What is Chord: Definition and 41 Discussions

A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes (also called "pitches") that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords (in which the notes of the chord are sounded one after the other, rather than simultaneously), or sequences of chord tones, may also be considered as chords in the right musical context.
In tonal Western classical music (music with a tonic key or "home key"), the most frequently encountered chords are triads, so called because they consist of three distinct notes: the root note, and intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music, jazz and almost any other genre.
A series of chords is called a chord progression. One example of a widely used chord progression in Western traditional music and blues is the 12 bar blues progression. Although any chord may in principle be followed by any other chord, certain patterns of chords are more common in Western music, and some patterns have been accepted as establishing the key (tonic note) in common-practice harmony—notably the resolution of a dominant chord to a tonic chord. To describe this, Western music theory has developed the practice of numbering chords using Roman numerals to represent the number of diatonic steps up from the tonic note of the scale.
Common ways of notating or representing chords in Western music (other than conventional staff notation) include Roman numerals, the Nashville Number System, figured bass, chord letters (sometimes used in modern musicology), and chord charts.

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  1. A

    MHB Formula to find arc radius using arc length, chord length, and/or segment angle

    I'm attempting to write some code using the Ruby programming language that will give me the radius of an arc but the only pieces of information I have to work with are the arc length (L), the chord length (C), and the circular segment angle in degrees (A): I'm hoping someone can show me how to...
  2. R

    I Arc diameter as a function of arc length and chord length

    I'm trying to determine if a certain bicycle tire size will fit my bike, and that determination is based on the inflated diameter (or width) of the tire. As such, I'm trying to come up with a formula that will give me the diameter of a bicycle tire as a function of the tire's carcass width and...
  3. T

    MHB Finding Chord length given arc length and arc height?

    I am in the process of making a tent and need to get two curved surfaces to meet. I need to find the length of a Chord of a circle given that I have the Arc length and Arc Height (that's all), no radius or anything else. I suspect that I will need a radius to find this. Or am I missing a...
  4. karush

    Chord Length: A Mathematical Observation

    Ok this should be just an observation solution .. But isn't the equation for chord length $$2r\sin{\frac{\theta}{2}}= \textit{chord length}$$ Don't see any of the options Derived from that..
  5. L

    B Finding Radius from chord length and tangent distance

    Ok, i have a question. First, i am an engineering student and have done all math requirements up to linear alg. HOWEVER, my geometry is terrible, oh so terrible and i need some spoon feeding right now because i am stuck on a problem. Ok, i saw a really cool tool the other day called a radius...
  6. S

    I Average chord length of a circle

    I would like to find the average chord length of a circle. And I have 2 methods, which gave different answers... [The chord is defined as the line joining 2 points on the circumference of the circle.] The general formula for a chord length is ##d=2R\sin(\delta/2)=2\sqrt{R^2-u^2}## Method 1...
  7. Const@ntine

    Tuning a Violin's Chord (Frequencies)

    Homework Statement A violin's chord has a length of 0.350 meters, and is tuned to the sound of the note Sol, with a frequency of fG = 392 Hz. a) How far from the edge of the chord does the violinist need to place his hand, in order to play a note La, with a frequency of fA= 440 Hz? b) If...
  8. A

    Rectangular hyperbola, chord, origin

    Homework Statement Prove that the chord joining the points P(cp, c/p) and Q(cq, c/q) on the rectangular hyperbola xy = c^2 has the equation x + pqy = c(p + q) The points P, Q, R are given on the rectangular hyperbola xy = c^2 . prove that (a) if PQ and PR are equally inclined to the axes of...
  9. A

    Ellipse chord subtending a right angle

    Homework Statement Show that the equation of the chord joining the points P(a\cos(\phi), b\sin(\phi)) and Q(a\cos(\theta), b\sin(\theta)) on the ellipse b^2x^2+a^2y^2=a^2b^2 is bx cos\frac{1}{2}(\theta+\phi)+ay\sin\frac{1}{2}(\theta+\phi)=ab\cos\frac{1}{2}(\theta-\phi). Prove that , if the...
  10. EverGreen1231

    Is Chord Factor the same thing as Winding Factor?

    My Father's friend repairs electric motors and, occasionally, he comes to me with questions that require more of an "engineering knowledge." He asked me this past Sunday if I could explain to him what are Chord and Chording Factor, and, as has happened to me before, I felt I had a pretty good...
  11. ATY

    Chord length and radius of a wind turbine rotor blade

    Hello, I have a question about the chord length of rotor blades from wind turbines. I do not really understand what the difference is to the radius of a wind turbine. I can not find a real explanation, but it seems to be very important. I know that the formula of the chord length depends on...
  12. G

    Toaster Cord Tension Angle Optimization

    Homework Statement A 1.26kg toaster is not plugged in. The coefficient of static friction between the toaster and a horizontal countertop is 0.395. To make the toaster start moving, you carelessly pull on its electric cord. For the cord tension to be as small as possible, you should pull at...
  13. T

    Area of A Segmented Circle Cut By A Chord

    Homework Statement Given a circle with a set diameter, how does one calculate the area of the segment below? Homework Equations The only information available is the diameter (in this particular example it is 14"), You may not use angles. Only the chord length. Thank you for your reply. Miguel
  14. Titan97

    Question on intersection of tangent and chord

    Homework Statement Show that The tangent at (c,ec) on the curve y=ex intersects the chord joining the points (c-1,ec-1) and (c+1,ec+1) at the left of x=c Homework Equations Legrange's mean value theorem The Attempt at a Solution f'(c)=ec Applying LMVT at c-1, c+1...
  15. Kostas Tzim

    A chord at the edges of a graph

    Greetings, i found an interesting exercise from my perspective, it's not about HW, i just want to see different approaches than the Greek math forum i posted yesterday, so we have: If $$ f $$ is a function, then a chord is a straight portion whose edges belong to $$ C_f $$ f is a continuous...
  16. A

    Free fall down (Chord) Tunnel through Earth

    Homework Statement I'm trying to show that any tunnel through the Earth (not necessarily through the center) will have a free-fall time that is the same. I heard this was true somewhere. Homework Equations acceleration of free-fall = GM / r^2 where r is changing I believe this involves trig...
  17. Z

    Question about ellipse and chord

    I drew an oval using the ellipse tool of a vector-based drawing program. It's 23.5 mm wide and 21.5 mm high. There is a chord 15 mm long perpendicular to the minor axis. So the question is, how do I calculate the distance from the chord to the end of the ellipse (i.e., the end of the major...
  18. ChimM

    How Do You Calculate the Length of a Chord and Tangential Line in a Circle?

    Homework Statement Attached here is a diagram. My questions are, how to compute for the value of the chord? How to compute for the value of the tangential line? Please help.. Thank you in advance.
  19. 1

    Can the Area of a Sector be Determined Without Calculus or Trig?

    Homework Statement Suppose we have a circle of radius r, and two points A and B on the circle. We want to know the area of the sector cut off by A and B as a function of radius r and AB (the length of SEGMENT AB) Without calculus or trig. Homework Equations The Attempt at a...
  20. P

    Mean Aerodynamic Chord and Area

    If I have a problem in which the laminar/turbulent transition point is said to be 50% the mean aerodynamic chord, how can I find the area of the wing over which there is laminar flow? Is it simply half the wing area?
  21. R

    MHB Find arc length given chord, radius

    The solution to this question (whose answer is pi) is eluding me: The radius of a circle is 3 feet. Find the approximate length of an arc of this circle, if the length of the chord of the arc is 3 feet also.
  22. U

    What is the minimum length chord of a circle passing through a specific point?

    Homework Statement px+qy=40 is a chord of minimum length of the circle (x-10)^2 + (y-20)^2 = 729 . If the chord passes through (5,15), then p^{2013}+q^{2013} is equal to Homework Equations The Attempt at a Solution Let chord length be L \frac{L}{2} = 729-...
  23. D

    Finding the Length of a Chord on a Circle

    Homework Statement Find the length of the chord which the circle 3x^2+3y^2-29x-19y+56=0 cuts off from the straight line x-y+2+=0. Find the equation of the circle with this chord as diameter Homework Equations x^2+y^2+2gx+2fy+c=0 The Attempt at a Solution I can solve the second part...
  24. A

    Chord PQ subtending Right angle at centre of ellipse.

    Homework Statement If P and Q are two points on ellipse [(x^2/a^2)+(y^2/b^2)]=1 such that PQ subtends a right angle at the centre O then.Prove that 1/[(OP)^2] + 1/[(OQ)^2] = [1/(a^2)] +[1/(b^2)] Homework Equations Parametric form of points P(acos(θ),bsin(θ))...
  25. K

    Question about circle chord midpt locus

    Homework Statement A is the pt where the circle with wquation x^2+y^2=25 cuts the positive x-axis. Find the midpts of the chords of this circle that contain the pt A Homework Equations The Attempt at a Solution Since it is about the midpt of chords, I try to set up a equation...
  26. U

    Prove that a variable chord of ellipse

    Homework Statement Prove that a variable chord of ellipse which subtends 90° at the centre is always tangent to a concentric circle Homework Equations The Attempt at a Solution I assume the simplest equation of ellipse to be \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1 and the variable chord...
  27. E

    Finding the gradient of a chord

    Homework Statement What is the gradient of the chord of the curve y = 2x^2 between the points x = 1 and x = 1+ h? Homework Equations differentiation by first principles dy/dx = f(x+h) - f(x)/hThe Attempt at a Solution use of the formula to receive 4x +2h
  28. D

    Simplify Condition for Chord Length Equals Angle?

    Consider the following: On a circle of radius 1, two points are marked: P1 and P2. Two lines are drawn from the center of the circle: one from the center to P1, the other from the center to P2. The angle between these two lines is \theta. One more line is drawn: from P1 directly...
  29. Jadaav

    Hi there,To find the gradient of a curve, we draw a chord on the

    Hi there, To find the gradient of a curve, we draw a chord on the curve and then makes the 2nd coordinates ( B ) tends to A ( 1st coordinates ). To find the gradient of the chord, i.e, ΔY/ΔX, we replace the two coordinates into the equation of the curve. But my question is why do we...
  30. J

    Chord Length Distribution in a Right Circular Cylinder

    Homework Statement chord length distribution in right circular cylinder for isotropic source of rays we start with solid angle relation dP/(d(fi)d(cos(theta)))=const.(1) Homework Equations dP/dl=integral[const.(1)*d(cos(theta)/dl)]d(fi) and similar...
  31. S

    Gravity in Tunnel Through Chord of a Planet

    Homework Statement An object of mass 104 kg moves in a smooth straight tunnel of length 1540 km dug through a chord of a planet of mass 3.2 × 1024kg and radius 1 × 109 m. Determine the effective force constant of the harmonic motion. Answer in units of N/mHomework Equations Force of gravity=...
  32. U

    Equation for Ellipse from a chord - no other parameters

    Equation for Ellipse from a chord -- no other parameters! Homework Statement Known conditions are: End points of the chord intersect the major and minor axis. Proximity to nearest parallel tangent. Known (hypothetical) values are: The length of the chord is 10. The chord is 1.25 from...
  33. Z

    Which is a Chord of a Hyperbola? AB or PQ?

    Homework Statement In the attached figure, which one is a chord of the hyperbola? is it AB or PQ? I am confused between both. If AB passes through the focus perpendicular to the axis, it is called latus rectum which is a focal chord. But in some figures I saw PQ as a chord. Please...
  34. G

    A circle where every chord intersects every other chord?

    I'm trying to do a project that requires me construct a circle with n chords. I need to find the maximum number of regions are obtained. I believe the way to do this is to have every new chord intersect every other chord without three chords intersecting at one point. In other words: is it...
  35. L

    Maximising the Area of a Chord.

    Homework Statement This is a problem within a problem. I need to differentiate the area of a chord of find the maximum area (and hopefully, in the process, radius). Homework Equations I found this equation on another site: A=R^2[(Pi/180*c - sin c)]/2 Where: • C is the central angle in...
  36. Saladsamurai

    When is arc length ≈ chord length

    Homework Statement Maybe this is precalculus? Either way, here is a question that I am curious about. Take a circle of radius R and sweep out an arc length SAB with endpoints 'A' and 'B' over angle theta. For a short enough arc length, I believe that we could approximate SAB by the chord...
  37. L

    Find the radius of a circle from a chord

    Hi, Can someone please explain to me how you get the equation: radius=(\sqrt{c}+m2)/2m c=length of chord m=distance from midpoint of chord to edge of the circle I would like to find the radius of the circle from only knowing those two quantities. I have found the equation on...
  38. J

    Bungee chord (standing waves and antinodes.)

    Homework Statement A 75 g bungee cord has an equilibrium length of 1.20 m. The cord is stretched to a length of 1.80 m, then vibrated at 20 Hz. This produces a standing wave with two antinodes. What is the spring constant of the bungee cord? Homework Equations f=nv/2L The...
  39. P

    Finding a Normal Chord of a Parabola to Minimize Area

    Hey, Homework Statement Putnam 1951 A6 Determine the position of a normal chord of a parabola such that it cuts off of the parabola a segment of minimum area. Homework Equations Standard Form of a Parabola {y} = {{{a}{{x}^{2}}} + {{b}{x}} +...
  40. B

    Identifying the Chord in the Image: Am or C?

    What is the chord in the attached image? *What is called (properly/formally)? (perhaps Am/C?)
  41. himanshu121

    Chord parallel to AB and 2CD=AB

    AB is the diameter of a circle CD is a chord parallel to AB and 2CD=AB. The tangent at B meets the line AC produced at E. Prove that AE=2AB. I'm finding no way to solve this ? Still i thought of applying AE*CE=BE2 but that is not enough to slove the pro ? Any other Hint to solve