Large Language Models like GPT-4 adjust their responses not only based on the question asked, but also on how it is emotionally phrased. We systematically vary the emotional tone of 156 prompts - spanning controversial and everyday topics - and analyze how it affects model responses. Our findings show that GPT-4 is three times less likely to respond negatively to a negatively framed question than to a neutral one. This suggests a "rebound" bias where the model overcorrects, often shifting toward neutrality or positivity. On sensitive topics (e.g., justice or politics), this effect is even more pronounced: tone-based variation is suppressed, suggesting an alignment override. We introduce concepts like the "tone floor" - a lower bound in response negativity - and use tone-valence transition matrices to quantify behavior. Visualizations based on 1536-dimensional embeddings confirm semantic drift based on tone. Our work highlights an underexplored class of biases driven by emotional framing in prompts, with implications for AI alignment and trust. Code and data are available at: https://github.com/bardolfranck/llm-responses-viewer