Yesterday, I was reading an online music lesson that was on learning a scale on the piano. The author defined a scale as a series of notes that ascends and descends. While nothing in that definition is untrue, there are many series of notes that ascend and descend that are not scales; arpeggios or any number of melodies immediately come to mind. We need a more specific definition.
Scales are nearly always linked to tonality. A scale is a collection of tones comprised of one occurrence of every tone that belongs to a given tonality or tone set. Tone sets that are not tonal include comprise the chromatic scale, the whole tone scale, and a serial tone row. The tones don’t have to be a particular interval apart, because we can easily find scales that have adjacent tones separated by a variety of intervals, including seconds (the most common) and thirds (as found in the pentatonic scales.)
The vast majority of melodies in all cultures move more by step and small intervals than by leaps. Because scales also move by steps or small intervals, they represent an accurate cross section of melodic material one is likely to encounter in preparing repertoire for performance. When a singer or player can negotiate scales, especially in all their possible permutations, he or she has developed a technique that will easily transfer to music, and that is even throughout the range of the instrument, and encompasses the entire range of the instrument. Because relatively few pieces cover the entire range and so many note combinations as comprehensive scale study, they are an efficient means of preparing a musician to perform a vast array of music. With this in mind, I would also offer as a definition of scales that they are a useful abstract from the overall repertoire of music that can be used to build fluency of playing or singing. The more different scales one masters, the more of the world’s music one is prepared to successfully practice and perform.
This brings me to another point; scales don’t have to be based on the major scale, or even on the Western system of equal temperment. There is the Hejaz scale of the middle east, and the Pelog and Slendro scales of Polynesian gamelan tradition, all of which have unevenly tempered intervals, making them unusable for Western major-minor tonality. These non-Western scales cannot be overlooked, because they are rooted in musical cultures and traditions every bit as important to the world’s music as Euro-centered art music. There are also the so-called “jazz scales.” These are evenly tempered but less common among many music students. They include the four bebop scales, lydian dominant, half-whole diminished, and major blues. Few conservatory trained classical musicians or high school students studying privately are fluent in these scales, yet working them into a practice routine adds rigor and virtuosity to anyone’s technique. Scales for the modes, including dorian, lydian, mixolydian and Phrygian cannot be overlooked either. Each of these scales fits our initial definition perfectly.
The chromatic scale is something of an oddity among scales. It is the only scale that cannot be used in its entirety as the pitch set for a tonal piece of music. Even the whole tone scale, though itself without tonality, has been successfully embedded into tonal music so that the listener can audiate a tonality by association with the context. The chromatic scale, however, includes all possible tones in the Western equal tempered system. When all twelve tones are used, tonality is all but obliterated with no contextual clues to bring us back. Such is the nature of serial or 12-tone music. We can define a particular chromatic scale within the arbitrary bounds of a given octave, but there is no hint to tonal functions among any of the equally-spaced tones of the scale, and there is no definite tone on which the scale begins or ends. Theoretically, the chromatic scale is comprised of a tone set made up of an infinite number of tones. It becomes manageable only by constraining it within arbitrarily chosen beginning and ending points. This makes the chromatic scale open to all sorts of permutations for practicing, including ascending seconds (whole tone up, half tone down, etc.) and any number of adjacent tones ascending and descending with no loss (because there isn’t any) of harmonic grounding.
Scales are, in effect, the universal alphabet of music. They can be formed from the pitch materials of any music, and can be the basis for composing and improvising in any conceivable tonality, even in cultures and traditions that do not include functional harmony. Because scales are linear and melodic, they do not require harmony, though one can use them to play over harmonic changes or to construct chords, as, for example, jazz musicians do regularly.