In this note we will describe the process of developing a high precision model of the Booster betatron tunes. The Booster is used as the pre-injector to the AGS for heavy ion, polarized proton, and high intensity proton operations. In addition, the Booster is currently being modified to supply slow extracted beams to the Booster Applications Facility (BAF) [3]. The Booster is capable of accelerating these various beams up to a maximum rigidity of 17 T-m. However, for AGS injection, the Booster never operates higher than about 10 T-m [1]. For BAF operations, the Booster will operate up to the highest rigidity for heavy ion beams and up to 13 T-m for proton beams [3]. In this note we will give a full description of the Booster tune quadrupoles and the arc dipoles. We will describe magnetic measurements and actual bare tune measurements. We will describe a 3 dimensional model we developed in order to understand various aspects of the tune quadrupole magnets that were or could not be measured directly. We will present data on tune shifts caused byḂ effects (e.g., vacuum chamber eddy currents) and results of a 3 dimensional model of eddy currents. Finally we will describe a high precision MAD model of the Booster tunes and the predicted tune control ranges at the highest Booster rigidities.