Music is always out of tune. Surprised? Well, if it's played by modern instruments, it is.
Some guy named Bach proved that, if you detune every instrument a little bit, you could play in any key. Previously, you had to tune instruments to specific keys: a clavichord tuned to G would sound like cats screwing if you played in E flat.
The point is that the only place one hears precisely in-tune music is a cappella vocals, because the singers, often without being aware, fudge or cheat every chord into precise tune. There is a tension to equal-tempered tuning that is absent in a cappella music, and it's refreshing to hear, it's almost like being able to take a deep breath for the first time.
I heard a recording of "Adeste Fidelis" by the Vienna Boys Choir in my 4th grade music class, and it changed my life. This wasn't opera, the posturing heavy-metal of the classical vocal world. This was straight-up singing, as pure as a human voice can be. No excessive art or artifice, no obvious tools or mechanics, no sounding forced. It was sounds like I had never heard, voices devoted to the melody and not the style.
It is said that the unchanged male voice is the most beautiful there is. While this is probably a wholly sexist viewpoint which has led in past centuries to horrible practices (castrati), this recording, of pre-pubescent males, was truly glorious.
Here is the Vienna Boys Choir in 1977 singing "Adeste Fidelis"
Here's the same vintage of the VBC singing "Maria Wiegenlied" (Maria's Lullaby); this is rock'n'roll: