Daily data on solar magnetism, available from May 1975 to April 2002, were analyzed by linear-nonlinear rhythmometry, with particular focus on the near-transyear, slightly longer than the calendar year. The time structure of solar magnetism is compared to that of solar activity, gauged by Wolf numbers. An about 27-day component corresponding to the solar rotation period, is common to both variables but differs in harmonic content. About 10-year component characterizes solar activity but not solar magnetism. A near-transyear with a period of about 1.05 years is detected in solar magnetism. In solar activity, a near-transyear is also found but its period of about 1.10 years is longer than that characterizing solar magnetism, and it may be paired with an about 0.9-year component to correspond to an about 10-year modulation in amplitude or phase of an about-yearly component.