  The emission processes active in the highly relativistic jets of gamma-ray
bursts (GRBs) remain unknown. In this paper we propose a new measure to
describe spectra: the width of the $EF_E$ spectrum, a quantity dependent only
on finding a good fit to the data. We apply this to the full sample of GRBs
observed by Fermi/GBM and CGRO/BATSE. The results from the two instruments are
fully consistent. We find that the median widths of spectra from long and short
GRBs are significantly different (chance probability $<10^{-6}$). The width
does not correlate with either duration or hardness, and this is thus a new,
independent distinction between the two classes. Comparing the measured spectra
with widths of spectra from fundamental emission processes -- synchrotron and
blackbody radiation -- the results indicate that a large fraction of GRB
spectra are too narrow to be explained by synchrotron radiation from a
distribution of electron energies: for example, 78% of long GRBs and 85% of
short GRBs are incompatible with the minimum width of standard slow cooling
synchrotron emission from a Maxwellian distribution of electrons, with fast
cooling spectra predicting even wider spectra. Photospheric emission can
explain the spectra if mechanisms are invoked to give a spectrum much broader
than a blackbody.
