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. I

    Form of symmetric matrix of rank one

    Homework Statement The question is: Let C be a symmetric matrix of rank one. Prove that C must have the form C=aww^T, where a is a scalar and w is a vector of norm one. Homework Equations n/a The Attempt at a Solution I think we can easily prove that if C has the form...
  2. I

    MHB Form of symmetric matrix of rank one

    The question is:Let $C$ be a symmetric matrix of rank one. Prove that $C$ must have the form $C=aww^T$, where $a$ is a scalar and $w$ is a vector of norm one.(I think we can easily prove that if $C$ has the form $C=aww^T$, then $C$ is symmetric and of rank one. But what about the opposite...
  3. E

    Deriving poroelastic equation in differential form

    Hi, I'm trying to fill in the gaps in my notes - looking at a poroelastic model of tissue. We have the simple spherical model below. The centre sphere is where liquid is produced, then the two following spheres are brain tissue with different permeabilities, and the final sphere is an...
  4. V

    Finding x for a certain quadratic form

    Homework Statement Suppose a,c>0 and b^2-4ac>0 . Explain how you could find x_1, x_2 ε ℝ such that a(x_1) ^2+bx_1x_2+c(x_2)^2<0 . Homework Equations q\begin{pmatrix}x_1\\x_2\end{pmatrix} = a(x_1)^2+bx_1x_2+c(x_2)^2 The Attempt at a Solution I'm not sure where to go with this...
  5. T

    Write the polar form of a complex number in the form of a+ib

    Homework Statement 4{cos(13∏/6)+isin(13∏/6)} = 4((√3/2)+(i/2)) = 2√3+2i Homework Equations The Attempt at a Solution This is an example from my textbook. The part which I do not understand is how to convert the cos and sin of radians into those fractions. Any help is greatly appreciated.
  6. L

    Why wouldn't black hole singularity evaporate before it can form?

    I assume people much more knowledgeable then me must have already thought this through, but the following line of thought has me very curious. I'm making a lot of intuitive leaps here though, so I am sure there is a lot of places I could have gone drastically wrong. Hawking radiation is...
  7. M

    Two two-level atoms and form of the Hamiltonian

    Hello, If we look at a system of two two-level atoms interacting with light, most papers start with a Hamiltonian H_{int}=(\sigma_{1}^{+}+\sigma_{2}^{+})a_{\textbf{k},\lambda} + h.c. That is, we absorb a photon and lost one excitation in the atoms or vice versa. Why do we never...
  8. M

    Linear recurrence = closed form?

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  9. M

    Integral Form of the Momentum Equation - Reducer Question

    Homework Statement The internal volume of the reducer is 0.2m^3 and its mass is 25 kg. The fluid being pumped is oil (specific gravity of 0.72). Evaluate the total force that must be provided to support the reducer. d1 = 0.4m d2 = 0.2m u1 = 3m/s p1 = 58.7 kPa p2 = 49kPa (gauge)...
  10. R

    Find a point charge a distance form a charged rod

    Homework Statement See image Homework Equations KQ/r^2 The Attempt at a Solution I have seen several different ways of working this problem, but they have all failed on me. I tried this using the equation above from my book E = (8.99x10^9)(1036 C)/(4x10^-6m) E= 2.328x10^18 N/C I also...
  11. Z

    The Relation between the integral and differential form of Amperes Law

    The integral form of Ampere's law in vacuum is ∫B\cdotdl=μ_{0}I (a) Using the relation between I and J, obtain the differential form of Ampere's law. You may ignore any displacement current. (b)Define the displacement current density J_{d} in terms of the displacement field D and show...
  12. R

    Finding the z component of vectors that form a triangle?

    For the vectors in the figure, with a = 1.1 and b = 2.6, what are (a) the z component of a x b, (b) the z component of a x c, and (c) the z component of b x c? Everything I've tried to look up involves vectors that are in unit notation, etc. I just don't understand how to do it when all you...
  13. S

    Number of ways to form a committee with men and women

    Homework Statement From a group of 5 women and 7 men, how many different committees con- sisting of 2 women and 3 men can be formed? What if 2 of the men are feuding and refuse to serve on the committee together? Part 1: my attempt: for men, we have 7 choose 3 for woman, we have 5 choose 2...
  14. T

    Simplified form of Voltage Formula

    In my book it gives the relationship between voltage and electric field as Vb-Va= -\int _a^{b} E dl which for a positively charged conducting sphere Q simplifies to \frac{Q}{4\pi\epsilon_0} (\frac{1}{b}-\frac{1}{a}) my questions is that shouldn't it be \frac{Q}{4\pi\epsilon_0}...
  15. alyafey22

    MHB Find a closed form interpretation for the integral :

    $\displaystyle \int^{\infty}_0 \, \frac{\log (1+e^{ax})}{1+e^{bx}}\, dx $ I am not sure whether it can be solved :confused:
  16. G

    Solve Spherical Shell Gauss Problem with Differential Form Only

    Homework Statement A hollow spherical shell carries charge density \rho=\frac{k}{r^2} in the region a<=r<=b, where a is the inner radius and b is the outer radius. Find the electric field in the region a<r<b. I'm not allowed to use integral form of Gauss's law, must use differential...
  17. R

    How to use the normal form of the Green's Theorem?

    Homework Statement Suppose that F = ∇f for some scalar potential function f(x, y) = 1/2(x2 + y2) Let C denote the positively oriented unit circle, parametrized by r(t) = (cos t, sin t), 0 ≤ t ≤ 2∏. Compute the flux integral of \ointF\bulletN ds, where N is the outward unit normal to C.Homework...
  18. K

    Understanding the Strong Form of Flux Conservation Law

    [b]1. The flux of a conserved quantity can be written q(x) = -x2 (du/dx)-u If the source term is f(x) = x, write the strong form of the conservation law. I know the form of the strong form is : d/dx(c du/dx)+f(x)=0 I have no idea where to begin for this problem. The examples my professor gave...
  19. L

    The proton elastic form factor (nuclear physics)

    Homework Statement The elastic form factors of the proton are well described by the form G(q2) = \frac{G(0)}{(1 + (\frac{q^{2}}{0.71})^{2}} with qw in GeV2. Show that an exponential distribution in the proton given by ρ(r) = ρoe-λr Homework Equations thought it to be the...
  20. M

    Jordan Normal Form: Find Basis B in $\mathbb{Z}_{5}^{3}$

    Hi Homework Statement Let f:\:\mathbb{Z}_{5}^{3}\rightarrow \mathbb{Z}_{5}^{3} be a linear operator and let [f]_{e_{3}}^{e_{3}}=A=\begin{pmatrix}3 & 1 & 4\\ 3 & 0 & 2\\ 4 & 4 & 3 \end{pmatrix} over \mathbb{Z}_{5}. Find a basis B of \mathbb{Z}_{5}^{3} such that...
  21. H

    The form of gravitational potential energy

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  22. M

    Determining the general form of an orthogonal vector

    Homework Statement Determine a vector that is orthogonal to both (1,2,-1) and (3,1,0) Homework Equations As above. The Attempt at a Solution The solution, from the back of the book, is "any vector of the form (a, -3a, -5a), but I'm not sure how they got there. I get the...
  23. S

    How to connect strain gauge in the form of wheatstone bridge

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  24. T

    Use exponential notation to form a+ib

    Homework Statement Use exponential notation to write (√3-i)(1+i√3) in the form a+ib. Homework Equations The Attempt at a Solution Let (√3-i) = z1 r1=|z1|=√((√3)2-i2) =√(3-1) =√2 Therefore, √3=√2cosθ and -1=√2sinθ cosθ = √3/√2 and sinθ = -1/√2 θ= arcsin(-1/√2) θ= -∏/4...
  25. 8

    Alternative form of the 2nd translation theorem proof

    hi guys, this is literally my first post here on physicsforums so i apologize in advance that my latex formatting sucks. Homework Statement prove the alternative form of the 2nd translation theorem of the laplace transform: L[f(t)u(t-a)]=e^{-sa}L[f(t+a)] where u(t-a) is the unit step...
  26. R

    Mathematica Mathematica or (preferably) maxima display exanded form

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  27. E

    Closed form solutions to integrals of the following type?

    For any integral where the integrand is of the form f(θ)^z, with z a complex number, and f(θ) = sin(θ), cos(θ), tan(θ), ... etc., θ being either real or complex. Is it possible to explicitly solve for an antiderivative? I'm not aware of any such way I could use residues/series representations...
  28. MarkFL

    MHB Limit of Arctan (x^2-4)/(3x^2-6x) as x Approaches 2

    Here is the question: Here is a link to the question: What is the limit of arctan( (x^2-4) / (3x^2-6x) ) as x approaches 2? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  29. M

    Can Metrics Reveal Flat Spaces Without Computing the Riemann Tensor?

    If you are given a metric gαβ and you are asked to find if it describes a flat space, is there any way to answer it without calculating the Riemman Tensor Rλμνσ? and how can I find for that given metric the coordinate transformation which brings it in conformal form? For example I'll give you...
  30. A

    Surds in polar form of imaginary number

    Homework Statement Find the polar form for zw by first putting z and w into polar form. z=2√3-2i, w= -1+i Homework Equations Tan-1(-√3/3)= 5∏/6 The Attempt at a Solution r= √[(2√3)2+(-2)2]=4 tanθ= -2/(2√3)=-1/√3=-√3/3=> acording to above... tan-1(-√3/3)= 5∏/6 so, in polar form z should be...
  31. S

    Block matrix transformation of specific form

    Hi everyone, I am trying to solve the following problem. Is there exist a transformation matrix T, different then the block diagonal, with all blocks the same, such that the form of the matrix A=[A1 A2 ; I 0], is preserved? All blocks of A are in R^{nxn}, I is identity and 0 is zero matrix. In...
  32. T

    Separating e^(xi) to form a-bi

    Homework Statement I am in dif eq, but just need to know how to separate a power. separate e^(xi) into the form a-bi, where x is a constant (in my homework, x is 4pi/3, but that's not too relevant) i is the imaginary number sqrt(-1) Homework Equations I don't know if there is some simple...
  33. G

    How does WolframAlpha use the gamma function to solve this integral?

    Hi I have this integral that I want to express in terms of a gamma function. Unfortunately I am unable to bring it in this form. So can you give me a hint how wolframalpha does thishttp://m.wolframalpha.com/input/?i=∫e%5E%28ix%29%2F%28ix%29%5E%281%2F5%29dx+from+-+infinity+to+infinity&x=10&y=3
  34. W

    Potential energy( electron moving away form proton)

    An electron is initially 2cm from a proton and is then give an initial velocity away from the proton. If v is 31m/s how far to the right does the electron move before it momentarily stops? is this right? http://i1341.photobucket.com/albums/o745/nebula-314/IMAG0112_zps5361921d.jpg
  35. R

    Proving Finite Order Elements Form a Subgroup of an Abelian Group

    Homework Statement Prove the collection of all finite order elements in an abelian group, G, is a subgroup of G. The Attempt at a Solution Let H={x\inG : x is finite} with a,b \inH. Then a^{n}=e and b^{m}=e for some n,m. And b^{-1}\inH. (Can I just say this?) Hence...
  36. K

    Differential Form: Closed/Exact

    1 & 3 I have this differential form: ##\omega = F_1 dx + F_2 dy + F_3 dz## And I concluded that ##\omega## is closed because I calculated the partials and found out that ##\displaystyle \frac{\partial F_i}{\partial x_j} = \frac{\partial F_j}{\partial x_i}##. Also, ##F_1## contains only...
  37. shounakbhatta

    Star collapse to form directly a black hole

    Hello, Does a star collapse directly to form a black hole without creating a supernova or whether a supernova forms some neutron stars which after crossing the TOV limit forms a black hole? Thanks.
  38. C

    How does water rise to form clouds if oxygen is heavier than nitrogen?

    1 - how does water rise to form clouds if oxygen is heavier than nitrogen? when it turns into a gas its hydrogen and oxygen---why does it rise (to form clouds) if oxygen is heavier than nitrogen, which makes up 78% of the Earth's atmosphere? *please note that I'm not confused as to the...
  39. B

    What kind of form is this general solution of a system?

    If this were the reduced row echelon form of an augmented matrix, 1 2 0 1 1 0 3 0 0 1 2 1 0 1 0 0 0 0 0 1 2 0 0 0 0 0 0 0 What is the form of the following answer given, and how can I understand it? (x1; x2; x3; x4; x5; x6) = (3; 0; 1; 0; 0; 2)+ t(1; 0; 1; 0; 1; 0)+ s(1; 0; 2; 1; 0...
  40. A

    A particle traveling at a speed V decays to form two photons (no mass)

    Conservation of relativistic momentum and energy, pion decays Homework Statement A small particle (pion), traveling at a velocity V, decays into two rays, γ1 and γ2. Find the Momentum and Energy of γ1 and γ2 if: a) γ1 is in line with V, and b) if γ1 is perpendicular to V. I drew out the...
  41. D

    Write 1-2i in Polar Form - Solve Confusion

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  42. V

    Index/Einstein notation: from/to matrix form

    So I've just started working with the index/einstein notation for matrices and vectors the other day. I've been doing a few exercises from a booklet I have, but I am still a bit confused. I am pretty sure my confusion is rather stupid though, so I apologize in advance. Homework Statement So...
  43. G

    Probability Question - using the combinations counting form C(n,k)

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  44. L

    Control system Transfer Function ( Time constant form)

    Why is time constant form of transfer function in control system better than pole zero form ? If a closed Loop transfer function is given to me how should i find D.C gain ?
  45. S

    Integrating a differential form on a manifold without parametric equations

    I am sure that this can be done, but I haven't been able to figure it out, Is there a way to integrate a differential form on a manifold without using the parametric equations of the manifold? So that you can just use the manifold's charts instead of parametric equations? If you a function...
  46. B

    What is a Closed Form for the Sequence?

    Homework Statement Let Ʃ 1\(n^2-1) from n=2 to k. It says find a closed for it and prove it using sum notation. Homework Equations The Attempt at a Solution I can easily prove it by induction but I don't know what a closed form means. I tried looking it up online but there really...
  47. heycoa

    Moment of inertia | Integral form

    Homework Statement Starting from the sum: I=Ʃ mα*ρα2 and replacing it by the appropriate integral, find the moment of inertia of a uniform thin square with side length 2*b, lying in the x-y plane, rotated about the x-axis. Calculate its moment of inertia. Homework Equations The integral form...
  48. S

    Magnetic field of a dipole in co ordinate free form

    Hello everybody! I am writing this topi because i got stuck in this!I have a cylindrical magnet with 1,5mm Radius,2mm thickness and Br 1,38 Tesla! I want to calculate the magnetic field in a distance s = [0 0 0.01](in meters) ,that means in 1cm distance while my magnet's position is α = [0 0...
  49. H

    Proof of the general form of the equipartition theorem

    Homework Statement For a Hamiltonian of the form H=\sum_{j=1}^m a_j p_j^2 + \sum_{j=1}^n b_j q_j^2 + H'(q_{n+1}, \dots, q_{sN}, p_{m+1}, \dots, p_{sN}) (for a system with n coordinates and m momenta, s degrees of freedom and N particles), show that \overline{a_jp_j^2}=\frac{kT}{2}, for...
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