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  2. Delphic Hymns - Wikipedia

    en.wikipedia.org/wiki/Delphic_Hymns

    The Second Hymn is composed in a different key from the First Hymn. The central note (mese) of the first section is D (in conventional notation), rather than C, making it the (Greek) Lydian mode. [20] Below the mese are the notes A and B ♭, and above it are E, E ♭, F, and G. The notes used in the second section are different from the first ...

  3. Harmonic series (music) - Wikipedia

    en.wikipedia.org/wiki/Harmonic_series_(music)

    For example, a perfect fifth, say 200 and 300 Hz (cycles per second), causes a listener to perceive a combination tone of 100 Hz (the difference between 300 Hz and 200 Hz); that is, an octave below the lower (actual sounding) note. This 100 Hz first-order combination tone then interacts with both notes of the interval to produce second-order ...

  4. Painlevé transcendents - Wikipedia

    en.wikipedia.org/wiki/Painlevé_transcendents

    The most general form of the sixth equation was missed by Painlevé, but was discovered in 1905 by Richard Fuchs (son of Lazarus Fuchs), as the differential equation satisfied by the singularity of a second order Fuchsian equation with 4 regular singular points on the projective line under monodromy-preserving deformations.

  5. Poincaré–Lindstedt method - Wikipedia

    en.wikipedia.org/wiki/Poincaré–Lindstedt_method

    The coefficients of the super-harmonic terms are solved directly, and the coefficients of the harmonic term are determined by expanding down to order-(n+1), and eliminating its secular term. See chapter 10 of [5] for a derivation up to order 3, and [8] for a computer derivation up to order 164.

  6. Musical note - Wikipedia

    en.wikipedia.org/wiki/Musical_note

    Notes in it include a prime symbol below the note's letter. Names of subsequent lower octaves are preceded with "sub". Notes in each include an additional prime symbol below the note's letter. The octave starting at tenor C is called the "small" octave. Notes in it are written as lower case letters, so tenor C itself is written c in Helmholtz ...

  7. List of musical symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_musical_symbols

    Musical symbols are marks and symbols in musical notation that indicate various aspects of how a piece of music is to be performed. There are symbols to communicate information about many musical elements, including pitch, duration, dynamics, or articulation of musical notes; tempo, metre, form (e.g., whether sections are repeated), and details about specific playing techniques (e.g., which ...

  8. Ordinary differential equation - Wikipedia

    en.wikipedia.org/wiki/Ordinary_differential_equation

    In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable.As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. [1]

  9. Spectral theory of ordinary differential equations - Wikipedia

    en.wikipedia.org/wiki/Spectral_theory_of...

    The following is a version of the classical Picard existence theorem for second order differential equations with values in a Banach space E. [2] Let α, β be arbitrary elements of E, A a bounded operator on E and q a continuous function on [a, b].