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  2. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [ a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted ...

  3. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or ⁠ ⁠, where a and b are both integers. [ 9] As with other fractions, the denominator ( b) cannot be zero. Examples include ⁠ 1 2 ⁠, − ⁠ 8 5 ⁠, ⁠ −8 5 ⁠, and ⁠ 8 −5 ⁠.

  4. Time signature - Wikipedia

    en.wikipedia.org/wiki/Time_signature

    Most time signatures consist of two numerals, one stacked above the other: The lower numeral indicates the note value that the signature is counting. This number is always a power of 2 (unless the time signature is irrational), usually 2, 4 or 8, but less often 16 is also used, usually in Baroque music. 2 corresponds to the half note (minim), 4 to the quarter note (crotchet), 8 to the eighth ...

  5. Harmonic progression (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Harmonic_progression...

    An excellent example of Harmonic Progression is the Leaning Tower of Lire. In it, uniform blocks are stacked on top of each other to achieve the maximum sideways or lateral distance covered. The blocks are stacked 1/2, 1/4, 1/6, 1/8, 1/10, … distance sideways below the original block.

  6. 7-limit tuning - Wikipedia

    en.wikipedia.org/wiki/7-limit_tuning

    7-limitor septimaltuningsand intervalsare musical instrument tunings that have a limitof seven: the largest primefactor contained in the interval ratiosbetween pitchesis seven. Thus, for example, 50:49 is a 7-limit interval, but 14:11 is not. For example, the greater just minor seventh, 9:5 (Playⓘ) is a 5-limitratio, the harmonic seventhhas ...

  7. List of Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/List_of_Runge–Kutta_methods

    List of Runge–Kutta methods. Runge–Kutta methods are methods for the numerical solution of the ordinary differential equation. Explicit Runge–Kutta methods take the form. Stages for implicit methods of s stages take the more general form, with the solution to be found over all s. Each method listed on this page is defined by its Butcher ...

  8. Approximations of π - Wikipedia

    en.wikipedia.org/wiki/Approximations_of_π

    The cells (±3, ±4) and (±4, ±3) are labeled. The 12 cells (0, ±5), (±5, 0), (±3, ±4), (±4, ±3) are exactly on the circle, and 69 cells are completely inside, so the approximate area is 81, and π is calculated to be approximately 3.24 because 81⁄52 = 3.24. Results for some values of r are shown in the table below: r.

  9. Fractional factorial design - Wikipedia

    en.wikipedia.org/wiki/Fractional_factorial_design

    The results of that example may be used to simulate a fractional factorial experiment using a half-fraction of the original 2 4 = 16 run design. The table shows the 2 4 - 1 = 8 run half-fraction experiment design and the resulting filtration rate, extracted from the table for the full 16 run factorial experiment .

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