Sona's Power Chord passive does affect towers. This increased damage applies regardless of the version of the enhanced auto you have (though her Q version adds more damage than her W and E).
Per the passive description, with my emphasis (source: the League of Legends wiki):
Sona's basic abilities generate a stack of Power Chord, which stacks up to 3 times. At 3 stacks, her next basic attack consumes them all to become empowered with an uncancellable windup, deal 20 − 240 (based on level) (+ 20% AP) bonus magic damage, and apply an additional effect based on the last basic ability cast.
Hymn of Valor (Q): The attack deals (x) damage instead.
Aria of Perserverence (W): The target deals (x) less damage for 3 seconds.
Song of Celerity (E): The target is slowed by (x) for 2 seconds.
This doesn't explicitly say it works against towers, but in testing, I've found this to be true. I briefly hover over the Power Chord buff (with Song of Celerity (E) as my Power Chord type) on my character in the following gif to verify that it is active before attacking the tower, dealing 34 damage. I then attack it a second time to showcase what a normal basic attack's damage looks like (17 damage).
This additional magic damage is increased when Hymn of Valor (Q) is your current Power Chord, as the unique effect of Hymn of Valor on Sona's Power Chord passive is to explicitly magnify the extra magic damage her Power Chord attack does.
Sona's Hymn of Valor (Q) spell also adds damage to her next basic attack, albeit as a short duration buff. This additional damage is also applied to attacks against towers.