Single-frequency optical synthesizers (SFOS) provide an optical ﬁeld with arbitrarily adjustable frequency and phase which is phase-coherently linked to a reference signal. Ideally, they combine the spectral resolution of narrow linewidth frequency stabilized lasers with the broad spectral coverage of frequency combs in a tunable fashion. In state-of-the-art SFOSs tuning across comb lines requires comb line order switching,1, 2 which imposes technical overhead with problems like forbidden frequency gaps or strong phase glitches. Conventional tunable lasers often tune over only tens of GHz before mode-hops occur. Here, we present a novel type of SFOSs, which relies on a serrodyne technique with conditional ﬂyback,3 shifting the carrier frequency of the employed frequency comb without an intrusion into the comb generator. It utilizes a new continuously tunable diode laser that tunes mode-hop-free across the full gain spectrum of the integrated laser diode. We investigate the tuning behavior of two identical SFOSs that share a common reference, by comparing the phases of their output signals. Previously, we achieved phase-stable and cycle-slip free frequency tuning over 28.1 GHz with a maximum zero-to-peak phase deviation of 62 mrad4 when sharing a common comb generator. With the new continuously tunable lasers, the SFOSs tune synchronously across nearly 17800 comb lines (1 THz). The tuning range in this approach can be extended to the full bandwidth of the frequency comb and the 110 nm mode-hop-free tuning range of the diode laser.