<?xml version="1.0"?>
<feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en">
	<id>https://en.formulasearchengine.com/w/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=99.109.198.230</id>
	<title>formulasearchengine - User contributions [en]</title>
	<link rel="self" type="application/atom+xml" href="https://en.formulasearchengine.com/w/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=99.109.198.230"/>
	<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/wiki/Special:Contributions/99.109.198.230"/>
	<updated>2026-08-26T08:20:39Z</updated>
	<subtitle>User contributions</subtitle>
	<generator>MediaWiki 1.47.0-wmf.7</generator>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Local_exchange_carrier&amp;diff=1577</id>
		<title>Local exchange carrier</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Local_exchange_carrier&amp;diff=1577"/>
		<updated>2013-05-18T21:07:46Z</updated>

		<summary type="html">&lt;p&gt;99.109.198.230: /* External links */  (broken link 5/18/13)&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{Refimprove|date=January 2013}}&lt;br /&gt;
[[File:HK 佐敦 Jordan 裕華國貨 Yue Hwa Chinese Products Emporium 琵琶 Music 二胡 String instruments.jpg|thumb|right|300px|Various stringed instruments of Chinese make on display in a shop.]]&lt;br /&gt;
&#039;&#039;&#039;String instruments&#039;&#039;&#039; are [[musical instrument]]s that produce sound from vibrating strings. In most strings instruments, the vibrations are transmitted to the body of the instrument, which also vibrate, along the air inside it.  In the [[Hornbostel-Sachs]] scheme of [[musical instrument classification]], used in [[organology]], they are called [[chordophone]]s. Some common instruments in the string family are [[violin family|violin]], [[guitar]], [[sitar]], [[electric bass]], [[viola]], [[cello]], [[harp]], [[double bass]], [[rabab]], [[banjo]], [[mandolin]], [[ukulele]], and [[bouzouki]].&lt;br /&gt;
&lt;br /&gt;
==History==&lt;br /&gt;
[[File:StringInstruMAPDF.JPG|thumb|325px|Various string instruments on display at the [[Museo de Arte Popular]] in Mexico City.]] &lt;br /&gt;
Early string instruments have been excavated in [[ancient Mesopotamia]], like the [[lyres of Ur]], which date to 2500 BC.&amp;lt;ref name=&amp;quot;mp&amp;quot;&amp;gt;{{cite book|author=Michael Chanan|title=Musica Practica: The Social Practice of Western Music from Gregorian Chant to Postmodernism|year=1994|publisher=Verso|isbn=978-1-85984-005-4|pages=170}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Types of instruments==&lt;br /&gt;
&lt;br /&gt;
===Construction===&lt;br /&gt;
String instruments can be divided in three groups. &lt;br /&gt;
#[[Lute]]s - instruments in which the strings are supported by a [[Neck (music)|neck]] and a bout (&amp;quot;gourd&amp;quot;), for instance a [[guitar]], a [[violin]], a [[baglama|saz]].&lt;br /&gt;
#[[Harp]]s - instruments in which the strings are contained within a frame.&lt;br /&gt;
#[[Zither]]s - instruments with the strings mounted on a body, such as a [[guqin]], a [[cimbalom]], an [[autoharp]], or a [[piano]].&lt;br /&gt;
&lt;br /&gt;
It is also possible to divide the instruments in groups focused on how the instrument is played.&lt;br /&gt;
&lt;br /&gt;
===Types of playing techniques===&lt;br /&gt;
[[File:Teach-yourself-guitar.png|thumb|right|300px|An [[acoustic guitar]] being strummed.]]&lt;br /&gt;
:&#039;&#039;For a full list, see [[List of string instruments]].&#039;&#039;&lt;br /&gt;
&lt;br /&gt;
All string instruments produce sound from one or more [[vibrating]] strings, transferred to the air by the body of the instrument (or by a pickup in the case of electronically amplified instruments). They are usually categorized by the  technique used to make the strings vibrate (or by the primary technique, in the case of instruments where more than one may apply.) The three most common techniques are plucking, bowing and striking.&lt;br /&gt;
&lt;br /&gt;
==== Plucking ====&lt;br /&gt;
{{main|Plucked string instrument}}&lt;br /&gt;
&lt;br /&gt;
Plucking is a method of playing on instruments such as the [[banjo]], [[ukulele]], [[guitar]], [[harp]], [[lute]], [[mandolin]], [[oud]], and [[sitar]], using either a finger, thumb, or quills (now plastic plectra) to pluck the strings.&lt;br /&gt;
&lt;br /&gt;
Instruments normally played by bowing (see below) may also be plucked, a technique referred to by the Italian term &#039;&#039;[[pizzicato]]&#039;&#039;.&lt;br /&gt;
&lt;br /&gt;
==== Bowing ====&lt;br /&gt;
{{main|Bowed string instrument}}&lt;br /&gt;
&lt;br /&gt;
Bowing                                  (&#039;&#039;Italian: Arco&#039;&#039;) is a method used in some string instruments, including the [[violin]], [[viola]], [[cello]], and the [[double bass]] (of the [[violin family]]) and the old [[viol]] family. The [[bow (music)|bow]] consists of a stick with many hairs stretched between its ends. Bowing the instrument&#039;s string causes a [[Stick slip Phenomenon|stick-slip phenomenon]] to occur, which makes the string vibrate.&lt;br /&gt;
&lt;br /&gt;
[[Ravanahatha]]  has been recognized as one of the oldest string instruments in the history,&lt;br /&gt;
Ancestors of the modern bowed string instruments are the [[rebab]] of the Islamic Empires, the Persian [[kamanche]] and the [[Byzantine lira]]. Other bowed instruments are the [[rebec]], [[hardingfele]], [[nyckelharpa]], [[kokyū]], [[erhu]], [[igil]], [[sarangi]] and [[K&#039;ni]]. The [[hurdy gurdy]] is bowed by a [[wheel]].&lt;br /&gt;
&lt;br /&gt;
Rarely, the [[bowed guitar|guitar can be played with a bow]] (rather than plucked) for unique effects.&lt;br /&gt;
&lt;br /&gt;
==== Striking ====&lt;br /&gt;
The third common method of sound production in stringed instruments is to strike the string. The piano uses this method of sound production.&lt;br /&gt;
&lt;br /&gt;
[[Violin family]] string instrument players are occasionally instructed to strike the string with the stick of the bow, a technique called &#039;&#039;[[col legno]]&#039;&#039;. This yields a percussive sound along with the pitch of the note. A well-known use of &#039;&#039;col legno&#039;&#039; for orchestral strings is the [[Gustav Holst]]&#039;s &amp;quot;Mars&amp;quot; movement from &#039;&#039;[[The Planets]]&#039;&#039; suite.&lt;br /&gt;
&lt;br /&gt;
==== Other methods ====&lt;br /&gt;
The [[aeolian harp]] employs a very unusual method of sound production: the strings are excited by the movement of the air.&lt;br /&gt;
&lt;br /&gt;
Some instruments that have strings have attached [[musical keyboard|keyboards]] that the player uses instead of directly manipulating the strings. These include the [[piano]], the [[clavichord]], and the [[harpsichord]].&lt;br /&gt;
&lt;br /&gt;
With these [[keyboard instrument]]s too, the strings are occasionally plucked or bowed by hand. [[Composer]]s such as [[Henry Cowell]] wrote music which asks for the player to reach inside the piano and pluck the strings directly, or to &amp;quot;bow&amp;quot; them with bow hair wrapped around the strings, or play them by rolling the bell of a [[brass instrument]] such as a [[trombone]] on the array of strings.&lt;br /&gt;
&lt;br /&gt;
Other keyed string instruments, small enough for a strolling musician to play, include the plucked [[autoharp]], the bowed [[nyckelharpa]], and the [[hurdy gurdy]], which is played by cranking a rosined wheel.&lt;br /&gt;
&lt;br /&gt;
Steel-stringed instruments (such as the guitar, bass, violin, etc.) can be played using a magnetic field. An [[E-Bow]] is small hand-held battery-powered device which can be used to excite the strings of an electric guitar. It provides a sustained, singing tone on the string which is magnetically vibrated.&lt;br /&gt;
&lt;br /&gt;
[[3rd bridge]] is a plucking method where the string is divided in two pieces and struck at the side which is unamplified. The technique is mainly used on electric instruments, because these have a pickup that amplifies only the local string vibration. It&#039;s possible on acoustic instruments as well, but lesser convenient. For instance press on the 7th fret on a guitar and pluck it at the head side and a tone will resonate at the opposed part. At electric instruments this technique can generate multitone sounds remniscent of a clock or a bell.&lt;br /&gt;
&lt;br /&gt;
==Changing the pitch of a vibrating string==&lt;br /&gt;
&lt;br /&gt;
There are three{{citation needed|date=December 2011}} ways to change the pitch of a [[vibrating string]]. String instruments are tuned by varying the strings&#039; tension because adjusting length or mass per unit length is impractical. Instruments with a [[fingerboard]] are then played by adjusting the length of the vibrating portion of the strings. The following observations all apply to a string that is infinitely flexible strung between two fixed supports. Real strings have finite curvature at the bridge and nut, and the bridge, because of its motion, are not exactly nodes of vibration. Hence the following statements about proportionality are (usually rather good) approximations.&lt;br /&gt;
&lt;br /&gt;
===Length===&lt;br /&gt;
&lt;br /&gt;
Pitch can be adjusted by varying the [[length]] of the string.  A longer string will result in a lower pitch, while a shorter string will result in a higher pitch. The frequency is inversely proportional to the length:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
f \propto \frac{1}{l}&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A string twice as long will produce a tone of half the frequency (one octave lower).&lt;br /&gt;
&lt;br /&gt;
===Tension===&lt;br /&gt;
&lt;br /&gt;
Pitch can be adjusted by varying the [[Tension (physics)|tension]] of the string. A string with less tension (looser) will result in a lower pitch, while a string with greater tension (tighter) will result in a higher pitch.  The frequency is proportional to the square root of the tension:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
f \propto \sqrt{T}&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=== Linear density ===&lt;br /&gt;
&lt;br /&gt;
The pitch of a string can also be varied by changing the [[linear density]] (mass per unit length) of the string. The frequency is inversely proportional to the square root of the linear density:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;&lt;br /&gt;
f \propto {1 \over \sqrt{\mu}}&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Given two strings of equal length and tension, the string with higher mass per unit length will produce the lower pitch.&lt;br /&gt;
&lt;br /&gt;
== String length or scale length ==&lt;br /&gt;
The length of the string from [[Nut (instrumental)|nut]] to [[Bridge (instrument)|bridge]] on bowed or plucked instruments ultimately determines the distance between different notes on the instrument. For example, a double bass with its low range needs a [[scale length (string instruments)|scale length]] of around {{convert|42|in|cm}}, whilst a violin scale is only about {{convert|13|in|cm}}. On the shorter scale of the violin, the left hand may easily reach a range of slightly more than two octaves without [[shifting position]], while on the bass&#039; longer scale, a single octave or a ninth is reachable in lower positions.&lt;br /&gt;
&lt;br /&gt;
== Contact points along the string ==&lt;br /&gt;
&amp;lt;!-- Note: This heading is linked to from the [[Flautando]] redirect. Please update the redirect if you change the heading. --&amp;gt;&lt;br /&gt;
[[Image:DuplexScaling.jpg|thumb|300px|The strings of a [[piano]]]]&lt;br /&gt;
In bowed instruments, the bow is normally placed perpendicularly to the string, at a point half way between the end of the fingerboard and the bridge.  However, different bow placements can be selected to change [[timbre]].  Application of the bow close to the bridge (known as &#039;&#039;[[sul ponticello]]&#039;&#039;) produces an intense, sometimes harsh sound, which acoustically emphasizes the upper [[harmonics]].  Bowing above the fingerboard (&#039;&#039;[[sul tasto]]&#039;&#039;) produces a purer tone with less overtone strength, emphasizing the [[Fundamental frequency|fundamental]], also known as &#039;&#039;flautando&#039;&#039;, since it sounds less reedy and more flute-like.&lt;br /&gt;
&lt;br /&gt;
Similar timbral distinctions are also possible with plucked string instruments by selecting an appropriate plucking point, although the difference is perhaps more subtle.&lt;br /&gt;
&lt;br /&gt;
In keyboard instruments, the contact point along the string (whether this be hammer, tangent, or plectrum) is a choice made by the instrument designer.  Builders use a combination of experience and acoustic theory to establish the right set of contact points.&lt;br /&gt;
&lt;br /&gt;
In harpsichords, often there are two sets of strings of equal length.  These &amp;quot;choirs&amp;quot; usually differ in their plucking points.  One choir has a &amp;quot;normal&amp;quot; plucking point, producing a canonical harpsichord sound; the other has a plucking point close to the bridge, producing a reedier &amp;quot;nasal&amp;quot; sound rich in upper harmonics.&lt;br /&gt;
&lt;br /&gt;
== Production of multiple notes ==&lt;br /&gt;
A string at a certain tension and length will only produce one note, so to obtain multiple notes, string instruments employ one of two methods. One is to add enough strings to cover the range of notes desired; the other is to allow the strings to be &#039;&#039;stopped&#039;&#039;. The piano and harp are examples of the former method, where each note on the instrument has its own string or [[Course (music)|course]] of multiple strings. (Many notes on a piano are strung with a &amp;quot;choir&amp;quot; of three strings tuned alike.)&lt;br /&gt;
&lt;br /&gt;
Some zithers combine stoppable (melody) strings with a greater number of &amp;quot;open&amp;quot; harmony or chord strings. On instruments with stoppable strings, such as the violin or guitar, the player can shorten the vibrating length of the string, using their fingers directly (or more rarely through some mechanical device, as in the [[nyckelharpa]] or the [[hurdy gurdy]]). Such instruments usually have a &#039;&#039;fingerboard&#039;&#039; attached to the neck of the instrument, that provides a hard flat surface athe player can stop the strings against. On some string instruments, the fingerboard has &#039;&#039;[[fret]]s&#039;&#039;, raised ridges perpendicular to the strings that stop the string at precise intervals, in which case the fingerboard is also called a &#039;&#039;fretboard&#039;&#039;.&lt;br /&gt;
&lt;br /&gt;
Moving frets during performance is usually impractical. The bridges of a [[Koto (musical instrument)|koto]], on the other hand, may be moved by the player, occasionally in the course of a single piece of music. Many modern Western harps include levers, either directly moved by fingers (on Celtic harps) or controlled by foot pedals (on orchestral harps), to raise the pitch of individual strings by a fixed amount. The middle Eastern zither, the [[Kanun (instrument)|qanun]], is equipped with small levers called &#039;&#039;mandal&#039;&#039; that allow each  course of multiple strings to be incrementally retuned &amp;quot;on the fly&amp;quot; while the instrument is being played. These levers raise or lower the pitch of the string course by a microtone, less than a half step.&lt;br /&gt;
&lt;br /&gt;
==Sympathetic strings==&lt;br /&gt;
{{main|Sympathetic string}}&lt;br /&gt;
Some instruments are employed with [[sympathetic string]]s, additional strings not meant to be plucked. These strings [[resonance|resonate]] along with the played notes. This system is for instance present on a [[sarangi]].&lt;br /&gt;
&lt;br /&gt;
== Sound production ==&amp;lt;!-- This section is linked from [[Violin]] --&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=== Acoustic instruments ===&lt;br /&gt;
{{See also|Musical acoustics}}&lt;br /&gt;
&lt;br /&gt;
A vibrating string on its own makes only a very quiet sound, so string instruments are usually constructed in such a way that this sound is coupled to a hollow resonating chamber, a soundboard, or both. On the violin, for example the tout strings pass over a bridge resting on a hollow box. The strings vibrations are distributed via the bridge and soundpost to all surfaces of the instrument, and are thus made louder. The correct technical explanation is that they allow a better match to the acoustic impedance of the air.&lt;br /&gt;
&lt;br /&gt;
It is sometimes said that the sounding board or soundbox &amp;quot;amplifies&amp;quot; the sound of the strings. Technically speaking, no amplification occurs, because all of the [[energy]] to produce [[sound]] comes from the vibrating string. What really happens is that the sounding board of the instrument provides a larger surface area to create sound [[waves]] than that of the string. A larger vibrating surface moves more air, hence produces a louder sound.&lt;br /&gt;
&lt;br /&gt;
All lute type instruments traditionally have a bridge, which holds the string at the proper action height from the fret/finger board. On acoustic instruments, the bridge performs an equally important function of transmitting string energy into the &amp;quot;sound box&amp;quot; of the instrument, thereby increasing the sound volume. The specific design, and materials the used in the construction of the bridge of an instrument, have a dramatic impact upon both the sound and responsiveness of the instrument.&lt;br /&gt;
&lt;br /&gt;
Achieving a tonal characteristic that is effective and pleasing to the player&#039;s and listener&#039;s ear is something of an art, and the makers of string instruments often seek very high quality woods to this end, particularly [[spruce]] (chosen for its lightness, strength and flexibility) and [[maple]] (a very hard wood). Spruce is used for the sounding boards of instruments from the violin to the piano. Instruments such as the banjo use a drum, covered in natural or synthetic skin as their soundboard.&lt;br /&gt;
&lt;br /&gt;
Acoustic instruments can also be made out of artificial materials, such as [[carbon fiber]] and [[fiberglass]] (particularly the larger instruments, such as cellos and basses).&lt;br /&gt;
&lt;br /&gt;
In the early 20th century, the [[Stroh violin]] used a diaphragm-type resonator and a metal horn to project the string sound, much like early mechanical gramophones. Its use declined beginning about 1920, as electronic amplification came into use.&lt;br /&gt;
&lt;br /&gt;
=== Electronic amplification ===&lt;br /&gt;
Most string instruments can be fitted with [[piezoelectric]] or magnetic [[Pick up (music technology)|pickup]]s to convert the string&#039;s vibrations into an electrical signal that is amplified and then converted back into sound by loudspeakers. Some players attach a pickup to their traditional string instrument to &amp;quot;electrify&amp;quot; it. Another option is to use a solid-bodied instrument, which reduces unwanted [[Audio feedback|feedback]] howls or squeals.&lt;br /&gt;
&lt;br /&gt;
Amplified string instruments can be much louder than their acoustic counterparts, which allows them to be used in relatively loud rock, blues, and jazz ensembles. Amplified instruments can also have their amplified tone modified by using electronic effects such as distortion, reverb, or [[wah-wah (music)|wah-wah]].&lt;br /&gt;
&lt;br /&gt;
Bass-register string instruments such as the double bass and the electric bass are amplified with [[bass instrument amplification|bass instrument amplifiers]] that are designed to reproduce low-frequency sounds. To modify the tone of amplified bass instruments, a range of electronic [[bass effects]] are available, such as distortion and chorus.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
{{commons category|String instruments}}&lt;br /&gt;
* &amp;quot;[[Essay on the fingering of the violoncello and on the conduct of the bow]]&amp;quot;&lt;br /&gt;
* [[List of string instruments]]&lt;br /&gt;
* [[Luthier]] (maker of stringed instruments)&lt;br /&gt;
* [[Musical acoustics]]&lt;br /&gt;
* [[Musical instrument]]&lt;br /&gt;
* [[Ravanahatha]]&lt;br /&gt;
* [[String instrument extended technique]]&lt;br /&gt;
* [[String instrument repertoire]]&lt;br /&gt;
* [[String orchestra]]&lt;br /&gt;
* [[Strings (music)]]&lt;br /&gt;
* [[Vibrating string]]&lt;br /&gt;
* [[Stringed instrument tunings]]&lt;br /&gt;
&lt;br /&gt;
== References ==&lt;br /&gt;
&amp;lt;references /&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== External links ==&lt;br /&gt;
* [http://www.phys.unsw.edu.au/jw/Bows.html The physics of the bowed string]&lt;br /&gt;
* [http://www.bsmny.org/features/iidviola Instruments in Depth: The Viola], an online feature presented by Bloomingdale School of Music (2010)&lt;br /&gt;
* {{Cite EB1911|wstitle=Stringed instruments}}&lt;br /&gt;
{{Instrument tunings}}&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:String Instrument}}&lt;br /&gt;
[[Category:String instruments| ]]&lt;br /&gt;
&lt;br /&gt;
[[it:Archi (musica)]]&lt;/div&gt;</summary>
		<author><name>99.109.198.230</name></author>
	</entry>
</feed>