Pronouncing "found" as "fyound": why?
Solution 1:
The historical phenomenon of palatalizing the velar consonants /k/ and /g/ before certain vowel sounds
I actually don't think Louise "Gyardner" would necessarily pronounce found as "fyound". My impression is that the kind of palatalization that Wolfe is describing in this passage only occured after the velar consonants /g/ and /k/, before certain vowel sounds that either had a phonetically "front" quality, or that historically had had a "front" quality. Specifically:
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I'm sure I remember reading that it occured before the sound /æ/, as in "cat" ("kyat").
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It also seemed to have occured before "ar" pronounced /ɑr/, as in your example of "Gyardner"; I guess the explanation for this is that the palatalization originated before "a" was turned into a back vowel [ɑ] in this position.
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For at least some speakers, it occured before the a-starting diphthong /aɪ/, as in "kind" ("kyind").
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I found one source that indicates that "k" could also be heard palatalized before the diphthong /aʊ/, as in "cow" (A Defence of Phonetic Spelling, by Robert Gordon Latham, 1872), but I'm not sure if that pronunciation might have a slightly different distribution, or different origin.
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It seems it could occur, although not as noticeably since the difference between the quality of the glide and the following vowel sound was smaller, before the front vowels /ɪ/ and /iː/ (e.g. Latham refers to "kin" being pronounced as "kyin").
Phonetically, velar consonants are often more prone to palatalization than others, and since the vowel /æ/ is phonetically "front", it is possible for it to impart a palatal quality to the preceding consonant. Similar phenomena exist (or have existed) in other languages: in French, /k/ and /g/ were palatalized before /a/, resulting ultimately in fricatives /ʃ/ and /ʒ/ as in chat "cat" and jardin "garden"; in Japanese, English loanwords that contain /kæ/ or /gæ/ are often adopted with palatalized consonants.
As mentioned in the extract, palatalizing velars before certain vowels became thought of as a kind of affection and seems to have passed out of common use in standard accents a long time ago; however, it apparently survives in some less well-known accents, like Jamaican English (Culture and Customs of Jamaica, by Martin Mordecai and Pamela Mordecai, 2001).
You can find references to this phenomenon in Walker (1791), among other sources, so it's pretty old and existed in British English as well as in American English.
"Fyound" might occur due to unconditional fronting of the first part of the diphthong /aʊ/
Since /f/ is not a velar sound, it doesn't participate in the sound change I described in the previous section. This section is just speculation, but if it's true that some people pronounce "found" in a way that sounds like "fyound", I think it is likely that this pronunciation is the result of fronting the first element of the dipthong /aʊ/, changing it to something like /æʊ/, which then develops a front onglide /jæʊ/ unconditionally. There are known to be accents of American English where the "cat" vowel has developed more or less unconditionally, not just after velars, to a diphthong with a very front first element (the Wikipedia article on the Northern Cities Vowel Shift says "cat and that as pronounced by a Rochester, New York resident may sound like "kyet" and "thyet" to a visitor") and it seems possible that this could also occur in some accents for the "mouth" diphthong. However, I am not familar with any description of an accent that has this feature.
Solution 2:
It’s a regional accent. The way you speak sounds outrageous to people who grew up in a different area than you also.