Steven Pinker -- How the Mind Works - Hampshire High Italian ...

530 | HOW THE MIND WORKSidioms, the notes are drumbeats with different timbres (coloring or quality).In others, the notes are pitches that are arrayed from high to low butnot placed at precise intervals. But in many idioms the notes are tones ofa fixed pitch; we label ours "do, re, mi,. . ." or "C, D, E, . . ." The musicalsignificance of a pitch cannot be defined in absolute terms, but only byan interval between it and a reference pitch, usually the stablest one inthe set.The human sense of pitch is determined by the frequency of vibrationof the sound. In most forms of tonal music, the notes in the inventory arerelated to the frequencies of vibration in a straightforward way. When anobject is set into a sustained vibration (a string is plucked, a hollowobject is struck, a column of air reverberates), the object vibrates at severalfrequencies at once. The lowest and often loudest frequency—thefundamental—generally determines the pitch we hear, but the objectalso vibrates at twice the fundamental frequency (but typically not asintensely), at three times the frequency (even less intensely), at fourtimes (less intensely still), and so on. These vibrations are called harmonicsor overtones. They are not perceived as pitches distinct from thefundamental, but when they are all heard together they give a note itsrichness or timbre.But now imagine disassembling a complex tone and playing each ofits overtones separately and at the same volume. Say the fundamentalfrequency is 64 vibrations a second, the second C below middle C on thepiano. The first overtone is a vibration at 128 cycles a second, twicethe frequency of the fundamental. Played by itself, it sounds higher than thefundamental but with the same pitch; on the piano, it corresponds tothe next C going up the keyboard, the C below middle C. The intervalbetween the two notes is called an octave, and all people—indeed, allmammals—perceive tones separated by an octave as having the samequality of pitch. The second overtone vibrates at three times the fundamentalfrequency, 192 times per second, and corresponds to G belowmiddle C; the interval between the pitches is called the perfect fifth.The third overtone, four times the fundamental (256 vibrations per second),is two octaves above it, middle C. The fourth overtone, five timesthe fundamental (320 vibrations a second), is the E above middle C, separatedfrom it by an interval called the major third.These three pitches are the heart of the pitch inventory in Westernmusic and many other idioms. The lowest and most stable note, C in ourexample, is called the tonic, and most melodies tend to return to it and