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  2. Beat (acoustics) - Wikipedia

    en.wikipedia.org/wiki/Beat_(acoustics)

    Monaural beats are combined into one sound before they actually reach the human ear, as opposed to formulated in part by the brain itself, which occurs with a binaural beat. This means that monaural beats can be used effectively via either headphones or speakers. It also means that those without two ears can listen to and receive the benefits."

  3. Music and mathematics - Wikipedia

    en.wikipedia.org/wiki/Music_and_mathematics

    Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of set theory, abstract algebra and number theory.

  4. Decidability of first-order theories of the real numbers

    en.wikipedia.org/wiki/Decidability_of_first...

    The theory of real closed fields is the theory in which the primitive operations are multiplication and addition; this implies that, in this theory, the only numbers that can be defined are the real algebraic numbers. As proven by Tarski, this theory is decidable; see Tarski–Seidenberg theorem and Quantifier elimination.

  5. Theory (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Theory_(mathematical_logic)

    The complete theory of a structure A is the set of all first-order sentences over the signature of A that are satisfied by A. It is denoted by Th(A). More generally, the theory of K, a class of σ-structures, is the set of all first-order σ-sentences that are satisfied by all structures in K, and is denoted by Th(K). Clearly Th(A) = Th({A ...

  6. List of first-order theories - Wikipedia

    en.wikipedia.org/wiki/List_of_first-order_theories

    The theory of an equivalence relation with exactly 2 infinite equivalence classes is an easy example of a theory which is ω-categorical but not categorical for any larger cardinal. The equivalence relation ~ should not be confused with the identity symbol '=': if x=y then x~y, but the converse is not necessarily true. Theories of equivalence ...

  7. Sentence (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Sentence_(mathematical_logic)

    Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.

  8. Beat (music) - Wikipedia

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

    Both terms correspond to the direction taken by the hand of a conductor. This idea of directionality of beats is significant when you translate its effect on music. The crusis of a measure or a phrase is a beginning; it propels sound and energy forward, so the sound needs to lift and have forward motion to create a sense of direction.

  9. List of mathematical theories - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_theories

    Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory; Brill–Noether theory; Catastrophe theory; Category theory; Chaos theory; Character theory; Choquet theory; Class field theory; Cobordism theory; Coding theory; Cohomology theory ...