Cross A is the old-time cross tuning, and on a mandolin it is the most committed of the three. The two lower courses each come up a whole tone, and what you are left with is an instrument whose four open courses sound exactly two letters: A and E, in two octaves each. Nothing about that set can be major or minor. That ambiguity is the sound, and it is why the tuning belongs to tunes rather than to chords.
The retune, course by course
Derived from pitch arithmetic against standard GDAE — each target octave is computed as the shortest move producing the named letter, not looked up:
| String | Standard | Cross A | Semitones |
|---|---|---|---|
| 4 | G3 | A3 | up 2 |
| 3 | D4 | E4 | up 2 |
| 2 | A4 | A4 | stays |
| 1 | E5 | E5 | stays |
AEAE — 2 courses move (4, 3).
What the open strings spell
The distinct letters now sounding are A, E, which reads as no triad at all. Two pitch classes across four courses is a stronger claim than “no triad”: there is no third available in the open set at all, so the tuning cannot resolve until a finger puts one there. Standard GDAE spells four letters and also reads as no triad, but for the opposite reason — too many notes rather than too few.
Eight strings, four tuners each way
Both moved courses go up, which is the direction that adds tension, and each is a pair. Four strings pulled tighter is a real load on a carved top, so bring them up in stages rather than one course at a time to full pitch, and let the instrument settle before you decide it is in tune. Then check each pair against itself: a unison that is a few cents out is barely noticeable under a chord and glaringly obvious under a drone, and this tuning is nothing but drones.
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 2 and 1 did not move, so the top half of the neck behaves normally and anything played entirely on those two courses is unchanged. The chop is gone, since a closed four-course shape cannot avoid the moved pair.
What you get in exchange is the reason people do this: the open A and E courses ring under everything you play on the top, so a tune in A accompanies itself. Play the melody from the A major scale map on the top courses and let the bottom two sound. That is the whole technique. Fiddle Warrior’s cross A page covers what the same tuning does for a bow, which is a different and equally long story.