The dialect Seoul hears as rough and sing-song, and the one that kept what Seoul lost: a lexical pitch accent, so that 가지 'branch' and 가지 'aubergine' differ by which syllable is high. Two vowels fall together — ㅡ and ㅓ are one sound, so 글 and 걸 rhyme — and the tense ㅆ is said as a plain ㅅ, so 쌀 comes out as 살. The grammar is clipped too: 밥 먹었어요? becomes 밥 뭇나?, and the endings -나, -노, -고 replace Seoul's -니, -지.
Where: the south-east — Busan, Daegu, the Gyeongsang provinces
The way in: Say 밥 뭇나? with the 뭇 high and short — and let ㅡ and ㅓ be the same vowel.
Try a word
Anything the spelling engine can transcribe, the accent can move. Slow it down to hear the shape.
Lexical pitch accent on top of the phrase melody: a word's high syllable is fixed and meaningful. Faster and more emphatic than Seoul, with the pitch range wide and the final syllables clipped. To a Seoul ear it sounds like an argument; to a Busan ear Seoul sounds affected.
What moves, one rule at a time
In the order the mouth applies them. Every before-and-after is playable — click the IPA. The pattern is the rule as the engine runs it, for the curious.
Consonants
tense ㅆ becomes plain ㅅ
s͈|ɕ͈ → s
How: Say the plain, slightly breathy s.
The south has no tense s: 쌀 'rice' is said 살, 씨 'seed; Mr' is 시. The other tense consonants (ㄲ ㄸ ㅃ ㅉ) stay tense — only ㅆ is lost.
Word
Reference
Accent
쌀
rice — now the same as 살 'flesh'
씨
seed; Mr — note the ɕ goes too
살
unchanged
Vowels
ㅡ and ㅓ become one vowel
ɯ → ʌ
How: Drop the tongue slightly from ɯ towards ʌ — the lips stay unrounded in both.
Gyeongsang has no /ɯ/: the flat vowel merges into ㅓ. 음악 'music' and 엄악 would be the same; 글 'writing' rhymes with 걸.