On one of my keyboards, I found an option to engage certain "tempered tunings". You also had to pick which key to put them in. I turned on one, and it sounded "thick". So what exactly are they?
They refer to the way notes are distributed in the octave. What western music normally uses is 12 EDO, short for 12 equal divisions of the octave. Another name is 12-TET, or 12-tone equal temperament. What those names mean is that we have 12 equally spaced divisions of our octave -- all the semitones. Since they are equally spaced, any key will harmonize in the same way, regardless of which note it starts on. That's why 12 EDO is popular. Some other 12-tone temperaments don't space the notes equally, so that intervals are better in tune. Mean tone scales are one option. They are constructed to put all the major thirds in tune. The "tempered tunings" option on your keyboard allows you to choose from a few different note arrangements, which change the pitches of the notes slightly to adjust the way they harmonize. Generally the goal is to increase consonance, but constructing a scale requires a few compromises to make it all work out. The mean tone scale, for example, produces one very sharp fifth, which you need to either flatten (messing things up a little), or avoid.
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