The purpose of this project is to create a useful tool for musicians that utilizes the harmonic content of their playing to recommend new, relevant chords to play. This is done by training various Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNNs) on the lead sheets of 100 different jazz standards. A total of 200 unique datasets were produced and tested, resulting in the prediction of nearly 51 million chords. A note-prediction accuracy of 82.1% and a chord-prediction accuracy of 34.5% were achieved across all datasets. Methods of data representation that were rooted in valid music theory frameworks were found to increase the efficacy of harmonic prediction by up to 6%. Optimal LSTM input sizes were also determined for each method of data representation.

Lossy compression is a form of compression that slightly degrades a signal in ways that are ideally not detectable to the human ear. This is opposite to lossless compression, in which the sample is not degraded at all. While lossless compression may seem like the best option, lossy compression, which is used in most audio and video, reduces transmission time and results in much smaller file sizes. However, this compression can affect quality if it goes too far. The more compression there is on a waveform, the more degradation there is, and once a file is lossy compressed, this process is not reversible. This project will observe the degradation of an audio signal after the application of Singular Value Decomposition compression, a lossy compression that eliminates singular values from a signal’s matrix.

This project examines the dynamics and design of control systems for a rocket in propulsive ascent and descent using a simplified model with motion constrained to a vertical plane. The governing differential equations are analyzed. They are then linearized, after which transfer functions are derived relating controllable input variables to controlled output variables. The effect of changes in various parameters as well as other aspects of the system are examined. Methods for controller design based on the derived transfer functions are discussed. This will include the discussion of control of the final descent and landing of the rocket. Lastly, there is a brief discussion about both the successes and limitations of the model analyzed.