Hi Yeleixingfeng,
Nice to see you back here!
Yes, your description is EXACTLY the one I worked out when I was young too, when first exposed to Mandarin
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There are a couple of additional subtle comments which can be important though (stuff I only found out in the last few years).
I believe (but I base this only on my own listening, not on accurate measurements or anything I read in linguistic articles):
1. The (Penang) Hokkien tone1 and the Mandarin tone1 are both level tones, but the Hokkien tone is lower than the Mandarin one (maybe 44 or 33, in contrast to Mandarin 55).
2. The (Penang) Hokkien3/7 tone and Mandarin tone3 are both low (or non-high, in any case), slightly falling, but the Hokkien tone3/7 never rises again, the way the Mandarin one does when at the end of the phrase.
3. The (Penang) Hokkien tone2 is considered ("psychologically") to correspond to the Mandarin tone4 - Penang Hokkien speakers consider both of them to be falling tones, but... in reality, the Mandarin tone4 is a very sharply falling tone (maybe 51), whereas the Penang Hokkien tone doesn't fall very much at all (maybe 53 or maybe even only 54 or 5-4.5). It is the fact that it starts higher than Hokkien tone1 which Penang Hokkien speaker use to distinguish it from Penang Hokkien tone1, rather than the actual falling itself.
This last fact was first brought to my attention by Ah-bin (when he was trying to improve his Penang Hokkien), and I now "believe it to be true", even though I still continue to *perceive* it as a falling tone! One of the ways I "prove" this to myself is to think of the contrast between how non-Penang Hokkien speakers say "i1 ho2" (= "he's good"), and how Penang Hokkien speakers say it. The former group have a much more dramatically falling Hokkien tone2, it's one of the things which make the two variants sound different. My current opinion (subject to change if the tones of the two are ever measured scientifically) is that the non-Penang Hokkien tone2 (rather than the Penang Hokkien tone2) is much closer to the Mandarin tone4 (because both fall quite sharply).
To sum up points 1 and 3 from a slightly different perspective: Mandarin speakers distinguish Mandarin tone1 and Mandarin tone4 from one another by the fact that the former remains level while the latter falls sharply (they both begin quite high), whereas Penang Hokkien speakers distinguish Hokkien tone1 and Hokkien tone2 from one another by the fact that the former starts lower than the latter (neither - specifically the latter - falls significantly).
The reason all this is worth pointing out is that when speakers of one language learn another language (especially as adults), the most normal thing is to map the sounds (and hence also tones) of the language they are learning to the one which they already know (i.e. their native language). This is a very well-established fact about the (non-native) acquisition of second languages. So, for all intents and purposes, the mapping that Yeleixingfeng (and I) make has the result that in our Mandarin tones are slightly different from how they would be spoken by a PRC Mandarin speaker (not that there is a standard completely uniform pronunciation in the PRC anyway, but just glossing over details to get the idea across).
It's taken me many years and a lot of thinking and listening to come to these conclusions, and I re-emphasize that the only way to *really* know is to measure them: get a native Penang Hokkien speaker, get a native PRC N. Mandarin speaker; get them to say the 4 tones (in a whole lot of situations and samples); record this, get the spectograms, and look at the resulting tone contours. That's the only way to *really* know, as all other methods go through our perception and linguistic processing systems, which can influence what we think we hear incredibly.
PS. I'd like to give another illustration of point 2 above (and also to support the statement that learners attempt to map the language they are learning to the system used in their native language). When I was young in Penang, nobody had the slight rise in Mandarin tone3, when the syllable was at the end of a phrase; i.e. they used the Hokkien tone3/7 in all situations where they needed the Mandarin tone3, when speaking Mandarin (I don't know if that has changed now, with more exposure to PRC Mandarin in TV, radio, films and YouTube). I found this "standard Mandarin tone3" rise-at-the-end very odd when I first started learning Mandarin again from PRC speakers, as an adult. Not only odd, but confusing, because I was used to Mandarin tone3 as low non-rising, and Mandarin tone2 as rising. THIS was what I used to distinguish Mandarin tone3 from Mandarin tone2 - the presence or absence of rising. In PRC Mandarin, tone3 at the end of the phrase rises slightly and that made it very difficult for me to distinguish from tone2.
Anyway, for Tainan I didn't have the same luck and they do sound a little bit differently.
). My question is, does Hokkien really have a tone like Mandarin tone 4? Most of my references I have for Taiwanese (except Maryknoll) show pitch graphs and none of the tones look like high-falling...