Scale Theory

In music, a scale is a systematic ordering of five to eleven notes within the octave. Fewer than five notes does not make a scale, whereas the full complement of 12 notes constitutes something called the chromatic scale. Scales are usually written with the lowest note first and the others in ascending order.

The Diatonic Scale

The diatonic scale is a central concept in Western music. The underlying principle is a seven-note scale that is built up from five whole-tone steps and two semitone steps. The two semitone steps have maximum separation within one octave, so that the sequence of steps remains whole-whole-half-whole-whole-whole-half or variations of it.

This interval disposition is rather neatly illustrated by looking at a piano keyboard, which has seven white and five black keys, the latter occurring between the former in all but two cases:

In case you're unsure, the trick is to look for the "2 group"—C is always found just to the left of the first of the pair of black keys.

The intervals of the diatonic scale are assymmetrical. No pattern is repeated except at the octave, which means that you can construct seven distinct modes from the scale.

Traditionally, these modes are named for the Greek modes of antiquity, which in their turn took their names from Greek tribes: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian. They are listed in this order since that's how they arrange themselves if you start on C and only use natural notes.

Ionian (C)

Step pattern: whole-whole-half-whole-whole-whole-half.

Interval pattern: root-maj2-maj3-perf4-perf5-maj6-maj7.

Dorian (D)

Step pattern: whole-half-whole-whole-whole-half-whole.

Interval pattern: root-maj2-min3-perf4-perf5-maj6-min7.

Phrygian (E)

Step pattern: half-whole-whole-whole-half-whole-whole.

Interval pattern: root-min2-min3-perf4-perf5-min6-min7.

Lydian (F)

Step pattern: whole-whole-whole-half-whole-whole-half.

Interval pattern: root-maj2-maj3-aug4-perf5-maj6-maj7.

Mixolydian (G)

Step pattern: whole-whole-half-whole-whole-half-whole.

Interval pattern: root-maj2-maj3-perf4-perf5-maj6-min7.

Aeolian (A)

Step pattern: whole-half-whole-whole-half-whole-whole.

Interval pattern: root-maj2-min3-perf4-perf5-min6-min7.

Locrian (B)

Step pattern: half-whole-whole-half-whole-whole-whole.

Interval pattern: root-min2-min3-perf4-dim5-min6-min7.

About the Modes

The seven diatonic modes are often referred to as church modes, since music theory came of age during medieval times, when the Catholic church was the dominant factor in music. In those days, there was a clear preference for the Dorian, Phrygian, Lydian and Mixolydian modes. The Ionian and Aeolian modes were deemed unworthy, unsuitable for serious music. Ironically, the Ionian and Aeolian modes eventually won out and became the major and minor scales, respectively—the foundation of modern tonality.

It is also possible to group six of the modes into broad categories based on their similarity to Ionian/major and Aeolian/minor:

• The Dorian mode has a major sixth instead of the minor sixth of the minor scale.
• The Phrygian mode as a minor second instead of the major second of the minor scale.
• The Lydian mode has an augmented fourth rather than the perfect fourth of the major scale.
• The Mixolydian mode has a minor seventh rather than the major seventh of the major scale.

Thus far I haven't really mentioned the Locrian mode. This is because it is a comparatively recent construction, just to put a name on that seventh scale. The reason why it was never used in the old days was because of the built-in instability: the first, third and fifth scale degrees constitute a diminished chord rather than a major or minor chord.

The Major and Minor Scales

Since the major and minor scales are derived from the Ionian and Aeolian modes, respectively, they are also considered to be diatonic scales. On the surface, the scales are indeed indistinguishable from the modes:

Major Scale (C)

Step pattern: whole-whole-half-whole-whole-whole-half.

Interval pattern: root-maj2-maj3-perf4-perf5-maj6-maj7.

Minor Scale (A)

Step pattern: whole-half-whole-whole-half-whole-whole.

Interval pattern: root-maj2-min3-perf4-perf5-min6-min7.

However, the terms "C major scale" and "C Ionian mode" are only interchangeable when taken out of their context, for instance scale patterns as played on a musical instrument such as the guitar. In the grander scheme of things, they represent two wildly different musical environments.

The use of the terms major and minor does not just refer to the scales used, or the chords that can be formed using those scales. The major/minor tonal system is a theoretical world in and of itself, with chord relationships that affirm or weaken the sense of key, etc. Church modes represent a simpler system that is based around a central note.

Harmonic and Melodic Minor Scales

One of the problems with the minor scale as shown above is that it lacks a natural leading note. Compare that to the major scale. Pick up any suitable musical instrument, play the natural notes starting on C, but stop at the B. What does it feel like? There is a strong gravitational force that almost begs for the resolution provided by going that extra half-step up to the high C.

Between the seventh and eighth note of this A minor scale, there is a whole step. Play a minor scale from A, but stop on G, and I'll bet that you will not get the same sense of tension. The scale might just as well drop back to E via F.

The solution to the problem is to sharpen the seventh to G♯:

This is called the harmonic minor scale as it opens up more harmonic possibilities. Try playing A through F and then G♯. It is almost guaranteed that you will feel that tension reverberate in the room.

However, raising the seventh of the minor scale creates another problem. All of a sudden, there is a rather awkward-sounding augmented second between the sixth and seventh (F and G♯, in A minor). The solution to that problem is simply to raise the sixth degree as well, to F♯:

This is the melodic minor scale, so called because it lends itself slightly better for melody writing and singing. The reason why I've chosen to depict it as both ascending and descending is because many music theory reference works state that the raised sixth and seventh degrees aren't necessary when descending. In actual music, things are a bit more nuanced. It probably makes more sense to regard the sixth and seventh degrees of the minor scale as variable—they can be either major or minor depending on the situation.

The unaltered minor scale is commonly referred to as the natural minor scale tell it apart from the variants we've just discussed.

Scale vs. Mode

There is a great deal of confusion about when to use the term scale as opposed to the term mode. If there are proper dictionary definitions, they are muddled by not only inconsistent day-to-day usage, but also how the meaning of the respective terms have changed over the centuries. This author presumes that "scale" and "mode" are interchangeable, but here are some ways to differentiate between them:

In one sense, a scale is a diatonic major or minor scale, implying a key center and the related bells and whistles. In that case, a mode is any other scale or note selection. This usage separates tonal music from modal music.

In another sense, a scale can be thought of as a recurring series of intervals, where no particular note is considered as the root. If you select a root note, then you have selected a mode of the scale. The diatonic scale has seven modes.

Pentatonic, Hexatonic and Octatonic Scales

So far, we have discussed seven-note scales. Seven is the magic number in music. Our system of musical notation is built on the idea of seven-note scales. On the eighth note, you're back where you started, but higher up, i.e. the octave.

However, as mentioned in the very first sentence of this article, scales can be constructed using anywhere between five and eleven notes. To classify scales by number of notes, we use Greek ordinals. The diatonic scale is a heptatonic scale, since in Greek, hepta means seven. If you know your Greek, you can construct labels for all types of scales between five and eleven notes.

The most common alternative scales (i.e. not seven notes) are the pentatonic, hexatonic and octatonic scales. They have five, six or eight notes, respectively.

The scales with fewer than seven notes can absolutely be subsets of the more fully featured diatonic scales. The composer or improviser might consciously omit a note or two for whatever reason, maybe to keep certain chord functions ambiguous, or just because it happens to suit the melody better. And even though a melody might use a comparatively sparse note material, the accompanying harmony could very well use everything from the full set of seven to the whole gamut of 12 notes.

Pentatonic Scales

There are obviously many possible ways of constructing pentatonic scales that can be construed as major or minor (the key note being the third degree), but over the years, two types have been crystallized and are currently regarded as the pentatonic scales:

The pentatonic major scale omits the fourth and seventh from the diatonic major scale, and consequently consists of the root, a major 2nd, a major 3rd, a perfect 5th and a major 6th. In C major, it would be spelt C D E G A.

The pentatonic minor scale is obviously based on the diatonic [natural] minor scale, but omits the 2nd and 6th. Hence, it containes the root, a minor 3rd, a perfect 4th, a perfect 5th and a minor 7th. In A minor, the notes are A C D E G.

The sharp-eyed reader will notice that these two scales contain the same notes. Indeed, the two most common pentatonic scales are relative to each other.

It might seem strange to talk about a sixth or a seventh in a scale that clearly has just five notes. In the case of penta- and hexatonic scales, it is often more convenient to label a note by its interval from the root note rather than merely counting scale steps. If nothing else, this underlines that these smaller scales are subsets of the full seven-note scales.

Hexatonic Scales

Since there are 12 notes to the octave, there is the interesting possibility to divide the octave into six equal parts. This creates a scale that is known as the whole-tone scale. It is so known because it contains only whole steps: no semitones. This has two consequences: since the intervals remain the same no matter how many times you transpose the scale, any of the notes can be considered the root, and only two whole-tone scales are needed to cover all 12 notes:

Hexatonic scale on C (or D, E, F♯, G♯, or A♯).

Hexatonic scale on D♭ (or E♭, F, G, A or B).

Blues music is stereotypically pentatonic in nature, but there are hexatonic variants that add for instance the major sixth to the minor pentatonic scale for a distinctly Dorian flavor. One can also play the natural minor scale minus the sixth, which is essentially the same thing as adding a major second to the minor pentatonic scale. One scale that is commonly referred to as the blues scale is a minor pentatonic scale with an added augmented fourth—the "blue note".

Octatonic Scales

Octatonic scales bring with them a certain form of chromaticism, thus also a notational problem, because Western music theory and notation is built on the notion of seven notes per scale. This is also the prime reason why there are few practical scales beyond seven or eight notes: there are so many semitone steps that it is difficult to grasp where the diatonic functionality ends and chromaticism begins.

The diminished scale is an oft-cited example of an octatonic scale. It is very common in jazz improvisation, where it is known as the octatonic scale. The diminished scale is symmetric and consists of alternating full and half steps:

This means that the scale has two modes: one that starts with the whole-step and one that starts with the half-step. Since both are symmetrical, they can only be transposed twice: three scales cover all keys.

The Chromatic Scale

The chromatic scale, as described in the beginning of this article, consists of all 12 notes. Consequently, it has only one mode and cannot be transposed, since there are no whole steps to differentiate between modes.

The chromatic scale is most often used as a coloristic effect in tonal music (12-tone music is beyond the scope of this essay), and it can be mentioned that it is written differently depending on whether it is ascending:

Or descending: