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2. Metronome - Wikipedia

   en.wikipedia.org/wiki/Metronome

   2 4 at 60 BPM. This track plays 5 measures, then goes silent for 2, 3, 4, and 8 measures (alternating with 2 measures played), a typical exercise to help internalize a stronger sense of tempo. Much of modern metronome technique aims to resolve timing problems without creating overdependence on the metronome.

3. Music and mathematics - Wikipedia

   en.wikipedia.org/wiki/Music_and_mathematics

   A whole tone is a secondary interval, being derived from two perfect fifths minus an octave, (3:2) 2 /2 = 9:8. The just major third, 5:4 and minor third, 6:5, are a syntonic comma , 81:80, apart from their Pythagorean equivalents 81:64 and 32:27 respectively.

4. Mathematics - Wikipedia

   en.wikipedia.org/wiki/Mathematics

   Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics) but often later find practical applications. [2] [3]

5. Exercise (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Exercise_(mathematics)

   At the Russian School of Mathematics, students begin multi-step problems as early as the first grade, learning to build on previous results to progress towards the solution. In the 1960s, collections of mathematical exercises were translated from Russian and published by W. H. Freeman and Company : The USSR Olympiad Problem Book (1962), [ 8 ...

6. Music theory - Wikipedia

   en.wikipedia.org/wiki/Music_theory

   Music theorists sometimes use mathematics to understand music, and although music has no axiomatic foundation in modern mathematics, mathematics is "the basis of sound" and sound itself "in its musical aspects... exhibits a remarkable array of number properties", simply because nature itself "is amazingly mathematical". [87]

7. Order of operations - Wikipedia

   en.wikipedia.org/wiki/Order_of_operations

   [2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of ...