Scale

Sing the opening of Beethoven's "Ode to Joy" and pay attention to the notes that turn up:

Hear the passage

Hear the passage

Fifteen notes, but only five different sounds: C, D, E, F and G. The melody goes back and forth among them, repeats, leaps. Now take out the repetitions and put the five in order, from low to high:

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That is no longer a melody. It is the material the melody was made of, lined up in a row. A scale is exactly that, carried up to the octave.

What a scale is

The word comes from the Latin scala, a ladder or staircase (Med 1996, ch. XV), and the image works: the notes are rungs, and what matters is how high each rung sits above the one before.

A scale is a series of successive notes separated by tones or semitones (Lacerda 1966, ch. XX). Med adds two more ideas to that. A scale is also the set of notes available in a given musical system, and an ordered succession of sounds within the span of an octave (Med 1996, ch. XV).

The three definitions describe the same thing from three sides. The first is about shape, rung after rung. The second is about purpose: the scale is the stock of notes a piece has at hand. The third says where the scale stops: at the octave, because above it the notes repeat under the same names.

The scale is not the music

Blatter makes a point that helps keep things apart. What characterises major and minor music is a set of pitches, each with its own function. Because that set is usually presented in order, going up or down, we speak of a major scale and a minor scale (Blatter 2007, part 2, art. 2).

The order, then, is a way of displaying the material, not a description of how the music moves. "Ode to Joy" never plays its scale from end to end, and hardly any melody does. Studying the scale is studying the stock; listening to the music is hearing what is done with it.

Ascending and descending

A scale can be ascending, from low to high, or descending, from high to low (Lacerda 1966, ch. XX). When a scale is studied in theory, the custom is to take it going up, and it is the ascending form that numbers the notes.

The note the scale starts on is the first degree, the next one the second, and so on, always in Roman numerals. In the descending scale the degrees keep the numbers of the ascending one: the seventh degree is still the seventh, whether the scale is going up or down (Lacerda 1966, ch. XX).

Diatonic and chromatic

Lacerda divides scales into two kinds by the size of their steps (Lacerda 1966, ch. XX).

A diatonic scale moves by tones and semitones. In it the seven letters all appear in a row, each one once, with or without an accidental:

Hear the passage

A chromatic scale moves by semitones only. Since the octave has twelve semitones and there are only seven letters, some letters have to repeat, with accidentals:

Hear the passage

On the piano, the chromatic scale is what you hear playing every key in a row, white and black. The right way to spell its notes, with sharps or flats, going up or down, belongs to the chromatic scale itself.

Seven scales on the white keys

The scale used most in Western music is the seven-note scale, and it repeats every seven notes (Lacerda 1966, ch. XX). But seven notes do not make just one scale.

Take the white keys of the piano and start on each of them in turn: C to C, D to D, E to E, all the way to B to B. The notes are the same in all seven scales. What changes is where the two semitones fall. From C to C they fall between the third and fourth degrees and between the seventh and eighth. From D to D they fall between the second and third and between the sixth and seventh:

Hear the passage

It sounds different, and it is different. Each of those seven ways of laying out the tones and semitones is a mode, and today two of them prevail, major and minor (Lacerda 1966, ch. XX).

That is why a scale has two names: that of the note it starts on, the tonic, and that of its mode. A scale that starts on C and is in the major mode is the C major scale; one that starts on A and is in the minor mode is the A minor scale (Lacerda 1966, ch. XX).

How many notes a scale has

Seven is the most familiar number, but not the only one. Med classifies scales by their number of notes (Med 1996, ch. XV):

Notes	Name
5	pentatonic
6	hexachordal
7	heptatonic
12	chromatic

The five-note scale is the pentatonic. With no semitones, it sounds open, and it is one of the most widespread scales in the world:

Hear the passage

Med also classifies scales by use, in three groups: the natural or diatonic scales, the artificial or chromatic scales, and the exotic scales, which have a singular make-up, such as the gypsy scales, the pentatonic scales and the whole-tone scale (Med 1996, ch. XV).

Well beyond seven

Blatter recalls that Western music rested for about a thousand years on the modes and the major-minor system, and that only in the nineteenth century did composers start looking for other systems, in the traditional music of other peoples and in invented scales (Blatter 2007, part 2, art. 10).

Even without leaving tones and semitones there is plenty of room. With exactly five whole tones and two semitones inside the octave, a whole family of seven-note scales can be built, and only a few of them belong to the modes and the major-minor system (Blatter 2007, part 2, art. 10). Beyond that family there are eight-note scales, scales of nine or more notes, and scales that reach past the octave, used in other cultures, in jazz and in the blues (Blatter 2007, part 2, art. 10).

The seven-note scale is the front door, not the whole house.

What comes next

With the idea of a scale in hand, each particular scale is a recipe of steps: the major, the minors, the pentatonic, the chromatic, the symmetric scales that repeat one pattern inside the octave. And each note of a scale has a role, which leads to scale degrees and to tonality.