General-purpose embedding is highly desirable for few-shot even zero-shot learning in many application scenarios, including audio tasks. In order to understand representations better, we conducted a thorough error analysis and visualization of HEAR 2021 submission results. Inspired by the analysis, this work experiments with different front-end audio preprocessing methods, including Constant-Q Transform (CQT) and Short-time Fourier transform (STFT), and proposes a Batch Embedding Covariance Regularization (BECR) term to uncover a more holistic simulation of the frequency information received by the human auditory system. We tested the models on the suite of HEAR 2021 tasks, which encompass a broad category of tasks. Preliminary results show (1) the proposed BECR can incur a more dispersed embedding on the test set, (2) BECR improves the PaSST model without extra computation complexity, and (3) STFT preprocessing outperforms CQT in all tasks we tested. Github:https://github.com/ankitshah009/general_audio_embedding_hear_2021