Can if I want

A very interesting investigation! While reading your post, I thought of the song 《恰似你的温柔》by 邓丽君 and《一生的朋友》by 费玉清. I've always wondered if people think the lyrics sound like “掐死你的温柔" and "你是我医生的朋友" haha

Brilliant Hoffman! I had often wondered this myself. I have always listened for a tone-melody connection when listening to Mandarin music but never found it.

But then you put up this stunning Cantonese example! I wonder how representative this is of Cantonese lyrical music. I also wonder to what extent the songwriter is conscious of the connection.

In English lyrics, meter is important, although the songwriter does not necessarily consciously try to match syllable lengths and stresses -- rather they just write what "sounds right". I have been listening to quite a bit of English lyrics lately composed by francophones, and, though creative, they often contain jarring "mistakes" in their meter. I guess it's hard to get it right coming from French.

But on topic again, if there is a general pattern along the lines of your findings, I wonder why Mandarin music seems to be tone-deaf...

I've always been fascinated by this topic! But it's extremely knotty. This amateur's intuition is that Cantopop Cantonese is a more rarefied language, and as a "high" form is more subject to the constraints of (pace Casti/Salieri/R. Strauss) prima le parole. That would be an element in explaining the prevailing culture of Cantopop, as opposed to Mandopop or Tâi-pop.

Whether Cantopop's tendency to tone-sensitive word setting has any relationship with the tonal phonology of the language itself... my guess is that it is related to the fact that in Hong Kong Cantonese, the number of pitch contours is rather low (three, moving towards two), with a dominance of level tones of relatively fixed or moderately falling pitches. This is lower than the number of pitch registers amongst the phonemic tones (three, moving toward four). I do hear the importance of keeping the rising tones intact when singing Cantopop: that distinctive portamento is super common, and seems to be realised whenever possible.

Though there are four lemma contours for Mandarin, in practice I've never heard the 上声 realised with any sort of pitch dip or raise in music, so these reduce to three clearly defined contours, and two pitch levels. To what extent are rising tones and falling tones (the latter of which are much more salient in spoken Mandarin of most varieties than in not-quite-modern Cantonese) realised in modern Mandopop sounds like a good project (can't quite check whether it's been done yet).

I don't know much Taiwanese (or any other form of) Hokkien, and haven't listened to much of its music; I can say that there are three contours (preserved in sandhi as well), and (depending on the grouping) two or three levels.

That big catch-all lifesaver of language- and song-intelligibility, "context", would be useful, but only if it can be properly quantified. Does the increasingly disyllabic nature of Mandarin make it easier to take context into account? Is there an interaction of stress with meter in Mandopop? If such an interaction exist, does it result in stressed tones being taken into account more commonly than unstressed tones?

Thai's five phonemic tones are composed, broadly speaking, of three registers and three contours, a lot like Mandarin. But why are tones (or at least tone contours) more salient in most Thai singing (especially the realisation of the falling tone) than in Mandarin? There's also tone-phonation interaction, such as in Vietnamese, where at least some of the creaky voice / glottalisation is preserved in singing. The phonation types can be considered as being added to two of the tones, although they are usually thought of in that way,

Another facet: to what extent is length involved? Like metrical stress and tonal register, phoneme length (whether it refers to vowel or consonant length) is directly affected by music. As the connection between Mandarin's tones and the length of its syllables is well-established, there needs to be some investigation into how these interact in music: is the Mandarin third tone realised as the "long" or "longer-than-standard" note? In Cantonese, vowel length relates to vowel quality (like in the vast majority of English varieties which have significant musical culture) but can influence tone too. In the cases that it can, does it?

(Of course, the length issue has repercussions for quite a lot of languages, including a large number of European ones. Czech and Hungarian are the languages with strong length contrasts as well as famous musical traditions, but any diction student of German or Italian knows of [and dreads?] the length-related pitfalls in those languages too).

Answers as clearly marked DOIs to be posted on a postcard somewhere on this forum.