I have my own ideas, but I’d like to hear yours 
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I saw someone post a headcanon on Tumblr that Rose would listen to music from her near future, and that she would walk around in 2005 or 2006 with a shirt from Olivia Rodrigo’s most recent tour, which I absolutely agree with!
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Well, we already know about Ryan…
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Bop.
Twelve characters
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I think 7 listens to ska
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15 obviously listens to Kylie Minogue.
And I can totally see Twelve rocking out to classic rock bands like AC/DC or Deep Purple.
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Both 7 and 8 listened to this song in the Doctor Who movie…
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If nothing else, 12 obviously likes “Pretty Woman” and “All the Young Dudes”.
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Oh, actually, 12 whistles “Another Brick in the Wall” at one point, and plays “Amazing Grace”, too. Honestly one of the more musical Doctors.
Amy and Rory danced to Queen’s “Crazy Little Thing Called Love” and James Morrison’s “You Give Me Something” at their wedding.
I’m tending to assume Mel liked the music in Delta and the Bannermen.
5 sings “I Want to be Happy” from Na, Na, Nanette.
Sarah Jane whistles “Daddy Wouldn’t Buy Me a Bow Wow”.
We know Susan listens to “John Smith and the Common Men”…
Pretty sure 6 is into Gilbert and Sullivan.
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During “The Nightmare Man: Part 1,” Luke Smith is playing "Bulletproof by La Roux on his radio, and I think of that episode whenever I hear that song. In the script for the episode (shoutout to the BBC for putting most Doctor Who and spinoff scripts online for free), the song that’s written down is “Omen” by The Prodigy, but that clearly changed between writing and broadcast.
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Seven canonically loves jazz, and Eight loves orchestral and classical music. I think Seven would also be passively into progressive rock and stuff like that.
I think Eight likes loads of weird alien music his companions find bewildering – Sam finds him at the console crying his eyes to what sounds like a series of atonal bloops and bleeps.
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I think Thirteen would listen to a lot of showtunes.
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Six definitely loves opera and classical, that’s canon. I headcanon him as having a very eclectic music taste though.
Peri canonically loves Elvis and metal (she cites Metallica specifically, says she’s a headbanger, and even dated a guy in a metal band). Again, I think she’d like a bit of everything.
Mel likes Olivia Newton-John 
Even more reason why she needs to have a proper adventure with Six.
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Doesn’t Three like opera?
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I feel that 9 would like stuff like Oasis and Stone Roses
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If The Invasion is anything to go by, Jamie loves 60’s (modern) pop, and 2 despises it.
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We do also know how Ian feels about the Beatles.
And Vicki’s been to their Memorial theatre and thinks of them as classical music…
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Definitely self projecting here but Tegan would totally listen to Midnight Oil. They’re an alt-rock band that started out in the 70s but hit peak fame in the 80s and 90s. You’ve probably heard of their biggest hit, Beds are Burning. Most songs tackle heavy themes like geopolitics, corporate greed, environmentalism, nuclear war, Indigenous rights and more, right up Tegan’s alley.
She may even have seen them live before they got big when they were doing the pub rock circuit in Sydney, as she lived there for a bit between Time Flight and Arc of Infinity in the early 80s.
Anyway, 10/10 would recommend, they have so many Bangers
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I think Susan, being as she is a time travelling teenager, goes through a phase of listening to just the wildest music from whatever time zone she can find, the kind of thing that would make the Doctor, and even Ian and Barbara, complain about modern music just being noise
On a related note, I was introduced to donk music through a friend recently (https://youtu.be/BZAQRUbYFpY?si=x6nHcAs9z7ToXL90) and I think that was what played in her mind on loop during Edge of Destruction
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11 would totally be into space theatre
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