  We report a new determination of muonium 1S-2S transition frequency and its
isotope shift with deuterium by recalibrating the iodine reference lines using
an optical frequency comb. The reference lines for the muonium and deuterium
1S-2S transitions are determined with a precision of 2.4*10^-10 and 1.7*10^-10
respectively. A new muonium-deuterium 1S-2S isotope-shift frequency is derived
from these references to be 11 203 464.9(9.2)(4.0) MHz, in agreement with an
updated bound-state quantum-electrodynamics prediction based on 2010
adjustments of Committee on Data for Science and Technology and 2.3 times
better in the systematic uncertainty than the previous best determination.
