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.
in the language of general relativity,we know that we can write
$$\nabla_{V}W $$
in this form such that:
$$\nabla_{V}W = = w^i d ( V^j e_j)/du^i = w^j e^i (V^j e_j ) = W( V)$$
where $$w^i * d/ (du^i) =W$$ will act on the vector V
where $$W = w^i d( ) /du^i $$ and W is a vector as a...
I've looked for a while and can't find an answer to this, hence the post. Ultimately this is a question about how the first pieces of "classical" matter formed from quantum matter. My study of self-organizing systems shows that you need a hierarchical build-up of structures to allow a complex...
I'm reading through Thomson's "Modern Particle Physics", and I've gotten stuck at a point in the derivation of the form factor for electron scattering in a static potential due to an extended charge distribution. It's just a mathematical "trick" i don't quite get.
He goes from
$$\int\int...
Good evening everybody.
This is my suggestion for answer.
The tensor is diagonal and the compression is a plane stress
equilibre equation div(σ)=0
so:
So, does that means that
= f(y.z) = Ay+Bz and
=f(x.z)= Cx+Dz
A,B,C and D are constants.
Is that what the question meant?
Thank you in...
I've just been learning about Gauss' law which as far as I can tell states that the net electric flux through a surface equals the enclosed charge divided by the permittivity of free space, and is often expressed as the integral $$\int_S {\bf{E} \cdot d \bf{A}} = \frac{Q}{\epsilon_0}$$In some...
By working with the following definition of minimum of a quadratic form ##r(\textbf{x})##,
##\lambda_1=\underset{||\textbf{x}||=1}{\text{min}} \ r(\textbf{x})##
where ##\lambda_1## denotes the smallest eigenvalue of ##r##, how would one tackle the above problem?
It is clear that the diagonal...
I just ran this pretty quick at work. But this is the general outline. Sorry for the slop, it will get better with time. Thanks in advance and any additional info can be supplied.
The material is from the Khan free course.
.....
A student is fed up with doing her kinematic formula homework...
How did you find PF?: google
Hi
I have a scenario where I just cannot make up my mind when creating this joint and hinge at the same time.
Obviously yellow is the hinge, red section to the left has two wings hanging off it held there by two hinges, 250 um.
thinking about ultra sonics to...
Hey! :o
I am looking at the following exercise:
Construct a composite Turing machine $M$ that has a word $w$ over the alphabet $A = \{a, b\}$ tests to see if it's made up of two equal parts, that is, if $w = uu$ with $u \in {a, b}^+$.
In this case, at the end of the method a $1$ has to be...
Hey! :o
I am looking the follwong exercise:
Using the method of Quine-McCluskey, determine the prime implicants for the following switching function and find a disjunctive minimal form. If available, also specify all other disjoint minimal forms.
The switching function is...
According to this image, in the attached files there is the demonstration of the ampere's law in differential form. Bur i have some difficulties in understanding some passages. Probably I'm not understanding how to consider those two magnetic vectors oriented and why have different name.
in...
Formula I have shows is probably for resulting harmonic? Does syntesizing mean writing the main formula? I havo no clue about effective value of signal and representation is probably done in excel or other graphing app.
As far as I know we can express the position and momentum operators in terms of ladder operators in the following way
$${\begin{aligned}{ {x}}&={\sqrt {{\frac {\hbar }{2}}{\frac {1}{m\omega }}}}(a^{\dagger }+a)\\{{p}}&=i{\sqrt {{\frac {\hbar }{2}}m\omega }}(a^{\dagger }-a)~.\end{aligned}}.$$...
Lets take for example Gauss's law in integral form. Suppose at time ##t## we have charge ##q(t)## (at the center of the gaussian sphere) enclosed by a gaussian sphere that has radius ##R>>c\Delta t##. At time ##t+\Delta t## the charge is ##q(t+\Delta t)## and if we apply gauss's law in integral...
Hey guys,
Sorry that it's been a decent amount of time since my last posting on here. Just want to say upfront that I am extremely appreciative of all the support that you all have given me over my last three or four posts. Words cannot express it and I am more than grateful for it all. But, in...
Hey guys,
I'm kind of in a rush because I'll have to go to my classes soon here at USF Tampa, but I had one last problem for Intermediate Analysis that needs assistance. Thank you in advance to anyone providing it.
Question being asked: "Let $A$ be a nonempty set of real numbers which is...
I was trying to solve a differential equation that I defined to study the dynamics of a system. Meanwhile, I encounter integration. The integration is shown in the image below. I tried some solutions but I am failed to get a solution. In one solution, I took "x" common from the denominator terms...
The only thing tripping me up here is that the answer needs to be in vector form. If the question was asking for the scalar form, then I would just find the distance between the charges (plot the charges according to their vector coordinates, then use pythagorean theorem to find the distance...
Summary: could you explain why this equality is a quadratic form identity?
i read this equality (4.26) here w depends on two variables. it is written that if B is bounded (L2) then it is a quadratic form identity on S. what does it mean? is it related to the two variables?
next the author...
Backstory - I have not been in school for 5ish years, and am returning to take some grad classes in the field of Solid Mechanics. I am freaking out a bit about the math (am rusty). I have not started class yet, but figured I would get my books and start working through problems. This problem...
I'm unclear on what exactly an annihilation or creation operator looks like in QFT. In QM these operators for the simple harmonic oscillator had an explicit form in terms of
$$
\hat{a}^\dagger = \frac{1}{\sqrt{2}}\left(- \frac{\mathrm{d}}{\mathrm{d}q} + q \right),\;\;\;\hat{a} =...
The Minkowski metric for inertial observers reads ##ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2##. Is there a way to show that if it had off diagonal terms, the inertial observers would not see light traveling with the same speed?
Is it appropriate to say that within classical physics the general form of Newton II is the Cauchy momentum equation?
This equation applies to an arbitrary continuum body. Therefore it is more general than the common form of Newton II which applies basically to point masses and centers of mass...
There are essentially three cases of the rational ODE $(ax+by+c)\,dx+(ex+fy+g)\,dy=0,$ since there are two straight line expressions multiplying the differentials. We will think of this geometrically, then translate to the algebraic approach. The tricky part to these problems is keeping track of...
I want to make a small item in Stainless Steel Sheet of 1.2 mm thick, 18 inch width & 24 inch length, by "Metal Forming & Punching of Holes". Please suggest me, which grade of Stainless Steel Sheet is more soft or ductile? It has to be economical as well. Thank you.
The integral has the form:
$$\frac{s^2\nu^4}{(2\pi)^2}\int_{-1}^1 u(1-u^2)k_f^5[|r_1\chi_1|^2+|r_1\chi_2|^2-|r_1|^2\chi_1^*\chi_2\cos(2k_f\sqrt{u^2-\nu^2}a)-|r_1|^2\chi_2^*\chi_1cos(2k_f\sqrt{u^2-\nu^2}a)]\, du$$
##r_1,\chi_1## and ##\chi_2## are also imaginary functions of u, because the form...
I am studying a beginner's book on QFT.
In a chapter on electromagnetic form factors, the authors have written, using normalized states,
$$\begin{eqnarray}
\langle \vec{p'}, s'| j_\mu (x) |\vec{p}, s \rangle \ = \ \exp(-i \ q \cdot x) \langle \vec{p'}, s'| j_\mu (0) |\vec{p}, s \rangle...
Hi,
The following is called normal form of the conic section equation:
x²+y²+2ax+2by+c=0
A circle is one of the conic sections when considered as a special of ellipse. I'm confused as to why the the given equation is called "normal form of the conic section equation" when, in my opinion, the...
From Thomas Moore A General Relativity Workbook I have the geodesic equation as,
$$ 0=\frac{d}{d \tau} (g_{\alpha \beta} \frac{dx^\beta}{d \tau}) - \frac{1}{2} \partial_\alpha g_{\mu\nu} \frac{dx^\mu}{d \tau} \frac{dx^\nu}{d \tau} $$
as well as
$$ 0= \frac{d^2x^\gamma}{d \tau^2} +...
Now that I think about this some more, nucleons can get close together if they are traveling at a very high speed. So maybe when the Earth first formed, stuff was moving fast (or at high temperature/pressure) and this forced nucleons together into nuclei? I don't really know what I'm talking...
Hello everyone, I'm trying to make lubrication out of paraffin, this is what I am doing, 1/3 melted paraffin wax, 1/3 paraffin oil, and 1/3 xylene. After melting the wax I add the oil, I then add the oil, mix it well to the correct consistency, I then transfer it to a glass container where I...
Determine if the set of vectors
$\begin{bmatrix}
x\\y\\5
\end{bmatrix}\in \Bbb{R}^3$
form a vector space
ok if I follow the book example I think this is what is done
$\begin{bmatrix} x_1\\y_2\\5 \end{bmatrix}
+\begin{bmatrix} x_2\\y_2\\5 \end{bmatrix}
+\begin{bmatrix} x_2\\y_2\\5...
Hi so I'm really new to stats, like I know mean, median, mode, and t-testsish and that is it. However, this topic really resonates with me because I know it can have real world applications. So these are my questions.
First off here is my real world problem. At my workplace, we sell food that...
I know that the height before the first bounce will be ##y = g * t * t + v_0 * t + y_0##.
After the first bounce, I can find y by pretending the ball was thrown from the ground with velocity ##e * -v_f## with ##v_f## being the velocity of the ball when hitting the ground, but I have to reset the...
Problem Statement: The effective charge density of the electron cloud in a hydrogen atom in its quantum mechanical ground state turns out to be given by pnot(e^-(r/rnot)), where pnot is a negative constant (the clouds charge density at r=0) and rnot is a constant (rnot=0.025nm). Use gauss's law...
Hello,
For my homework I am supposed to get-
into the form of a Bessel equation using variable substitution. I am just not sure what substitution to use.
Thanks in advance.
nmh{896} mnt{347.21}
consider th non-homogeneous first order differential system
where $x,y,z$ are all functions of the variable t
\begin{align*}\displaystyle
x'&=-4x-3y+3z\\
y'&=3x+2y-3z+e^t\\
z´&=-3x-3y+2z
\end{align*}
write a system in the matrix form $Y'=AY+G$
Akio coaches the girls volleyball team. He needs to select players for the six different starting positions from his roster of 16 players. On Akio’s teams, each position has its own special responsibility: setter, front left-side and middle hitters, back right- and left side passers, and...
In my last post I asked about the general form of the Lorentz Transformation for time. Now I am trying to understand the final form of it, and how it makes sense based on what's happening physically. The final form for t is:
t = γt1 + (γv/c2/)x1
It's the second part of this equation, the...
Hi.
I've the following charge density: ## \rho = \rho_0 \frac {r}{R} ##
I'm getting a trouble to calculate the potential inside a sphere of radius R located in the center of axis with the given charge density (using poisson equation):
the Laplacian in spherical coordinates is: ##\frac {1}{r^2}...
Express -3-3i in polar form.
I know that r=3√2.
And I understand that now we take tan^-1(b/a) which I did. tan^-1(-3/-3) = π/4. So I put my answer as z = 3√2 [cos(π/4) + isin(π/4)].
However the answer manual told me this was incorrect I am unsure of where I went wrong...