Music Theory A Mathematical Approach
|
Music is a nonverbal form of communication discovered by mankind to reach the soul of individuals. It not only soothes the soul but also relaxes the mind.
|
|
It is no more just a source of entertainment but is being used in a number of useful therapies to fight many ailments and diseases. Music is also being linked with mathematics. It is being claimed that mathematics is involved in some way or the other in all the activities.
Music therapists are making use of mathematics to understand music structure, to understand musical scales etc. It is being connected with algebra, number theory, golden theory and Fibonacci numbers. In musical set theory a set of tones could form motives or chords. With the application of transposition, inversion which preserves the intervals between tones in a set, deep structures in music can be discovered. Abstract algebra has also been used to analyze music, the notes in an equal octave form of an abelian group with 12 elements. Modern theory of just intonations is fully based on fundamental theorem of arithmetic. The golden ratio is also used by different musicians in which they mark their keys out in intervals 34, 21, 13 and 8 etc.
There are many tracks also composed in homage of the golden ratio. Even while tuning irrational numbers or interval size comparisons are often used. A tuning based on the perfect consonants, perfect octave, perfect fifth and perfect fourth is called Pythogorean tuning. If ratios constituting a scale in just intonations are taken, the largest prime number could be found among their prime factorizations. A scale which uses only the primes 2, 3 and 5 is called a 5-limit scale; in such a scale, all tones are regular number harmonics of a single fundamental frequency.
A scale which uses only the primes 2, 3 and 5 is called a 5-limit scale; in such a scale, all tones are regular number harmonics of a single fundamental frequency. In equal temperament, the equal division of the octave into twelve parts, each semitone (half step) is an interval of the twelfth root of two, so that twelve of these equal half steps add up to exactly an octave. There are many features of relation between music and mathematics and the important ones have been covered above. However there are many aspects of music and it is impossible to explain rationally as it is dependant on human perception and psychology.
|
|
|
