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30° and 60°. The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
Algebraic fraction. In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are and . Algebraic fractions are subject to the same laws as arithmetic fractions. A rational fraction is an algebraic fraction whose numerator and denominator are both polynomials.
A unit fraction is a positive fraction with one as its numerator, 1/ n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, ...
In mathematics, the plastic ratio is a geometrical proportion close to 53/40.Its true value is the real solution of the equation x 3 = x + 1.. The adjective plastic does not refer to the artificial material, but to the formative and sculptural qualities of this ratio, as in plastic arts.
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.
Quarter-comma meantone, or 1 4 -comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma ( 81 : 80 ), with respect to its just intonation used in Pythagorean tuning (frequency ratio 3 ...
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 ...
Simple quintuple meter can be written in 5. 4 or 5. 8 time, but may also be notated by using regularly alternating bars of triple and duple meters, for example 2. 4 + 3. 4. Compound quintuple meter, with each of its five beats divided into three parts, can similarly be notated using a time signature of 15. 8, by writing triplets on each beat of ...