The nodes of a vibrating string are harmonics.

A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency. Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 50 Hz, 75 Hz, 100 Hz etc.

Characteristics[link]

Many oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, are more or less periodic, and so composed of harmonics.

Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at not one, but several frequencies known as partials. When the oscillator is long and thin, such as a guitar string, or the column of air in a trumpet, many of the partials are integer multiples of the fundamental frequency; these are called harmonics. Sounds made by long, thin oscillators are for the most part arranged harmonically, and these sounds are generally considered to be musically pleasing. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic. Instruments such as cymbals, pianos, and strings plucked pizzicato create inharmonic sounds.^[1][2]

The untrained human ear typically does not perceive harmonics as separate notes. Rather, a musical note composed of many harmonically related frequencies is perceived as one sound, the quality, or timbre of that sound being a result of the relative strengths of the individual harmonic frequencies. Bells have more clearly perceptible inharmonics than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic partials or multiphonics.

Harmonics and overtones[link]

The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion. This chart demonstrates how they are counted:

Harmonics are not overtones, when it comes to counting. Even numbered harmonics are odd numbered overtones and vice versa.
In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g., recorder) this has the effect of making the note go up in pitch by an octave; but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. The extended technique of playing multiphonics also produces harmonics. On string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a unison the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found half way down the highest string of a cello produces the same pitch as lightly fingering the node 1/3 of the way down the second highest string. For the human voice see Overtone singing, which uses harmonics.

While it is true that electronically produced periodic tones (e.g. square waves or other non-sinusoidal waves) have "harmonics" that are whole number multiples of the fundamental frequency, practical instruments do not all have this characteristic. For example higher "harmonics"' of piano notes are not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure harmonic series. This is especially true of instruments other than stringed or brass/woodwind ones, e.g., xylophone, drums, bells etc., where not all the overtones have a simple whole number ratio with the fundamental frequency.

The fundamental frequency is the reciprocal of the period of the periodic phenomenon.

 This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

Harmonics on stringed instruments[link]

Playing a harmonic on a string

The following table displays the stop points on a stringed instrument, such as the guitar (guitar harmonics), at which gentle touching of a string will force it into a harmonic mode when vibrated. String harmonics are described as having a "flutelike, silvery quality that can be highly effective as a special color" when used and heard in orchestration.^[3] It is unusual to encounter natural harmonics higher than the fifth partial on any stringed instrument except the double bass, on account of its much longer strings.^[4]

Table[link]

Table of harmonics of a stringed instrument with colored dots indicating which positions can be lightly fingered to generate just intervals up to the 7th harmonic

Other information[link]

Harmonics may be either used or considered as the basis of just intonation systems. Composer Arnold Dreyblatt is able to bring out different harmonics on the single string of his modified double bass by slightly altering his unique bowing technique halfway between hitting and bowing the strings. Composer Lawrence Ball uses harmonics to generate music electronically.

See also[link]

	Violin harmonics Violin natural harmonic stop points on the A string Harmonics 110x16 Demonstration of 16 harmonics using electronic sine tones, starting with 110 Hz fundamental, 0.5s each. Note that each harmonic is presented at the same signal level as the fundamental; the sample tones sound louder as they increase in frequency
Problems listening to these files? See media help.

• Aristoxenus
• Artificial harmonic
• Harmonics (electrical power)
• Electronic tuner
• Formant
• Fourier series
• Fundamental frequency
• Harmonic oscillator
• Harmonic series (music)
• Harmony
• Inharmonic
• Just intonation
• Overtones
• Pinch harmonic
• Pure tone
• Pythagorean tuning
• Scale of harmonics
• Singing bowl
• Spherical harmonics
• Stretched octave
• Subharmonic
• Tap harmonic
• Xenharmonic

References[link]

External links[link]

• Harmonics, partials and overtones from fundamental frequency
• Discussion of Sciarrino's violin etudes and notation issues
•  Chisholm, Hugh, ed. (1911). "Harmonic". Encyclopædia Britannica (11th ed.). Cambridge University Press. 
• Harmonics

Lee Oskar
Lee Oskar (standing 3rd from right) with War in 1976
Background information
Birth name	Oskar Levetin Hansen
Born	(1948-03-24) 24 March 1948 (age 64)
Origin	Copenhagen, Denmark
Genres	Rock, Funk, Blues, Jazz
Occupations	Musician, Songwriter, CEO
Instruments	Harmonica
Years active	1966–present
Associated acts	War, S.O.B. (Same Old Band), Lowrider Band
Website	http://www.leeoskar.com/

Lee Oskar (born March 24, 1948, Copenhagen, Denmark)^[1] is a Danish harmonica player,^[2] notable for his contributions to the sound of the rock-funk fusion group War, which he formed with Eric Burdon,^[3] his solo work, and as a harmonica manufacturer.^[4] He currently plays with Lowriderband, with Harold Brown, Howard Scott and B.B.Dickerson

Early life and career[link]

Born in Copenhagen, Denmark in 1948, Oskar was six years old when a family friend gave him his first harmonica.^[5] "I came from an area where every kid on the block had a harmonica," he remembers.^[6] He grew up listening to Danish radio, enjoying all types of music and cites Ray Charles as the biggest influence from that period.^[7] When he was 17, Oskar decided that the United States was where a harmonica player should make his career,^[6] so he moved to New York at the age of 18 with little more than a harmonica in his pocket.^[5] With no money, Oskar played harmonica in the streets of New York.^[6] Eventually arriving in Los Angeles, California, via Toronto and San Francisco, Oskar soon met and joined forces with Eric Burdon who had recently disbanded The Animals and was searching for new collaborators.^[8] Together, the harp-playing Dane (born Oskar Levetin Hansen^[9]) and the British blues-rock singer made the rounds of the L.A. clubs, eventually hooking up with the soon-to-be members of War.^[10] Burdon agreed to the novel idea of pairing up Oskar's harmonica with Charles Miller's saxophone to form a horn section. This team-up set War apart from the start, giving Oskar room to display the full spectrum of his improvisational prowess. Oskar's harmonica magic was always a vital element in War's music and performances. Oskar continued with War for 24 years non-stop. At the end of 1992 he made the decision to end his association with that group in order to have the time to pursue his solo career.^[10]

War[link]

Lee Oskar who has been described as "a virtuoso,"^[11] "the harmonica whiz"^[12] "a war hero,"^[13] "legendary,"^[5] "musical wizardry,"^[14] and as "generally regarded to be among the best rock-blues-soul harmonica players."^[15] His role as a founding member and former lead harmonica player of the pioneer funk-jazz group War won him international renown for over two and a half decades (1969–1993). Oskar's signature solos helped to define the War sound from the band's beginning in 1969, adding dashes of color to its R&B, jazz, rock, and Latin influences.^[14] Oskar's position with War was a prominent one from its early days with singer Eric Burdon onward.^[16] "My playing has become more aggressive over the years," he says. "In the beginning, my role was playing horn lines. Today, it's evolved to the point where I'm playing a lead instrument. If I'm not doing a solo, I'm playing counterlines—I try to paint within certain spaces in the music to help create the overall picture."

Solo career[link]

The eclectic, multicultural nature of War's music is also evident in Oskar's solo projects.^[17] Three well regarded albums released between 1976 and 1981 (and recently rereleased on CD) brought critical and popular acclaim^[18] including being voted No. 1 Instrumental Artist of the Year for 1976 in not one, but three major industry mags: Billboard, Cashbox and Record World.^[19] The albums, like Oskar's live performances, show the diverse influences of his musicality. A composer, his compositions have been featured on movie sound tracks and television commercials. He has been the recipient of many Gold and Platinum recordings and honored with special ASCAP Writing Awards.

Lee Oskar harmonica[link]

In 1983 Oskar formed a company to manufacture high-quality harmonicas. His company, Lee Oskar Harmonica, sells harmonicas suited to many different styles of music, including blues, folk, rock, R&B and country. The harmonicas themselves are manufactured by Tombo.^[1] Oskar's harmonica company celebrated its 25th anniversary in 2008 at the NAMM Show (Oskar playing one of his harmonicas at the 2008 NAMM Show).

Influences[link]

Several modern musicians, such as Mike Tetrault, cited Oskar as an important influence. When Junior Wells died, he was buried with a tray of Lee Oskar harmonicas.^[20]

References[link]

External links[link]

• http://www.leeoskar.com Lee Oskar Harmonica Company official website
• http://www.leeoskarproductions.com/ Lee Oskar Production Company official website
• Lee Oskar at the Internet Movie Database