What I recall (from years ago) is to go with the average of the planting distances.
X inches + Y inches / 2
Thus, 6" between corn seeds plus 12 inches between bean seeds is 18 inches. Dividing by two gives us a 9" interval between plants.
However, no matter what the initial measurements are, in short order you are going to come across a multiple that calls for both seeds to occupy the same hole.
Plants aren't that precise.
I use interplanting (where each plant uses the space differently) and succession planting (where the first plant matures in time to surrender the space to a second plant for the balance of the season).
As an example of interplanting, I might plant lettuce at the base of peas being sent up a trellis. The peas provide some shade and lots of nitrogen for the lettuce, the lettuce serves as a living mulch and helps keep the soil moist. Succession planting sees garlic planted behind a legume such as beans. The garlic occupies the soil until June / July. Beans like hot weather. When the garlic comes out I dig in the existing compost that was serving as a mulch and plant innoculated beans to rebuild the N level in the soil. Then, somewhere after the first hard frost, the beans come out and the garlic goes in again.
There are lots of other combinations. You might like to add squash to your mix and plant in hills in the grouping Native Americans call "three sisters". The squash runs between the hills, the beans run up the corn and the corn reaches for the sky. You have to watch where you step when picking, but you get a lot of yield for the amount of sq ft involved.
Bill