### 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.