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. B

    A Calculating Nabla w V in General Relativity

    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...
  2. H

    I How did the initial dust particles form?

    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...
  3. Fosheimdet

    A Understanding the Form Factor in Electron Scattering

    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...
  4. lachgar

    How to form the stress tensor component from the equilibrium equation?

    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...
  5. E

    B Determining whether the non-integral form of Gauss' law applies

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  6. Arman777

    I Radial Vector in Cartesian form

    If I wanted to write ##\hat{r}##in terms of ##\hat{x}##and ##\hat{y}##, is it ##\frac{\hat{x} + \hat{y}}{\sqrt{2}}## ?
  7. S

    I Find the minimum and maximum value of a quadratic form

    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...
  8. Delta_Craig

    Kinematic in Quadratic Form Equation (missing something simple)

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  9. mikesydwest

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  10. M

    MHB TM: Is the given string of the form uu?

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  11. M

    MHB Prime implicants and disjunctive minimal form

    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...
  12. D

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  13. M

    Engineering Adding Harmonics to Form the Final Signal

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  14. M

    A rather weird form of a coherent state

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  15. Delta2

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  16. AutGuy98

    MHB Prove that the 12-th roots of unity in C form a cyclic group

    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...
  17. AutGuy98

    MHB Proof of an Infimum Being Equal to the Negative Form of a Supremum ()

    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...
  18. anita chandra

    A Does this integration have a closed form solution?

    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...
  19. M

    Question on Calculating Coulomb force in VECTOR FORM

    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...
  20. H

    B Understanding the Quadratic Form Identity in Two-Variable Equations

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  21. B

    Show that the Kronecker delta retains its form under any transformation

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  22. Q

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  23. K

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  24. K

    I Is this the only form of the Minkowski metric?

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  25. V

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  26. Ackbach

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  27. P

    Which grade of Stainless Steel is more soft or ductile in Sheet form?

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  28. amjad-sh

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  29. Wrichik Basu

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  30. karush

    MHB Can You Solve This Initial Value Problem and Determine Its Solution Interval?

    Given #11 $\quad\displaystyle xdx+ye^{-x}dy=0,\quad y(0)=1$ a. Initial value problem in explicit form. $\quad xdx=-ye^{-x}dy$ separate $\quad \frac{x}{e^{-x}}\, dx=-y\, dy$ simplify $\quad xe^x\, dx=-y\, dy$ rewrite $\quad y\,dy=-xe^x\,dx$ integrate (with boundaries) $\quad \int_1^y...
  31. berlinspeed

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  32. PainterGuy

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  33. Jason Bennett

    I Alternative form of geodesic equation for calculating Christoffels

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  34. V

    MHB Rewrite in logarithmic form: e^(-1) = c

    Rewrite in logarithmic form: e^(-1) = c
  35. V

    MHB Rewrite in exponential form: Log(6) 1294 = 4

    Rewrite in exponential form: Log(6) 1294 = 4 Log(w) v = t Ln(1/4) = x Evaluate Log(4) 64 = ? Log(16) 4 = ?
  36. F

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  37. Dene

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  38. karush

    MHB 10.2 Determine if the set of vectors form a vector space

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  39. J

    MHB Form some model to predict a food items probability of you know being sold

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  40. K

    Which Form of Maxwell's Equations is More Useful? (Integral versus Differential)

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  41. B

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  42. J

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  43. I

    Use a variable substitution to get into a Bessel equation form?

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  44. karush

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  45. P

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  46. N

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  47. K

    Calculate potential form poisson equation

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  48. V

    Finding Polar Form Expressions: -3-3i & 2√3-2i

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