  The {\alpha}-element abundances of the globular cluster (GC) and field star
populations of galaxies encode information about the formation of each of these
components. We use the E-MOSAICS cosmological simulations of ~L* galaxies and
their GCs to investigate the [{\alpha}/Fe]-[Fe/H] distribution of field stars
and GCs in 25 Milky Way-mass galaxies. The [{\alpha}/Fe]-[Fe/H] distribution go
GCs largely follows that of the field stars and can also therefore be used as
tracers of the [{\alpha}/Fe]-[Fe/H] evolution of the galaxy. Due to the
difference in their star formation histories, GCs associated with stellar
streams (i.e. which have recently been accreted) have systematically lower
[{\alpha}/Fe] at fixed [Fe/H]. Therefore, if a GC is observed to have low
[{\alpha}/Fe] for its [Fe/H] there is an increased probability that this GC was
accreted recently alongside a dwarf galaxy. There is a wide range of shapes for
the field star [{\alpha}/Fe]-[Fe/H] distribution, with a notable subset of
galaxies exhibiting bimodal distributions, in which the high [{\alpha}/Fe]
sequence is mostly comprised of stars in the bulge, a high fraction of which
are from disrupted GCs. We calculate the contribution of disrupted GCs to the
bulge component of the 25 simulated galaxies and find values between 0.3-14 per
cent, where this fraction correlates with the galaxy's formation time. The
upper range of these fractions is compatible with observationally-inferred
measurements for the Milky Way, suggesting that in this respect the Milky Way
is not typical of L* galaxies, having experienced a phase of unusually rapid
growth at early times.
