THE AUDIBLE FREQUENCY SPECTRUM

Every musical culture of the world uses only a certain number of frequencies from the audible spectrum. Few cultures use the same selection of pitches, and few approach the entire gamut of frequencies.

Most cultures, however, make use of the octave. An octave is an acoustic and scientific relationship between two pitches, one of which vibrates twice as fast as the other and thus sounds higher. How the octave is divided is unique to each culture. Remember that this eight-part structure is unique to Western music. Other musical cultures do not necessarily divide pitches within an octave the way we do. Not surprisingly, each culture labels pitches differently. We name ours with seven letters –A, B, C, D, E, F, and G.

In European-based music, the octave represents an eight-pitch structure, but if you count the number of white and black piano keys in an octave, you will count thirteen. These thirteen keys represent the smallest divisions of the octave in the Western tradition. These divisions, called half steps, occur between two adjacent keys: from a white key to a black key and vice versa or, where there is no intervening black key, from a white key to a white key. There are twelve half steps in an octave.

Dividing the octave into more than twelve half steps results in smaller distances between pitches than are found in Western music. Some cultures, such as that of Bali (Indonesia), use fewer pitches with wider distance between them; others use more pitches – twenty-two in Indian music, twenty-four in Arabic music.

When two half steps are added together, they equal a whole step, represented on the piano by two keys separated by an intervening key. Whole steps occur between two white keys, two black keys, and in some cases, a black key and a white key. Half steps and whole steps are examples of what are called intervals – specifiable distances between two pitches. To refer to a pitch one half step higher than a particular pitch, we use the designation sharp. Thus, the black key to the right of C is C sharp. To refer to a pitch a half step lower, we use the designation flat. Thus, the black key to the left of D is D flat.

We have just given two names to the same key. We say that C sharp and D flat are enharmonic because they sound the same but have different names. But pitches not just those of the black keys, have at least two enharmonic designations. This is because "sharp" and "flat" can apply to any pitch. Thus, C is enharmonic to B sharp, because "sharp" simply means a pitch is raised a half step. Similarly, E is enharmonic to F flat. Remember that a sharp or flat is not necessarily a black key.

The terms we have learned – pitch, octave, interval, half step, whole step, enharmonic and related terms – are basic to any discussion of melody. They refer to the constituent parts of melody and are therefore fundamental to understanding its qualities, which we will discuss next.