Tyler Wynn
The presence of overtones in sounds is a topic that has been widely explored in music and acoustics. Overtones, also known as harmonics or resonances, are higher-frequency standing waves that occur when a note is played on an instrument, and the different modes of the instrument vibrate, each contributing its own frequency. This creates a rich and warm tone quality, but it can also make the pitch less distinct. The overtone series plays a crucial role in the analysis of musical instruments and tone quality, and composers often use overtones to create harmonies by playing notes with simple frequency relationships, causing the notes to 'blend together'. However, not all sounds have overtones, and pure notes, for example, have a shape that is a sine wave without any overtones. Additionally, some instruments may produce overtones that are slightly sharper or flatter than true harmonics, resulting in dissonance.
| Characteristics | Values |
|---|---|
| Definition of Overtone | A partial (a "partial wave" or "constituent frequency") that can be either a harmonic partial (a harmonic) other than the fundamental, or an inharmonic partial. |
| Harmonic Frequency | An integer multiple of the fundamental frequency. |
| Inharmonic Frequency | A non-integer multiple of a fundamental frequency. |
| Pure Note | A pure note, one with no overtones, has a shape that is a sine wave. |
| Musical Instruments and Overtones | For most string instruments and other long and thin instruments, the first few overtones are quite close to integer multiples of the fundamental frequency, producing an approximation to a harmonic series. |
| Wind Instruments and Overtones | Wind instruments manipulate the overtone series in the normal production of sound, but techniques like "overblowing" can cause notes to split into their overtones. |
| Non-Western Instruments and Overtones | Non-Western wind instruments like the didgeridoo are highly dependent on the interaction and manipulation of overtones achieved by the performer changing their mouth shape. |
| High-Quality Instruments and Overtones | "High-quality" instruments are usually built so that their individual notes do not create disharmonious overtones. |
| Singing and Overtones | Singers practicing polyphonic overtone singing can amplify the overtones of the voice by creating a second resonance chamber in the mouth with tongue positioning. |
| Hearing Overtones | With training, it is possible to hear overtones. Once you start hearing them, it becomes hard not to notice them. |
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What You'll Learn
Pure notes and sine waves
A pure note, or pure tone, is a sound with a sinusoidal waveform, or a sine wave, of constant frequency, phase shift, and amplitude. Pure tones are used in psychoacoustics and signal processing. In signal processing, a pure tone is a purely sinusoidal signal, such as voltage.
Pure tones have been used by physicists to support theories about how the ear functions. For example, in Ohm's acoustic law, musical tones are perceived as a set of pure tones. The pitch is dependent on the frequency of the most prominent tone. Unlike musical tones, which are made up of several harmonically related sinusoidal components, pure tones only contain one such waveform. When presented in isolation, and when its frequency pertains to a certain range, pure tones give rise to a single pitch percept, which can be characterized by its frequency.
Pure tones are also used in clinical audiology for pure-tone audiometry to characterize hearing thresholds at different frequencies. When looking at the waveform of a pure tone on an oscilloscope, it appears as a sine wave. The y-axis represents air pressure or air displacement (loudness), and the x-axis represents time, with the wave period defining pitch.
A pure note, or a note with no overtones, has the shape of a sine wave. Overtones are partial waves or frequencies that are either harmonic or inharmonic partials. Harmonic overtones are integer multiples of the fundamental frequency, while inharmonic overtones are non-integer multiples. When a note is sounded on an instrument, all the different modes of the instrument can start vibrating, and each mode contributes its own frequency to the overall sound produced, resulting in overtones.
By adding additional sine waves with different frequencies to a pure tone, the waveform transforms from a sinusoidal shape into a more complex shape. This allows for the independent control of tone quality without affecting the pitch.
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String instruments and overtones
An overtone is any resonant frequency above the fundamental frequency of a sound. In other words, overtones are all pitches higher than the lowest pitch within an individual sound. The fundamental frequency is usually heard most prominently, but overtones are present in any pitch except a true sine wave.
String instruments can also produce multiphonic tones when strings are divided into two pieces or the sound is somehow distorted. The sitar, for example, has sympathetic strings that help bring out the overtones while playing. Western string instruments, such as the violin, may be played close to the bridge (a technique called "sul ponticello" or "am Steg"), which causes the note to split into overtones. The violin can be plucked or bowed, and these two ways of playing the note sound different even if the pitch and the instrument are the same. What is changing is the amount of each overtone contributing to the tone quality.
The stiffness of the string also affects the overtone series and the tone quality. A violin string has some stiffness, while a guitar string is more flexible, and a piece of thread or dental floss is perfectly flexible. Piano strings are so stiff that they are rather hard to work with. As the stiffness of a string increases, the overtones become higher than they should be, and the musical term for this is that the overtones become "sharper". Ultimately, the strings become so stiff that the overtones will be too far out of tune to sound good.
For most string instruments and other long and thin instruments such as a bassoon, the first few overtones are quite close to integer multiples of the fundamental frequency, producing an approximation to a harmonic series. Depending on how the string is plucked or bowed, different overtones can be emphasized. However, some overtones in some instruments may not be of a close integer multiplication of the fundamental frequency, thus causing a small dissonance. "High-quality" instruments are usually built in such a manner that their individual notes do not create disharmonious overtones.
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Wind instruments and overtones
Wind instruments manipulate the overtone series significantly in the normal production of sound. However, various playing techniques may be used to produce multiphonics, which bring out the overtones of the instrument. On many woodwind instruments, alternate fingerings are used. "Overblowing", or adding intensely exaggerated air pressure, can also cause notes to split into their overtones. In brass instruments, multiphonics may be produced by singing into the instrument while playing a note simultaneously, causing the two pitches to interact. If the sung pitch is at specific harmonic intervals with the played pitch, the two sounds will blend and produce additional notes by the phenomenon of sum and difference tones.
Non-Western wind instruments also exploit overtones in playing, and some may highlight the overtone sound exceptionally. Instruments like the didgeridoo are highly dependent on the interaction and manipulation of overtones achieved by the performer changing their mouth shape while playing, or singing and playing simultaneously. Likewise, when playing a harmonica or pitch pipe, one may alter the shape of their mouth to amplify specific overtones. Though not a wind instrument, a similar technique is used for playing the jaw harp: the performer amplifies the instrument's overtones by changing the shape and, therefore, the resonance of their vocal tract.
Brass instruments originally had no valves and could only play the notes in the natural overtone or harmonic series. Brass instruments still rely heavily on the overtone series to produce notes. The tuba typically has 3-4 valves, the tenor trombone has 7 slide positions, the trumpet has 3 valves, and the French horn typically has 4 valves. Each instrument can play (within their respective ranges) the notes of the overtone series in different keys with each fingering combination (open, 1, 2, 12, 123, etc). The first valve lowers the major 2nd, the second valve lowers the minor 2nd, the third valve lowers the minor 3rd, and the fourth valve lowers the perfect 4th.
The French horn, for example, was originally a valveless instrument that could only play the notes of the harmonic series. Similar arguments apply to vibrating air columns in wind instruments, although these are complicated by the possibility of anti-nodes (i.e., the air column is closed at one end and open at the other), conical as opposed to cylindrical bores, or end-openings that run the gamut from no flare, cone flare, or exponentially shaped flares (such as in various bells).
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Harmonics and pitch
The presence of overtones is what gives each musical instrument its unique sound. An overtone is a partial or "constituent frequency" that can be either a harmonic partial (a harmonic) other than the fundamental frequency, or an inharmonic partial. In other words, an overtone is any higher-frequency standing wave, while a harmonic is a wave whose frequency is an integer multiple of the fundamental frequency.
When a note is played on an instrument, all the different modes of the instrument start vibrating, and each mode contributes its own frequency to the overall sound produced. This is what makes each instrument sound different or gives it its unique tone quality or timbre. However, not all sounds have overtones. A pure note, one with no overtones, has a shape that is a sine wave.
Harmonics and overtones are closely related. The overtone series is a sequence of frequencies that plays an important role in the analysis of musical instruments and musical tone quality. The first overtone is the second harmonic, the third overtone is the third harmonic, and so on. When harmonics are added to the fundamental frequency, the shape of the wave changes, but not its pitch. This allows for independent control of tone quality without affecting pitch.
Different playing techniques can be used to manipulate overtones on various instruments. For example, on string instruments, the way a string is plucked or bowed can emphasize different overtones. On woodwind instruments, alternate fingerings or "overblowing" (adding intense air pressure) can be used to produce multiphonics and bring out the overtones. In brass instruments, singing into the instrument while playing a note can create additional notes through the phenomenon of sum and difference tones.
The design of instruments also takes into account the interaction of harmonics and overtones. For example, the flared end of a brass instrument is not to make the instrument sound louder but to correct for tube length "end effects" that would otherwise affect the overtones. In guitars, the bridge is angled so that the thinner strings are slightly shorter than the thicker strings to avoid inharmonious chords. Similarly, the construction of piano strings involves considerations of tension and diameter to manage the stiffness of the strings and the resulting overtones.
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The overtone series in orchestration
The overtone series is a sequence of harmonics or musical tones whose frequencies are integer multiples of a fundamental frequency. In other words, overtones are all pitches higher than the lowest pitch within an individual sound. The fundamental frequency is the lowest pitch and is usually heard most prominently. However, overtones are present in any pitch except a true sine wave.
The overtone series is highly significant in orchestration, as it can be used as a guide for arranging chords and composing music. Nikolai Rimsky-Korsakov, in his treatise "Principles of Orchestration," emphasised the importance of the overtone series in orchestration. He demonstrated how to voice a C major triad according to the overtone series, utilising partials 1, 2, 3, 4, 5, 6, 8, 10, 12, and 16.
Orchestration involves both technique and creativity, and the overtone series serves as a valuable tool for composers and orchestrators. By understanding the overtone series, they can utilise its characteristics for musical storytelling. The overtone series provides a sense of familiarity to the human ear, as it has been a part of our auditory experience since ancient times. This familiarity can be leveraged to create a sense of home or resolution in a musical piece.
Additionally, the overtone series helps composers and orchestrators understand the unique characteristics of different instruments. Each instrument produces a distinct set of overtones, contributing to its individual timbre or tone colour. This knowledge is crucial for arranging and blending instruments in an orchestra to create a harmonious sound.
Furthermore, playing techniques can be employed to manipulate the overtone series and bring out the overtones of an instrument. For example, on woodwind instruments, alternate fingerings and "overblowing" techniques can be used to produce multiphonics and emphasise overtones. Similarly, brass instruments can create multiphonics by singing into the instrument while playing a note, resulting in the interaction of different pitches.
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Frequently asked questions
Overtones are partials or frequencies that are generated when a note is played on an instrument. These overtones are what give each instrument its own unique sound or timbre.
All sounds are technically made from a combination of sine waves that form a timbre. However, a pure note, one with no overtones, has a shape that is a sine wave.
Overtones are important in creating harmonies in music. Composers often play notes together that have simple frequency relationships, causing the notes to blend together' and create a single sound.
