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. Sanchayan Ghosh

    I Canonical form derivation of (L1'AL1)

    Hello everyone, I actually had a problem with understanding the part where they have defined L'AL = Λ. There, they have taken γΛγ1 = Σy2λ = 1. Why have they taken that? Is it arbitary or does it come as a result of a derivation? Thank you
  2. M

    MHB Determine a matrix C such that T = CA has echelon form

    Hey! :o Let $$A=\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{pmatrix}\in \mathbb{R}^{3\times 3}$$ I want to determine a matrix $C\in GL_3(\mathbb{R})$ such that $T:=C\cdot A$ has echelon form. Performing an elementary row operation is equivalent to multiplying an invertible matrix...
  3. Mr Davis 97

    Showing that subgroups of G form a lattice

    Homework Statement Prove that the set of all subgroups of a group ##G## is a lattice with respect to the partial order relation given by containment. Note: You need not prove that containment is a partial order relation but you do need to prove that if ##H\leq G## and ##K\leq G## then there...
  4. V

    I Are three zeros always required in the third row for a matrix in echelon form?

    I need to find the echelon form of: 1 1 2 8 -1 -2 3 1 3 -7 4 10 and so far I have: 1 1 2 8 0 10 -50 -90 0 0 -52 -104 I was just wondering if I was required to put another zero in my third row. Am I always required to have three zeros in the third row? I'm assuming I do, but when I looked at...
  5. M

    MHB Change the form of equation of surface

    Hey! :o We consider the surface $S$ of the space $\mathbb{R}^3$ that is defined by the equation $2(x^2+y^2+z^2-xy-xz-yz)+3\sqrt{2}(x-z)=1$. I want to find (using symmetric matrices) an appropriate orthonormal system of coordinates $(x_1, y_1, z_1)$ for which the above equation has the form...
  6. A

    A What volume of interstellar space is needed to form a star?

    So, let me preface by saying I’m neither a scientist nor a mathematician, so am requesting some talented help here checking the accuracy of my source information and math. Regarding star formation, I got curious about how much volume of space in the interstellar medium is actually required to...
  7. arpon

    I Form factors and Interaction term of the Action

    Consider, two fields interact with each other and the interaction term of the action is given. Now the Lagrangian density is Fourier transformed and the interaction term of the action is expressed as an integral over the momentum space. How is the integrand related to the form factor?
  8. lfdahl

    MHB Is the definite integral ∫ [arcsin(1/x)-1/x]of indeterminate form?

    Is the definite integral $$\int_{1}^{\infty}\left(\arcsin \left(\frac{1}{x}\right)-\frac{1}{x} \right)\,dx$$ of indeterminate form or not? Prove your statement.
  9. V

    Solving Limits: Finding a, b, c, and d for ∞-∞ Form

    Homework Statement lim x~∞ 〈√(x⁴+ax³+3x²+ bx+ 2) - √(x⁴+ 2x³- cx²+ 3x- d) 〉=4 then find a, b, c and d[/B]Homework Equations all the methods to find limits The Attempt at a Solution it can be said that the limit is of the form ∞-∞.I am completely stuck at this question.the answer is a=2...
  10. V

    What is the limit of the form 0/0?

    Homework Statement lim x~a 〈√(a⁺2x) -√(3x)〉 ÷ 〈√(3a+x) - 2√x〉[/B]Homework Equations rationalisation and factorisation[/B]The Attempt at a Solution i had done rationalisation but the form is not simplifying.pleasez help me.[/B]
  11. Pushoam

    Show: Vectors e.g.(a,b,1) do not form vector space.

    Homework Statement Homework Equations definition of null vector, [/B] The Attempt at a Solution null vector : ## |0 \rangle = (0,0,0) ## inverse of (a,b,c) = ( - a, -b, -c) vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same...
  12. T

    570 million year old animal life form

    Seems that us animals got an even earlier start than we thought. Short popular version: https://www.livescience.com/63289-ediacaran-leaf-fossil-is-animal.html Longer version: http://www.dailymail.co.uk/sciencetech/article-6043177/Animal-kingdom-OLDER-previously-thought-scientists-reveal.html...
  13. Mr Davis 97

    Showing that upper triangular matrices form a subgroup

    Homework Statement Let ##n \in \mathbb{Z}^+## and let ##F## be a field. Prove that the set ##H = \{(A_{ij}) \in GL_n (F) ~ | ~ A_{ij} = 0 ~ \forall i > j \}## is a subgroup of ##GL_n (F)## Homework EquationsThe Attempt at a Solution So clearly the set is nonempty since ##I_n## is upper...
  14. Ken Gallock

    I Covariance Matrices and Standard form

    Hi. I have a question about covariance matrices (CMs) and a standard form. In Ref. [Inseparability Criterion for Continuous Variable Systems], it is mentioned that CMs ##M## for two-mode Gaussian states can be symplectic transformed to the standard form ##M_s##: ## M= \left[ \begin{array}{cc}...
  15. opus

    B Expressing Velocity in Vector Form

    Let me start off by stating a given problem: A baseball is hit, and leaves the bat at a speed of 100 mph and at an angle of 20° from the horizontal. Express this velocity in vector form. So we're given the velocity and the angle at which the ball is hit. The speed corresponds to the vector's...
  16. Spinnor

    I Noble gases with even nuclear spin form superfluids?

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  17. Astronuc

    New cracks form - Grand Teton National Park near Yellowstone

    US National Park service issued the following notification: Hidden Falls Area Emergency Closure Closure updated July 10, 2018. Temporary closure remains in effect until rescinded. It is unknown how long the closure at Hidden Falls and Inspiration Point areas will be in place. Closure and...
  18. J

    My E&M textbook claims that fields are a form of matter

    I'm studying out of Classical Electrodynamics by Ohanian and in chapter 2 (Electrostatics) he makes the following claim while discussing the electric field: I'm a little confused by this, and I can't seem to find any sources that share this view. I'm even more confused because in the...
  19. binbagsss

    Infinitesimal form of the Lorentz Transformation

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  20. Alphonso2001

    B Conversion of parametric form to polar for the rose curve

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  21. JTC

    What causes pressure in form drag?

    Consider a ball flying through the air. When there is turbulence, and the flow separates, say on a SMOOTH ball, then in the rear, there is circulation in the wide wake. There is pressure on the front, but no pressure on the rear due to the fact that the fluid is "busy" circulating around. So...
  22. R

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    <Moderator's note: Moved from a technical forum and thus no template. Effort in post #3.> What is the condition of tangency of a line y=mx+c on parabola with vertex(h,k) ,say for parabola (y-k)2=4a(x-h)? I could only find the condition of tangency on standard form of parabola, in the internet...
  23. N

    On deriving the standard form of the Klein-Gordon propagator

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  24. M

    MHB Deriving Extremas of Homogeneous Functions: A Chain Rule Comparison

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  25. M

    A Pressure in the proton, from gravitational form factors?

    A paper in Nature is getting some press, for having calculated "the pressure distribution inside the proton". But the theory behind the calculation seems a little odd. Apparently the data pertains to the scattering of an electron from a quark via the exchange of two photons. But each photon...
  26. L

    MHB Standard formula for solving simultaneous equations of the form ax + by + c = 0

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  27. N

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    Hi, I am going around in circles, excuse the pun, with phasors, complex exponentials, I&Q and polar form... 1. A cos (ωt+Φ) = Acos(Φ) cos(ωt) - Asin(Φ)sin(ωt) Right hand side is polar form ... left hand side is in cartesian (rectangular) form via a trignometric identity? 2. But then...
  28. I

    Transform differential equations into state space form

    Homework Statement I have derived the differential equations of a system. They are like the following: a\ddot{\theta} - b\ddot{x} + c \theta = 0 \\ d\ddot{\theta} + e\ddot{x} = F(t) where a,b,c,d,e are constants. I'm having trouble putting it into state space form, since I have the highest...
  29. bananabandana

    I Deriving Covariant Form of $E_{1}E_{2}|\vec{v}|$

    Given a two particle scattering problem with (initial) relative velocity $|\vec{v}|$, apparently the product $E_{1}$E_{2}|\mathb{v}|$ can be expressed in the covariant form: $$ E_{1}E_{2}|\vec{v}| = \sqrt{ (p_{1}\cdot p_{2} - m_{1}^{2}m_{2}^{2}} $$ My textbook gives no further explanation -...
  30. T

    MHB Simple closed form for integral

    How may we go about to show that, $$\int_{0}^{1}t\cos(2t\pi)\tan(t\pi)\ln[\sin(t\pi)]\mathrm dt=\color{green}{1\over \pi}\cdot\color{blue}{{\ln 2\over 2}(1-\ln 2)}$$
  31. A

    A How to calculate the second fundamental form of a submanifold?

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  32. T

    MHB A hard integral gives a simple closed form, π/(4a)^3

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  33. binbagsss

    GR: 3-d star metric deriving from a general form

    Homework Statement attached: I am stuck on question 2, and give my working to question 1 - the ##B(r) ## part I am fine with the ##A(r)## part which clearly is the same in both regions seen by looking at ##G_{rr}## , and attempt, however I assume I have gone wrong in 1 please see below for...
  34. Physics345

    Finding a Vector in Cartesian form

    Homework Statement Find u→ in Cartesian form if u→ is a vector in the first quadrant, ∣u→∣=8 and the direction of u→ is 75° in standard position. Round each of the coordinates to one decimal place. Homework Equations none The Attempt at a Solution I'm certain this is correct, but some guy at...
  35. P

    A Prove 2-D Lorentzian Metric is Locally Equivalent to Standard Form

    Hi, how can I prove that any 2-dim Lorentzian metric can locally be brought to the form $$g=2 g_{uv}(u,v) \mathrm{d}u \mathrm{d}v=2 g_{uv}(-\mathrm{d}t^2+dr^2)$$ in which the light-cones have slopes one? Thanks!
  36. L

    Identify the quadratic form of the given equation

    <Moderator's note: Moved from a technical forum and thus no template.> Hello I am given the following problem to solve. Identify the quadratic form given by ##-5x^2 + y^2 - z^2 + 4xy + 6xz = 5##. Finally, plot it. I cannot seem to understand what I have to do. The textbook chapter on...
  37. T

    B Understanding the Conversion of Energy Forms in Particle Interactions

    Different forces (e.g. electromagnetism, colour) are mediated via different force-carrying particles (e.g. photon, gluon). When converting from one form of energy to another, what force-carrying particles are involved in converting acceleration (or more generally a change in kinetic energy) of...
  38. bluejay27

    A What form of the Schrodinger equation do you use for intensity?

    I am trying to see how I can use the schrodinger equation to quantify the changes in the intensity of light. My closest guess is using the time dependent pertubation theory
  39. B

    A Solving Schwarzschild Field Equations in this Form

    Applying Cartan's first and second structural equations to the vielbein forms \begin{align} e^t = A(r) dt , \ \ \ \ \ e^r = B(r) dr , \ \ \ \ \ e^{\theta} = C(r) d \theta , \ \ \ \ \ e^{\phi} = C(r) \sin \theta d \phi , \end{align} taken from the metric \begin{align} ds^2 = A^2(r) dt^2 - B^2(r)...
  40. N

    I Representing a Hamiltonian in an operator form

    Given a Hamiltonian in the position representation how do I represent it in operator form? for example I was asked to calculate the expectancy of the Darwin correction to the Hydrogen Hamiltonian given some eigenstate (I think it was |2,1> or something bu that doesn't matter right now), now I...
  41. N

    How to Input a Weak Form Equation in COMSOL for Simulation?

    Consider the weak form Input this equation in COMSOL Homework EquationsThe Attempt at a Solution test(ux) -exp(x)*test(u)
  42. V

    B Time it takes to convert one form of energy to another?

    How much time does it take to convert one form of energy to another. Say ball dropped from a height 'H' its PE convert to KE. Can it be be defined in a time frame?
  43. B

    A Strange Tetrad Form of Einstein-Hilbert Action

    I have seen it the claimed that the Einstein-Hilbert action can be written in terms of a tetrad ##e_{\mu} \, ^a## as \begin{align} S &= \int d^n x \, e R(e_{\mu} \, ^a, \omega_{\mu a} \, ^b (e)) \\ &= \int d^n x \, e (T_{ca} \, ^a T^{cb} \, _{b} - \frac{1}{2} T_{ab \ c} T^{ac \ b} -...
  44. M

    Electric field vector in component form

    Homework Statement A -12nC charge is located at (x,y) = (1.0cm, 0cm). What are the electric fields at the positions (x,y) = (5.0cm, 0cm), (-5.0cm, 0cm), and (0cm, 5.0cm)? Write each electric field vector in component form. Homework Equations E=k(q/r2) The Attempt at a Solution I was able to...
  45. binbagsss

    Order of zero of modular form from its expansion at infinity

    1. Homework Statement order of zero of a modular form ? 2. Homework Equations 3. The Attempt at a Solution Apologies if this is a stupid question but I'm pretty confused. So, a modular form ##f(t) \in M_k ## is usually given by it's expansion about ##\infty## expressed in the variable...
  46. DeathbyGreen

    I Loop Integral Form: Finding a Workable Solution without Regularization

    Hi, I'm trying to calculate an integral which looks unfortunately divergent. The structure is similar to a loop integral but the appendix in the Peskin textbook didn't have a useable form. The integral form is (I did a u substitution to make it easier to look at) \int_x^{\infty}du...
  47. LeInvertedPenguine

    I How elementary particles form matter

    Hello, So i wonder how elementary particles which are said to have no physical extension on a larger scale are able to form what is known to us as matter? Aka stuff with an observable physical extension.
  48. T

    How do you always put a complex function into polar form?

    Homework Statement It's not a homework problem itself, but rather a general method that I imagine is similar to homework. For a given elementary complex function in the form of the product, sum or quotient of polynomials, there are conventional methods for converting them to polar form. The...
  49. I

    Which elements form covalent bonds?

    This might be a very basic question. What are the elements that are in the world of creating covalent bonds, distinguishing themsevels from the elements that never form covalent bonds? Many thanks!
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