question: why does the sound of a musical note differ with instruments?
comment: In short, overtones / harmonics, which impact a given note’s timbre, which can be thought of as the individual hue of a sound. Most sounds you hear aren’t at all just one single frequency - many factors combine to affect a given instrument’s (or person’s, or animal’s) “voice”. The vibrating or oscillating elements give their own unique tones to the sound’s timbre, the geometry and resonance of the chamber contribute a shape, mathematically-related harmonics are generated, and our ear perceives a novel tone. Try playing with additive synthesis to hear this come alive for yourself :)
passages: In simple terms, timbre is what makes a particular musical sound have a different sound from another. For instance, it is the difference in sound between a guitar and a piano playing the same note at the same volume. Both instruments can sound equally tuned in relation to each other as they play the same note, and while playing at the same amplitude level each instrument will still sound distinctively with its own unique tone color. Experienced musicians are able to distinguish between different instruments of the same type based on their varied timbres, even if those instruments are playing notes at the same fundamental pitch and loudness.
   Section::::History.:Modern.:Classical and Romantic.
   Musical tones produced by the human voice and all acoustical musical instruments incorporate noises in varying degrees. Most consonants in human speech (e.g., the sounds of "f", "v", "s", "z", both voiced and unvoiced "th", Scottish and German "ch") are characterised by distinctive noises, and even vowels are not entirely noise free. Wind instruments include the whizzing or hissing sounds of air breaking against the edges of the mouthpiece, while bowed instruments produce audible rubbing noises that contribute, when the instrument is poor or the player unskilful, to what is perceived as a poor tone. When they are not excessive, listeners "make themselves deaf" to these noises by ignoring them.
   Timbre, sometimes called "color" or "tone color" is the quality or sound of a voice or instrument. Timbre is what makes a particular musical sound different from another, even when they have the same pitch and loudness. For example, a 440 Hz A note sounds different when it is played on oboe, piano, violin or electric guitar. Even if different players of the same instrument play the same note, their notes might sound different due to differences in instrumental technique (e.g., different embouchures), different types of accessories (e.g., mouthpieces for brass players, reeds for oboe and bassoon players) or strings made out of different materials for string players (e.g., gut strings versus steel strings). Even two instrumentalists playing the same note on the same instrument (one after the other) may sound different due to different ways of playing the instrument (e.g., two string players might hold the bow differently).
   Accompanying the changes to timbre and volume was a shift in the typical pitch used to tune instruments. Instruments meant to play together, as in an orchestra, must be tuned to the same standard lest they produce audibly different sounds while playing the same notes. Beginning in 1762, the average concert pitch began rising from a low of 377 vibrations to a high of 457 in 1880 Vienna. Different regions, countries, and even instrument manufacturers preferred different standards, making orchestral collaboration a challenge. Despite even the efforts of two organized international summits attended by noted composers like Hector Berlioz, no standard could be agreed upon.
   Timbre composition with acoustic instruments is usually very subtle. Minute altercations in performance change the sound produced by the instrument. Percussionists use specific sticks and mallets to yield desired timbres. Players of wind instruments alter the tone simply by changing the pressure of their lips. One could argue that the act of choosing which instrument to play or write for is in itself timbre composition.
  
  Timbre composition is used in vocal techniques such as throat-singing where the main focus of the music is timbre as opposed to pitch.
   Section::::Classification.:Ancient systems.
   Melody may be described as a phrase or collection of musical notes played in succession. Rhythm, or harmony, occurs when one or more notes are played at the same time. A lead instrument is usually monophonic (only able to sound one note at a time), such as a horn or voice. A rhythm or backing instrument(s) may be monophonic, working together to create harmony, or polyphonic, generating harmony on its own.
  
  Section::::Orchestra.
   The physical characteristics of sound that determine the perception of timbre include the spectrum, envelope and overtones of a note or musical sound. For electric instruments developed in the 20th century, such as electric guitar, electric bass and electric piano, the performer can also change the tone by adjusting equalizer controls, tone controls on the instrument, and by using electronic effects units such as distortion pedals. The tone of the electric Hammond organ is controlled by adjusting drawbars.
  
  Section::::Elements.:Description of elements.:Expression.
   The physical characteristics of sound that determine the perception of timbre include spectrum and envelope. Singers and instrumental musicians can change the timbre of the music they are singing/playing by using different singing or playing techniques. For example, a violinist can use different bowing styles or play on different parts of the string to obtain different timbres (e.g., playing sul tasto produces a light, airy timbre, whereas playing sul ponticello produces a harsh, even and aggressive tone). On electric guitar and electric piano, performers can change the timbre using effects units and graphic equalizers.
   Section::::History.:Modern.:Twentieth century to present.
   Section::::Classification.:Hornbostel–Sachs.
  
  Erich von Hornbostel and Curt Sachs adopted Mahillon's scheme and published an extensive new scheme for classification in "Zeitschrift für Ethnologie" in 1914. Hornbostel and Sachs used most of Mahillon's system, but replaced the term "autophone" with "idiophone".
  
  The original Hornbostel–Sachs system classified instruments into four main groups:
  
  BULLET::::- Idiophones, which produce sound by vibrating the primary body of the instrument itself; they are sorted into concussion, percussion, shaken, scraped, split, and plucked idiophones, such as claves, xylophone, guiro, slit drum, mbira, and rattle.
   Section::::History.:Modern.
  
  Section::::History.:Modern.:Renaissance.
   An ancient Hindu system named the "Natya Shastra", written by the sage Bharata Muni and dating from between 200 BC and 200 AD, divides instruments into four main classification groups: instruments where the sound is produced by vibrating strings; percussion instruments with skin heads; instruments where the sound is produced by vibrating columns of air; and "solid", or non-skin, percussion instruments. This system was adapted to some degree in 12th-century Europe by Johannes de Muris, who used the terms "tensibilia" (stringed instruments), "inflatibilia" (wind instruments), and "percussibilia" (all percussion instruments). In 1880, Victor-Charles Mahillon adapted the "Natya Shastra" and assigned Greek labels to the four classifications: "chordophones" (stringed instruments), "membranophones" (skin-head percussion instruments), "aerophones" (wind instruments), and "autophones" (non-skin percussion instruments).
   When used in the name of an instrument, these terms are relative, describing the instrument's range in comparison to other instruments of its family and not in comparison to the human voice range or instruments of other families. For example, a bass flute's range is from C to F, while a bass clarinet plays about one octave lower.
  
  Section::::Other classifications.
   BULLET::::- Aerophones, which produce a sound with a vibrating column of air; they are sorted into free aerophones such as a bullroarer or whip, which move freely through the air; flutes, which cause the air to pass over a sharp edge; reed instruments, which use a vibrating reed; and lip-vibrated aerophones such as trumpets, for which the lips themselves function as vibrating reeds.
   Timbre
  
  In music, timbre ( , also known as tone color or tone quality from psychoacoustics) is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. It also enables listeners to distinguish different instruments in the same category (e.g., an oboe and a clarinet, both woodwind instruments). 
   Examples of percussion instruments with definite pitch:
  
  BULLET::::- Chimes/Tubular bells
  
  BULLET::::- Crotales
  
  BULLET::::- Glass harmonica
  
  BULLET::::- Glass harp
  
  BULLET::::- Glockenspiel
  
  BULLET::::- Handbells
  
  BULLET::::- Marimba
  
  BULLET::::- Mridangam
  
  BULLET::::- Rototom
  
  BULLET::::- Steelpan
  
  BULLET::::- Tabla
  
  BULLET::::- Timpani
  
  BULLET::::- Tuned Triangle
  
  BULLET::::- Vibraphone
  
  BULLET::::- Wind chimes
  
  BULLET::::- Xylophone
  
  BULLET::::- Xylo-marimba
  
  Section::::Classification.:By musical function or orchestration.:Indefinite pitch.
  
  Instruments in this group are sometimes referred to as "non-pitched", "unpitched", or "untuned". Traditionally these instruments are thought of as making a sound that contains such complex frequencies that no discernible pitch can be heard.
   Timbre is principally determined by two things: (1) the relative balance of overtones produced by a given instrument due its construction (e.g. shape, material), and (2) the envelope of the sound (including changes in the overtone structure over time). Timbre varies widely between different instruments, voices, and to lesser degree, between instruments of the same type due to variations in their construction, and significantly, the performer's technique. The timbre of most instruments can be changed by employing different techniques while playing. For example, the timbre of a trumpet changes when a mute is inserted into the bell, the player changes their embouchure, or volume.
   In the case of a musical note, the lowest frequency of its timbre is designated as the sound's fundamental frequency. For simplicity, we often say that the note is playing at that fundamental frequency (e.g. "middle C is 261.6 Hz"), even though the sound of that note consists of many other frequencies as well. The set of the remaining frequencies is called the overtones (or the harmonics) of the sound. In other words, the fundamental frequency alone is responsible for the pitch of the note, while the overtones define the timbre of the sound. The overtones of a piano playing middle C will be quite different from the overtones of a violin playing the same note; that's what allows us to differentiate the sounds of the two instruments. There are even subtle differences in timbre between different versions of the same instrument (for example, an upright piano vs. a grand piano).
   Three factors relating to the walls of a resonator will affect how it functions: the material it is made of, the thickness of its walls, and the type of surface it has. The resonance characteristics of a musical instrument obviously will vary with different materials and the amount of material used will have some effect.
   Music instrument technology
  
  Music instrument technology refers to the construction of instruments and the way they have changed over time. Such change has produced modern instruments that are considerably different from their historical antecedents.
  
  An example is the way in which many instruments commonly associated with a modern symphony orchestra are markedly different from the same instruments for which European composers were composing music centuries ago.
   Section::::Construction.
   In rock music from the late 1960s to the 2000s, the timbre of specific sounds is important to a song. For example, in heavy metal music, the sonic impact of the heavily amplified, heavily distorted power chord played on electric guitar through very loud guitar amplifiers and rows of speaker cabinets is an essential part of the style's musical identity. You could not take the heavily amplified electric guitar part and substitute it with the same notes played on a grand piano or pipe organ.
  
  Section::::Psychoacoustic evidence.
   BULLET::::- I.A: no tension (free solid, for example, xylophones, cymbals, or claves);
  
  BULLET::::- I.B: linguaphones (lamellophones) (solid fixed at only one end, such as a kalimba or thumb piano);
  
  BULLET::::- I.C: chordophones (solid fixed at both ends, i.e. strings such as piano or harp)); plus drums
  
  BULLET::::- II: instruments that make sound from vibrating air (such as clarinets, trumpets, or bull-roarers.)
  
  The system agrees with Mahillon and Hornbostel–Sachs for chordophones, but groups percussion instruments differently.
  