Exercises in mental cartography: making new maps.

IN 1698, an Italian named Bartolomeo Cristofori built the world's first piano. This happened more than two millennia after Pythagoras invented Western music by discovering that the relationships between musical notes could be expressed as numerical ratios. Cristofori designed his pianoforte (literally "soft loud") for Florence's Medici family, but the new instrument didn't catch on until the late eighteenth century. Even Bach first called the piano a clumsy instrument that would be too difficult to master. But as Romanticism spread across Europe, the piano came to be lauded for its expressive capabilities. By this time, a modified tuning system had been developed that separated each octave into twelve separate tones. This is the tuning system we use in music today.

A modern piano has eighty-eight keys and can produce eighty-eight tones. Each unique tone is produced when a hammer strikes a string, causing it to vibrate. Hit a middle-A, and a string will vibrate at 440 cycles per second. Hit an A-flat, one half-step down, and a different string vibrates at around 422 cycles per second, a difference of only eighteen cycles per second, or hertz. This difference separates each note on the piano. By putting two tones together, we can create an interval. Then we can give the interval a name based on its size. A major third, for example, contains four half-steps. A minor third contains only three. With a mere eighteen-hertz difference, we have created a complex language that helps us use music to communicate all kinds of emotions. The interval we call a major third sounds happy, pleasant or calming to us. Think of the standard ding-dong of a doorbell. The interval known as a minor third sounds angry, menacing, or foreboding. Think of the opening notes of Beethoven's Fifth symphony. Why do these associations exist? Does the music have some intrinsic quality that we understand instinctively? Hardly. We associate certain sounds with certain feelings because this is what we have been taught to do. This is what we have been learning since the day we were born.

While poetry may be the most efficient way to communicate with words, music offers another world of even more highly abstracted communication. The ability of humans to abstract from our experience with whatever language we choose (verbal or otherwise) allows us to make maps of the territories we encounter. Maps are infinitely useful for communicating, especially on abstract levels. But when we allow the map--the symbol--to presuppose the territory, we are taking a shortcut to avoid thinking for ourselves. This is relatively harmless in music, except that the inability of most people to understand more than one musical map causes all of one culture's music to sound the same to ...