Tuning processes implemented by an auto-tune controller are provided for measuring and adjusting the combustion dynamics and the emission composition of a gas turbine (GT) engine via a tuning process. Initially, the tuning process includes monitoring parameters, such as combustion dynamics and emission composition. Upon determining that one or more of the monitored parameters exceed a critical value, these “out-of-tune” parameters are compared to a scanning order table. Upon comparison, the first out-of-tune parameter that is matched within the scanning order table is addressed. The first out-of-tune parameter is then plotted as overlaid slopes on respective graphs, where the graph represents a fuel-flow split. Typically, the slopes are plotted as a particular out-of-tune parameter against a particular fuel-flow split. The slopes for each graph are considered together by taking into account the combined impact on each out-of-tune parameter when a fuel-flow split is selected for adjustment.