Abstract
Mathematics of music and sound production brings to bear the physical and practical application of Mathematics in the field of Music. The composition of songs involves the principle of key scaling, their respective interval as calculated with the aid of an appropriate key division which suites the generality of songs composed in different keys with the keyboard. Melodies, harmonies and rhythms produced in the stage of rendition is characterized by transposition and inversion of key to suite each song. With the aid of keyboard, elements of Symmetric group are used to compose songs.
Highlights
1.1 THE PYTHAGOREAN SCALE AND THE EQUAL TEMPERED SCALEPythagorean scales are generated by a single pure interval
Insisting that each new note be related by a perfect fifth to some previous note in our scale does not ensure that arbitrary pairs of notes have any kind of nice harmonic relationship
It fails to ever generate a perfect octave.One historical solution to this problem was to temper the Pythagorean scale by flattening the twelfth ratio into a perfect octave as proposed by Steven [6]
Summary
Pythagorean scales are generated by a single pure interval. The simplest non-trivial harmonic ratios are 3/2 (the perfect fifth) and 2/3, which normalizes (i.e., scaled by the appropriate power of two to lie in the “fundamental” octave of intervals between 1 and 2) to 4/3 (the perfect fourth). The difference between the seven octave and the twelve fifth of the Pythagorean scale was seen from the difference in its ratio and inequality in comparison With this difference involved, it became difficult for musician to play music on this scale as one would not be able to play several keys of songs using this scale. After a long research and hard work, a geometric progression approach was applied where a=1 and r = 12 2 which divides the scale in twelve equal intervals thereby measuring the interval in cent; that 12 2 is 100 cent par intervals It was the perfect scale for music composition and highly adopted and used by musicians in playing song having different keys. It is intended as a supplemental text (not a replacement text) for a music fundamentals course, or as reading for a course on music and mathematics, or on diatonic set theory
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