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.
Homework Statement
"The complex power spectral density is :
S(jw)=(1/(w*(w^2+a^2))*e^j90
Find the form and duration of the signal."
Homework Equations
Any ideas on how to solve this ?[/B]The Attempt at a Solution
What I've managed to calculate so far is:
http://tinypic.com/r/zydamr/9
Hi. I was investigating through this week why there are the differential forms, why are they anti-symmetric, why do we have the Jacobian when expressing the volume in a different coordinate system. This was just fantastic! I found all the connections between these topics. And I found that all of...
Specifically how did the stars collapse into themselves. If gravity varies by the distance squared and gas pressure varies by the volume cubed, how could a cloud of hydrogen, or any gas for that matter, collapse into itself? Not to mention the fact that the heat increases which would also...
Homework Statement
I guess this is a general question. in the book, it was originally in a normal form, but it was then converted into a double angle form, which I would have to use double angle forumla to compute, so what's the point of simplifying in the first place?
Homework EquationsThe...
Homework Statement
The question asks me to express the system shown in the image in state-space form, firstly by using the transfer function which was fine but the second part asks to express in state-space form by using the components A,B,C,D as the states x1,x2,x3,x4
Homework Equations
U(s)...
Homework Statement
I'm fine with the first part. Part b) is causing me trouble
http://imgur.com/xA9CG5G
Homework EquationsThe Attempt at a Solution
I tried subbing in the solution y1 into the given equation, but I'm not sure how to differentiate this, i thought of using integration by parts...
Homework Statement
I've used z* to mean z conjugate.
Given the equation z + 2iz* = 8 + 7i, express z in the form a + ib.
From SQA Advanced Higher Mathematics 2005 Exam Paper
Homework Equations
n/a
The Attempt at a Solution
I substituted a+ib and its conjugate in for z and z*, which, after...
Dear all:
I am studying the finite difference method for black scholes equation(heat equation form), and my Prof. asked me to use the Crank Nicolson and Compact Scheme to do it. But I cannot reach second order for the space, i.e., x . The error only reach 1st order and sometimes not stable, it...
Hello, so while i was doing my own revision. When putting tan^-1(1/-√3) i receive the answer as -30. however, (im doing demovoier's theorem) in the revision book it says the answer should be 5π/6 .
Help to brighten me? thanks.
Homework Statement
[/B]
"Absorption spectra of gaeous HCl show a line at 3.5 μm which results form molecular vibration (oscillation from interatomic distance)" How do I get the frequency of vibration from this?
Homework Equations
? If I knew this, then I could probably solve the problem
The...
Homework Statement
you are given the standard form z = 3 - 3i
Homework EquationsThe Attempt at a Solution
so to convert this to polar form, i know that ##r = 3√2## but how do i find theta here? There are so many mixed answers it seems online that I can't tell... i know that ##(3,-3)## is in...
I am working on a lab where we were measuring how magnetic force between two parallel conductors varies with current and the separation between the two conductors. I need to find a formula for the dependence of Force on current to create a fit line on the data in my graph that shows the relation...
I am basically just rewriting a question that was posted on other forums.
While watching videos of a MIT lecture on the eigenstates of angular momentum (video: '16. Eigenstates of the Angular Momentum II' by MIT OpenCourseWare) the professor visualized different spherical harmonics for low...
Homework Statement
well this is not exactly a homework, i had an argument whith my teacher about my grade in a test, because i put a complex number in the form of R,theta and she claims that the form was costheta+isentheta, and i know that but i need to prove in a book that...
Homework Statement
A beam of length L is fixed on one end and roller supported on the other end. An axial force P is applied on the ends of the beam. The beam is loaded with a uniform distributed load (q) along its entire length. The beam has constant EI. Find an expression for the maximum...
Few months back, in the final rounds of biology olympiad for Highschool students, i was asked, "Plants distributes sugar in the phloem as sucrose molecules, why did plant do this, and is there any advantages? Why not other form of sugar like glucose?"Can anyone help me? :3
Also i was wondering...
Homework Statement
Find the Jordan canonical form of the matrix ##
\left( \begin{array}{ccc}
1 & 1 \\
-1 & 3 \\ \end{array} \right)##.
Homework EquationsThe Attempt at a Solution
So my professor gave us the following procedure:
1. Find the eigenvalues for each matrix A. Your characteristic...
Hi all,
I was doing some math and I stumbled upon a very interesting thing. When I do ln(-1), I get πi, and when I turn that into polar coordinates on the calculator, it gives me πeiπ/2 . Why is that? I'm very curious to know, because they are so intertwined!
Thank you
Let $a, b \in \Bbb R$ and $u, v \in \Bbb R^2$, with $u = (0, 1)$ and $v = (1, 0)$. Show that every vector in $\Bbb R^2$ is of the form $au + bv$. Under what conditions is this true for general vectors $u = (u_1, u_2)$ and $v = (v_1, v_2)$?
No idea where to begin. Would appreciate any help.
Hello all, I am posting this question here in this thread and not the homework thread since it is not a homework problem but something I have been working on myself.
Let us imagine a fluid flowing through a pipe, we can measure pipe diameter and fluid velocity. The density of the fluid is also...
Homework Statement
Write the density operator
$$\rho=\frac{1}{3}|u><u|+\frac{2}{3}|v><v|+\frac{\sqrt{2}}{3}(|u><v|+|v><u|, \quad where <u|v>=0$$
In matrix form
Homework Equations
$$\rho=\sum_i p_i |\psi><\psi|$$
The Attempt at a Solution
[/B]
The two first factors ##\frac{1}{3}|u><u|##...
I have known what Ornstein-Zernike equation is. I try to plug in the form as follow to the isotropic materials:
Still, I cannot show the pair correlation function as follow.
Can anyone know what I have missed?
Homework Statement
[/B]
The door is held open by the means of 2 chains. If the tension in AB and CD is Fa = 300 N and Fc = 250 N, respectively, express each of these in Cartesian Vector Form
Homework Equations
Sin / cos / tan
The Attempt at a Solution
The angle of FA at B is...
I am unsure whether I am posting in the right place, but was hoping someone could help me out.
I was wondering if anyone knows the shape of the material at the beginning of the manufacturing process of a stub axle, and how the shape will vary depending on the quantity of products being made...
Dear all,
I have a question regarding the computation of the area of an ellipse. The parametric form of the ellipse with axes a and b is
$$x(t) = a\cos{(t)}, \ \ \ y(t) = b\sin{(t)} $$
Using this to evaluate the area of the ellipse, usually one takes one halve or one quarter of the ellipse...
Homework Statement
Using only NOT and XOR, construct a compound statement having the same truth table as:
(a) p OR q
(b) p AND q
Homework Equations
XOR is "exclusive OR." p XOR q = (p OR q) AND NOT (p AND q).
I have been working under the assumption that I can use parentheses.
The...
I thought that z= 7.5 was the maximum for galaxies to form after re ionization but this paper puts it at z=8.38,
can galaxies have formed this early?
arXiv:1703.02039 [pdf, other]
Dust in the reionization era: ALMA observations of a z=8.38 Galaxy
Nicolas Laporte, Richard S. Ellis, Frederic...
Homework Statement
Homework Equations
r=sqrt(a^2+b^2)
θ=arg(z)
tan(θ)=b/a
The Attempt at a Solution
for a)[/B]
finding the polar form:
r=sqrt(-3^2+(-4)^2)=sqrt(7)
θ=arg(z)
tan(θ)=-4/-3 = 53.13 °
300-53.13=306.87°
-3-j4=sqrt(7)*(cos(306.87+j306.87)
I don't know if my answer is correct...
I cannot find any explanation of the mathematical form of the single-mode photon number states, i.e. the |n>.
I take them to be functions with domain {0,1,2,3, …} and appropriate associated outputs.
So |3> I take to have outputs {0,0,0,1, 0, …} , |0> to have outputs {1,0,0,0, 0, …} and...
Hello
I was solving a problem in probability. Here is the statement.
Seven terminals in an on-line system are attached to a communications line to the central computer. Exactly four of these terminals are ready to transmit a message. Assume that each terminal is equally likely to be in the ready...
Hi, I was just looking at an example for a certain problem and noticed that in the second step they went to arctan(epsilon). I know there's a form that is equal to arctan but am a little unsure.
I've come across formulas on the web such as
arctan(x) = ∫(dt)/(a2+t2)
but nothing else that would...
Is there a closed form for the constant given by:
$$\sum_{n=2}^\infty \frac{Ei(-(n-1)\log(2))}{n}$$
(Where Ei is the exponential integral)?
Could we generalize it for:
$$I(k)=\sum_{n=2}^\infty \frac{Ei(-(n-1)\log(k))}{n}$$
?
My try: As it is given that k will be a positive integer, I have...
Homework Statement
Show that the set GL(n, R) of invertible matrices forms a group under matrix multiplication. Show the same for the orthogonal group O(n, R) and the special orthogonal group SO(n, R).
Homework EquationsThe Attempt at a Solution
So I know the properties that define a group are...
Homework Statement
Show that every matrix A ∈ O(2, R) is of the form R(α) = cos α − sin α sin α cos α (this is the 2d rotation matrix -- I can't make it in matrix format) or JR(α). Interpret the maps x → R(α)x and x → JR(α)x for x ∈ R 2
Homework EquationsThe Attempt at a Solution
So I know...
After series of algebraic simplifications, I ended up with the following integral:
##\int_0^\infty \exp(-Kx) \arctan(x) dx ##
As far as I searched, there is no closed form solution for the integral. But, K is my design variable that I need to optimize later. To do this, I need to take K out of...
Is the Hubble's law(recessional velocity linearly proportional to distance) valid for all cases even when the spacetime is curved? Is there a nonlinear model for Friedman models or it's always linearly proportional?
From Courant's Differential and Integral Calculus p.13,
In an ordinary system of rectangular co-ordinates, the points for which both co-ordinates are integers are called lattice points. Prove that a triangle whose vertices are lattice points cannot be equilateral.
Proof: Let ##A=(0,0)...
Homework Statement
3 charges are placed like shown:
Q1 __4cm____ Q2 ______6cm___________Q3
Q1=-2nC
Q2= 1nC
Q3= 3nC
Find the resultant force and its direction upon the charge Q3.
Homework Equations
F=k0*(Q1Q2)/r2
k0-constant, equals to 9*10^9
r-distance
The Attempt at a Solution...
Homework Statement
I need help when changing the formula of the yellow circled part to red-circled part ...
Homework EquationsThe Attempt at a Solution
I tried , but i didnt get what the author got ... Here's my working ... Which part of my working is wrong ?
Homework Statement
[/B]
Suppose a quadratic equation in 3 variables is put into a standard form represents a hyperboloid of one sheet. This hyperboloid has the property that:
• the cross section through z= 0 is a circle of radius 1;
• the cross section through x= 1 is the two straight lines...
Homework Statement
Let |z+1| + |z-1| = 7 where z are complex numbers. Show that the solutions to this equation form an ellipse with foci at (+/-)1
Homework Equations
(x^2 / a) + (y^2 / b) = 1 equation for an ellipse
The Attempt at a Solution
I set z = a + bi and so |z-1| = ((a-1)^2 + b^2)^1/2...
Homework Statement
\frac{z-1}{z+1}=i
I found the cartesian form, z = i, but how do I turn it into polar form?The Attempt at a Solution
|z|=\sqrt{0^2+1^2}=1
\theta=arctan\frac{b}{a}=arctan\frac{1}{0}
Is the solution then that is not possible to convert it to polar form?
Homework Statement
Hi,
As part of the proof that :
the set of periods ##\Omega_f ## of periods of a meromorphic ##f: U \to \hat{C} ##, ##U## an open set and ##\hat{C}=C \cup \infty ##, ##C## the complex plane, form a discrete set of ##C## when ##f## is a non-constant
a step taken in the...
I have recently been attempting to solve a problem that has been bugging me for quite some time. I've gotten back into calculus and integrals to attempt to solve a little formula I'm trying to build for a simulation test. Over-all, if I have ##\int _0^bv^2x\ dx## I'd expect the outcome to be...
I understand the concept of Kmaps, Quine method and forming a logic diagram but I'm lost at forming an equation from an addition and subtraction equation
For example: a 2 bit plus a 3 bit binary integer. I would have a 4 bit sum and 3 carries. However, how does one form the appropriate equation...
Homework Statement
Find the closed form of the impulse response of the system y[n] = 7y[n-1]-12y[n-2]+x[n] using the peel away and guess method. Ie, by using Python code to find the geometric ratios and amplitudes of the outputs as n grows large, then calculate residuals, and find the...
I have been studying the Higg's field and ran across a particular equation that made me realize I need to better understand Sturm-Liuoville. So naturally I went looking through my differential calculus textbooks but was surprised they didn't cover this detail. While the article covers how to get...
Homework Statement
I'd like to know how to convert Maxwell's Equations from Differencial form to Integral form.
Homework Equations
Gauss' Law
Gauss' Law for Magnetism
Faraday's Law
The Ampere-Maxwell Law
The Attempt at a Solution
Convert using properties of vector analysis (as Divergence and...
Why is i that two cones connected at their vertices is not a manifold? I know that it has to do with the intersection point, but I don't know why. At that point, the manifold should look like R or R2?