The reason we avoid E# and B# is to get nice-sounding chords by only using the white keys.
and only 12 notes per octave. With more notes per octave you can distinguish between F# and Gb without losing much accuracy in the most common keys.
In fact, before we understood twelfth roots, people used to tune pianos so that the ratios above were exactly 5⁄4, 4⁄3, and 3⁄2. This made different scales sound different. For instance, the C major triad might have notes in the ratios 4:5:6, while a D major triad might have different ratios, close to the above but slightly off.
Nitpick: I’m no expert in historical tunings, but AFAIK medieval music used pure fifths, where near-pure major thirds are hard to reach. This became a problem in Renaissance music so keyboard instruments started to favor meantone tunings with more impure fifths, to make 4 fifths modulo octave a better major third in the most common keys. (The video demonstrating the major scale/chords generated by a fifth of 695 cents shows this rationale.) As soon as people began to value pure major thirds in their music the fifths in keyboard music became more tempered. Keyboard tunings with both pure 3/2s and pure 5/4s were not widely used, because of the syntonic comma.
In Renaissance music 12-equal was used for lutes for example, which shows that even though people knew about 12 equal temperament and could approximate 2^(1/12) well they didn’t like to use it for keyboard instruments. The tuning of the keyboard gradually changed to accommodate all 12 keys of modern Western music as the style of music started to call for more modulations in circa 18th century. But you are overall correct that different keys in the twelve-tone keyboard sounded different. (even in the 18th century.)
On the one hand, it’s a standard textbook exercise that the difference between pitches of a note in two different tuning systems is never large enough for the human ear to hear it. So, most of the time, the tuning systems are impossible to distinguish.
I find it hard to believe this. If these differences were mostly not significant there would be no reason for the existence of different tuning systems. What kinds of differences between tuning systems are you talking about?
and only 12 notes per octave. With more notes per octave you can distinguish between F# and Gb without losing much accuracy in the most common keys.
Nitpick: I’m no expert in historical tunings, but AFAIK medieval music used pure fifths, where near-pure major thirds are hard to reach. This became a problem in Renaissance music so keyboard instruments started to favor meantone tunings with more impure fifths, to make 4 fifths modulo octave a better major third in the most common keys. (The video demonstrating the major scale/chords generated by a fifth of 695 cents shows this rationale.) As soon as people began to value pure major thirds in their music the fifths in keyboard music became more tempered. Keyboard tunings with both pure 3/2s and pure 5/4s were not widely used, because of the syntonic comma.
In Renaissance music 12-equal was used for lutes for example, which shows that even though people knew about 12 equal temperament and could approximate 2^(1/12) well they didn’t like to use it for keyboard instruments. The tuning of the keyboard gradually changed to accommodate all 12 keys of modern Western music as the style of music started to call for more modulations in circa 18th century. But you are overall correct that different keys in the twelve-tone keyboard sounded different. (even in the 18th century.)
I find it hard to believe this. If these differences were mostly not significant there would be no reason for the existence of different tuning systems. What kinds of differences between tuning systems are you talking about?