It used to hold true. In the time of J.S. Bach, C# and Db were two different keys on the clavier and harpsichord. When Bach wrote
The Well-Tempered Clavier
, that's what he was referring to. The temperament of keyboard instruments were such that there was approximately 1/8th of a step between C# and Db. The difference also appeared with other chromatics as well. Nowadays, there is no difference, since modern keyboards use the "mean" temperament, which is a little more precisely calculated, and is less prone to dissonance. It's still not quite the Pythagorean temperament, but I'm not one to work the algorithms for it, I'll leave that up to the mathematicians.
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- The Well-Tempered Clavier
, that's what he was referring to. The temperament of keyboard instruments were such that there was approximately 1/8th of a step between C# and Db. The difference also appeared with other chromatics as well. Nowadays, there is no difference, since modern keyboards use the "mean" temperament, which is a little more precisely calculated, and is less prone to dissonance. It's still not quite the Pythagorean temperament, but I'm not one to work the algorithms for it, I'll leave that up to the mathematicians.