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. W

    Would the water remain in lquid form?

    Lets say Earths atmospheric pressure was reduced to 0.10 bar which is 10% Earths atmospheric pressure. The boiling point at this pressure is 113 degrees F. Due to the atmosphere being thinner there is a greater temperature difference with higher highs and lower lows in a 24 hour period. Lets say...
  2. M

    Jordan form of f^​2 and f^​3 knowing that m. polynomial of f is x^​7

    The problem statement Let V be a vector space of dimension 8 and f (endomorphism) such that the minimal polynomial of f is x^​7. If B={v1,...,v8} is the Jordan basis of f, find the Jordan form and a Jordan basis for f^​2 and f^​3. The attempt at a solution Ok, I am having some trouble to...
  3. gauss44

    How does circular DNA wrap around a histone to form a chromosome?

    How does circular DNA wrap around a histone to form a chromosome? Or does it? I am having a hard time visualizing this for any sort of circular DNA: prokaryotes, mitochondria, etc. (This question was inspired by my reading about biology and reading that circular DNA does, in fact, form...
  4. J

    Does the ionised form of a drug produce a pharmacological effect?

    Hi all, I was just wondering, does the ionised form of a drug produce a pharmacological effect? I know that an ionised drug is lipid-insoluble so it cannot traverse across the membrane. However, my question is, what happens to them if they remain in the gastrointestinal tract? Does it still...
  5. L

    Complex numbers rectangular form

    Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression: Z = Z1 X Z2 / Z1 + Z2 If Z1 = 4 + j10 and Z2 = 12 - j3, calculate the impedance Z in both rectangular and polar form. Homework Equations Multiplication and division of complex...
  6. J

    Derivation of trigonometric identities form rotation on the plane

    Homework Statement I want to derive the trig identities starting with rotation on the plane. Homework Equations One rotation through a given angle is given by $$x' = xcosθ - ysinθ $$ $$y' = xsinθ + ycosθ$$ The Attempt at a Solution What if I wanted to rotated through any...
  7. R

    Statics: Forces in Cartesian Vector form

    Homework Statement For cable AD it is known that the magnitude is 14 kips, x-component has a value of -6.216, the direction angle in the z-direction is 83.63°, and Fy is less than zero. Find forces in Cartesian vector form, coordinates of point D if it lies on the x-z plane and point A is (0...
  8. V

    Solve these differential equations by converting to Clairaut's form

    The question comprises of three subparts which need to be converted to Clairaut's form and then solved : (a) x p2 - 2yp + x + 2y = 0 (b) x2 p2 + yp (2x + y) + y2 = 0 (c) (x2+y2)(1+p)2-2(x+y)(1+p)(x+yp)+(x+yp)2=0 Note : p = dy/dx I understand that Reducing to Clairaut's form...
  9. R

    Odd Form Of Eigenvalue - Coupled Masses

    Odd Form Of Eigenvalue -- Coupled Masses This isn't strictly homework, since it's something I'm trying to self-teach, but it seems to fit best here. Homework Statement It's an example of applying eigenvalue methods to solve (classical) mechanical systems in an introductory text to QM...
  10. L

    What Is the Non-Compact Form of the SU(2) Algebra in String Theory?

    I read that in string theory the Virasoro algebra contains an ##SL(2,R)## subalgebra that is generated by ##L_{-1}, L_{0}, L_{1}##. I read that this is the non-compact form of the ##SU(2)## algebra. Also, that as ##SU(2)## and ##SO(3)## have the same Lie algebra, so do ##SL(2,R)## and...
  11. M

    2D life form can exist with alimentary canal

    Hi, as I read in one of Hawking books, he predicted that a 2D life-form with an alimentary canal can not exist because it would fall apart. I was wondering about that, because I thought of an easy solution for this: with two movable chainings its still possible. I have made a graphic and...
  12. A

    Second fundamental form and Mean Curvature

    Homework Statement Metric ansatz: ds^{2} = e^{\tilde{A}(\tilde{\tau})} d\tilde{t} - d\tilde{r} - e^{\tilde{C}(\tilde{\tau})} dΩ where: d\tilde{r} = e^{\frac{B}{2}} dr Homework Equations How to calculate second fundamental form and mean curvature from this metric? The Attempt at a...
  13. K

    Show that the forces form a couple (algebraic)

    Homework Statement A Triangle ABC has sides of length a, b and c labelled according to the usual convention. Forces of magnitude ka, kb and kc act along BC, CA and AB respectively, with the direction given by the order of the letters. By considering the vector sum of the forces, or otherwise...
  14. D

    Angular momentum operators on matrix form

    Homework Statement Hi. I'm given a 3-dimensional subspace H that is made up of the states |1,-1\rangle, |1,0\rangle and |1,1\rangle with the states defined as |l,m\rangle and l=1 as you can see. The usual operator relations for L_{z} and L^{2} applies, and also: L_{+} = L_{x}+iL_{y} L_{-} =...
  15. C

    Express Laplace Transform of y(t) in given form.

    Homework Statement y(t) solves the following IVP y''(t) + 2y'(t) + 10y(t) = r(t) y(0) = 2 y'(0) = 3 r(t) = 0 if t < 0 t if 0 ≤ t ≤ 1 0 if t > 1 Demonstrate that the laplace transform of y(t) is Y(s) = \frac{2s+7}{s^{2}+2s+7} + \frac{e^{-s}}{s(s^{2}+2s+7)} +...
  16. D

    Calculate flux with normal form of Green's theorem

    Homework Statement Let R be the region bounded by the lines y=1 , y=0 , xy=1 , and x=2 . Let \vec{F} = \begin{bmatrix} x^4 & y^2-4x^3y \end{bmatrix}^T . Calculate the outward flux of \vec{F} over the boundary of R . Homework Equations Green's theorem (normal form): \int_{\partial...
  17. J

    Understanding the Integration by Parts Method: Solving Exercise 3

    Homework Statement Use integration by parts to show that ∫(sqrt(1-x^2) dx = x(sqrt(1-x^2) + ∫ (x^2) / sqrt(1 - x^2) write x^2 = x^2 -1 + 1 in the second integral and deduce the formula ∫(sqrt(1-x^2) dx = (1/2)x(sqrt(1-x^2) + (1/2)∫ 1 / sqrt(1 - x^2) dx I actually found a...
  18. B

    Quadratic form of strain energy

    Hi, I have some confusion about strain energy. When using Lagrange's equations to derive the EOM of vibrating structures, the strain energy is written as : U = q^{T}Kq ; (q is the vector of generalized coordinates, and K is the stiffness matrix). Writing it in this form makes it easy to...
  19. C

    Line element under coordinate transformation to get polar form

    Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...
  20. N

    Quantization of hamiltonian with complex form

    In most of textbooks, the canonical quantization procedure is used to quantize the hamiltonian with a simple form, the quadratic form. I just wonder how should we deal with more complex form hamiltonian, such like the ones including interaction terms?
  21. J

    Question about determinate form of plane

    Homework Statement I was just curious about determinate form of a plane if anyone has any info. If you check out number 18 on wolfram I was pondering about this form. http://mathworld.wolfram.com/Plane.html Homework Equations The Attempt at a Solution I would like to know why if...
  22. C

    Finding a surface form the intersection of two surfaces- Stokes' Thrm.

    Homework Statement Let \vec{F}=<xy,5z,4y> Use Stokes' Theorem to evaluate \int_c\vec{F}\cdot d\vec{r} where C is the curve of intersection of the parabolic cylinder z=y^2-x and the circular cylinder x^2+y^2=36 Homework Equations Stokes' Theorem, which says that \int_c\vec{F}\cdot...
  23. marellasunny

    Easy study material to define the normal form of a differential system

    Could someone suggest me an easy guide to transforming a system of differential equations into normal form around a particular point? As I understand, normal forms are used in border collision bifurcations to define the new set of coordinates around the parameter value \mu _0. By doing this...
  24. Z

    Indeterminate limit of the form 1/0

    When finding lim(x->1) (1+2ln(x))^(1/(x-1)) = 1^(infinity) I let y = (1+2ln(x))^(1/(x-1)) then ln both sides giving ln(y) = ln(1+2ln(x)))/(x-1) Taking the limit of ln(y) gives 1/0, which is indeterminate and hence the limit does not exist. However, I typed this into MS Mathematics and got...
  25. M

    Definition of isometry in components form

    From the book of Nakahara "Geometry, Topology and Physics": A diffeomorfism ##f:\mathcal{M}\to \mathcal{M}## is an isometry if it preserves the metric: ## f^{*}g_{f(p)}=g_{p} ## In components this condition becomes: ## \frac{\partial y^{\alpha}}{\partial x^{\mu}}\frac{\partial...
  26. B

    MHB Limit involving non-indeterminate form

    I've been studying this kind of limits today and most of them were solved by the technique I mentioned in my previous topic, except for the one you just showed me how to solve and this one: \lim_{x->0} (1 - cos(x))^{1/x} (It approaches 0 from the left, but I don't know how to write it here)...
  27. O

    Radical and its rational exponential form

    Can someone explain how these are equivalent. sqrt((-3)^2) = (-3)^2/2 =sqrt(9) and (-3)^1 3 is not equal to -3 (-3)^2/2 can be expressed as: (-3^2)^1/2 and (-3^1/2)2 (9)^1/2 and (sqrt(-1)sqrt(3))^2...
  28. Barioth

    MHB Is There Another Method to Evaluate This Limit Without Using Taylor Series?

    Hi, I have a question that is very close the the one of the OP so I tough I should post in here instead of making a new thread. (Hope no one mind ) Let's say \lim_{x->\pm\infty}x(log \sqrt{x} - log(\sqrt{x}-y)-\frac{y}{\sqrt{x}} )=\frac{y^2}{2} Now I could use taylor series to evaluate it, is...
  29. C

    Gaussian distribution other than standard form

    what changes does there occur in the result of the gaussian distribution "integration e^-alpha*x^2 dx=sqrt(pi/alpha) if i substitute that x^2 with some (x-a)^2? then what should be the integral result ?
  30. R

    Engineering Proving the Form of a Homogenous LC Circuit?

    Homework Statement I have a circuit with input source x(t), which contains also an inductor and a capacitor in series which I have found to be related to the output voltage y(t) (across the capacitor) like so: LC*d2y/dt2 + y(t) = x(t). I have also found its roots through the quadratic...
  31. MarkFL

    MHB Anakin1369's Limit of (tanh(x))^x: Yahoo Answers

    Here is the question: Here is a link to the question: What is the limit of (tanh(x))^x as x approaches infinity? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  32. O

    HTML/CSS Can a Fortran 95 Program Run Online Using a HTML Form?

    I've got a Fortran 95 program (which basically does few calculations) and I'd like to use it online. So that, the users will input data into a HTML form, the program will run, and it will display the results. Would it be possible to do it in the following way? To run a little program (e.g...
  33. marcus

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    The basic equation of GR has a curvature constant Λ on the lefthand (geometric) side. The Friedman equation is derived from the Einstein Field Equation by making a simplifying assumption of uniformity. As a spacetime curvature Λ can be written either in units of reciprocal area or reciprocal...
  34. U

    Proper form of schrodinger's equation?

    I feel a bit silly asking this, but I've been working through some QM lately and there's one aspect of Schrodinger's equation that's puzzling me. I've typically understood the equation as i\hbar \frac{d|\psi\rangle}{dt}=\hat H |\psi\rangle, but I've also seen it written as i\hbar \frac{\partial...
  35. B

    Why does everything in the Universe form a ball or Sphere?

    I want to know why everything in the universe forms a Ball or Sphere? Is gravity the cause of this? If so why? For example, If we were to pick the sphere apart can we see the source of gravity? Is gravity also a ball or sphere and can we grasp and see it? Why do we not ever see square planets or...
  36. C

    Find phasor current (impedance, etc.), finding polar form

    Homework Statement A 90Ω resistor, a 32 mH inductor, and a 5μF capacitor are connected in series across the terminals of a sinusoidal voltage source Vs = 750cos(5000t + 30)V. Calculate the phasor current. Homework Equations phasor current i = V/Z V in polar form = (Magnitude)(cos a + j sin...
  37. V

    Equation of motion in tensorial form (relativistic)

    Homework Statement How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge e and mass m, with 4-momentum p^a and electromagnetic field tensor F_{ab} of a constant magetic field \vec B perpendicular to the plane of motion...
  38. G

    Predicting the form of solution of PDE

    Predicting the functional form of solution of PDE How do you conclude that the solution of the PDE u(x,y)\frac{∂u(x,y)}{∂x}+\upsilon(x,y)\frac{∂u(x,y)}{∂y}=-\frac{dp(x)}{dx}+\frac{1}{a}\frac{∂^{2}u(x,y)}{dy^{2}} is of the functional form u=f(x,y,\frac{dp(x)}{dx},a) ? I know this...
  39. B

    Complex exponetial form of Fourier series

    I have some rather technical questions about the complex exponential form of the Fourier series: 1) What is the motivation behind the complex exponential form? Why not just use the real form (i.e. with sine and cosines)? 2) Surely the complex exponential form is an orthogonal set, i.e...
  40. M

    He most general form of the metric for a homogeneous, isotropic and st

    What is the most general form of the metric for a homogeneous, isotropic and static space-time? For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) signature) ds^2=dt^2+a^2(t)g_{ij}(\vec x)dx^idx^j Now the static condition. If I'm not mistaken...
  41. sunrah

    How to Calculate the Form Factor of a Nucleus?

    Homework Statement Calculate form factor of nucleus (A, Z given). Radius R = 1.2\cdot10^{-15}A^{\frac{1}{3}}Homework Equations F(\textbf{q}) = \frac{1}{Ze} \int d^{3}\textbf{r} \rho(r)e^{i\textbf{q}\cdot \textbf{r}}The Attempt at a Solution using polar coords d^{3}\textbf{r} = r^{2}dr...
  42. MarkFL

    MHB Convert 7sqrt5 cis(tan−1 (2)) to Rectangular Form - Yahoo! Answers

    Here is the question: Here is a link to the question: Express in the form a + bi, where a and b are real numbers.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  43. N

    Can You Help Me Solve the Infinitely Large Integral ∫|r|-3dV in Gauss Law?

    Hey. I want to use integrals-math to get from Gauss law in divergence form to the one in integral form. I know you can do it by simply accepting ∇*E dV = ρ/ε => ∫ ∇*E dV= ∫ρ/εdV = Q/ε = ∫E*dA, but I want to do it another way. I want to begin with ∫∇*E*dV and end up with Q/ε. So: E =...
  44. A

    Will a Sun Collapse Form a Black Hole?

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  45. F

    MHB Logic involving knowing when a form is ready to be submitted

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  46. N

    Electrical: Reduce the expression to the form V_mcos(wt+theta)

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  47. Petrus

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  48. M

    How to Solve Laplace Equation in Polar Coordinates?

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  49. H

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  50. K

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