Names in this corner of the repertoire are contested. Sawmill is used for G D G D by most players and for A E A E by some, and "cross tuning" can mean either depending on who is talking. So this page leads with the notes and lets the name follow: G D G D, derived below, whatever anyone calls it.
What the arithmetic shows is that this is cross A transposed. Every string sits exactly two semitones below its cross A pitch, so both tunings share an interval shape and differ only in key.
The retune, string by string
Derived from pitch arithmetic against standard GDAE:
| String | Standard | Sawmill | Semitones |
|---|---|---|---|
| 4 (G) | G3 | G3 | stays |
| 3 (D) | D4 | D4 | stays |
| 2 (A) | A4 | G4 | down 2 |
| 1 (E) | E5 | D5 | down 2 |
GDGD — 2 strings move (2, 1).
What the open strings spell
The distinct letters now sounding are G, D, which reads as no triad at all. Two pitch classes across four strings, exactly as in cross A — because it is cross A, moved. No third in the open set, nothing major or minor about it until a finger decides.
The drone, and the bow arm
The mirror-image of cross A: there, the two lower strings came up; here the two upper strings come down. So the ringing pairs sit at the other end of the instrument, and the melody tends to live on the lower strings with the drone above it rather than below. That is a genuinely different sound and a slightly different arm — the bow spends more time on the inner strings, and the crossing to reach the drone is upward. The bowing pages cover the arm; the tuning just decides where it goes.
What survives, and what does not
The standard double-stop library does NOT apply here — a stopped string moved, so any pair naming an interval against it now names a different one. Strings 4 and 3 are untouched, which is the opposite half from cross A: your low strings are exactly where you left them, and the two that moved are the ones carrying the melody in most first-position tunes.
That makes sawmill the friendlier of the pair to start with, because the notes under your fourth finger on the low strings are unchanged. Take a G tune — June Apple is the obvious one — and play it against the ringing G and D. The scale map at G major is where the melody comes from; first position is where all of this happens.