by Danlee Mitchell and Jack Logan, Ph.D.

A series of different pitches with one following the other in time creates the basic musical element of Melody. Producing different pitches all of which occur at the same time creates the basic musical element of Harmony.
There are some very interesting aspects of pitch that relate to the physical world when comparing one vibrating object with another. If the pitches of two solid objects of the same material were compared, the smaller of the two would be higher in pitch when set in vibration. If the vibration of two equal lengths of string were compared, the tighter one would be higher in pitch when set in vibration. If the vibrations of two unequal lengths of string were compared with each having the same tension, the shorter one would be higher when set in vibration. Stating these relationships in another way, smaller or tighter vibrating objects are higher in pitch, and conversely, larger and looser vibrating objects are lower in pitch.
Amplitude is the physical measurement of levels of loudness and softness in sound, and, in music, the psychological term used to describe gradations of amplitude is dynamics. Loud sounds are generally associated with vigor, turmoil and conflict, while soft sounds are associated generally with repose, tranquillity and calmness. Various degrees of loudness, can sometimes cause a particular passage of music to have the foregoing characteristics. Amplitude also has a periodicity aspect about it in that music may have patterns of dynamic intensity as well as patterns of pitch length.
Timbre (Harmonic Profile) is the quality of a sound or sonic event. A few questions may lead to a more practical understanding of harmonic profile or timbre. Is it possible to determine the identity of a friend in a dark room by the "quality" of their voice? Is it possible to know who says "Hello" on the telephone before they identify themselves? Is it possible to identify the sound of a neighbor’s automobile as it approaches? Is it possible to hear the difference between the singing voices of Michael Jackson and Prince? Is it possible to hear the difference between a flute, oboe, clarinet, trumpet or saxophone if they play the same note with one instrument following the other in time? Is it possible to hear the difference between an acoustic guitar and an electric guitar? If the answer to any of the preceding questions is "yes," it is probable that humans have a natural sensitivity to timbre.
Sound vibrations are also known as sound waves or sound wave forms. The simplest sound vibration or sound wave is illustrated below in Figure 1.

When sound waves vibrate through the medium of air, they form themselves into patterns an example of which is found below in Figure 2 .

An electronic oscilloscope provides pictures of sound waves: (1) nodes are non-moving points along the field of movement, (2) the nodal axis is an imaginary straight line between nodal points, and (3) the nodal axis represents the vibrating source at rest.
The intensity (loudness or softness) of a sound is known as . A louder sound has a wider wave form than a softer sound. Figure 3 shows a comparison of two sounds (one louder-one softer) each with a different wave form.

Comparison of Two Sound Waves with Different Amplitude

A louder sound has more energy (force) than a softer sound. Faster oscillations are higher in pitch and slower oscillations are lower in pitch.

Comparison of Wave Lengths of High and Low Tones and Loud and Soft Tones

The Harmonic Series
If a listener concentrates well while hearing a single, sustained pitch (or looks at the sound waves of the pitch on an oscilloscope) the listener hears not only the strong tone of the pitch but also higher and softer pitches above the more noticeable lower tone. These additional higher and fainter pitches that occur above the stronger and lower pitch are produced by the vibrating object. Because they are softer than the lower tone they are much harder to hear. A listener must concentrate intensely to be aware of these acoustical phenomena; however, they are seen quite easily on an oscilloscope.
These higher and softer pitches occurring above the lower and louder tone are called harmonics, overtones or partials. With subtle distinctions, the words are used interchangeably. The lower tone is called the fundamental . Sometimes the word "sympathetic" is attached to the word "harmonics" because harmonics are generated (produced) by the fundamental itself and therefore vibrate sympathetically above (and faster than) the fundamental. The word "overtone" is formed from the combination of the words over and tone; thus, the reality of the physical phenomenon is made apparent in the word used as its descriptor.
Every vibrating object in nature vibrates a pitch comprised of a fundamental (the lowest and most predominant pitch) and higher sympathetic pitches called harmonics (softer and less noticeable pitches). Harmonics are generated (produced) by a fundamental sound wave that divides its length into smaller vibrating sections (which sound higher and softer). This series of divisions begins with a division of the whole wave into two (2) equal parts; then, in order from low to high: three (3) equal parts, four (4) equal parts, five (5) equal parts, six (6) equal parts, seven (7) equal parts, eight (8) equal parts and continues successively to infinity. These divisions of the whole fundamental sound wave are called harmonics, overtones or partials.

The harmonic series is illustrated below with the fundamental at the bottom and harmonics above the fundamental.

The Harmonic Series as the Basis of Intervals, Melody, Harmony, and Timbre
The "distance" between two pitches is known as an interval. If two different objects are vibrating at exactly the same pitch, the interval produced is known as a unison and has a mathematical ratio of 1:1 (one to one). If one of two different pitches vibrates at exactly twice the speed of the other (a 2:1 ratio), the interval produced is known as an octave.
The octave is the lowest interval in the harmonic series and enjoys its unique and characteristic sound quality because of the distance between the fundamental tone and the first overtone of the harmonic series. Most World music cultures recognize the music interval known as the octave and most divide the octave into sub-intervals that comprise the particular pitches for the scales unique to each World culture.
Scale may be defined as the number of pitches that divide an octave and the intervals between those pitches. All World music cultures have different numbers of pitches in their scales, different intervals between pitches and different methods of creating scales. However, scales of all World cultures have two elements in common -- they use some division of the octave and the interval between the first and last tones of all scales is the octave.

Harmonic Profile, Sound Signature, and Voice Print
When listening to a tone with its fundamental and overtones a listener should be aware that certain harmonics are stronger than others or they are missing entirely. The visual pattern (generated on an oscilloscope) of relative strength of harmonics of a given pitch, produced by a given source, constitute what may be called the harmonic profile or sound signature of that source.
Every individual, whether speaking or singing, produces (with each pitch spoken or sung) a fundamental plus a series of harmonics. The pattern of relative strength of these harmonics is different in each individual voice and this individual harmonic series pattern determines the voice quality of an individual. Sound "quality" is determined by the harmonic profile or sound signature as a direct result of the specific pattern of intensity of individual components of the harmonic series of the sound source. The friend-in-the-dark's voice or the initial "Hello" on the telephone are both determined by the quality (harmonic pattern) of the voice. The human ear is very sensitive to harmonic profile or sound signature. In the world of crime detection, the unique quality of a specific human voice is called a "voice print". Individuals may be identified accurately by electronic analysis of their recorded voices.
Music instruments also possess a unique harmonic profile and individuals discern the difference between musical instruments by their unique tone quality. All musical instruments of the same family have the same general tone quality.
If a natural sound source has its harmonic profile electronically filtered and the harmonics of the source completely removed (or even partially removed), it is very difficult for the human ear to determine the source of the sound. A sound wave without any harmonic content is called a pure sine wave. Artificial sounds may be produced by electronic synthesis, and, for a given electronic sound, any number of harmonic profile combinations may be synthesized. By electronic synthesis the sounds of natural, acoustic instruments and human voices may be approximated, but individuals can often differentiate between natural sounds and electronically synthesized sounds. Synthesized sound technology is used extensively in all types of current musical activity, from the musical fine arts to popular culture and from movies to rock and roll.

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