The lowest resonant frequency of a tube or string is the fundamental; the higher ones are overtones, and all of them are called harmonics. All resonant frequencies are whole-number multiples of the fundamental. A plucked string makes pulses that travel both ways, and because its ends are fixed, nodes appear at the ends and a standing wave forms; the first mode of a string, the fundamental or first harmonic, shows half of a wavelength. An octave is a ratio of 2:1 in frequency, and in equal temperament an octave has 12 equal semitones. In equal temperament each semitone has a frequency ratio of about 1.059, which is 2 to the power one twelfth. By convention the note A4 is often set at 440 hertz. Doubling the power of a sound adds 3 decibels, yet doubling the power does not make a huge difference to the loudness.
The same arithmetic applies to air. A tube open at both ends has a fundamental frequency twice what it would have if closed at one end. The longest wavelength in an open cylinder is twice its length, but in a closed one, like a clarinet, it is four times the length; a tube closed at one end has only odd multiples of the fundamental, while an open tube also has the even ones, so an open tube sounds richer. The low register of the clarinet has mainly odd harmonics. A trumpet is a closed tube when pressed to the lips, so it naturally makes every other overtone of the harmonic series; a woodwind has a long, thin column of air, and the lowest note is played with all the tone holes closed, when the column is longest.
The violin emerged in northern Italy in the early sixteenth century. On a violin the bridge transfers some of the string's vibration energy to the body, and the body pushes air because it has a large surface area. The belly, the top plate, is the most important part of the body for pushing air; a small post inside the violin connects the flexible belly to the stiffer back and helps keep the belly from collapsing under the string tension. The bass bar under the bass side of the bridge spreads that foot's motion across a large area of the belly. The air inside the body is important, especially for the low range; the more complex the shape of a sounding box, the greater its ability to resonate over a wide range of frequencies.
A drumhead's overtones are inharmonic, which means they are not whole-number multiples of the fundamental. A drum body acts as a resonant cavity: a frame drum with no enclosure sounds loud but lacks depth, while a bigger enclosure gives a fuller, deeper sound. Like a string, a drumhead gives a higher pitch when its tension goes up. An African talking drum has two drumheads joined by cords, and the drummer squeezes the cords to change the pitch and mimic the tones of speech. The cuica of Brazil is a friction drum with a stick attached inside the drumhead; rubbing the stick makes vibrations, and the player changes pitch by adjusting tension. In 1914 Erich von Hornbostel and Curt Sachs published a system for sorting instruments by how they make sound. It had four classes: idiophones, chordophones, membranophones and aerophones. An idiophone is an instrument whose own body vibrates, often by being struck; a membranophone is an instrument in which a membrane or thinly stretched material is vibrated. An aerophone is an instrument in which vibrating air produces the sound. In 1940 Sachs added a fifth class, electrophones, whose sound is made by electrical means.
Bartolomeo Cristofori, who worked for the Medici family in Florence, Italy, built the first piano in the early 1700s. A harpsichord's notes came when a plectrum made from a bird's quill or leather struck the string, and the harpsichord could not change how loud a note was. Cristofori made a harpsichord that can play quietly and loudly, and the name was soon shortened to pianoforte; he built only about twenty pianos before he died in 1731. His hammers were covered in deer leather and hit the strings from below, and a piano hammer must rebound at once so the string is left to vibrate freely. The soft pedal was invented by Cristofori and so appeared on the very earliest pianos; a piano's string vibrations pass through a bridge to a soundboard.
The Leipzig Gewandhaus Orchestra was organized in 1781 from a merchants' concert society. The orchestra grew bit by bit from 1600 to 1900 but changed very little during the twentieth century. Wagner's score for Das Rheingold calls for no fewer than seven harps. Every orchestra section has a principal who generally leads the group, and the principal first violin is called the concertmaster. An orchestra has four groups of instruments: strings, woodwinds, brass and percussion. In a double-blind test, 21 professional violinists played six violins, and only 8 of the 21 chose an old violin to take home. One of the new violins was chosen most often as the take-home instrument. The test was double-blind: neither the players nor the people handing them violins could know which was which; the Stradivari family of violin makers of Cremona lived from 1644 to 1737.
One of the oldest flutes was made from the naturally hollow wing bone of a griffon vulture, with five finger holes and a V-shaped mouthpiece. Its pieces were found in 2008 at Hohle Fels, a Stone Age cave in southern Germany. Researchers say early music may have helped the first modern humans in Europe communicate and form tighter social bonds. In 1995 researchers in Slovenia found a juvenile cave bear's thigh bone with a line of small holes at a site called Divje Babe. As of 2026 scientists still disagree about how the holes were made: by people or by ice age hyenas. A replica made by a Boston University biologist suggested hyenas can make one hole, but not a row of nice, round holes all in one bone. Bone flutes between 7,000 and 9,000 years old were found at Jiahu, a site in China. Chinese researchers dated the site with 20 radiocarbon dates from charcoal, plant ash and human bone.
Robert Moog's 1964 paper described the foundation for a voltage controlled oscillator, which many later synthesizers built on. Robert Moog was fascinated by the theremin as a boy and built his first from plans in the magazine Wireless World. On a theremin the player's hand and an antenna form the two plates of a capacitor; as the hand nears the pitch antenna, the pitch gets higher; the Minimoog was the first synthesizer sold in retail music stores, and it let keyboard players compete with guitarists in solos. A joint Penn Museum and British Museum expedition to Ur in southern Iraq began in 1922; Woolley began a massive excavation there in 1926 and uncovered nearly 2,000 burials. The diggers found a great lyre with a gold and lapis lazuli bull's head, made about 2550 BCE.
Words to know
- harmonics: overtone family
- octave: a 2:1 jump
- temperament: tuning system
- inharmonic: not whole multiples
- electrophones: electric instruments
- aerophone: air instrument
