What is Composition: Definition and 386 Discussions
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.
Let u (not equal to 0) be a vector in R^2 and let
T: v --> proju(v)
1. Show that T is a linear transformation.
2. Describe the composition T T.
3. If ~u = [1,−1], find the standard matrix for T.
I'm good with 1 and 3, but I'm not sure what 2 is asking. Excuse the poor notation...
Homework Statement
[PLAIN]http://img230.imageshack.us/img230/4203/vectoro.jpg
Homework Equations
The Attempt at a Solution
I know I need to find (f\circ p)'(0) which is 2-dimensional vector and then show it equals \alpha (a,1) where the number \alpha depends on v_1 and v_2 but...
We have three functions: f:A->A, g:A->A and h:A->A
with both f and g bijective and h bijective.
We know that f ° h = h ° g for every x in A.
Is it true that f=g for every x in A?
I have tried to solve it and I am pretty sure it is true but I cannot find neither a counterexample nor a...
We have three functions: f:A->A, g:A->A and h:A->A
with both f and g bijective and h bijective.
We know that f ° h = h ° g for every x in A.
Is it true that f=g for every x in A?
I have tried to solve it and I am pretty sure it is true but I can find neither a counterexample nor a...
I understand that the sun is made of 91% hydrogen, 8.7% Helium, and 0.3% other stuff. I looked up the atomic spectrum for helium and hydrogen [within the visible portion] and they leave most of the spectrum blank, albeit few lines of colour here and there, yet the white light that reaches us has...
I'm planning to plot phase diagrams of Temperature vs Composition. I found the formula ln(x) = \frac{\Delta H}{R} (\frac{1}{T_A} - \frac{1}{T}) from the Clapeyron equation.
Its a ideal solution of 2 metals in L state and regular solution in S state. Eutectic temperature is at 850C and enthalpy...
Homework Statement
A fuel has the following composition on a molar basis: 40.0% CH4,
24.0% C2H4, 16% C3H8, 10% CO2, 10% H2O. What is the composition of the fuel on a dry
basis? What is the composition of the fuel on a mass basis? What is the average molecular
weight of the fuel? [Relative...
the composition of ozone is O3 and the oxygen O2 present in atmosphere.considering the masses of O3 and O2 , the O3 is more heavier than O2 then also ozone is situated above the oxygen (O2) present in atmosphere. why is it so?
advanced thanks.
Show that when basic rotations are combined to find composite rota-
tional transformations, if the rotation is about one of the principal axes of
OXYZ (the fixed frame) the previous resultant rotation matrix is premulti-
pled by the new rotational transformation, and if the rotation is about...
Show that when basic rotations are combined to find composite rota-
tional transformations, if the rotation is about one of the principal axes of
OXYZ (the fixed frame) the previous resultant rotation matrix is premulti-
pled by the new rotational transformation, and if the rotation is about...
Is it always true that the domain of f(g(x)) is the intersection of the domains of f(x) and g(x)?
I've been having trouble with this and this answer would make me fully understand this concept.
Thanks to everyone!
Homework Statement
I have a problem with the next exercise:
Given de function f(x,y)=\begin{Bmatrix} \displaystyle\frac{xy^2}{x^2+y^2} & \mbox{ if }& (x,y)\neq{(0,0)}\\0 & \mbox{if}& (x,y)=(0,0)\end{matrix} with \vec{g}(t)=\begin{Bmatrix} x=at \\y=bt \end{matrix},t\in{\mathbb{R}}
a) Find...
Homework Statement
A certain metal hydroxide, M(OH)2, contains 32.8% oxygen by mass. What is the identity of the metal M?
Homework Equations
O = 16.00 g x2
H = 1.008 g x2
The Attempt at a Solution
I thought that 1g = 1% of the mass because there are 32g of O and it composed of...
Homework Statement
4.0 g of sulfur and 10.0 g of zinc are heated together, how much zinc will remain unreacted?
Homework Equations
The Attempt at a Solution
If these two elements are heated together, wouldn't the total mass (g) be 14.0 by adding the amount of sulfur and zinc...
Homework Statement
J represents a 3x2 matrix and H represents and 2x4 matrix. y = Hx and z = Jy, where y is a 2x1 matrix, z is a 3x1 matrix, and x is a 4x1 matrix. Form the composition J○H and simplify z = J○Hx.
The Attempt at a Solution
I don't know what my answer is going to look...
Homework Statement
I have a question regarding how to compose 2 transformations, a rotation and a translation, of a linear algebra problem.
Suppose we have a quadratic curve like the following one:
(i) x^2 + y^4 - 6xy +2x -3y +6 = 0
We want to transform the above into its standard...
Can h(x)=(cos x)^x be written as a composition of two functions f and g where f(x)=x^n and g(x)=cosx ? where h=fog
REASON FOR ASKING: I am wondering this in connect with a differentiation I was having trouble with (but can now solve thanks to this forum). I mistakenly thought that I could...
Homework Statement
This is a problem from D'Inverno's "Introducing Einstein's Relativity".
If vAB is the velocity of B with respect to A, vBC is the velocity of C with respect to B, and vAC is the velocity of C with respect to A (all velocities are in relativistic units, that is, c=1)...
Okay, so I see this pizza chart a lot on the web that points physical matter with mass making up 4.6% of all matter in the universe, followed by dark matter with 23% and dark energy with the rest.
Where the heck did old fashion, normal energy go? is it not good enough to get it's own place...
Homework Statement
Make [; f: A \rightarrow B ;], [; g: C \rightarrow D ;], [; h: E \rightarrow F ;] functions in which [; \text{Im} f \subseteq C;] and [; \text{Im} g \subseteq E;]. Show that [; f \circ ( g \circ h ) ;] and [; h \circ ( g \circ f ) ;] are valid if, and only if, [; f...
I was organizing pennies into categories based on what they were composed of; before 1982 (I believe) pennies were made out of 95% Cu, and after they were made primarily out of zinc. I thought that the ideal penny for a voltaic cell would use a Copper penny, and a Nickel. However, I found that...
Hello, I have been given the following problem and am hoping for some help...
You have 1000 unlabeled gas cylinders, each are 0.25m3 and need to be able to identify the contents. They mostly contain oxygen and helium, but some contain xenon and uranium hexafluoride. You are given a scale...
Homework Statement
Is the composition of two differentiable functions always differentiable?
E.x.
h(x) = sin(x)
k(x) = 1/x for x not equal 0
Does this automatically mean h(k(x)) is differentiable?
Thank you,
M
Homework Statement
Consider the following functions:
Modified Dirichlet Function
f(x) = 1/n if x=m/n of lowest forms, and f(x) = 0 if x is irrational
find an integrable function g(x) such that the composition of g and f is NOT integrable
The Attempt at a Solution
Let g(x) = nx for all n in...
I will state here what I understand in this topic which I am a little confused:
If I have 2 sinusoidal signals perfectly in phase, with distinct power levels, say -13dBm and -10dBm, the composition ("sum") of both signals is -8.23dBm. Or, for -10dBm and -10dBm signals, the sum is -7dBm...
Homework Statement
Find the partial derivatives with respect to u,v of \bar{U}(\bar{x}(u,v)), where \bar{U} is the unit normal to a surface given by the parametrization \bar{x}(u,v). (This, of course, is part of a larger problem, but I just am looking for advice with the calculus.)...
Homework Statement
Suppose r and s are two positive real numbers. Let Dr and Ds be defined as in part 3 of Example 4.3.1. What is D_r \circ D_s? Justify your answer with a proof. (Hint: In your proof, you may find it helpful to use the triangle inequality.)
Homework Equations
Example 4.3.1...
Homework Statement
I keep getting what I think is the "right answer", but it's not one of my choices :^(
Here are the problems and answer choices.
1).
2).
Homework Equations
nothing really...or at least I don't think besides the fact that e^-x = 1/e^x
The Attempt at a Solution
1).
x + 14...
Hello,
I am trying to take the Laplace transform of floor(f(t)) in order to solve the differential equation f'(t)=floor(f(t)).
I know that http://functions.wolfram.com/IntegerFunctions/Floor/22/04/" gives L(floor(t)) = (e^(-s))/(s(1-e^(-s))) instead -- are these equivalent?) and L(f(t)) =...
Hello,
I am trying to take the Laplace transform of floor(f(t)) in order to solve the differential equation f'=floor(f(t)). I know that L(floor(t)) = (e^(-s))/(s(1-e^(-s))) and that L(f(t)) = F(t) (of course), but I realized that I have no idea how to take the Laplace transform of a...
Homework Statement
how to show using MVT that cos(cos x) is a contraction.
Homework Equations
| d/dx (cos(cos x)) | = | sin(cos x) sin(x) | < sin 1 < 1
The Attempt at a Solution
Using that relation, the original problem is easily solved. My question is, how do we know:
|...
I've been looking at different math books that have analysis problems to get more perspectives on how to approach various analysis problems. I was following along in the "Derivatives" section of the book "Mathematical Thinking" by D'Angelo and West, second edition, and arrived at a lemma with...
If our solar system originated from the same dust / gas cloud, why do we see such differences in abundance of elements from one body to another. I can come up with two possible answers:
1. Rotation of cloud centrifuged heavier elements towards edge (Almost certainly not true, because it would...
Homework Statement
(-3x^2-15x-12)(√5)
Homework Equations
Quadratic formula?
The Attempt at a Solution
hmm, i know how to solve the first set of bracets, but what do i do with the radical? how do i multiply it to the polynomial?
Homework Statement
The substance CoBr3 dot 4 NH3 dot 2 H2O ha a molar conductivity of 42 kS/m at infinite dilution. Indicate the composition of the coordination sphere.
Homework Equations
I don't know any relevant equations.
The Attempt at a Solution
Where can we read about how...
[b] I'm in desperate need of some help. I am so lost on this:
1. imagine a rocket ship R moving eastward with speed v with respect to the Earth and a rocket ship S moving westward with speed −v with respect to the earth, we wish to know the speed of R with respect to S.
a. Go to a reference...
I need prove or disprove the following statement:
If f: R^2->R^2 is a differentiable function whose derivative at (0,0) is not invertible, then there does not exist a differentiable function g: R^2->R^2 such that:
(g o f)(X)=X
I've been trying to find counter examples like crazy...
Homework Statement
f and g are differentiable functions that have the following properties:
i. f(x) < 0 for all values of x
ii. g(5) = 2
If h(x)= f(x) / g(x) and h'(x) = f '(x) / g(x), then g(x) = _____?
Homework Equations
Quotient Rule with f(x) and g(x)
The Attempt at a...
I need to write a loop that iterates several times to find the limit of this function
f(x) = 5x(-x+1) lim f^n(0.75) n->
For[n = 0, n < 5, n++,
x=0.75;
f[x_] := 5x(-x+1)
];
]
what am i doing wrong?
Homework Statement
An astronaut crew is preparing for a space mission. As part of their preparation,
they must spend a block of consecutive days training in a flight simulator. Each day,
the crew is required to spend either 1, 2, or 3 hours in the simulator. The training
ends once they...
Homework Statement
Suppose T is a rotation by 30 degrees about the point 2, and S is a rotation by 45 degrees about the point 4. What is T composed with S? Can you describe this transformation geometrically?
Homework Equations
none
The Attempt at a Solution
I know T composed with S...
Homework Statement
Form the composition f o g o h and give the domain.
f(x) = x - 1, g(x) = 4x, h(x) = x2
Homework Equations
The Attempt at a Solution
f(g(h(x))) = 4x2-1
The domain of x is any real number.
Homework Statement
Does there exist a continuous function f: R -> R such that f'(f(x)) = x ?
Homework Equations
The Attempt at a Solution
I was trying to find an example, but wasn't able to, and if I had to take a guess whether such a function exists or not, I'd say no. Here...
I am trying to find the chemical composition for basic, college chemistry lab quality thermite. I saw that it was a white/grey powder substance. Trying to figure out what the exact chemical composition might be. :)
% (by mass) composition
Homework Statement
Dopamine, C8 H11 O2 N is a neutroransmitter. Determine the percent (by mass) composition of each of the elements in dopamite.Homework Equations
The Attempt at a Solution
8C atoms= 12 (12.0) = 44.0amu
11H atoms = 11 (1.0) = 11.0 amu
2O atoms = 2...
1. Show that the set {f:R-{0,1}\rightarrow [b]R-{0,1}}, of functions under composition, is isomorphic to S _{3}
f_{1} = x
f_{2} = 1 - x
f_{3} = \frac {1}{x}
f_{4} = 1 - \frac {1}{x}
f_{5} = \frac {1}{1 - x}
f_{6} = \frac {x}{x - 1}
Homework Equations
The Attempt at a Solution...
I have a homework problem as follows:
Let f(x) = 2x, (-inf < x < inf). Can you think of functions g and h which satisfy the two equations g \circ f = 2gh and h \circ f = h^2 - g^2?
I know that g \circ f = g(f(x)), which then = g(2x) for the first question. I can't figure out how to work...