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. avito009

    Why Does More Vapour Form When Taking a Bath in Colder Weather?

    When the temperature in a city is lower and one has a bath in the bathroom then why does more vapour get created? More vapour than it would be created when the temperature is higher?
  2. Kuzon

    How do covalent bonds of the same molecule form?

    There is no difference in electronegativity, so how do bonds form? Take for example C-C, they both want 4 electrons for a full valence shell to become more stable - they meet each other, but how come they share 4 electrons? There is no difference in electronegativity for them to attract each...
  3. Cobalt101

    I Time to Form Black Hole? | Observer Slows Time at Event Horizon

    Is it correct that, from the perspective of an observer, time slows down and ultimately stops at the event horizon of a black hole, implying that no black holes have had time to form in the universe ?
  4. C

    Circled Part Formula in Double Integral: Explaining the Use of dA in Polar Form?

    Homework Statement can someone explain about the formula of the circled part? Why dA will become r(dr)(dθ)? Homework EquationsThe Attempt at a Solution A = pi(r^2) dA will become 2(pi)(r)(dr) ? why did 2(pi) didnt appear in the equation ?
  5. stevendaryl

    I Asymptotic Behavior of Modified Bessel Functions

    Does anyone know whether the following integral has a closed-form solution? If not, is anything known about the asymptotic behavior? f(x) = \int_{-\infty}^{+\infty} \frac{e^{iux}}{\sqrt{u^2 + 1}} du
  6. Ali Durrani

    Integral form of momentum equation

    Hello guys! can i get the derivation for this equation ?
  7. munirah

    Reduced Density operator in matrix form

    Homework Statement I already read book of Quantum Computation and Quantum Information by Nielsen and Chuang according to reduced density operator and I already understand how to do the reduced density using Dirac notation, Ket Bra.Homework Equations [/B] My problem here I want to know the...
  8. F

    Alternative form of Reynold's number

    Homework Statement in the third picture , we know that π2 can be written as function of π1 , where π2 is inverse of reynold number , how if i want to change it to π1 = function of π2 , can i write it as (Reynold number ) = F / ρ (D^2)(v^2) ? p/s : π1 is actually inverse of reynold number...
  9. F

    I Integral form of Navier-Stokes Equation

    The Navier-Stokes equation may be written as: If we have a fixed volume (a so-called control volume) then the integral of throughout V yields, with the help of Gauss' theorem: (from 'Turbulence' by Davidson). The definition of Gauss' theorem: Could someone show me how to go from the...
  10. J

    A Form factor and new EFT operators for a WIMP on a nucleon

    Hi, On the third paragraph(right column) of page 1 of the paper, http://journals.aps.org/prc/pdf/10.1103/PhysRevC.89.065501 , It says on form factor, "Because the momentum transfer in the scattering is large compared to the inverse nuclear size, form factors are generally included ". I...
  11. F

    Alternative form of buckingham theorem

    Homework Statement http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/dimension/node9.html in the link above , the author stated that F / (rho)(D^2)(v^2) = f( (rho)(v)(D) / (μ) ) , Homework EquationsThe Attempt at a Solution can i rewrite in in anotgher way ...
  12. 5

    Complex numbers in the form a+bi

    Homework Statement How would I go about solving 1/z=(-4+4i) The answer that I keep on getting is wrong The Attempt at a Solution [/B] What I did z=1/(-4+4i)x(-4-4i)/(-4-4i) z=(-4-4i)/(16+16i-16i-16i^2) z=(-4-4i)/32 z=-1/8-i/8 This is the answer that I got however it says that it is...
  13. M

    MHB Find all the matrices in Jordan form

    Hey! :o I want to find all the matrices in Jordan form with characteristic polynomial the $(x+2)^2(x-5)^3$. Let $\mathcal{X} (x)=(x+2)^2(x-5)^3$. The possible minimal polynomials $m(x)$ are the ones that $m(x)\mid \mathcal{X} (x)$, so $(x+2)^2(x-5)^3$ $(x+2)(x-5)^3$ $(x+2)(x-5)^2$...
  14. Evangeline101

    Function: expressing functions in vertex form.

    Homework Statement 2. Homework Equations The Attempt at a Solution a) [/B]f(x) = -5x2 + 20x + 2 y = -5x2 + 20x + 2 Factor -5 from the first two terms: y = -5x2 + 20x + 2 = -5 (x2 – 4x) +2 Complete the square in the bracket: (1/2 b)2 = [1/2 (-4)]2 = (-2)2 = 4 Group the perfect...
  15. J

    Does AC form a closed loop circuit?

    Some say that AC should form a closed loop circuit for electricity utilization but is there really an loop from the Power station(hot wire) to the Ground(neutral) and then from Ground to power station so that it forms a loop?
  16. D

    Solving e^z=w in Polar Form | Abs(right hand side)=2 without ln 2 in Solution

    Homework Statement $$2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2} $$ Then i write the right side as polar form and the abs(right hand side)=2 , and then multiplied with an angle. But in the answer there is only pi/4*i. which is the angle i get, but since the abs(right hand side)=2...
  17. odietrich

    I General form of symmetric 3x3 matrix with only 2 eigenvalues

    I'm looking for the general form of a symmetric 3×3 matrix (or tensor) ##\textbf{A}## with only two different eigenvalues, i.e. of a matrix with the diagonalized form ##\textbf{D}=\begin{pmatrix}a& 0 & 0\\0 & b & 0\\0 & 0 & b\end{pmatrix} = \text{diag}(a,b,b)##. In general, such a matrix can be...
  18. V

    Mesh current equation in matrix form

    i3 -? This is how I tried to solve using cramer's rule (denominator is the determinant of the matrix, while numerator is the determinant of the modified matrix) I ignored the prefix Kilo, but the method is right. So I get a different value for i3. Does anyone know what's wrong?
  19. I

    I Form of Wavefunctions: Exploring Outside of e^ikx

    Hi all! I'm currently watching MIT 8.04 (Quantum Physics I) on MIT open courseware. I have just finished lecture 5. In the past 2 lectures, they introduced opperators, specifically momentum, energy and position. To prove/derive (I'm not sure what the correct term is) the momentum and energy...
  20. S

    A Theories that respect one form of the equivalence principle but violate another

    This extract is taken from Sean Carroll's textbook. It talks about a theory that respects the Weak Equivalence Principle but violates the Einstein Equivalence Principle. we could imagine a theory of gravity in which freely falling particles begin to rotate as they moved through a gravitational...
  21. EnigmaticField

    A The Fierz-Pauli action takes the form of the Maxwell action

    I read in a paper arXiv:1002.3877 a Higgs mechanism for massive gravity can be constructed by introducing 4 scalar fields (they play the role of the Higgs fields) \phi^A with A=0,1,2,3 and then considering the Fierz-Pauli action S_{\rm{FP}}=\frac{m^2}{2}\int...
  22. F

    I Spatial homogeneity and the functional form of two-point functions

    Consider a two-point function $$f(\mathbf{r}_{1},\mathbf{r}_{2})$$ If one requires homogeneity, then this implies that for a constant vector ##\mathbf{a}## we must have $$f(\mathbf{r}_{1},\mathbf{r}_{2})=f(\mathbf{r}_{1}+\mathbf{a},\mathbf{r}_{2}+\mathbf{a})$$ How does one show that if this is...
  23. G

    Weak form of Navier-Stokes and heat transfer coupling(COMSOL)

    I am asked to simulate a 2-D coupled problem in COMSOL(Navier stokes with Heat transfer) of a simple room. I'm not sure if COMSOL already has preexisting physics for navier stokes and heat tranfer that I could use directly but I am provided with two differential equations and boundary...
  24. A

    Is it possible for heat to be a physical form?

    By physical form I mean stored chemical or actual be a physical thing you can touch. Yes I understand it already is a physical form in atoms but I mean is it possible to have a jar of heat.
  25. Kirito123

    Changing standard form to slope intercept form.

    Homework Statement Write the equation 4x – 7y – 14 = 0 in the form y = mx + b. Homework Equations "Y= mx + b" and "standard form". The Attempt at a Solution4x – 7y – 14 = 0 (add 14 to both sides of the equation) 4x – 7y = 14 (subtract 4x from both sides of the equation) -7y = -4x + 14...
  26. C

    I Is the Higgs Field a new form of an old idea?

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  27. Kingyou123

    Disjunctive Normal form to Combinatorial Circuit

    Homework Statement Draw the combinatorial circuit corresponding to the disjunctive normal form. Homework Equations DNF of f(x,y,z)=xyz+Not(xy)z The Attempt at a Solution f(x,y,z)=xyz+not(xy)z =z(xy+not(xy)) Wouldn't the xy and not xy cancel out? That's my current problem with this...
  28. kolawoletech

    General Form of Canonical Transformations

    Homework Statement How do I go about finding the most general form of the canonical transformation of the form Q = f(q) + g(p) P = c[f(q) + h(p)] where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and...
  29. kolawoletech

    A Most General form of Canonical Transformation

    How do I go about finding the most general form of the canonical transformation of the form Q = f(q) + g(p) P = c[f(q) + h(p)] where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and conjugate momentum in...
  30. M

    MHB Solution of the problem in interlaced form

    Hey! :o We consider the differnetial equation $$(x-xy(x))+(y(x)+x^2)y'(x)=0$$ I have found the integrating factor $\mu (x,y)=\sqrt{x^2+y^2}$. Using this I have to find the solution of the problem in interlaced form. Could you give me some hints what I am supposed to do? (Wondering) I...
  31. C

    B Can all elements, (not including gases) form Ionic Bonds?

    I've been looking all over the internet, can calcium and iron form an ionic bond, Gold and Radium, Sodium and Tin. If those elements happened to run into each other. Also, another thing I don't understand is why don't the atoms in my hand bond with atoms on the wall when they come into contact.
  32. B

    Finding Jordan canonical form of these matrices

    Homework Statement For each matrix A, I need to find a basis for each generalized eigenspace of ## L_A ## consisting of a union of disjoint cycles of generalized eigenvectors. Then I need to find the Jordan canonical form of A. The matrices are: ## a) \begin{pmatrix} 1 & 1\\ -1 & 3...
  33. Adraasa Kynuei

    B What would be the minimum size for a galaxy to have a disk form?

    So looking at pictures of dwarf galaxies and how they're just an irregular (pun intended) mess and they do not have the disk shape that we, ironically, associate with galaxies despite a small minority of galaxies being big enough to have and maintain their disk shape. Like apparently the...
  34. karush

    MHB Solving Polar Form of $\sin x$: Simple Equations

    $$y=\sin\left({x}\right) $$ write in polar form This reduces to $$r=1$$ So that's not = plots Not sure why I can't get these simple equations
  35. karush

    MHB Can the Polar Form of $y=x^3$ be Plotted on W|A?

    $y=x^3$ in polar form I got to this but it didn't plot ${x}^{3}$ $$r=\pm\sqrt{\frac{\sin\left({x}\right)}{\cos^3\left({x}\right)}}$$
  36. N

    How to know what binding agent to use? (powder into pseudo solid form)

    Hey all, th easiest way to make a powdered non-salt based powder into pseudo solid form is the use of a binding agent (the way medical compounds are made into pills), how does one know what is the best binding agent for a compound r mix of compounds? Any links/table names/advice appreciated.
  37. F

    Form differential equation by substituition

    Homework Statement dy/dx = (x-y+2) / (x+y-2) , by using x=X and y=Y+2 , form a differential equation . Homework EquationsThe Attempt at a Solution the author gave the answer as (Y^2) +(2XY) -(X^2)+A= 0 , while my answer is (Y^2) +(2XY) -(X^2)+A(X^4)= 0 is there anything wrong with my answer?
  38. F

    A Can Discrete Parameters Be Used in Limit Calculations?

    I'm trying to calculate this limit to answer a question in Quantum Mechanics: \mathop {\lim }\limits_{{t_1} \to 0} \,\,{\left( {\frac{m}{{2\pi \hbar i{t_1}}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}{e^{im{{(x' - x)}^2}/2\hbar...
  39. M

    Rearranging x=x0e^-lambda t in the form y=mx+c

    Hi, How could I rearrange x=x0e^-lambda t into the form y=mx+c, where y is equal to ln x and x is equal to t? Thank you in advance I tried to solve the problem myself, by taking the natural log of both sides, this left me with: ln x = -lambda t * lnx0 However, I am not sure if this answer is...
  40. EverGreen1231

    I How do we derive an Algebraic Companion Form equation set?

    Hello, I'm trying to study a settingless relaying scheme for Power System protection. The method is fairly well known and requires that one model a piece of equipment (like a transformer) with differential equation sets and compare that computational model with the actual operating behavior. If...
  41. tomdodd4598

    I What is a Blunt Form Factor?

    Hi there - a very simple question. On Wikipedia, it is stated that for the drag equation to be accurate, "the objects must have a blunt form factor and the fluid must have a large enough Reynolds number to produce turbulence behind the object". My question is what is a 'blunt form factor'? I...
  42. A

    Light what is it really ? past just another form of energy?

    Light is electric magnetic waves alternating. But are electric magnetic waves?, What are they composed of. electric and magnetic fields ? But what are they composed of ? is there any physical part of a wave to imagine. light is energy but is that the best description to what light is. We know...
  43. Stephanus

    B Is Extra Terrestrial Life Possible in This Universe?

    Dear PF Forum, I would like to know if LIFE in exoplanet is possible. And if it is, how? When I drove my Pastor to my mother funeral, he asked me out of the blue while I was driving my car. "Do you believe there is another earth?" My immediate response would be, in parallel universe where there...
  44. NATURE.M

    Stuck on obtaining a closed form for parameter using MLE

    Homework Statement We have a Markov Random Field with the log likelihood as such: $$ l(\theta) = \sum\limits_{i=1}^L \log p(x^{(i)}|\theta) = \sum\limits_{i=1}^L \left( \sum\limits_{s \in V} \theta_{s} x_{s}^{(i)} - \log \sum\limits_{x} \exp \left\lbrace \sum\limits_{s \in V} \theta_{s} x_{s}...
  45. G

    Dy/dx = (y^2) /x , form differential equation

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  46. D

    Discover the form of real solution set

    Homework Statement ##|4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x| > 8*6^x(8^{x-1}+6^x)## For some numbers ##a, b, c, d## such that ##-\infty < a <b < c <d < +\infty ## the real solution set to the given inequality is of the form ##(-\infty, a] \cup [b, c] \cup [d, +\infty)## Prove it by arriving at...
  47. Odious Suspect

    Deriving this "familiar arccosine form" of integral

    I posted a question about this yesterday, but realized I had made a stupid mistake in my derivation. Orbital dynamics: "The familiar arc-cosine form" That error has been corrected. I still have a deeper question. I believe this expression can be developed using the geometry of an ellipse in...
  48. Odious Suspect

    Orbital dynamics: "The familiar arc-cosine form"

    This arises in Joos's discussion of planetary motion, at the following URL: https://books.google.com/books?id=wFl2MkpcY6kC&lpg=PP1&pg=PA91#v=onepage&q&f=false I've modified the notation in obvious ways. He asserts that the following expression is "the familiar arc-cosine form": $$-\int...
  49. F

    Prove that three functions form a dual basis

    Homework Statement Homework Equations[/B] The Attempt at a Solution From that point, I don't know what to do. How do I prove linear independence if I have no numerical values? Thank you.
  50. A

    Is this considered factored form

    Homework Statement 6(2x+5)^2(6x-1)^5+(2x+5)^3(30)(6x-1)^4 this is what i got from deriving (2x+5)^3(6x-1)^5 and now i have to express my answer in factored form, does this classify as factored from even though it has a '+' in it? Homework EquationsThe Attempt at a Solution
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