled in frequency (i.e., their octaves). The problem is that various scales were invented before it was realized that there were twelve notes, and not seven, and we have suffered with sharp/flat notation since, as well as unfortunate facts like a "fifth" is really the seventh semitone. Rather than suffer notation like "going from one string to another is a 4th," it seems better to say, "going from one string to another is plus five semitones." When you start to think about semitones instead of "whole steps" (two semitones) and "half-steps," (one semitone) it becomes much easier to understand what is going on in chords and scales, since you can think of sets of notes and transformations.

Semitone	Typical Terminology
0	unity
1	flat 2nd
2	2nd
3	minor 3rd
4	major 3rd
5	4th
6	flat 5th
7	5th
8	flat 6th
9	6th
10	flat 7th
11	7th
12	octave

Anything higher is not really needed; for example, 15 mod 12 = 3, so that's just a minor 3rd (m3).

Appendix

Here is the above table for a seven-string guitar:

B1	E2	A2	D3	G3	C4	F4
C2	F2
		B2	E3	A3	D4	G4
D2	G2	C3	F3
				B3	E4	A4
E2	A2	D3	G3	C4	F4
F2						B4
	B2	E3	A3	D4	G4	C5
G2	C3	F3
			B3	E4	A4	D5
A2	D3	G3	C4	F4
					B4	E5
B2	E3	A3	D4	G4	C5	F5
C3	F3
		B3	E4	A4	D5	G5
D3	G3	C4	F4
				B4	E5	A5
E3	A3	D4	G4	C5	F5
F3						B5
	B3	E4	A4	D5	G5	C6
G3	C4	F4
			B4	E5	A5	D6
A3	D4	G4	C5	F5
					B5	E6
B3	E4	A4	D5	G5	C6	F6

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I added another fake string to the seven string guitar to show how one can extend the pattern of fourths. When you get up to twelve strings the guitar can be turned into a toroid.

B1	E2	A2	D3	G3	C4	F4
C2	F2						B4
		B2	E3	A3	D4	G4	C5
D2	G2	C3	F3
				B3	E4	A4	D5
E2	A2	D3	G3	C4	F4
F2						B4	E5
	B2	E3	A3	D4	G4	C5	F5
G2	C3	F3
			B3	E4	A4	D5	G5
A2	D3	G3	C4	F4
					B4	E5	A5
B2	E3	A3	D4	G4	C5	F5
C3	F3						B5
		B3	E4	A4	D5	G5	C6
D3	G3	C4	F4
				B4	E5	A5	D6
E3	A3	D4	G4	C5	F5
F3						B5	E6
	B3	E4	A4	D5	G5	C6	F6
G3	C4	F4
			B4	E5	A5	D6	G6
A3	D4	G4	C5	F5
					B5	E6	A6
B3	E4	A4	D5	G5	C6	F6

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Kleanthes Koniaris, email.