How do Chinese speakers convey emotions by speech?
How can Chinese express emotion if tones determine the meaning of a word? This should be one of the top 2 or 3 items on a Chinese language FAQ. It seems to be a constant source of puzzlement and a goad to much odd speculation.

The problem is that the word 'tone' when applied to Chinese does not mean what people think it does. Or perhaps people do not think carefully about what they think tone means when speaking of it in their own language.

For most people, it seems that tone is simply emotion embedded in language. This is much too simplistic to provide any insights into how we judge emotion in speech.  What is an angry or frightened tone? Put in these terms, it's purely subjective.  

For Chinese tones, however, it is possible to give a much more objective statement of what they consist of.  Jerry Norman's book Chinese (published by Cambridge UP) gave what I thought was a very clear description: Tone consists of primarily of pitch, but duration and volume (Norman says intensity) are "important secondary cues." These are all relative, not absolute.

Much of what people tend to interpret as the emotional content of speech is in the departure of one of these from what has come before or what comes after.

This might seem puzzling, but perhaps a comparison with English might help. English indicates interrogative with a rising pitch. In contrast, many people interpret angry or strong emphasis with a falling pitch.  Is it possible to ask an angry question in English? I think this is not at all difficult, using increased volume and duration and perhaps less of a rise in pitch than is common.

Emotional inflection in Chinese works in similar ways, with increased or decreased volume and duration. Pitch certainly does not work the way in Chinese that it does in English, and this can make it easy to misinterpret the emotional inflection of speech for those who do not know the language.

I have often heard learners complain that it sounds like Chinese speakers are arguing or angry all the time, and this was certainly my first impression when I heard people speaking in the Minnan dialect. In fact, however, I think that misjudging emotional content is common with most languages that one is unfamiliar with.