The 18th century solution to the keyboard temperament problem

Abstract

The interval relationships between the tones of the scale varied in the past. Applying historical temperament systems to performance affects music interpretation. In the 20th century equal tempered system, all semitones are equally spaced; therefore, melodic and harmonic effects in various keys are identical except for being higher or lower in pitch. Well-tempered 18th century semitones are unequally spaced. This results in melodies and harmonies having varying effects when they are transposed. Whereas the 20th century temperament divides the ditonic comma into 12 equal parts, the 18th century temperaments divide the ditonic comma into two to six parts equally or unequally in such a manner that the most used keys produce harmonies close to just intonation while the least used keys produce harmonies that are highly tempered but still musically acceptable. The 18th century tradition determined that major thirds should change in size progressively throughout the circle.