In a Sound Symbolism sense, "high" contains a high pitch vowel, "low" a low pitch. Therefore, Ger. "hell" (bright) is a better translation than "hoch" (high), and "dunkel" ("dark") fits better than "tief" ("deep") (although, make no mistake, most cognates have o and u vowels - Ain't talking about dub).
The "young" and "alt" voice brought up in a comment is ironic, because Lt. "alto" means "high, deep". Alto is the lowest female register, above tenor (cp. tension) and below soprano (cp. super).
Similar to the flute analogue brought up before, a string instrument produces high pitch when gripping close to the head, and a low pitch when gripping close to the base. Perhaps that's why it's called Bass (Lt. "bassus" - thick, fat, stumpy, short, low, base; Agr. "βᾰ́σῐς", "básis" - step, rhythm, foot, foundation, base), but perhaps, as the Agr. glosses indicate, it related to drums, cp. base-drum (which may explain the etymology of vase; even Ger. "Fass", "Gefäß"; "tonne" is close to "tone", too, but that's only superficial, so far, and besides the point).
"Thick" and "thin" in turn would have to relate to the thickness of the instrument's strings.
The lowest formant of a sound is also called the fundamental frequency. The imagery is quite strong. In musical theory, the baseline is the foundation of a melody.
The analogy to the movement of the larynx up and down is rather obvious, too.