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.

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  1. R

    I Is (u,v) = (x square - x, x+1) a Parametric Form of a Parabola?

    Hello. How can I verify that (u,v) = (x square - x, x+1) is a parametric form of a parabola? Thank you!
  2. O

    A Justify matrices form basis for SO(4)

    I am given the following set of 4x4 matrices. How can i justify that they form a basis for the Lie Algebra of the group SO(4)? I know that they must be real matrices, and AA^{T}=\mathbb{I}, and the detA = +-1. Do i show that the matrices are linearly independent, verify these properties, and...
  3. F

    Euler Lagrange equation issue with answers final form

    Homework Statement For the following integral, find F and its partial derivatives and plug them into the Euler Lagrange equation $$F(y,x,x')=y\sqrt{1+x'^2}\\$$ Homework Equations Euler Lagrange equation : $$\frac{dF}{dx}-\frac{d}{dy}\frac{dF}{dx'}=0$$ The Attempt at a Solution...
  4. P

    B Why Need Covarient Form of Electrodynamics?

    hello this is my first topic here and i hope good discussion or answer to my question As i understand the Maxwell equation keep its form in all frames so why i need to make a covarient formulation form of electrodynamics ? for example what the covarient form of continuity equation give me !
  5. binbagsss

    I Modular form quick question translation algebra

    Please see attached. I am trying to show that ## T_{p} f (\tau + 1) = T_{p} f (\tau ) ## ##f(\tau) \in M_k ## and so can be written as a expansion as ##f(\tau)=\sum\limits^{\infty}_{0}a_{n}e^{2 \pi i n \tau } ## ##f(\tau + 1) = f(\tau) ## since ##e^{2\pi i n} = 1## Similarly ##f(p\tau + p) =...
  6. FallenApple

    I Does analysis form a bridge to geometry?

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  7. A

    Expressing a quadratic form in canonical form using Lagrange

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  8. C

    Proving discontinuity for rational numbers (reduced form)

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  9. binbagsss

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  10. Vitani11

    Potential energy as a form of mass?

    Homework Statement Let's say we have a mass of 5kg at a height of 3 m so it's potential energy is mgh = 147J/1.6e-19 = 9.19 e20 eV. Now we know that E = mc^2... so when finding the mass of this potential energy we get 10.2e3 kg. What the hell is that supposed to mean? Homework Equations None...
  11. karush

    MHB S6.12.25 find v in component form

    $\tiny{s6.12.25}$ $\textsf{If $v$ lies in the first quarter and makes an angle }\\$ $\textsf{$\pi/3$ with the positive x-axis and $\left| v \right|$=4} $ $\textsf{find $v$ in component form.}$ \begin{align} \displaystyle v&=\langle 2\sqrt{3},2\rangle \\ \end{align} this is probably correct...
  12. R

    Can H2S Molecules Form Hydrogen Bonds?

    can H2s form hydrogen bonds i read that H2s can , but I'm not so sure about it .
  13. john augustine

    Dy/dx = xe^(y-2x), form differntial eqaution

    dy/dx = xe^(y-2x) , i am asked to form differential equation using this equation . the ans given is (e^-y) = 0.5(e^-2x)(x+0.5) + a , how to get the answer? btw , i have attached my working
  14. S

    A Pontryagin densities and Chern-Simons form

    Dear All It is known that pontryagin densities are defined in even dimension space, let's say i am concerned with 4 dim space time. We also have a certain group G. What is the formula of pontryagin densities for arbitrary group? Larger group?
  15. S

    A How Does the Volume Form on the Unit Sphere Relate to Its Position Vector?

    The volume form on the unit sphere ##S^{n}## in ##\mathbb{R}^{n+1}## is given by $$i_{{\bf r}}\ dx^{1}\wedge \dots \wedge dx^{n+1}=\sum (-1)^{i-1}x^{i}dx^{1}\wedge\dots \widehat{dx^{i}} \dots \wedge dx^{n+1}.$$ Why must the volume form ##dx^{1}\wedge \dots \wedge dx^{n+1}## act on the vector...
  16. A

    Conservation law form of Navier Stokes Equation

    I am pretty confused about how to write Navier-Stokes Equation into conservation form, it seems that from my notes, first, the density term with the pressure gradient dropped out. and second, du^2/dx seems to be equal to udu/dx. Why is it so? I attached my notes here for your reference.
  17. garylau

    I How to write the relationship of B and E in vector form

    http://www.physicspages.com/2014/08/22/electromagnetic-waves-in-vacuum/ Sorry i have no idea how to get the last step in the vector form how to convert and mix it?thank you
  18. lep11

    Problem reducing quadratic to diagonal form

    Homework Statement Reduce ##xy+zy## to diagonal form. Homework Equations The desired diagonal form is ##Q(\vec{x})=(\alpha_1(\vec{x}))^2+...+(\alpha_k(\vec{x}))^2-(\alpha_{k+1}(\vec{x}))^2-...-(\alpha_{k+l}(\vec{x}))^2,## where ##\alpha_i## are linearly independent linear functions. Also known...
  19. R

    Stuck on expressing a complex number in the form (a+bi)

    Homework Statement Express the complex number (−3 +4i)3 in the form a + bi Homework Equations z = r(cos(θ) + isin(θ)) The Attempt at a Solution z = -3 + 4i z3 = r3(cos(3θ) + isin(3θ)) r = sqrt ((-3)2 + 42) = 5 θ = arcsin(4/5) = 0.9273 ∴ z3 = 53(cos(3⋅0.9273) + isin(3⋅0.9273)) a = -117 b...
  20. P

    Momentum and Position Operator Commutator Levi Civita Form

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  21. C

    Change (9-16cos theta) ^1.5 into another form

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  22. C

    Coulomb's law in its vector form?

    sorry I have use the image I made. Since I don't know how to perform the formula on forum :( This is the problem I am having.
  23. F

    I Formation of Bound Systems, Stars & Galaxies in General Relativity

    In particular how does matter "clump" together to form stars and planets, and how do Galaxy/star systems form? For the latter question is the answer simply that near massive enough bodies, the spacetime curvature is significant enough that the geodesics within its vicinity are closed curves...
  24. C

    Transforming Force Equations with Substitution

    Homework Statement in this question , solving equation 1 and 2 , how to get the F1 = (A1E1 P ) / ( 2A1E1 + A2E2) ? and also F2 ? Homework EquationsThe Attempt at a Solution we know that F2 = P -2F1 ) I have tried to sub (F2 / A2E2 ) in F1 = (A1E1 P ) / ( 2A1E1 + A2E2) , but i ended up...
  25. kostoglotov

    Which inverse Laplace form can I use?

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  26. L

    A Ricci Form Notation: Need Help Understanding

    The material I am studying express the Ricci form as ##R = i{R_{\mu \bar \nu }}d{z^\mu } \wedge d{{\bar z}^\nu } = i\partial \partial \log G## where ##G## is the determinant of metric tensor, but I am not sure what does ##\log G## here, can anybody help?
  27. G

    I Differential form of Gauss' law: All three terms the same value?

    Hi. Is the Maxwell equation $$\nabla\cdot\vec{E}=\frac{\rho}{\varepsilon_0}$$ even true in the stronger form $$\frac{\partial E_i}{\partial x_i}=\frac{\rho}{3\cdot\varepsilon_0}\enspace ?$$ I guess not, since I haven't found a source suggesting this. But shouldn't the isotropic electric field...
  28. ramzerimar

    I Finite Element Method: Weak form to Algebraic Equations?

    Okay, I'm following a series of video lectures on applications of finite element method to engineering, and the tutor started by demonstrating the mathematical background of FEM using a simple heat transfer problem. He derived the governing equation (in just one dimension): (1)...
  29. M

    MHB From quadratic form to vertex form

    $-x^2+4x-1$ should be converted to the vertex form of $y=k-(x-h)^2$ How can this be solved by factoring or any other method ? My attempt to solve this problem , I will be using the completing the square method, $\left(-x^2+4x+\frac{-b}{2a}\right)=1+\frac{-b}{2a}$ Here $\frac{-4}{-2}=2$...
  30. Green dwarf

    Is electromagnetic radiation a form of kinetic energy?

    Hi, I'm a high school science teacher. Most textbooks classify EM radiation as kinetic energy. But this doesn't seem right to me. As a photon is massless it's hard to see how it can have kinetic energy which is 1/2 mv^2. It could be said that it has energy hf and therefore mass hf/c^2. Then its...
  31. M

    A Time Independent Form of Klein Gordon Eqn.: How to Reach (gδ3(x))

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  32. stephen8686

    B How does Gauss's Law relate to E=(2kλ)/r for an infinite line of charge?

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  33. Y

    MHB Solving a Complex Logical Equivalence in CNF Form

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  34. nysnacc

    Rewrite Cartesian in Cylindrical form

    Homework Statement Homework Equations Cartesian to Cylindrial The Attempt at a Solution What I was doing is that, I changed the limits of z, and the function.
  35. Dewgale

    Is the Lorentz Force Law Consistent with \( P^\mu P_\mu = -m^2 \)?

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  36. H

    What is the relationship between hull shape and form drag on sailboats?

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  37. K

    MHB Simpify Factored Form Equation

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  38. R

    Expressing force in cartesian vector form

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  39. M

    Newton's Second Law Integral Form

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  40. S

    MHB Operator form of integro-differential equation

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  41. toforfiltum

    Proving a form ##z=f(r)## to be a surface of revolution

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  42. D

    I Lie derivative of a differential form

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  43. Captain1024

    Fourier Transform in the Form of Dirac-Delta Function

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  44. Gabriel Golfetti

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  45. wolram

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  46. terhje

    Complex numbers. write equation on form "a+bi"

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  47. Marcin H

    Complex Numbers (Exponential/Rectangular Form)

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  48. Destroxia

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  49. N

    I Help evaluating complex function in form m+ni?

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  50. evinda

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