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肃 supplies the sound through historical drift: sù → xiāo, attested in
萧 (mugwort, also a surname),
潇 (waterfall sound),
啸 (to whistle). Faint semantic flavor fits beautifully too — the xiao
箫 is the instrument of solemn court music and Daoist hermits, its breathy tone associated with quiet dignity, exactly the 'solemn, hushed' core of
肃.