We investigate the dynamics of interdependence between realized variances and realized semivariances of six major currencies across frequencies and time scales. The empirical results are derived, first, through constructing daily measures of realized variance and semivariance from a high frequency 5-min interval data, and second, by fitting wavelet squared coherence and wavelet cohesion measure with time-varying weights. The realized volatilities of the currencies and their cross-currency influences are found to increase during the global financial crisis. The realized volatilities of the Euro, Swiss Franc, and British Pound are closely synchronized over the short-term horizon. However, over the long-run, the Euro, Swiss Franc, and Japanese Yen lead the realized volatilities of the British Pound, Australian Dollar, and Canadian Dollar. The synchronization structure of positive and negative realized volatilities indicates asymmetric dependence among the currencies across time horizons. We further observe strong positive (negative) cohesion among the realized volatilities over the medium- and long-term horizons. Finally, significant counter cyclical comovements among the currencies are observed over the medium- and long-term horizons. These findings have important implications for foreign exchange portfolio managers.