Last year I made
this post listing some tone correspondences between Mandarin and Cantonese. I have a bit more experience with Cantonese now, and now I'd like to post a more elaborate version of that.
So, first, the useful tone correspondences between Mandarin and Cantonese, when a Cantonese syllable ends in a vowel, -m, -n or -ng. Judging very informally from my experience learning pronunciations, I estimate they're reliable perhaps 93%-95% of the time (alternatively read: the correspondence doesn't work for about 1 in 14 syllables or perhaps 1 in 20 syllables).
Mandarin 1st tone ~ Cantonese 1st tone
Mandarin 2nd tone ~ Cantonese 4th tone
Mandarin 3rd tone ~ Cantonese 2nd or 5th tone
Mandarin 4th tone ~ Cantonese 3rd or 6th tone
Examples:
Mandarin 1st tone ~ Cantonese 1st tone
開心 kai1xin1 ~ hoi1sam1 'happy'
分鐘 fen1zhong1 ~ fan1jung1 'minute'
Mandarin 2nd tone ~ Cantonese 4th tone
成為 cheng2wei2 ~ sing4wai4 'to become'
人員 ren2yuan2 ~ yan4yun4 'staff, staff member'
Mandarin 3rd tone ~ Cantonese 2nd or 5th tone
跑錶 pao3biao3 ~ paau2biu2 'stopwatch'
永遠 yong3yuan3 ~ wing5yun5 'forever'
可以 ke3yi3 ~ ho2yi5 'can, be allowed to'
軟體 ruan3ti3 ~ yun5tai2 'software'
Mandarin 4th tone ~ Cantonese 3rd or 6th tone
世界 shi4jie4 ~ sai3gaai3 'world'
互動 hu4dong4 ~ wu6dung6 'interaction'
教授 jiao4shou4 ~ gaau3sau6 'professor'
大眾 da4zhong4 ~ daai6jung3 'the masses'
However, if the Cantonese syllable ends in -p, -t or -k, then the Mandarin tone is a lot more unpredictable. A very large proportion (I very informally estimate 55%-65% from experience) has a 4th tone in Mandarin, and when that's not the case they tend to have 2nd tone (I very informally estimate 25%-30%). Instances of corresponding Mandarin 1st tone and 3rd tone are a lot less common, but do happen, including a few common morphemes (切 qie1 ~ chit3, used in 一切 yi4qie1 ~ yat1chit3 'everything; all Xs'). There are ultimately no highly reliable correspondences between Mandarin and Cantonese for -p/-t/-k syllables.
Example syllable morphemes with all possible combinations of correspondence:
出 chu1 ~ cheut1, 貼 tie1 ~ tip3, 夕 xi1 ~ jik6
得 de2 ~ dak1, 察 cha2 ~ chaat3, 獨 du2 ~ duk6
北 bei3 ~ bak1, 百 bai3 ~ baak3, 蜀 shu3 ~ suk6
必 bi4 ~ bit1, 各 ge4 ~ gok3, 辣 la4 ~ laat6
Also, an aside note on that old post:
In that same post from a year ago, I also mentioned 於 (simplified character: 于) as an exception of the tone correspondences for words ending in a vowel or -m/n/ng:
Ser wrote:There are some exceptions such as 於 (simplified 于) which is yu2 in Mandarin and yu1 in Cantonese, but these are thankfully few!
However, since then, I've learned the reason why this exception exists: the two characters used to represent two entirely separate words as recently as the Yuan Dynasty (Mongol conquest 1234, proclaimed 1271, fallen 1368 after Emperor's flight). It was some time after that they began being considered the same word because of their similar sound and and very similar meanings, and it seems Mandarin and Cantonese ended up with non-corresponding tones due to this.
In the Qieyun, published in 601 AD, 於 appears listed with a pronunciation that would've been similar to [ʔiɔ], and 于 with [ɦio], both with the medieval level tone (平聲). According to Edwin Pulleyblank in his Outline of Classical Chinese Grammar, the Zhongyuan Yinyun (a dictionary of Old Mandarin pronunciations made by 1324 under Mongol rule) lists them as [ʔy] but still bearing different tones, with 於 being in a different tone register (light level tone, 陰平聲, "light" like typical voiceless-initial syllables with e.g. [ʔ] in Qieyun) than the reading of 于 (dark level tone, 陽平聲, "dark" like typical voiced-initial syllables with e.g. [ɦ] in Qieyun). Their expected descendants by regular changes should in fact still be different: 於 = Mandarin yu1 and Cantonese yu1, and 于 = Mandarin yu2 and Cantonese yu4.
However, the problem is that besides having very similar pronunciations, 于 had been an obsolete word for a long time. From the very shapes of the characters (the "phonetic series"), we know that around 1000 BC 於 sounded something like [ʔa] and 于 like [ɢʷa] later [ɦʷa] (Zhengzhang Shangfang's reconstructions). The early pre-classical Chinese around and a little after this time distinguished 於 'be at [a place]; in, at, on' and 于 'go to [a place]; to(ward), into', but within classical times 於 took over the uses of 于, relegating 于 to a life as an uncommon character of not much use aside from very old texts.
Interestingly, when both started being used with the same pronunciation, it appears that Mandarin and Cantonese kept the opposite choices. Mandarin retains the reading of 于 (yu2), but Cantonese seems to retain that of 於 (yu1)! Then when the Traditional Chinese standard was established in late Qing, 于 was deemed a mere character variant of 於 under a lack of awareness of the old distinction. Later on the People's Republic of China specified 于 as the Simplified form of Traditional 於... 於 and 于 are now widely considered the same "word", but they still weren't as recently as ~800 years ago.