Here is some context behind musical tuning systems, and how harmony works: Musical harmony in Western music is based on physical properties of the way material

Here is some context behind musical tuning systems, and how harmony works: Musical harmony in Western music is based on physical properties of the way materials vibrate. When you vibrate something resonant through plucking, striking, forcing air through, etc, it vibrates at a fundamental frequency, and integer multiples of that fundamental frequency. So for instance 400 Hz, 800 Hz, 1200 Hz, etc. The power of two multiples sound like the same note in a higher octave. Human hearing is logarithmic, and the same note one octave higher is double the frequency. The non power of 2 multiples do NOT sound like the same note. These notes are what "sounds good" with the base frequency, and generally the lower frequency multiple it comes from the better it sounds. So for instance, starting with 400 Hz, 400 x 3 = 1200. Divide that back down below 800 to 600 to put it in the same "octave", and you have the interval called a 5th. 400 Hz x 5 = 2000, divide it back down to 500 Hz. That's a major 3rd? I think? It might be a 4th, I don't remember. Notice that these frequencies are defined by exact ratios to each other, not by consistent logarithmic increases which can be repeated in a pattern (a scale). So, how can you split up an octave in the way that most closely appoximates these exact ratios? Turns out dividing an octave into 12 steps is much better than any number before or after until you get to 24. Thus the 12 note system of western music. All the different tuning systems mentioned by others are trying to tune these 12 notes for different purposes. Older pre-modern systems usually tuned to C most exactly, and left small errors in every other key. These small errors gave different character to different keys in music of the time. Newer tuning systems (equal temperament), have the key errors balanced out evenly across every key, so every key now sounds the same in character.