Composition Definition and 388 Threads

Musical composition, music composition or simply composition, can refer to an original piece or work of music, either vocal or instrumental, the structure of a musical piece or to the process of creating or writing a new piece of music. People who create new compositions are called composers. Composers of primarily songs are usually called songwriters; with songs, the person who writes lyrics for a song is the lyricist. In many cultures, including Western classical music, the act of composing typically includes the creation of music notation, such as a sheet music "score," which is then performed by the composer or by other musicians. In popular music and traditional music, songwriting may involve the creation of a basic outline of the song, called the lead sheet, which sets out the melody, lyrics and chord progression. In classical music, orchestration (choosing the instruments of a large music ensemble such as an orchestra which will play the different parts of music, such as the melody, accompaniment, countermelody, bassline and so on) is typically done by the composer, but in musical theatre and in pop music, songwriters may hire an arranger to do the orchestration. In some cases, a pop or traditional songwriter may not use written notation at all and instead compose the song in their mind and then play, sing or record it from memory. In jazz and popular music, notable sound recordings by influential performers are given the weight that written or printed scores play in classical music.
Although a musical composition often uses musical notation and has a single author, this is not always the case. A work of music can have multiple composers, which often occurs in popular music when all members of a band collaborate to write a song or in musical theatre, when one person writes the melodies, a second person writes the lyrics and a third person orchestrates the songs.
A piece of music can also be composed with words, images or, since the 20th century, with computer programs that explain or notate how the singer or musician should create musical sounds. Examples range from 20th century avant-garde music that uses graphic notation, to text compositions such as Karlheinz Stockhausen's Aus den sieben Tagen, to computer programs that select sounds for musical pieces. Music that makes heavy use of randomness and chance is called aleatoric music and is associated with contemporary composers active in the 20th century, such as John Cage, Morton Feldman and Witold Lutosławski. A more commonly known example of chance-based, or indeterminate, music is the sound of wind chimes jingling in a breeze. The study of composition has traditionally been dominated by examination of methods and practice of Western classical music, but the definition of composition is broad enough to include the creation of popular music and traditional music songs and instrumental pieces, and to include spontaneously improvised works like those of free jazz performers and African percussionists such as Ewe drummers.
In the 2000s, composition is considered to consist of the manipulation of each aspect of music (harmony, melody, form, rhythm and timbre), according to Jean-Benjamin de Laborde (1780, 2:12):

Composition consists in two things only. The first is the ordering and disposing of several sounds...in such a manner that their succession pleases the ear. This is what the Ancients called melody. The second is the rendering audible of two or more simultaneous sounds in such a manner that their combination is pleasant. This is what we call harmony and it alone merits the name of composition.

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  1. Math Amateur

    MHB Composition of Functions - in the context of morphisms in algebraic geometry

    I am reading Dummit and Foote (D&F) Section 15.1 on Affine Algebraic Sets. On page 662 (see attached) D&F define a morphism or polynomial map of algebraic sets as follows: ----------------------------------------------------------------------------------------------------- Definition. A map...
  2. Z

    Archived Vapor composition from bubble-point temp.

    Suppose you have a mixture of 30 mol% pentane and 70 mol% hexane at 1 atm and 60oC. If the Tbubble-point = 55.1oC, calculate the composition of vapor of the first bubble as the mixture is heated. I found p*pentane = 1392.95 and p*hexane = 484.96 using Antoine's equation with T = 55.1. Now I...
  3. S

    Composition > Illustrative Essay On Radio

    Composition > Illustrative Essay On "Radio" Goal: 2-3 page essay on a topic of your choice. Must provide relevant photo's. My topic of choice is electromagnetism. I chose this topic because we live in a wireless age. I thought it'd be neat to provide some back round info on how it all...
  4. W

    What is the Composition of an Exoplanet 50 Light Years Away?

    Lets say there is an exoplanet 50 light years away. The radius of this planet is 2x Earths with 8x Earths mass and a density of 5.52 g cm/3. What is the composition of this planet?
  5. R

    Why will a composition function of an even function always be even?

    I apologize in advance if the answer to this is really simple; I often overlook simple solutions when something trips me up. For example, if f(x)=x2 and g(x)=x3/2, and g(f(x)) is therefore, after simplification, x3, why is that still an even function if x3 graphed under other circumstances is...
  6. M

    Composition: Arithmetic is futile

    Please watch from 0:00 to 1:23 Goal: Complete a short essay on my greatest accomplishment achieved. I have not achieved it yet, but my greatest accomplishment will be the language of mathematics. I thought about this last night, "The difference between arithmetic in algebra &...
  7. P

    Ice/Water Composition in Basic Thermodynamics

    Homework Statement So we are given an insulating container with two compartments between which, heat can flow. In the left one, there exists m_1 of water at temp T_1 and on the right there exists m_2 of ice at temp T_2. What is the final composition and temperature? Homework Equations...
  8. MarkFL

    MHB Kendra Leota's Calculus Questions @ Yahoo Answers

    Here are the questions: I have posted a link there to this topic so the OP can see my work.
  9. B

    Stable linear transformations under composition

    Hi, Let f be a linear transformation over some finite field, and denote f^{n} := f \circ f \circ \cdots \circ f, n times. What do we know about the linear maps f such that there exist an integer n for which f^{N} = f^n for all N \geq n? Also, how about linear maps g satisfying g = g \circ f^i...
  10. S

    Matrix Multiplication and Function Composition

    I am doing linear algebra and want to fully understand it, not just pass the class. I was recently taught matrix multiplication and decided to look up how it works. The good part is that I understand the concept. Matrices are a way of representing linear transformations. So matrix multiplication...
  11. S

    Phase Diagram Composition Determination

    Homework Statement Reference the Cu-Zr phase diagram. If you make the alloy CuZr and heat it to 300°C, what percentage of the material will be Cu10Zr7 and what percentage of the material will be CuZr2? Homework Equations Phase diagram attached. The Attempt at a Solution I used the lever...
  12. MarkFL

    MHB Solve Functions Question: Speed/Distance/Time & Composition

    Here is the question: Here is a link to the question: HELP WITH THIS FUNCTIONS QUESTION!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  13. A

    MHB Determine Compositions of Functions

    This question is killing me. I'm finding it difficult to do and it's a problem with my homework. Given that f(x)=2x^2-x+1,\,g(x)=2\sin(x)\text{ and }h(x)=3^x, determine the following. You need not simplify the expressions. f(g(-\pi))=? \left(h^{-1}\circ f \right)(x)=? g(f(h(x)))=? I am...
  14. N

    Reverse Composition to find composition of a derivative

    Homework Statement I\!f~ f(x+1)=\sqrt{x^2-2x}~~~and~~~g(x)=f(\!\sqrt{x}) Find: g'(x-1) Homework Equations In order to find g'(x-1) I know the following steps have to be taken: f(x+1) \rightarrow f(x) \rightarrow f(\sqrt{x}) = g(x) \rightarrow g'(x) \rightarrow g'(x-1) The Attempt at a...
  15. C

    Does angular diameter distance vary with composition of the Universe?

    I was just reading about how the redshift-relation for angular diameter distance is calculated, and the example in my textbook used a matter-dominated universe to calculate the formula. It seems to rely heavily on the relationships between t, a(t) and H(t), which are different in radiation...
  16. A

    Exploring the Mystery of Dark Matter: Evidence and Composition

    Did The Dark Matter Really exist ? did we have an evidence ? and What is the compositions Of The Dark Matter ?
  17. Fernando Revilla

    MHB Jacqueline's question at Yahoo Answers (Eigenvalues of a composition)

    Here is the question: Here is a link to the question: Denote by A the 3x3 matrix which rotates by 90 degrees around the z-axis? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  18. S

    Riemann Integrability of Composition

    Homework Statement Let ψ(x) = x sin 1/x for 0 < x ≤ 1 and ψ(0) = 0. (a) If f : [-1,1] → ℝ is Riemann integrable, prove that f \circ ψ is Riemann integrable. (b) What happens for ψ*(x) = √x sin 1/x? Homework Equations I've proven that if ψ : [c,d] → [a,b] is continuous and for every set...
  19. T

    Composition Factors cyclic IFF finite group soluble

    Hey, just trying to get my head around the logic of this. I can see that if composition factors are cyclic then clearly the group is soluble, since there exists a subnormal series with abelian factors, but I am struggling to see how the converse holds. If a group is soluble, then it has a...
  20. Z

    Composition of the Universe can be Derived from PI?

    New data from NASA's Cosmic Background Explorer (COBE), the Wilkinson Microwave Anisotropy Probe (WMAP), and Planck have found evidence that the composition of the universe: Matter - 4.9 % Dark Matter - 26.8 % Dark Energy - 68.3 % These numbers seem almost too coincidental to numbers...
  21. F

    Composition of meromorphic functions

    Homework Statement If f is meromorphic at a in ℂ^ (extended complex plane), and g is meromorphic at b = f(a) in ℂ^, show that h := g ° f is meromophic at a, with an exception. If f takes on the value b in ℂ^ with multiplicity m at a and g assumes the value c = g(b) in ℂ^ with multiplicity n...
  22. S

    Diffnt suppliers, same composition (AlTiB) yielding 2 different Grains

    I work at an Aluminum sheet casting plant, we use AlTiB as the grain refiner for our cast products.Ti:B ratio as indicated on certificates is 5:1 .We recently received a new consignment of AlTiB from another supplier in India.The certificates from our new supplier show that the The AlTiB we...
  23. I

    MHB Find Counterexample for Expression about Limit of Composition Function

    Suppose that $U$ is open in $\mathbb{R}^{m}$, that $L\in U$ and that $h:U\setminus \left \{ L \right \}\rightarrow \mathbb{R}^{p}$ for some $p\in N$. If $L=\lim_{x\rightarrow a}g(x)$ and $M=\lim_{y\rightarrow L}h(y)$. Then $\lim_{x\rightarrow a}(h\circ g)(x)=M$. (Someone told me that this...
  24. S

    Determing the composition of a state

    Hey, I have a question on determing the composition of a state of a system of composed of only two eigenvectors, the question is displayed below: I initially assumed that the ket v was given by: |v>=a|\omega_{1}>+b|\omega_{2}> Where 'a' and 'b' are constants which will determine...
  25. M

    Automotive Metal Composition of Motorcycle Chassis

    Hello guys, I wonder and would like to know what kind of metal to made a motorcycle chassis such as Yamaha YZF-R1 and Yamaha Raptor 700R? Is it solid or hollow? Is it cast or extrude? Thank you MyMachine
  26. M

    Limits of composition of two functions.

    Homework Statement Let A, B be subsets of ℝ and f : A → ℝ and g : B → ℝ and f(x)\inB for every x \in A. Prove: If f(x)→L as x → a, for x\in I and g is continuous at L \in B then lim x->a g(f(x)) = g(lim x->a f(x)). Homework Equations f is said to be continuous at a point a iff given ε>0 there...
  27. J

    Composition of two equivalence relations

    Homework Statement The question is let E1 and E2 be equivalence relations on set X. A new relation R is defined as the E1 o E2, the composition of the two relations. We must prove or disprove that R is an equivalence relation.Homework Equations The Attempt at a Solution I know that we must...
  28. mnb96

    Question on Jacobian with function composition and inverse functions

    Hello, let's suppose I have two functions \phi:U\rightarrow V, and T:V\rightarrow V that are both diffeomorphisms having inverse. Furthermore T is linear. I consider the function f(u) = (\phi^{-1}\circ T \circ \phi)(u), where \circ is the composition of functions. Since T is linear, we...
  29. P

    MHB Finding Composition Series of Groups

    My sum total of knowledge of composition series is: the definition, the jordan holder theorem and the fact that the product of the indices must equal the order of the group. With this in mind, can someone help with me with finding a composition series for the following:(1) Z60 (2) D12...
  30. K

    Integral of Composition Functions

    Homework Statement http://sphotos-h.ak.fbcdn.net/hphotos-ak-snc6/282312_368248176595083_1229435302_n.jpg Homework Equations To subtitute x into U, but that did not work. The Attempt at a Solution I have tried subtituting x into U like this ...
  31. T

    Showing a composition is isomorphic

    Prove that if S: U-->V and T: V-->W are isomorphisms, then TS (composition) is also an isomorphism. Idea: So my idea was since both S, T are both isomorphic that means they both have inverses S-1 and T-1. Now this is where I'm a little grey, in order to show that TS is isomorphic, is it...
  32. STEMucator

    What is the Proof for f=h when fog=x and goh=x in Composition?

    Homework Statement Can't believe I forgot how to do this... Prove if fog = x and goh = x then f=h for all x. Homework Equations Obviously the associativity of composition here. The Attempt at a Solution So we know : fog = goh fogoh = gohoh fo(goh) = (goh)oh I've...
  33. K

    Showing composition of functions are uniformly continuous

    Showing the sum of functions are uniformly continuous Homework Statement Suppose f and g are uniformly continuous on an interval I. Prove f + g are uniformly continuous on I. Homework Equations The Attempt at a Solution Let ε >0 By definition, since f and g are uniformly...
  34. K

    Showing IVP with composition of functions

    Homework Statement Suppose that f has the intermediate value property on an interval J, that g has the intermediate value property on an interval I and that g(I) is a subset of J. Prove that f°g has intermediate value property on I. Homework Equations The Attempt at a Solution I...
  35. S

    Preimage and function composition?

    Homework Statement Let f:S→T and let A\subseteqT. Define the preimage of A as f-1(A)={x in S: f(x) is in A}. Demonstrate that for any such map f and B\subseteqran(f), f(f-1(B)) = B. I am going to use set inclusion to prove this, but can I use function composition in the portion in red? I...
  36. D

    MHB Function Composition: Restrictions for Domains

    Given three functions $F,G,H$ what restrictions must be placed on their domains so that the following four composite functions can be defined? $$ G\circ F,\quad H\circ G,\quad H\circ (G\circ F),\quad (H\circ G)\circ F. $$ I need a hint or something.
  37. I

    Mathematica Composition of Vector Functions in Mathematica

    I want to define something like: A\left(\begin{matrix} x \\ y\end{matrix}\right) = \left(\begin{matrix} 1 & -1 \\ -1 & 1 \end{matrix}\right)\left(\begin{matrix} x \\ y\end{matrix}\right) B\left(\begin{matrix} x \\ y\end{matrix}\right) = \left(\begin{matrix} 0 & 1 \\ 2 & -1...
  38. F

    Composition of infinite deformation retracts

    I'm trying to give an answer to the following problem, I hope someone could come in help! Consider a smooth n-dimensional manifold M with smooth (nonempty) boundary \partial M, and suppose given a function f: M\setminus \partial M \to \mathbb{R} (which one can assume to be differentiable)...
  39. P

    Particle composition vs particle decay

    Ive read that elementary particles can decay. I am trying to understand how this can be with a particle that has no composition. So i have two questions: If elementary particle A decays into particles B and C, then why can't we say that A is composed of B and C? If an elementary particle can...
  40. H

    Why does the genetic composition of sex cells of an individual vary ?

    Why does the genetic composition of sex cells of an individual vary since the genome of an individual is same throughout his/her body.
  41. 1

    Finding the Composition of Relations

    Homework Statement R = { (1,2), (3,5), (2,2), (2,5) } S = { (2,1), (5,3), (5,1), (5,5) } Explicitly find the relation R^-1 o S^-1 Homework Equations The Attempt at a Solution This was on my test. First I just wrote down the inverses: R^-1 = { (2,1), (5,3), (2,2), (5,2)...
  42. M

    Measuring metallurgical composition of melt in furnace

    When mixing special grades of alloys, or even in commercial production of common alloys, furnaces are often used where metals or additives are added and mixed, then samples taken at the core and characterized, then adjustments are made by adding additives until the desired composition is...
  43. K

    Are Beta Particles Made of Electrons and Anti-Neutrinos?

    Does a Beta(?) Particle as a whole, comprise electrons and anti-neutrino?? or just a electron??
  44. L

    Bijective functions and finding a composition function fg

    Homework Statement Give a genuinely new (i.e. not discussed in class or in the book or in tutorial) example of: two sets X and Y , and two functions f : X →Y and g : Y → X, such that the composition g ◦ f is the identity function 1X : X → X, but neither f nor g are bijective. (Reminders: if...
  45. G

    How Do You Find g(x) When f(g(x)) Equals a Different Function?

    Homework Statement Find g(x) if f(x) = (3x-1)/(2x+5) and f(g(x)) = (x+9)/(12x-11) Homework Equations N/A, as far as I know The Attempt at a Solution I tried doing it as though g(x) = y and it turned out like this: (3y-1)/(2y+5)=(x+9)/(12x-11) I very quickly saw that that wouldn't...
  46. H

    Proof that a function composition is differentiable

    Homework Statement Let f:R->R, differentiable, f(1)=1 and f'(1)=2. Homework Equations Prove that g:R->R such that g(x)=f(x)Arctg(f(x)) is differentiable in x=1 and calculate g'(1)The Attempt at a Solution I would prove it saying that if a function is differentiable then the product and...
  47. L

    Composition Series and simple groups

    Homework Statement For each m >= 2, find a group with a composition series of length 1 with a subgroup of length m. Homework Equations Simple groups iff length 1. If G is abelian of order p1^k1...pr^kr, then length G = k1 + ... + kr If G has a composition series and K is normal...
  48. Z

    Composition of Two Isometries, Rotation & Glide Reflection

    Homework Statement R is a rotation around the origin by ∏/4, G is a glide reflection; the reflection is across y=x and the glide is by (2,2). Find the compositions R°G and G°R and characterize them. If you find a glide reflection, specify both the mirror line and the "glide" vector...
  49. P

    What are the domains and codomains of composed functions?

    Homework Statement Define Function f: [0,1]x[0,2∏)→ℝ2 by f(r,θ)= (r(2+cos5θ)cosθ) (r(2+cos5θ)sinθ) Let g: [0,2∏)→[0,1]x[0,2∏) be defined by g(t)= (1) (t) Compute the function δ=f°g, what are the domain and codomain of δ? Homework Equations The Attempt at a Solution Replacing r with 1...
  50. J

    Linear Algebra Proof on Composition of One-to-One Functions

    Homework Statement Prove that the composition of one-to-one functions is also a one-to-one function. Homework Equations A function is one-to-one if f(x1)=f(x2) implies x1=x2. Composition is (f*g)(x)=f(g(x)). Proof-based question. The Attempt at a Solution A...
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