Cross A is the old-time cross tuning, and the derived table below shows why it is the most committed of the four. Both lower strings come up a whole tone, and what is left is a fiddle whose four open strings sound exactly two letters, A and E, in two octaves each. There is no third in the set and there cannot be, because the set has only two pitch classes in it.
The retune, string by string
Derived from pitch arithmetic against standard GDAE — each target octave is computed as the shortest move that produces the named letter, not looked up from a table:
| String | Standard | Cross A | Semitones |
|---|---|---|---|
| 4 (G) | G3 | A3 | up 2 |
| 3 (D) | D4 | E4 | up 2 |
| 2 (A) | A4 | A4 | stays |
| 1 (E) | E5 | E5 | stays |
AEAE — 2 strings move (4, 3).
What the open strings spell
The distinct letters now sounding are A, E, which reads as no triad at all. That is a stronger statement than the "no triad" standard tuning gives: standard has too many letters to stack, cross A has too few. Which is why the tuning sounds neither major nor minor until your fingers say so, and why tunes in it tend to hang around a mode rather than resolve.
The drone, and the bow arm
Both A strings and both E strings are now adjacent to something they match. Play the melody on the second string and the ringing A below it is one string away; play on the first and the E below it is one string away. A drone you can reach without a full crossing is a drone you can hold for a whole tune, and that is the entire practical payoff — the crossing page covers the arm movement, which barely changes at all.
The other half is bow placement. With two strings ringing sympathetically the instrument gets loud fast, so a lighter contact point nearer the fingerboard keeps the drone underneath the melody rather than on top of it.
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 2 and 1 did not move, so anything played entirely on the top two is unchanged, and your position geometry is unchanged everywhere: a first-position hand is still a first-position hand, it simply produces different pitches on the two retuned strings.
Take the melody from the A major scale map, play it on the top strings, and let the bottom two ring. Then read the pairs on the double-stop pages as standard-tuning statements — they are correct there and off by a whole tone on the strings that moved. Calico is this tuning with the top string dropped to add the third back, if the ambiguity is not what you are after.