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

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (May 2011)

The Datsuns
Background information
Origin	Cambridge, New Zealand
Genres	Hard rock, garage rock revival, heavy metal
Years active	2000–present
Labels	In-Fidelity, V2, Cooking Vinyl
Associated acts	Cold Ethyl
Website	www.thedatsuns.com
Members
Dolf de Borst Phil Somervell Ben Cole Christian Livingstone
Past members
Matt Osment

The Datsuns are a hard rock band from Cambridge, New Zealand,^[1] formed in 2000. To date they have released four albums and several singles, most of which have charted in New Zealand and/or the United Kingdom. Their projected fifth album is currently in the production stage.

History[link]

In 1995, while still at school, Rudolf de Borst (vocals, bass), Phil Somervell (guitar), and Matt Osment (drums) formed a band under the name Trinket. Christian Livingstone joined the band in 1997 as a second guitarist. They entered and won the 1999 89FM Battle of the Bands competition in Hamilton, New Zealand.

By 2000 the band had renamed themselves 'The Datsuns'. In August 2000 they released their first single, "Super Gyration!," on 7 inch vinyl only. In July 2002, after featuring several times on John Peel's programme on the UK's BBC Radio 1 and being hailed as "the future of rock" by the British music press, the band signed with the V2 record label. Their self-titled debut album made a strong impression in the UK, as well as in Australia and New Zealand. The Datsuns toured Australia in 2002 with Melbourne band The Specimens and The Casanovas as well as playing a live to air on PBS radio.

The Datsuns won numerous awards over this period, including NME 's 'Best Live Band' and New Zealand Music Awards for 'Best Album', 'Best Group' and 'Breakthrough Artist'.

They played Ozzfest in 2003 on the mainstage alongside the likes of Ozzy Osbourne, Marilyn Manson, Korn and Disturbed. They also played the main stage of the 2004 and 2009 Big Day Out festival and opened for Metallica in their Australian tour in 2004. Metallica drummer Lars Ulrich had previously praised The Datsuns on the revival debut of Headbangers Ball before playing their video for "In Love." Their second album, Outta Sight, Outta Mind, was produced by Led Zeppelin's John Paul Jones. It did not receive the same praise as the first, as critics gave it only a lukewarm response.

In October 2006, the Datsuns came back with Smoke & Mirrors, heralded as a return to form in Australia and New Zealand. The album was met with generally positive reviews, although it was not reviewed as widely as the band's first two efforts. After the release of the third album, drummer Matt Osment was replaced by Ben Cole.^[1]

The Datsuns went on a New Zealand tour with Shihad during the Christmas/New Year's period 2006/07.

The band then completed a tour of Europe to promote Smoke & Mirrors. Although playing mostly locations the band had not previously visited, The Datsuns still managed to sell out the majority of the European dates.

The band's fourth album, Head Stunts (an anagram of The Datsuns), was released on 6 October 2008. The band recently toured New Zealand, Australia and America to try out new songs such as "Eye Of The Needle", "Human Error", "So Long", "Hey Paranoid People What's In Your Head", "Your Bones" and the limited edition single "Highschool Hoodlums".

To coincide with the release of Head Stunts, the quartet embarked on a tour of the UK and Europe.^[1]

The Datsuns are currently mixing their fifth studio album, which was produced by former Hellacopters frontman Nicke Andersson. The album, titled Death Rattle Boogie, was recorded at Gutterview Recorders in Stockholm, with additional work at Roundhead Studios in New Zealand, and is due for release in 2012.

Discography[link]

Singles[link]

References[link]

External links[link]

• The Datsuns' official website
• Interview with The Datsuns about Head Stunts