What method of tuning keyboard instruments divides all semitones equally within the octave, allowing for performance "in tune" in all keys?

The method that divides all semitones equally within the octave is known as equal temperament. This tuning system allows for each of the twelve semitones in an octave to be spaced equally apart, which means that each note is adjusted slightly to ensure that the overall tuning remains consistent across all keys. This is particularly advantageous for keyboard instruments as it facilitates the ability to modulate into different keys without sounding dissonant.

Equal temperament is widely used in Western music and is considered the modern standard, as it provides the flexibility needed for diverse musical styles and compositions. Instruments tuned in equal temperament can perform more uniformly across various pieces, ensuring a balance and coherence in harmony regardless of the key being played.

In contrast, the other tuning systems such as just intonation, Pythagorean tuning, and mean-tone temperament prioritize different harmonic relationships and may sound “in tune” in specific keys but would often be discordant when applied to others, limiting a musician's options for modulation.