Chinese is a tonal language. Qieyun (切韵), a rhyme dictionary published in 601 AD, organizes Middle Chinese syllables by their four tones. The four Middle Chinese tones are Ping (平), Shang (上), Qu (去), and Ru (入). Although linguists are not too sure about the exact pitch contours of the tones, good guess can be made from their names and descriptions. For example, Ping is a level tone, and Ru, although the exact tone value is not known, are made up of syllables end with voiceless stops [p], [t], or [k].

Modern Standard Mandarin also has four tones: Yin Ping (阴平), Yang Ping (阳平), Shang (上), and Qu (去) (aka the 1st, 2nd, 3rd, and 4th tone respectively）. Note that they are different from the Middle Chinese ones. In cool Chinese fashion, the tone change from Middle Chinese to modern mandarin has been summarized in 12 syllables: 平分阴阳, 浊上变去, 入派四声.

1. 平分阴阳 [pein22 fun33 yim33 yiaŋ22] Ping splits into Yin and Yang.

The Middle Chinese Ping syllables split into two tones: Yin Ping and Yang Ping. Syllables with unvoiced beginning consonants (清音)¹ become Yin Ping with tonal value 55. Syllables with voiced beginning consonants (浊音)²  turn into Yang Ping  with tonal value 35.

2. 浊上变去. [dək32 siaŋ32 bein33 hui33] Voiced Obstruent Shang merges into Qu.

The Middle Chinese Shang syllables with voiced obstruent (全浊)³ beginning consonants merge into the Qu tone.

3. 入派四声 [yip21 pai33 ɬi33 sein33] Ru redistributed to the Four Tones.

The Middle Chinese Ru syllables are redistributed to the four tones of modern mandarin. There're no obvious rules for the redistribution. Note that mandarin does not have the Ru tone anymore.

The Four Tones of Middle Chinese and Mandarin