Sawmill is cross A in another key, and the derivation proves it rather than asserting it: every course sits exactly two semitones below its cross A pitch. Same interval shape, same two-letters-only open set, same modal refusal to be major or minor — just built on G instead of A, which is where a great many old-time tunes actually live.
What differs on a mandolin is which end of the instrument you disturb. Cross A raises the two low courses; sawmill lowers the two high ones. The arithmetic is a mirror, and the practical consequences are not.
The retune, course by course
Derived from pitch arithmetic against standard GDAE:
| String | Standard | Sawmill | Semitones |
|---|---|---|---|
| 4 | G3 | G3 | stays |
| 3 | D4 | D4 | stays |
| 2 | A4 | G4 | down 2 |
| 1 | E5 | D5 | down 2 |
GDGD — 2 courses 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, no third, exactly as in cross A — because it is cross A, transposed. If you know one tuning you know the other; the shapes are identical and your hand simply sits two frets lower.
Lowering is the kinder direction
Both moved courses come down, which means four strings losing tension rather than gaining it. That is easier on the instrument and harder on the tone: the E course dropped to D on light strings can go slack enough to lose its bite, which on a mandolin is most of what you are playing with. This is the tuning where gauge earns its keep — the strings guide covers the trade, and a slightly heavier top pair is the usual answer if you spend real time here.
Unison discipline still applies, and slack pairs drift faster than tight ones. Expect to touch the top course again after the first tune.
What survives
The standard chord library does NOT apply here — a fretted course moved, so every fret in it that touches that course is off by the course’s delta. Courses 4 and 3 are untouched, so anything living on the two low courses is exactly where you left it. That is the opposite half of the neck from cross A, and it changes what the tuning is good for: sawmill keeps your bass notes and moves your melody strings, so it suits tunes you back as much as tunes you lead.
The shapes on the chord pages are standard-tuning shapes and will be wrong on the top two courses by a whole tone each. Learn the G drone as its own map instead of transposing in your head, and take the melody from the G major scale map. Fiddle Warrior’s sawmill page has the bowed version, where the same tuning is about which strings ring under the bow.