The principle of tuning all notes to be closed under musical transposition.

That is, if a piece of music is played on an instrument tuned in equal temperament, it can be shifted up or down an arbitrary number of notes and sounds exactly the same: the relative distances of all the intervals are preserved, only the overall pitch is affected. This has been the standard way of tuning instruments in Western "classical" music for the last, say, 200 years, while in earlier times, it was merely considered a mathematical curiosity, hardly suitable for serious use.

Yes, my friend, the way our pianos are tuned is hardly suitable for Western music written before 1750. You have to realise that in equal temperament, literally >every chord is out of tune. Until 1720, musical scales with more than two accidentals were outright curiosities, and chords remained very close to the natural harmonics of octaves, fifths, fourths and thirds; consequently, instruments would be tuned so as to make these most common intervals sound just or very nearly so, at the expense of the intervals that were never used. As musical transposition became more popular, the number of accidentals employed became higher, and tuning had to shift away from keeping just fifths and thirds, towards having better sounding scales and chords with more accidentals.

For a while, there was much discussion and experimentation with tuning; different authors proposed different compromises between making the most common intervals sound as just as possible and being able to play chords with many accidentals. Composers started to employ scales with more accidentals (2, 3, 4, 5) and each scale would have its unique character, owing to the unequal temperament.

We can see this development in the title of Johann Sebastian Bach's Well-Tempered Clavier, which is a suite of 48 pairs of pieces in every possible musical key, written to prove that such a thing was musically feasible with these new "well-tempered" tuning systems. The debate could only come to an end with one conclusion, namely, the universal adoption -- for Western classical instruments -- of the equal temperament system, which is taught as the only possible one in today's introductory courses in Western music theory.

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