Sonata form (also sonata-allegro form or first movement form) is a musical structure consisting of three main sections: an exposition, a development, and a recapitulation. It has been used widely since the middle of the 18th century (the early Classical period).
While it is typically used in the first movement of multi-movement pieces, it is sometimes used in subsequent movements as well—particularly the final movement. The teaching of sonata form in music theory rests on a standard definition and a series of hypotheses about the underlying reasons for the durability and variety of the form—a definition that arose in the second quarter of the 19th century. There is little disagreement that on the largest level, the form consists of three main sections: an exposition, a development, and a recapitulation; however, beneath this general structure, sonata form is difficult to pin down to a single model.
The standard definition focuses on the thematic and harmonic organization of tonal materials that are presented in an exposition, elaborated and contrasted in a development and then resolved harmonically and thematically in a recapitulation. In addition, the standard definition recognizes that an introduction and a coda may be present. Each of the sections is often further divided or characterized by the particular means by which it accomplishes its function in the form.
After its establishment, the sonata form became the most common form in the first movement of works entitled "sonata", as well as other long works of classical music, including the symphony, concerto, string quartet, and so on. Accordingly, there is a large body of theory on what unifies and distinguishes practice in the sonata form, both within and between eras. Even works that do not adhere to the standard description of a sonata form often present analogous structures or can be analyzed as elaborations or expansions of the standard description of sonata form.
Lets say Earths atmospheric pressure was reduced to 0.10 bar which is 10% Earths atmospheric pressure. The boiling point at this pressure is 113 degrees F. Due to the atmosphere being thinner there is a greater temperature difference with higher highs and lower lows in a 24 hour period.
Lets say...
The problem statement
Let V be a vector space of dimension 8 and f (endomorphism) such that the minimal polynomial of f is x^7. If B={v1,...,v8} is the Jordan basis of f, find the Jordan form and a Jordan basis for f^2 and f^3.
The attempt at a solution
Ok, I am having some trouble to...
How does circular DNA wrap around a histone to form a chromosome? Or does it?
I am having a hard time visualizing this for any sort of circular DNA: prokaryotes, mitochondria, etc.
(This question was inspired by my reading about biology and reading that circular DNA does, in fact, form...
Hi all,
I was just wondering, does the ionised form of a drug produce a pharmacological effect? I know that an ionised drug is lipid-insoluble so it cannot traverse across the membrane. However, my question is, what happens to them if they remain in the gastrointestinal tract? Does it still...
Homework Statement
Given the equivalent impedance of a circuit can be calculated by the expression:
Z = Z1 X Z2 / Z1 + Z2
If Z1 = 4 + j10 and Z2 = 12 - j3, calculate the impedance Z in both rectangular and polar form.
Homework Equations
Multiplication and division of complex...
Homework Statement
I want to derive the trig identities starting with rotation on the plane.
Homework Equations
One rotation through a given angle is given by
$$x' = xcosθ - ysinθ $$
$$y' = xsinθ + ycosθ$$
The Attempt at a Solution
What if I wanted to rotated through any...
Homework Statement
For cable AD it is known that the magnitude is 14 kips, x-component has a value of -6.216, the direction angle in the z-direction is 83.63°, and Fy is less than zero. Find forces in Cartesian vector form, coordinates of point D if it lies on the x-z plane and point A is (0...
The question comprises of three subparts which need to be converted to Clairaut's form and then solved :
(a) x p2 - 2yp + x + 2y = 0
(b) x2 p2 + yp (2x + y) + y2 = 0
(c) (x2+y2)(1+p)2-2(x+y)(1+p)(x+yp)+(x+yp)2=0
Note : p = dy/dx
I understand that Reducing to Clairaut's form...
Odd Form Of Eigenvalue -- Coupled Masses
This isn't strictly homework, since it's something I'm trying to self-teach, but it seems to fit best here.
Homework Statement
It's an example of applying eigenvalue methods to solve (classical) mechanical systems in an introductory text to QM...
I read that in string theory the Virasoro algebra contains an ##SL(2,R)## subalgebra that is generated by ##L_{-1}, L_{0}, L_{1}##. I read that this is the non-compact form of the ##SU(2)## algebra. Also, that as ##SU(2)## and ##SO(3)## have the same Lie algebra, so do ##SL(2,R)## and...
Hi,
as I read in one of Hawking books, he predicted that a 2D life-form with an alimentary canal can not exist because it would fall apart. I was wondering about that, because I thought of an easy solution for this: with two movable chainings its still possible. I have made a graphic and...
Homework Statement
Metric ansatz:
ds^{2} = e^{\tilde{A}(\tilde{\tau})} d\tilde{t} - d\tilde{r} - e^{\tilde{C}(\tilde{\tau})} dΩ
where: d\tilde{r} = e^{\frac{B}{2}} dr
Homework Equations
How to calculate second fundamental form and mean curvature from this metric?
The Attempt at a...
Homework Statement
A Triangle ABC has sides of length a, b and c labelled according to the usual convention. Forces of magnitude ka, kb and kc act along BC, CA and AB respectively, with the direction given by the order of the letters. By considering the vector sum of the forces, or otherwise...
Homework Statement
Hi.
I'm given a 3-dimensional subspace H that is made up of the states |1,-1\rangle, |1,0\rangle and |1,1\rangle with the states defined as |l,m\rangle and l=1 as you can see.
The usual operator relations for L_{z} and L^{2} applies, and also:
L_{+} = L_{x}+iL_{y}
L_{-} =...
Homework Statement
y(t) solves the following IVP
y''(t) + 2y'(t) + 10y(t) = r(t)
y(0) = 2
y'(0) = 3
r(t) =
0 if t < 0
t if 0 ≤ t ≤ 1
0 if t > 1
Demonstrate that the laplace transform of y(t) is
Y(s) = \frac{2s+7}{s^{2}+2s+7} + \frac{e^{-s}}{s(s^{2}+2s+7)} +...
Homework Statement
Let R be the region bounded by the lines y=1 , y=0 , xy=1 , and x=2 . Let \vec{F} = \begin{bmatrix} x^4 & y^2-4x^3y \end{bmatrix}^T . Calculate the outward flux of \vec{F} over the boundary of R .
Homework Equations
Green's theorem (normal form): \int_{\partial...
Homework Statement
Use integration by parts to show that
∫(sqrt(1-x^2) dx = x(sqrt(1-x^2) + ∫ (x^2) / sqrt(1 - x^2)
write x^2 = x^2 -1 + 1 in the second integral and deduce the formula
∫(sqrt(1-x^2) dx = (1/2)x(sqrt(1-x^2) + (1/2)∫ 1 / sqrt(1 - x^2) dx
I actually found a...
Hi,
I have some confusion about strain energy. When using Lagrange's equations to derive the EOM of vibrating structures, the strain energy is written as :
U = q^{T}Kq ; (q is the vector of generalized coordinates, and K is the stiffness matrix). Writing it in this form makes it easy to...
Homework Statement
Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me:
3.20 (P. 91)
In the 2-space with line element
ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}}
and...
In most of textbooks, the canonical quantization procedure is used to quantize the hamiltonian with a simple form, the quadratic form. I just wonder how should we deal with more complex form hamiltonian, such like the ones including interaction terms?
Homework Statement
I was just curious about determinate form of a plane if anyone has any info.
If you check out number 18 on wolfram I was pondering about this form. http://mathworld.wolfram.com/Plane.html
Homework Equations
The Attempt at a Solution
I would like to know why if...
Homework Statement
Let \vec{F}=<xy,5z,4y>
Use Stokes' Theorem to evaluate \int_c\vec{F}\cdot d\vec{r}
where C is the curve of intersection of the parabolic cylinder z=y^2-x and the circular cylinder x^2+y^2=36
Homework Equations
Stokes' Theorem, which says that \int_c\vec{F}\cdot...
Could someone suggest me an easy guide to transforming a system of differential equations into normal form around a particular point?
As I understand, normal forms are used in border collision bifurcations to define the new set of coordinates around the parameter value \mu _0. By doing this...
When finding lim(x->1) (1+2ln(x))^(1/(x-1)) = 1^(infinity) I let
y = (1+2ln(x))^(1/(x-1)) then ln both sides giving
ln(y) = ln(1+2ln(x)))/(x-1)
Taking the limit of ln(y) gives 1/0, which is indeterminate and hence the limit does not exist.
However, I typed this into MS Mathematics and got...
From the book of Nakahara "Geometry, Topology and Physics":
A diffeomorfism ##f:\mathcal{M}\to \mathcal{M}## is an isometry if it preserves the metric:
##
f^{*}g_{f(p)}=g_{p}
##
In components this condition becomes:
##
\frac{\partial y^{\alpha}}{\partial x^{\mu}}\frac{\partial...
I've been studying this kind of limits today and most of them were solved by the technique I mentioned in my previous topic, except for the one you just showed me how to solve and this one:
\lim_{x->0} (1 - cos(x))^{1/x}
(It approaches 0 from the left, but I don't know how to write it here)...
Can someone explain how these are equivalent.
sqrt((-3)^2) = (-3)^2/2
=sqrt(9) and (-3)^1
3 is not equal to -3
(-3)^2/2 can be expressed as:
(-3^2)^1/2 and (-3^1/2)2
(9)^1/2 and (sqrt(-1)sqrt(3))^2...
Hi, I have a question that is very close the the one of the OP so I tough I should post in here instead of making a new thread. (Hope no one mind )
Let's say
\lim_{x->\pm\infty}x(log \sqrt{x} - log(\sqrt{x}-y)-\frac{y}{\sqrt{x}} )=\frac{y^2}{2}
Now I could use taylor series to evaluate it, is...
what changes does there occur in the result of the gaussian distribution "integration e^-alpha*x^2 dx=sqrt(pi/alpha) if i substitute that x^2 with some (x-a)^2?
then what should be the integral result ?
Homework Statement
I have a circuit with input source x(t), which contains also an inductor and a capacitor in series which I have found to be related to the output voltage y(t) (across the capacitor) like so: LC*d2y/dt2 + y(t) = x(t). I have also found its roots through the quadratic...
Here is the question:
Here is a link to the question:
What is the limit of (tanh(x))^x as x approaches infinity? - Yahoo! Answers
I have posted a link there to this topic so the OP can find my response.
I've got a Fortran 95 program (which basically does few calculations) and I'd like to use it online. So that, the users will input data into a HTML form, the program will run, and it will display the results.
Would it be possible to do it in the following way?
To run a little program (e.g...
The basic equation of GR has a curvature constant Λ on the lefthand (geometric) side.
The Friedman equation is derived from the Einstein Field Equation by making a simplifying assumption of uniformity. As a spacetime curvature Λ can be written either in units of reciprocal area or reciprocal...
I feel a bit silly asking this, but I've been working through some QM lately and there's one aspect of Schrodinger's equation that's puzzling me. I've typically understood the equation as i\hbar \frac{d|\psi\rangle}{dt}=\hat H |\psi\rangle, but I've also seen it written as i\hbar \frac{\partial...
I want to know why everything in the universe forms a Ball or Sphere? Is gravity the cause of this? If so why? For example, If we were to pick the sphere apart can we see the source of gravity? Is gravity also a ball or sphere and can we grasp and see it? Why do we not ever see square planets or...
Homework Statement A 90Ω resistor, a 32 mH inductor, and a 5μF capacitor are connected in series across the terminals of a sinusoidal voltage source Vs = 750cos(5000t + 30)V.
Calculate the phasor current.
Homework Equations
phasor current i = V/Z
V in polar form = (Magnitude)(cos a + j sin...
Homework Statement
How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge e and mass m, with 4-momentum p^a and electromagnetic field tensor F_{ab} of a constant magetic field \vec B perpendicular to the plane of motion...
Predicting the functional form of solution of PDE
How do you conclude that the solution of the PDE
u(x,y)\frac{∂u(x,y)}{∂x}+\upsilon(x,y)\frac{∂u(x,y)}{∂y}=-\frac{dp(x)}{dx}+\frac{1}{a}\frac{∂^{2}u(x,y)}{dy^{2}}
is of the functional form
u=f(x,y,\frac{dp(x)}{dx},a) ?
I know this...
I have some rather technical questions about the complex exponential form of the Fourier series:
1) What is the motivation behind the complex exponential form? Why not just use the real form (i.e. with sine and cosines)?
2) Surely the complex exponential form is an orthogonal set, i.e...
What is the most general form of the metric for a homogeneous, isotropic and static space-time?
For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) signature)
ds^2=dt^2+a^2(t)g_{ij}(\vec x)dx^idx^j
Now the static condition. If I'm not mistaken...
Homework Statement
Calculate form factor of nucleus (A, Z given). Radius R = 1.2\cdot10^{-15}A^{\frac{1}{3}}Homework Equations
F(\textbf{q}) = \frac{1}{Ze} \int d^{3}\textbf{r} \rho(r)e^{i\textbf{q}\cdot \textbf{r}}The Attempt at a Solution
using polar coords d^{3}\textbf{r} = r^{2}dr...
Here is the question:
Here is a link to the question:
Express in the form a + bi, where a and b are real numbers.? - Yahoo! Answers
I have posted a link there to this topic so the OP can find my response.
Hey. I want to use integrals-math to get from Gauss law in divergence form to the one in integral form. I know you can do it by simply accepting ∇*E dV = ρ/ε => ∫ ∇*E dV= ∫ρ/εdV = Q/ε = ∫E*dA, but I want to do it another way. I want to begin with ∫∇*E*dV and end up with Q/ε.
So: E =...
I am creating a form using IBM Form Experience Builder. I want to create a survey as follows (content in [] denotes possible answers)
Do you still require a specified asset? [yes/no/I'm not the owner]
Do you know who the owner is? [yes/no]
Specify: []
Survey is complete
The...
Homework Statement
Reduce the Expression:
15sin(wt-45°) + 5cos(wt-30°) + 10cos(wt-120°)
to the form Vmcos(wt+θ)
Homework Equations
The Attempt at a Solution
My theta value at the end isn't coming out right.
My first step was to put make sure each term was in terms...
Hello MHB,
calculate \left(\frac{1}{2}+i\frac{\sqrt{3}}{2} \right)^{100} in the form a+ib
progress:
I start to calculate argument and get it to r=1 (argument)
then \cos\theta=\frac{1}{2} \ sin\theta=\frac{\sqrt{3}}{2} we se it's in first quadrant( where x and y is positive)...
Homework Statement
Solve the BVP:
r^{2}u_{rr} + ru_{r} + u_{ψψ} = 0
0 ≤ r ≤ 1, 0 < ψ < 2π
u(1,ψ) = 0.5(π - ψ)
Homework Equations
The Attempt at a Solution
I've derived the general solution of u(r,ψ) = C + r^{n}Ʃ_{n}a_{n}cos nψ + b_{n}sin nψ, where a,b, C are...
I have a set of questions concerning the perennial sum
\large \sum_{k=1}^{n}k^p
and its properties.
1. For p \ge 0, the closed form of this is known (via Faulhaber's formula).
I know little about divergent series, but I've read that in some sense there exists a value associated with these sums...
The Laguerre polynomials,
L_n^{(\alpha)} = \frac{x^{-\alpha}e^x}{n!}\frac{d^n}{dx^n}\left(e^{-x}x^{n+\alpha} \right)
have n real, strictly positive roots in the interval \left( 0, n+\alpha+(n-1)\sqrt{n+\alpha} \right]
I am interested in a closed form expression of these roots...