Overtone

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Vibrational modes of an ideal string, dividing the string length into integer divisions, producing harmonic partials f, 2f, 3f, 4f, etc. (where f means fundamental frequency). Harmonic partials on strings.svg
Vibrational modes of an ideal string, dividing the string length into integer divisions, producing harmonic partials f, 2f, 3f, 4f, etc. (where f means fundamental frequency).

An overtone is any frequency greater than the fundamental frequency of a sound. [1] In other words, overtones are higher pitches resulting from the lowest note or fundamental. While the fundamental is usually heard most prominently, overtones are actually present in any pitch except a true sine wave. [2] The relative volume or amplitude of various overtone partials is one of the key identifying features of timbre, or the individual characteristic of a sound. [3]

Contents

Using the model of Fourier analysis, the fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental (including the fundamental, which is 1 times itself). These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. [4] (See etymology below.) The model of Fourier analysis provides for the inclusion of inharmonic partials, which are partials whose frequencies are not whole-number ratios of the fundamental (such as 1.1 or 2.14179).

main tone (110 Hz) and first 15 overtones (16 harmonic partials) (listen)
Allowed and forbidden standing waves, and thus harmonics Allowed and forbidden standing waves.png
Allowed and forbidden standing waves, and thus harmonics

When a resonant system such as a blown pipe or plucked string is excited, a number of overtones may be produced along with the fundamental tone. In simple cases, such as for most musical instruments, the frequencies of these tones are the same as (or close to) the harmonics. Examples of exceptions include the circular drum – a timpani whose first overtone is about 1.6 times its fundamental resonance frequency, [5] gongs and cymbals, and brass instruments. The human vocal tract is able to produce highly variable amplitudes of the overtones, called formants, which define different vowels. [6]

Explanation

Most oscillators, from a plucked guitar string to a flute that is blown, will naturally vibrate at a series of distinct frequencies known as normal modes. The lowest normal mode frequency is known as the fundamental frequency, while the higher frequencies are called overtones. Often, when an oscillator is excited — for example, by plucking a guitar string — it will oscillate at several of its modal frequencies at the same time. So when a note is played, this gives the sensation of hearing other frequencies (overtones) above the lowest frequency (the fundamental).

Timbre is the quality that gives the listener the ability to distinguish between the sound of different instruments. The timbre of an instrument is determined by which overtones it emphasizes. That is to say, the relative volumes of these overtones to each other determines the specific "flavor", "color" or "tone" of sound of that family of instruments. The intensity of each of these overtones is rarely constant for the duration of a note. Over time, different overtones may decay at different rates, causing the relative intensity of each overtone to rise or fall independent of the overall volume of the sound. A carefully trained ear can hear these changes even in a single note. This is why the timbre of a note may be perceived differently when played staccato or legato.

A driven non-linear oscillator, such as the vocal folds, a blown wind instrument, or a bowed violin string (but not a struck guitar string or bell) will oscillate in a periodic, non-sinusoidal manner. This generates the impression of sound at integer multiple frequencies of the fundamental known as harmonics, or more precisely, harmonic partials. 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. Thus, in music, overtones are often called harmonics. Depending upon 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. In fact, 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 make the overtones significantly different from integer harmonics. This is illustrated by the following:

Consider a guitar string. Its idealized 1st overtone would be exactly twice its fundamental if its length were shortened by ½, perhaps by lightly pressing a guitar string at the 12th fret; however, if a vibrating string is examined, it will be seen that the string does not vibrate flush to the bridge and nut, but it instead has a small “dead length” of string at each end. [7] This dead length actually varies from string to string, being more pronounced with thicker and/or stiffer strings. This means that halving the physical string length does not halve the actual string vibration length, and, hence, the overtones will not be exact multiples of a fundamental frequency. The effect is so pronounced that properly set up guitars will angle the bridge such that the thinner strings will progressively have a length up to few millimeters shorter than the thicker strings. Not doing so would result in inharmonious chords made up of two or more strings. Similar considerations apply to tube instruments.

Musical usage term

Physical representation of third (O3) and fifth (O5) overtones of a cylindrical pipe closed at one end. F is the fundamental frequency; the third overtone is the third harmonic, 3F, and the fifth overtone is the fifth harmonic, 5F for such a pipe, which is a good model for a panflute. Overtones (most properly numbered) of closed pipe.png
Physical representation of third (O3) and fifth (O5) overtones of a cylindrical pipe closed at one end. F is the fundamental frequency; the third overtone is the third harmonic, 3F, and the fifth overtone is the fifth harmonic, 5F for such a pipe, which is a good model for a panflute.

An overtone is 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. A harmonic frequency is an integer multiple of the fundamental frequency. An inharmonic frequency is a non-integer multiple of a fundamental frequency.

An example of harmonic overtones: (absolute harmony)

FrequencyOrderName 1Name 2Name 3
1 · f =   440 Hzn = 1 fundamental tone 1st harmonic1st partial
2 · f =   880 Hzn = 21st overtone2nd harmonic2nd partial
3 · f = 1320 Hzn = 32nd overtone3rd harmonic3rd partial
4 · f = 1760 Hzn = 43rd overtone4th harmonic4th partial

Some musical instruments[ which? ] produce overtones that are slightly sharper or flatter than true harmonics. The sharpness or flatness of their overtones is one of the elements that contributes to their sound. Due to phase inconsistencies [9] between the fundamental and the partial harmonic, this also has the effect of making their waveforms not perfectly periodic.

Musical instruments that can create notes of any desired duration and definite pitch have harmonic partials. A tuning fork, provided it is sounded with a mallet (or equivalent) that is reasonably soft, has a tone that consists very nearly of the fundamental, alone; it has a sinusoidal waveform. Nevertheless, music consisting of pure sinusoids was found to be unsatisfactory in the early 20th century. [10]

Etymology

In Hermann von Helmholtz's classic "On The Sensations Of Tone" he used the German "Obertöne" which was a contraction of "Oberpartialtöne", or in English: "upper partial tones". According to Alexander Ellis (in pages 24–25 of his English translation of Helmholtz), the similarity of German "ober" to English "over" caused a Prof. Tyndall to mistranslate Helmholtz' term, thus creating "overtone". [4] Ellis disparages the term "overtone" for its awkward implications. Because "overtone" makes the upper partials seem like such a distinct phenomena, it leads to the mathematical problem where the first overtone is the second partial. Also, unlike discussion of "partials", the word "overtone" has connotations that have led people to wonder about the presence of "undertones" (a term sometimes confused with "difference tones" but also used in speculation about a hypothetical "undertone series").

"Overtones" in choral music

In barbershop music, a style of four-part singing, the word overtone is often used in a related but particular manner. It refers to a psychoacoustic effect in which a listener hears an audible pitch that is higher than, and different from, the fundamentals of the four pitches being sung by the quartet. The barbershop singer's "overtone" is created by the interactions of the upper partial tones in each singer's note (and by sum and difference frequencies created by nonlinear interactions within the ear). Similar effects can be found in other a cappella polyphonic music such as the music of the Republic of Georgia and the Sardinian cantu a tenore . Overtones are naturally highlighted when singing in a particularly resonant space, such as a church; one theory of the development of polyphony in Europe holds that singers of Gregorian chant, originally monophonic, began to hear the overtones of their monophonic song and to imitate these pitches - with the fifth, octave, and major third being the loudest vocal overtones, it is one explanation of the development of the triad and the idea of consonance in music.

The first step in composing choral music with overtone singing is to discover what the singers can be expected to do successfully without extensive practice. The second step is to find a musical context in which those techniques could be effective, not mere special effects. It was initially hypothesized that beginners would be able to: [11]

Singers should not be asked to change the fundamental pitch while overtone singing and changing partials should always be to an adjacent partial. When a particular partial is to be specified, time should be allowed (a beat or so) for the singers to get the harmonics to "speak" and find the correct one. [11]

String instruments

Playing a harmonic on a string. Here, "+7" indicates that the string is held down at the position for raising the pitch by 7 half notes, that is, at the seventh fret for a fretted instrument. Flageolette.svg
Playing a harmonic on a string. Here, "+7" indicates that the string is held down at the position for raising the pitch by 7 half notes, that is, at the seventh fret for a fretted instrument.

String instruments can also produce multiphonic tones when strings are divided in two pieces or the sound is somehow distorted. The Sitar has sympathetic strings which help to bring out the overtones while one is playing. The overtones are also highly important in the Tanpura, the drone instrument in traditional North and South Indian music, in which loose strings tuned at octaves and fifths are plucked and designed to buzz to create sympathetic resonance and highlight the cascading sound of the overtones.

Western string instruments, such as the violin, may be played close to the bridge (a technique called "sul ponticello [12] " or "am Steg") which causes the note to split into overtones while attaining a distinctive glassy, metallic sound. Various techniques of bow pressure may also be used to bring out the overtones, as well as using string nodes to produce natural harmonics. On violin family instruments, overtones can be played with the bow or by plucking. Scores and parts for Western violin family instruments indicate where the performer is to play harmonics. The most well-known technique on a guitar is playing flageolet tones or using distortion effects. The Ancient Chinese instrument the Guqin contains a scale based on the knotted positions of overtones. Also the Vietnamese Đàn bầu functions on flageolet tones. Other multiphonic extended techniques used are prepared piano, prepared guitar and 3rd bridge.

Violin

Viola

Cello

Double Bass

Guitar

Wind instruments

Wind instruments manipulate the overtone series significantly in the normal production of sound, but 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 [13] ", 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 at the same time, 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

Brass instruments originally had no valves, and could only play the notes in the natural overtone, or harmonic series. [14]

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 role of each valve or rotor (excluding trombone) is as follows: 1st valve lowers major 2nd, 2nd valve lowers minor 2nd, 3rd valve-lowers minor 3rd, 4th valve-lowers perfect 4th (found on piccolo trumpet, certain euphoniums, and many tubas). [15] The French horn has a trigger key that opens other tubing and is pitched a perfect fourth higher; this allows for greater ease between different registers of the instrument. [15] Valves allow brass instruments to play chromatic notes, as well as notes within the overtone series (open valve = C overtone series, 2nd valve = B overtone series on the C Trumpet) by changing air speed and lip vibrations.

The tuba, trombone, and trumpet play notes within the first few octaves of the overtone series, where the partials are farther apart. The French horn sounds notes in a higher octave of the overtone series, so the partials are closer together and make it more difficult to play the correct pitches and partials. [14]

Overtone singing

Overtone singing is a traditional form of singing in many parts of the Himalayas and Altay; Tibetans, Mongols and Tuvans are known for their overtone singing. In these contexts it is often referred to as throat singing or khoomei, though it should not be confused with Inuit throat singing, which is produced by different means. There are also possibility to create the overtone out of fundamental tone without any stress on the throat.

Also, the overtone is very important in singing to take care of vocal tract shaping, to improve color, resonance, and text declamation. During practice overtone singing, it helps the singer to remove unnecessary pressure on the muscle, especially around the throat. So if one can "find" a single overtone, then one will know where the sensation needs to be in order to bring out vocal resonance in general, helping to find the resonance in one's own voice on any vowel and in any register. [16]

Overtones in Music Composition

The primacy of the triad in Western harmony comes from the first four partials of the overtone series. The eighth through fourteenth partials resemble the equal tempered acoustic scale:

Overtone

When this scale is rendered as a chord, it is called the lydian dominant thirteenth chord. [17] This chord appears throughout Western music, but is notably used as the basis of jazz harmony, features prominently in the music of Franz Liszt, Claude Debussy, [18] Maurice Ravel, and appears as the Mystic chord in the music of Alexander Scriabin. [19] [20] [21]

Rimsky-Korsakov's voicing of a C major triad, consisting of the fundamental and partials 1, 2, 3, 4, 5, 7, 9, 11, and 15. Rimsky-korsakov-overtone-chord-deomonstration.png
Rimsky-Korsakov's voicing of a C major triad, consisting of the fundamental and partials 1, 2, 3, 4, 5, 7, 9, 11, and 15.

Because the overtone series rises infinitely from the fundamental with no periodicity, in Western music the equal temperament scale was designed to create synchronicity between different octaves. [2] [22] This was achieved by de-tuning certain intervals, such as the perfect fifth. A true perfect fifth is 702 cents above the fundamental, but equal temperament flattens it by two cents. The difference is only barely perceptible, and allows both for the illusion of the scale being in-tune with itself across multiple octaves, and for tonalities based on all 12 chromatic notes to sound in-tune. [23]

Western classical composers have also made use of the overtone series through orchestration. In his treatise "Principles of Orchestration," Russian composer Nikolai Rimsky-Korsakov says the overtone series "may serve as a guide to the orchestral arrangement of chords." [24] Rimsky-Korsakov then demonstrates how to voice a C major triad according to the overtone series, using partials 1, 2, 3, 4, 5, 7, 9, 11, and 15.

In the 20th century, exposure to non-Western music and further scientific acoustical discoveries led some Western composers to explore alternate tuning systems. Harry Partch for example designed a tuning system that divides the octave into 43 tones, with each tone based on the overtone series. [25] The music of Ben Johnston uses many different tuning systems, including his String Quartet No. 5 which divides the octave into more than 100 tones. [26]

Spectral music is a genre developed by Gérard Grisey and Tristan Murail in the 1970s and 80s, under the auspices of IRCAM. Broadly, spectral music deals with resonance and acoustics as compositional elements. For example, in Grisey's seminal work Partiels , the composer used a sonogram to analyze the true sonic characteristics of the lowest note on a tenor trombone (E2). [2] The analysis revealed which overtones were most prominent from that sound, and Partiels was then composed around the analysis. Another seminal spectral work is Tristan Murail's Gondwana for orchestra. This work begins with a spectral analysis of a bell, and gradually transforms it into the spectral analysis of a brass instrument. [2] Other spectralists and post-spectralists include Jonathan Harvey, Kaija Saariaho, and Georg Friedrich Haas.

John Luther Adams is known for his extensive use of the overtone series, as well as his tendency to allow musicians to make their own groupings and play at their own pace to alter the sonic experience. [27] For example, his piece Sila: The Breath of the World can be played by 16 to 80 musicians and are separated into their own groups. The piece is set on sixteen "harmonic clouds" that are grounded on the first sixteen overtones of low B-flat. Another example is John Luther Adam's piece Everything That Rises, which grew our of his piece Sila: The Breath of the World. Everything That Rises is a piece for string quartet that has sixteen harmonic clouds that are built off of the fundamental tone (C0) [28]

See also

Related Research Articles

Brass instrument Class of musical instruments

A brass instrument is a musical instrument that produces sound by sympathetic vibration of air in a tubular resonator in sympathy with the vibration of the player's lips. Brass instruments are also called labrosones or labrophones, from Latin and Greek elements meaning 'lip' and 'sound'.

Harmonic series (music) Sequence of frequencies

A harmonic series is the sequence of frequencies, musical tones, or pure tones in which each frequency is an integer multiple of a fundamental.

Musical tuning Terms for tuning an instrument and a systems of pitches

In music, there are two common meanings for tuning:

Pitch of brass instruments

The pitch of a brass instrument corresponds to the lowest playable resonance frequency of the open instrument. The combined resonances resemble a harmonic series. The fundamental frequency of the harmonic series can be varied by adjusting the length of the tubing using the instrument's valve, slide, key or crook system, while the player's embouchure, lip tension and air flow serve to select a specific harmonic from the available series for playing. The fundamental is actually missing from the resonances and is impractical to play on some brass instruments, but the overtones account for most pitches.

Trumpet Musical instrument

The trumpet is a brass instrument commonly used in classical and jazz ensembles. The trumpet group ranges from the piccolo trumpet with the highest register in the brass family, to the bass trumpet, which is pitched one octave below the standard B or C Trumpet.

Harmonic

A harmonic is any member of the harmonic series. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as sinusoidal waves. A harmonic is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is also called the 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz, 150 Hz, 200 Hz and any addition of waves with these frequencies is periodic at 50 Hz.

An nth characteristic mode, for n > 1, will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at L and L, where L is the length of the string. In fact, each nth characteristic mode, for n not a multiple of 3, will not have nodes at these points. These other characteristic modes will be vibrating at the positions L and L. If the player gently touches one of these positions, then these other characteristic modes will be suppressed. The tonal harmonics from these other characteristic modes will then also be suppressed. Consequently, the tonal harmonics from the nth characteristic modes, where n is a multiple of 3, will be made relatively more prominent.

Transposing instrument Musical instrument for which notated pitch differs from sounding pitch

A transposing instrument is a musical instrument for which music notation is not written at concert pitch. For example, playing a written middle C on a transposing instrument produces a pitch other than middle C; that sounding pitch identifies the interval of transposition when describing the instrument. Playing a written C on clarinet or soprano saxophone produces a concert B, so these are referred to as B instruments. Providing transposed music for these instruments is a convention of musical notation. The instruments do not transpose the music, rather their music is written at a transposed pitch. Where chords are indicated for improvisation they are also written in the appropriate transposed form.

Inharmonicity

In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency.

Piano acoustics are the physical properties of the piano that affect its sound. It is an area of study within musical acoustics.

Overblowing is a technique used while playing a wind instrument that causes the sounded pitch to jump to a higher one primarily through the manipulation of the supplied air rather than by a fingering change or the operation of a slide. Depending on the instrument, and to a lesser extent the player, overblowing may involve a change in the air pressure, in the point at which the air is directed, or in the resonance characteristics of the chamber formed by the mouth and throat of the player. In some instruments, overblowing may also involve the direct manipulation of the vibrating reed(s), and/or the pushing of a register key while otherwise leaving fingering unaltered. With the exception of harmonica overblowing, the pitch jump is from one vibratory mode of the reed or air column, e.g., its fundamental, to an overtone. Overblowing can be done deliberately in order to get a higher pitch, or inadvertently, resulting in the production of a note other than that intended.

Pedal tone

Pedal tones are special low notes in the harmonic series of brass instruments. A pedal tone has the pitch of its harmonic series' fundamental tone. Its name comes from the foot pedal keyboard pedals of a pipe organ, which are used to play 16' and 32' sub-bass notes by pressing the pedals with the player's feet. Brasses with a bell do not naturally vibrate at this frequency.

Tanpura Indian drone instrument

The tanpura is a long-necked plucked string instrument, originating from India, found in various forms in Indian music. It does not play melody but rather supports and sustains the melody of another instrument or singer by providing a continuous harmonic bourdon or drone. A tanpura is not played in rhythm with the soloist or percussionist: as the precise timing of plucking a cycle of four strings in a continuous loop is a determinant factor in the resultant sound, it is played unchangingly during the complete performance. The repeated cycle of plucking all strings creates the sonic canvas on which the melody of the raga is drawn. The combined sound of all strings, each string a fundamental tone with its own spectrum of overtones, supports and blend with the external tones sung or played by the soloist.

Piano tuning

Piano tuning is the act of adjusting the tension of the strings of an acoustic piano so that the musical intervals between strings are in tune. The meaning of the term 'in tune', in the context of piano tuning, is not simply a particular fixed set of pitches. Fine piano tuning requires an assessment of the vibration interaction among notes, which is different for every piano, thus in practice requiring slightly different pitches from any theoretical standard. Pianos are usually tuned to a modified version of the system called equal temperament.

Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology, physiology, music theory, ethnomusicology, signal processing and instrument building, among other disciplines. As a branch of acoustics, it is concerned with researching and describing the physics of music – how sounds are employed to make music. Examples of areas of study are the function of musical instruments, the human voice, computer analysis of melody, and in the clinical use of music in music therapy.

A multiphonic is an extended technique on a monophonic musical instrument in which several notes are produced at once. This includes wind, reed, and brass instruments, as well as the human voice. Multiphonic-like sounds on string instruments, both bowed and hammered, have also been called multiphonics, for lack of better terminology and scarcity of research.

Acoustic resonance resonance phenomena in sound and musical devices

Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration.

In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways. While the overtone series is based upon arithmetic multiplication of frequencies, resulting in a harmonic series, the undertone series is based on arithmetic division.

String harmonic

Playing a string harmonic is a string instrument technique that uses the nodes of natural harmonics of a musical string to isolate overtones. Playing string harmonics produces high pitched tones, often compared in timbre to a whistle or flute. Overtones can be isolated "by lightly touching the string with the finger instead of pressing it down" against the fingerboard.

Moodswinger

The Moodswinger is a twelve-string electric zither with an additional third bridge designed by Yuri Landman. The rod which functions as the third bridge divides the strings into two sections to cause an overtone multiphonic sound. One of the copies of the instrument is part of the collection of the Musical Instrument Museum in Phoenix, Arizona.

3rd bridge

The 3rd bridge is an extended playing technique used on the electric guitar and other string instruments that allows a musician to produce distinctive timbres and overtones that are unavailable on a conventional string instrument with two bridges. The timbre created with this technique is close to that of gamelan instruments like the bonang and similar Indonesian types of pitched gongs.

A third bridge can be devised by inserting a rigid preparation object between the strings and the body or neck of the instrument, effectively diving the string into distinct vibrating segments.

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