Form Definition and 1000 Threads

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.

View More On Wikipedia.org
  1. YogiBear

    Finding a parametric form and calculating line integrals.

    Homework Statement Let C be the straight line from the point r =^i to the point r = 2j - k Find a parametric form for C. And calculate the line integrals ∫cV*dr and ∫c*v x dr where v = xi-yk. and is a vector field Homework EquationsThe Attempt at a Solution For parametric form (1-t)i + (2*t)j...
  2. M

    When do roots of a polynomial form a group?

    I've been studying for my final exam, and came across this homework problem (that has already been solved, and graded.): "Show that the Galois group of ##f(x)=x^3-1## over ℚ, is cyclic of order 2." I had a question related to this problem, but not about this problem exactly. What follows is...
  3. R

    Converting a limit to integral form or vice-versa

    What is the proof for this $$ \int_a^b f(x) dx = 1/n\lim_{n\to\infty} (f(a) + f(a+h) + f(a+2h) +...+ f( a+ (n-1)h)) $$ h = (b-a)/n Also I think there is some summation form which can be converted to integral form how?
  4. binbagsss

    Why do proton and neutron form isospin doublet? I3 or I?

    As far as I understand, ##I_{3}##, the component of isospin in a certain direction is additive, but ##I## is to be treated as a vector sum, is this correct? So, ##I_{3}=1/2## for ##u## quark, ##I_{3}=-1/2 ## for ##d## quark. Adding ##I_{3}## then for a proton we find ##I_{3}=1/2## and for a...
  5. R

    How to Calculate the Magnetic Field Using Ampere's Law in Differential Form?

    Homework Statement A long cylindrical wire of radius R0 lies in the z-axis and carries a current density given by: ##j(r)= j_0 \left( \frac{r}{R_0} \right)^2 \ \hat{z} \ for \ r< R_0## ##j(r) = 0 \ elsewhere## Use the differential form of Ampere's law to calculate the magnetic field B inside...
  6. M

    MHB Help converting two standard form equations to slope intercept form?

    Hi guys, I have a few tries at this but I keep coming up wrong, so can anyone show me how to convert these two standard form equations into slope intercept form? 2x - 11y = 2, -6x + 3y = 9. Greatly appreciate any help offered :) Thank you!
  7. KevinMWHM

    Trouble understanding differential k form

    Homework Statement data[/B] Solving differential k forms. Homework Equations I don't want to give any exact problems from my problem set. The Attempt at a Solution solution.[/B] The text I'm using, CH Edwards, is very abstract in this section and the explanation over a sped up, last class...
  8. E

    Is xTAx always non-zero for a real, symmetric, nonsingular matrix A?

    Basic question, I think, but I'm not sure. It is a step in a demonstration, so it would be nice if it were true. True or false? Why? If A is a real, symmetric, nonsingular matrix, then xTAx≠0 for x≠0.
  9. NaturalSymphony

    Geophysics: Dynamic form factor and Equipotential surfaces

    I've got the following problem which I need help with. I'm used to calculating coefficients when the problem is about ellipsoids and first order approximations. But when it comes to spheres and coefficients J_n I really don't know how to approach the problem. Can somebody help me out? Consider...
  10. S

    MHB Solving System of ODEs: Matrix Form, Eigenvalues/Vectors

    Getting stuck on something I think that could be trivial. Maybe someone can see my mistake. consider the system: $x' = -2x + y$ and $y' = 2x - 3y$ a) Write the system in matrix form my solution $\overrightarrow{X} = (^x_y)$ so: $X' = (^{x'}_{y'})$ so $A = $ \begin{bmatrix} -2 & 1 \\ 2 & -3...
  11. topsquark

    MHB Confusion about the Killing form for A1

    This is a long one if you have to follow all of my steps. If you are reasonably familiar with Killing forms then you can probably just skip to the three questions. Okay, I'm on my latest project which is to get some idea about how Dynkin diagrams and Coxeter labels work. (How do you pronounce...
  12. U

    Form Factor - Simply take the real part?

    Homework Statement Show that the Form factor is ##\frac{3(sin x - x cos x)}{x^3}##. Homework EquationsThe Attempt at a Solution [/B] I know that the form factor is simply the Fourier transform of the normalized charge density: F(q) = \int \frac{\rho}{Z} e^{-i (\Delta \vec k) \cdot \vec r}...
  13. ELB27

    Determining Uniqueness of Reduced Echelon Form

    Homework Statement Is the reduced echelon form of a matrix unique? Justify your conclusion. Namely, suppose that by performing some row operations (not necessarily following any algorithm) we end up with a reduced echelon matrix. Do we always end up with the same matrix, or can we get different...
  14. T

    How do I graph in vertex form with an equation like (x+1/2)^2 = 12(y - 3)?

    I've run into stumbling block here, is some sort of conversion required when your equation looks like: (x+1/2)^2 = 12(y - 3). Do I move it to standard form or can I graph it as is?
  15. S

    Understanding Phasors: How to Sketch a Voltage Phasor in Polar Form

    Hello Excuse me, but how do I sketch the phasor of a voltage that it's V=5cos(10t+30degrees) and how the V=5sin(10t+30degrees) ? I know that these can be converted as the R<angle polar form, with R being the Vmax, ie the 5, and the angle the phase. But what doesn't it matter if I have cos or...
  16. J

    MHB Can $\mathbb{Z}[\sqrt{-3}]$ Be Proven as a Principal Ideal Domain?

    Hi, Im trying to prove that a prime $p\neq 3$ is of the form $p=x^2 + 3y^2$ if $p \equiv 1 \pmod{3}$. I have think in a prove as follows: As we know that $-3$ is a quadratic residue mod p, we know that the ideal $(p)$ must divide $(x^2 + 3) = (x + \sqrt{-3})(x - \sqrt{-3})$ in the ring...
  17. C

    Finding the Value of cot(pi/8) in the form a + b*sqrt(2)

    Homework Statement Show that sin(2θ) / (1 + cos(2θ) = tan(θ) - I've completed this part Hence find the value of cot(π/8) in the form a + b√(2), where a, b ∈ ℤ Homework Equations cot(θ) = (1 + cos(2θ)) / sin(2θ) The Attempt at a Solution I did the math, got (1 + cos(π/4)) / sin(π/4) = (1 +...
  18. S

    Rutherford scattering - electromagnetic form factor

    Homework Statement Hi there. This is not really a problem, I am only trying to understand something but I simply can't. So Rutherford scattering says that $$ \frac{d\sigma }{d\Omega}=(\frac{Ze^2m}{8\pi \varepsilon _0 p^2})^2\frac{1}{\sin ^4(\Theta/2)}|F(q)|^2$$ where $$F(q)=\int \rho (\vec...
  19. S

    MHB Determine equation of line described. put in slope intercept form if possible

    okay so as usual I am stumped ( I am not sure if I dislike math, or simply those who proclaim to be teachers of it. Spouting off steps is not the same thing as teaching ) Anyway, I have a problem that requires me to determine the equation of the line described: Through (6,-4), perpendicular to...
  20. Z

    Putting non-Calculus Physics problems in Calculus form

    I'm a sophomore Physics major currently taking Mechanics, and I recently noticed something when I was going over some homework. I am really good at Calculus, and I noticed I tend to do way better on the calculus based problems (i.e. work, finding force from potential energy etc) than some of the...
  21. ichabodgrant

    Prove arcsin x for its logarithm form

    Homework Statement Given sin x = (eix - e-ix) / 2i, I want to prove that arcsin x = -i ln(ix + √1 - x2) Homework Equations I know about the Euler's formula and complex number. But I have never learned about complex logarithms. The Attempt at a Solution I try to use x = sin y. But it seems...
  22. Abtinnn

    Formation of X-Ray Binaries Outside Black Holes

    Just curious... I mean they don't form inside the event horizon, so how would they form outside? How does accretion do this?
  23. R

    Gauss's Law (Differential Form)

    Homework Statement Find the electric field inside and outside a sphere of radius R using the differential form of Gauss's law. Then find the electrostatic potential using Poisson's equation. Charge density of the sphere varies as ##\rho (r) = \alpha r^2 \ (r<R)## and ##\rho(r)=0 \...
  24. manogyana25

    Can energy transferred from one body to the other be of same form?

    Suppose some energy, say light energy transfers from one body to another .. Then will the light energy transferred to the second body also be in the form of light energy? I mean are there any chances that the energy transferred between two different bodies be of same kind of energy? If yes...
  25. T

    Three electrons form an equilateral triangle

    1. Homework Statement Three electrons form an equilateral triangle 1.00nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges? Known Variables: s = 1.00 × 10-9m p+ Charge = 1.60 × 10-19C e- Charge = -1.60 × 10-19C r = s/√(3) = 5.77 ×...
  26. J

    General form for 2 x 2 unitary matrices

    I'm trying to show that any unitary matrix may be written in the form \begin{pmatrix}e^{i\alpha_1}\cos{\theta} & -e^{i\alpha_2}\sin{\theta}\\ e^{i\alpha_3}\sin{\theta} & e^{i\alpha_4}\cos{\theta}\end{pmatrix} Writing the general form of a unitary matrix as U=\begin{pmatrix} u_{11} & u_{12}\\...
  27. anemone

    MHB Find closed form expression for a given sum

    Find a closed form expression for \sum_{k=1}^{n^2}\dfrac{n-\lfloor\sqrt{k-1}\rfloor}{\sqrt{k}+\sqrt{k+1}}.
  28. M

    Why is the general form of the wave equation a second order partial derivative?

    When I deduct the the general form of wave equation, I noticed it has a second order partial derivative form. I am wondering why wave equation has a second order partial derivative form nor a first order partial derivative form?
  29. P

    Find all orthogonal 3x3 matrices of the form

    Homework Statement Find all orthogonal 3x3 matrices of the form \begin{array}{cc} a & b & 0 \\ c & d & 1\\ e & f & 0 \\\end{array} Homework Equations There are many properties of an orthogonal matrix. The one I chose to use is: An n x n matrix is an orthogonal matrix IFF $$A^{T}A = I$$. That...
  30. baby_1

    Find theta angle in complex form

    Homework Statement Here is my equation that I want to find theta angle Homework EquationsThe Attempt at a Solution I try to set different value of cos (theta) to find theta but it failed , I want to know the main solving strategy Thanks
  31. M

    The Cooper pair box Hamiltonian in the matrix form

    Hello, In my problem I need to We are advised to create the Cooper pair box Hamiltonian in a matrix form in the charge basis for charge states from 0 to 5. Here is the Hamiltonian we are given H=E_C(n-n_g)^2 \left|n\right\rangle\left\langle...
  32. S

    How Does Angular Momentum Operate in Exponential Form?

    Hey! How does the operator of angular momentum operates in exponential form? $$ e^{-i\theta J}\vert l, m \rangle = ?? $$ where $$J\vert \Psi \rangle = J\vert l, m \rangle$$ and $$J^2\vert \Psi\rangle = \hbar^2 l(l+1)\vert \Psi\rangle $$ Also, how do you operate $$J_-$$ and $$J_+$$...
  33. C

    FEM: How the weak form is related to an inner product

    Hi all, I am a final year maths student and am doing my dissertation in the finite element method. I have gotten a little stuck with some parts though. I have the weak form as a(u,v)=l(v) where: $$a(u,v)=\int_{\Omega}(\bigtriangledown u \cdot\bigtriangledown v)$$ and $$l(v)=\int_\Omega...
  34. Y

    How does the dark and bright fringes form ?

    When there is a water wave in a ripple tank( not involving any interference experiment ) there will be a pattern on the bottom of the ripple tank , that is the the dark and bright fringes. How does the bright fringes and dark fringes form for only water waves experiment in ripple tanks ? It...
  35. evinda

    MHB Find solution that satifies the differential equations and has a specific form

    Hello! (Smile) I am looking at the following exercise: Let $I=(0,1)$. Find the solution $\phi$ that has a continuous derivative in $\mathbb{R}$ and satisfies : $$y''=0 \text{ in } I \\y''+k^2y=0 \text{ apart from } I, \text{ where } k>0$$ and furthermore $\phi$ has the form...
  36. caffeinemachine

    MHB Natural Isomorphism b/w Dual Spaces Tensor Prod & Multilinear Form Space

    I am trying to prove the following. Let $V_1, \ldots, V_k$ be finite dimensional vector spaces over a field $F$. There is a natural isomorphism between $V_1^*\otimes\cdots\otimes V_k^*$ and $\mathcal L^k(V_1, \ldots, V_k;\ F)$. Define a map $A:V_1^*\times\cdots\times V_k^*\to \mathcal L^k(V_1...
  37. I

    MHB Convert infinite solution to vector form

    I know the solution has an infinite number of solutions. It is represented as follows: x1= 4/3 + (1/3)x3 - (5/3)x4 x2= 2 + (1/3)x3 + (1/3)x4 x3= Free x4= Free How do I put the above solution into vector form as illustrated in the original question?
  38. binbagsss

    Understanding Homogeneity & Isotropy in FRW Metric

    So in deriving the metric, the space-time can be foliated by homogenous and isotropic spacelike slices. And the metric must take the form: ##ds^{2}=-dt^{2}+a^{2}(t)\gamma_{ij}(u)du^{i}du^{j}##, where ## \gamma_{ij} ## is the metric of a spacelike slice at a constant t QUESTION: So I've read...
  39. B

    Polynomial fractions simplest form?

    I was taught that when you have a polynomial fraction where the denominator is of a higher degree than the numerator, it can't be reduced any further. This seems wrong to me for a couple of reasons. 1. If the denominator can be factored some of the terms may cancel out 2. Say you have the...
  40. S

    MHB Solving the separable equation, putting it in explicit form

    Find the solution of the given initial value problem in explicit form. Determine interval which solution is defined. (which i think is the same thing as saying find the interval of validity) $y' = (1-2x)y^2$ , $y(0) = -1/6$ So here is what I have so far.. $\int y^{-2}dy = x - x^2 + C$ $=...
  41. S

    MHB Need reassurance on "implicit" and "explicit" form

    When dealing with this separable equation for example, if I'm told to solve the given D.E. $y' = x^2/y$ so after manipulation and taking the integral I got $\frac{y^2}{2} = \frac{x^3}{3} + C$ This is the implicit form correct? Would the explicit form be $y = \sqrt{\frac{2}{3} x^3 + C}$
  42. J

    How to Solve Pendulum Forces in Component Form?

    Homework Statement Hi, I need help in solving question c) (a pendulum) The required data, problem and relevant equation is in the pictureThe Attempt at a Solution I am not sure how to solve it but here are my thoughts: since mg is working at j y(t)j= mg does that mean K(r-L0) x(t) direction? I...
  43. binbagsss

    When can a metric be put in diagonal form?

    I'm looking at deriving the Schwarzschild metric in 'Lecture Notes on General Relativity, Sean M. Carroll, 1997' and the comment under eq. 7.8, where he seeks a diagnoal form of the metric... - Is it always possible to put a metric in diagonal form or are certain symmetries required? - What...
  44. S

    MHB Solving the IVP, leaving it in Implicit Form

    Solve the IVP. $(2x-y)dx + (2y-x)dy = 0 $. $y(1) = 3$. Leave solution in implicit form. So I got: $\frac{dy}{dx} = \frac{-(2x-y)}{2y-x}$ Would this be correct since I didn't explicitly solve for $dy$ ?
  45. driesvdb

    Optimised Shin Guard for Slalom Skiing

    Hello everyone, I'm a young alpine skier and looking for ways to be faster. Slalom guards haven't changed in form since over a decade! I want to make a shin guard that could decrease the impact of the slalom gate on your shins so it doesn't make you slower. I added some videos in slow motion...
  46. C

    MHB Proving coercivity for weak form

    I have the weak form of the poisson equation as $a(u,v)=l(v)$ where $$a(u,v)=\int_\Omega \bigtriangledown u\cdot\bigtriangledown v$$ I have been proving existence and uniqueness of the solution using the Lax-Milgram Thm. I am stuck on proving that the bilinear form $$a(u,v)$$ is coercive. I...
  47. D

    What is the polar complex form of a wave with amplitude and phase?

    Homework Statement What is the amplitude and phase of the complex function? f(t) = (1-2i)e^(iwt) Homework Equations None/unknown Normal Polar Form = Real*e^imaginary i = e^pi/2*i The Attempt at a Solution [/B]I am trying to bring this into a normal polar form to easily see the phase and...
  48. U

    How Do Nuclear Form Factors Change with Scaling in Scattering Experiments?

    Homework Statement [/B] b) For a Form factor of form ##\theta_{(1-r)}## and ##\frac{1}{1 + e^{\frac{r-R}{a}}}##, how will these change when ##r \rightarrow 2r##? c) How would one accelerate and observe scattered protons? Homework EquationsThe Attempt at a Solution Part(b) [/B] Rate of...
  49. N

    Standard form, vertex form. Something isn't right here

    I mainly just need some clarification here. I was doing my homework and then browsing the web to find an answer to my problem and came across mathewarehouse' definition of Standard form and then I looked at my homework and went..."huh?" I don't understand if my homework is listening this wrong...
  50. S

    Does a diffraction grating with a shape form fourier image

    i just wanted to get this cleared that a beam falling on a diffraction grating with a shape gives the Fourier images of the grating object which can be reobtained by placing a biconvex lens that would converge the rays and form a focussed Fourier image at its focal length and the image of the...
Back
Top