I'm not sure if you can call the fractions of semi-tones of the equal tempered scale (used in most modern Western music) as neat. Indeed, its widespread introduction was very controversial because it was always considered a compromise on the purity of the sound. Never the less, its incredible convenience prevailed.
When we talk about "pure" sounds. The sound intervals that sound best to the human ear form simple numeric frequency ratios. However, if you tune a scale in a way that is closer to this ideal, not every semi-tone is interchangeable and playing pieces in certain keys sounds down right horrible.
That's why, choosing the key of a piece, once actually had a relatively larger impact on how it would sound, depending on how the instrument was tuned. Dissonance in some keys was even sometimes exploited by certain composers. Unfortunately we lose the impact of how these pieces would have sounded when played on modern instruments. We're talking here about pieces from composes as recent as Chopin.
When we talk about "pure" sounds. The sound intervals that sound best to the human ear form simple numeric frequency ratios. However, if you tune a scale in a way that is closer to this ideal, not every semi-tone is interchangeable and playing pieces in certain keys sounds down right horrible.
That's why, choosing the key of a piece, once actually had a relatively larger impact on how it would sound, depending on how the instrument was tuned. Dissonance in some keys was even sometimes exploited by certain composers. Unfortunately we lose the impact of how these pieces would have sounded when played on modern instruments. We're talking here about pieces from composes as recent as Chopin.