Thermosphere Ionosphere Mesosphere Energetics and Dynamics/Sounding of the Atmosphere using Broadband Emission Radiometry (TIMED/SABER) temperature measurements between 20 and 110\ km altitude and {\textpm}50{\textdegree} latitude during 2002{\textendash}2015 are employed to reveal the climatological characteristics of the quasi-6\ day wave (Q6DW) and evidence for secondary waves (SW) resulting from its nonlinear interactions with solar tides. The mean period is 6.14d with a standard deviation (*σ*) of 0.26d. Multiyear-mean maximum amplitudes (3{\textendash}5\ K, *σ* \~{} 4\ K) occur within the mesosphere-lower thermosphere (MLT) region between 75 and 100\ km during day of year (DOY) 60{\textendash}120 and 180{\textendash}300 in the Northern Hemisphere and DOY 0{\textendash}110 and 200{\textendash}300 in the Southern Hemisphere. Amplitudes approach 10\ K in some individual years. At midlatitudes downward phase progression exists from 100 to 35\ km with a mean vertical wavelength of about 70\ km. Signatures of SW due to Q6DW-tide interactions appear at distinct space-based zonal wave numbers (*k*_{s}) in temperature spectra constructed in the reference frame of the TIMED orbit. However, SW produced by several different tides can collapse onto the same (*k*_{s}) value, rendering their relative contributions indistinguishable. Nevertheless, by determining the space-based wave amplitudes attached to these values of (*k*_{s}), and demonstrating that they are a large fraction of the interacting wave amplitudes, we conclude that the aggregate contributions of the SW to the overall wave spectrum must be significant. Because the SW have periods, zonal wave numbers, and latitude-height structures different from those of the primary waves, they contribute additionally to the complexity of the wave spectrum. This complexity is communicated to the ionosphere through collisions or through the dynamo electric fields generated by the total wave spectrum.