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In mathematics, subharmonic and superharmonic functions are important classes of functions used extensively in partial differential equations, complex analysis and potential theory. Intuitively, subharmonic functions are related to convex functions of one variable as follows.
One can see that at some parameter values and initial conditions, the system’s oscillation spectrum is heavily contributed (almost dominated) by the \(3^{\text {rd }}\) subharmonic, i.e. the Fourier component of frequency \(\omega / 3 \approx \omega_{0}\).
Subharmonic frequencies are frequencies below the fundamental frequency of an oscillator in a ratio of 1/ n, with n a positive integer. For example, if the fundamental frequency of an oscillator is 440 Hz, sub-harmonics include 220 Hz ( 1 ⁄ 2 ), ~146.6 Hz ( 1 ⁄ 3 ) and 110 Hz ( 1 ⁄ 4 ).
That is, f is harmonic on every complex line. A function f: U → R ∪ { − ∞} is plurisubharmonic, sometimes plush or psh for short, if it is upper-semicontinuous and for every a, b ∈ Cn, the function of one variable ξ ↦ f(a + bξ) is subharmonic (whenever a + bξ ∈ U ).
A Closer Look for Vocalists. Learn exactly what subharmonic singing is, how to hear it in yourself and others, and when it occurs for vocalizers of all genres, voice types, and disciplines.
1 de abr. de 2020 · Click here to read more about Subharmonics at http://www.bass2yang.comTL;DW: Sing a note, slightly move toward vocal fry while staying on the same note, boom...
10 de feb. de 2020 · This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity.
