We have a Delonghi Bean-to cup coffee machine similar to the one shown at the right and it has an internal coffee grinder with a coarseness setting of between 1(fine) and 7(coarse) with factory default of 5 and we have it preferentially set at 5.5 for our preferred off-the-shelf Aromas LA Deluxe blend of coffee.
Our Breville benchtop grinder has a scale of 1(fine) to 60(coarse).
The relationship is not linear (i.e. it's not 1~7 = 1~60) because with the Delonghi set at 5.5 the grinds are visibly slightly coarser than those from the Breville set at 22/23, which is the coarse end of what Breville indicate as suitable for the 'espresso' grind range.
So we did some visual comparative grind tests and we think we figured out the relationship, It seems semi-logarithmic as per this graph we created:
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