TODO
Consider creating a Cover Page, Create a proper TOC, Define and solidify scope of book, Organize all sections/modules into broad Units/Parts/Chapters, Remove topics which are beyond the scope of the book, Use Template:stages or Template:decistages to indicate relative completeness of particular sections/modules
This book discusses tonal music theory, specifically of the common practice period onwards, including jazz, blues, rock, and other modern styles. It focuses mostly on Western (i.e., Western European, Euro-American, and Afro-American) styles, however, all styles of music are discussed.
What is a pitch? How is a keyboard set up? How is Western music notated? What are keys, modes and chords? What about scales? What is part-writing? What is figured bass?
Harmony is the underlying foundation of music of the Common Practice period. To study harmony is to study how particular sonorities are related and function with respect to a primary tonal region based upon a central pitch class.
The Mathematical definition of harmony: Presume that waves X and Y are of wavelengths A and B. In other words X(nA) = X(mA), and Y(nB) = Y(mB), where n and m are any 2 real numbers.
Now, presume that wave Z is a combination of X and Y. In other words Z(n) = X(n) + Y(n), where n is any number. Because Z is a function of X+Y, Z only repeats at any point where X and Y both repeat. This point is the lowest common multiple of A and B, which will henceforth be referred to as value C. C is the combined wavelength of X and Y.
The nature of tonal harmony is that the lower the value of C, the more harmonized the notes are. This is why octaves are the most harmonized; a note's octave repeats twice as often as the note itself, so if 2n is the wavelength of any note, n is its octave. Obviously, the lowest common multiple of N and 2N is 2N itself, which makes the wavelength of a note combined with its octave just the wavelength of the note itself, and the shortest possible combine wavelength of 2 notes.
The study of how melodic lines best interact in order to create functional and logical harmonic progressions. The term "counterpoint" comes from the Latin 'punctus contra punctum' or point against point (note against note).
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