Sometimes I do, mainly with certain ballads, but also has happened with some more energetic music. Usually breakdowns and transitions are the most common 'cause'.
Also things like certain scenes in certain movies that makes me shiver quite a lot; A notable example is from my all-time favorite movie where there's a scene of this wolf howling out into the distance that always makes me shiver every single time, even after having watched it half a dozen times throughout the years.
But generally these aren't that major and quite specific, not really anything I feel very strongly on a regular basis. It's kinda only caused in certain quite specific situations under the right circumstances.
I am very affected by music, though it's mostly just mental stimulation rather than physical feelings. Music that carries a lot of emotion is also what I usually listen to. Not necessarily really as in the "Emo"-genre but more in the way of music that delivers a lot of feelings and emotions. Be it happy music with a lot of energy, sad music with an overall dull tone, inspirational music with a positive and interesting tone or some heavy metal with an angry/upset theme etc.. Thus a lot of alternative rock and a little bit of metalcore is mainly what you'll find in my music library~
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ASMR however, that's something I very much enjoy on a regular basis. I quite often put on my headphones and bring up some videos on Youtube that is made specifically to induce ASMR as I find it to be very stimulating and relaxing.
I need to be able to relax and focus on the ASMR contend, mainly the sounds, with minimal distractions before I'm really affected by it myself and start feeling the tingles. Though once I get to that point it's quite often the tingles sort of progress from the back of my head and help cause chills/shivers throughout the rest of my body.