tonal language

A Tonal language is a language that uses tone to distinguish words. Tone is a phonological trait common to many languages around the world (though rare in Europe, the Middle East, South Asia, and the Pacific). Chinese is perhaps the most well-known of such languages.
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Noun
1. a language in which different tones distinguish different meanings
(synonym) tone language
(hypernym) natural language, tongue
(hyponym) contour language
(part-meronym) tone system, tonal system

Tone-sandhi occurs in tonal languages, such as Chinese, when a sequence of tones in words or phrases affect the tones involved. One might say that the tones of the Chinese language will adapt to the tune currently being played.

The three basic rules for tone-sandhi in Mandarin Chinese are:
The character "" (yi1) is pronounced 1) in the 1:st tone when counting, 2) in the 2:nd tone before a syllable with the 4:th tone and 3) in the 4:th tone in all other cases.
The character "" (bu4) is pronounced 1) in the 2:nd tone before a syllable with the 4:th tone and 2) in the 4:th tone in all other cases.
When two or more syllables with the 3:rd tone follow in a row, all but the last syllable will get the 2:nd tone.

Further reading: Chinese phonetics, tones 

Chinese and all Sino-Tibetan languages are tonal languages, which mean that it is important to pronounce most every single syllable with the correct tone or accent. Tones are absolutely vital to make a correct distinction between syllables that are otherwise phonetically identical. In Mandarin Chinese there are four distinct tones. In some cases, the tones will affect each other according to tone-sandhi. For both Pinyin and Bopomofo transliterations, the tones are generally marked with the following accents above the central vowels:

Further reading: Chinese phonetics, tone-sandhi