[2.2] Chromatic Scale and Temperament

Most of us have some familiarity with the chromatic scale and know that it must be tempered, but what are their precise definitions? Why is the chromatic scale so special and why is temperament needed? We first explore the mathematical basis for the chromatic scale and tempering because the mathematical approach is the most concise, clear, and precise treatment. We then discuss the historical/musical considerations for a better understanding of the relative merits of the different temperaments. A basic mathematical foundation for these concepts is essential for a good understanding of how pianos are tuned. For information on tuning, see White, Howell, Fischer, Jorgensen, or Reblitz in the Reference section at the end of this book.