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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:

   
 
   
 
     
 
       
 
 
 
C
 
D
 
E
 
F
 
G
 
A
 
B

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)

   
 
   
 
     
 
       
 
 
 
C
 
D
 
E
 
F
 
G
 
A
 
B
Ionian mode on C

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

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

Dorian (D)

 
 
   
 
     
 
       
 
     
 
D
 
E
 
F
 
G
 
A
 
B
 
C
Dorian mode on D

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

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

Phrygian (E)

 
 
     
 
       
 
     
 
   
 
 
E
 
F
 
G
 
A
 
B
 
C
 
D
Phrygian mode on E

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

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

Lydian (F)

   
 
       
 
     
 
   
 
 
 
F
 
G
 
A
 
B
 
C
 
D
 
E
Lydian mode on F

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

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

Mixolydian (G)

         
 
     
 
   
 
     
 
 
G
 
A
 
B
 
C
 
D
 
E
 
F
Mixolydian mode on G

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

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

Aeolian (A)

     
 
     
 
   
 
     
 
   
 
 
A
 
B
 
C
 
D
 
E
 
F
 
G
Aeolian mode on A

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

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

Locrian (B)

 
 
     
 
   
 
     
 
   
 
   
 
B
 
C
 
D
 
E
 
F
 
G
 
A
Locrian mode on B

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

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

About the Modes

These seven 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. They can be discussed separately or in various groups.

Here are the modes divided by character:

Or by suitability:

The Locrian mode is not listed either way, because it was never used in the old days. The name for it is therefore a rather recent invention, just to round out the set of seven modes possible with the diatonic scale. The Locrian mode is a more theoretical construction, since its tonic chord is an unstable diminished triad.

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)

   
 
   
 
     
 
       
 
 
 
C
 
D
 
E
 
F
 
G
 
A
 
B
C major scale

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

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

Minor Scale (A)

     
 
     
 
   
 
     
 
   
 
 
A
 
B
 
C
 
D
 
E
 
F
 
G
Aeolian mode on 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.

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.

One of the most important considerations is that usually, scales with fewer notes than seven are most often conscious note selections on the part of the composer or improviser. The harmony is more often than not drawn from the full gamut of seven (or up to 12) notes available in a key.

The natural conclusion is that the most frequently encountered pentatonic and hexatonic scales are derived from either the major or the minor (seven-note) scale. It is a mere matter of selecting which note or notes to omit. One of the reasons this might be is that the composer or performer wants to keep certain chord functions ambivalent.

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:

Pentatonic major scale on C

The pentatonic major scale omits the fourth and seventh from the heptatonic 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.

Pentatonic minor scale on A

The pentatonic minor scale is obviously based on the seven-note 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 appear thoughtless to talk about a sixth or a seventh in a scale that clearly has just five notes. However, it only goes to show that the pentatonic scale is a simplified heptatonic scale. Since music theory is built on the seven-note scale, with heptatonic scales, the scale steps and interval names happen to coincide. With scales that have fewer notes, one tends to discuss a note's distance from the root rather than its number in a sequence.

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:

Whole-tone scale on C Whole-tone scale on D flat

Many hexatonic scales are simply diatonic scales where one note has been omitted.

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:

Diminished scale on C

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:

Ascending chromatic scale

Or descending:

Descending chromatic scale