Music Theory: Scales

Scales

Scale tones are designated by number or by name. When using numbers, there are two common terms: degree and step (not to be confused with half-steps or whole steps). The first note can be called the first degree or first step; the second note can be called the second degree or second step; and so forth. Kundera uses the step terminology in the quote at the top of the introduction. I prefer the degree terminology, since it avoids confusion with half-steps and whole steps.

There are two different types of names for scale tones. The first type simply replaces the degree or step numbers with names that don't mean anything. This type should be familiar to anyone who has heard the "doe-a deer" song from "The Sound of Music." It uses what are called Solfège syllables to name the different scale tones, as follows:

1. do ("doe")
2. re ("ray")
3. mi ("me")
4. fa (as in "far")
5. sol ("so")
6. la
7. ti ("tea")
8. do

This system and its variants (and other systems like it) are primarily used by students who are learning to sight-sing written music.

The second kind of scale tone name refers to a note's function within a given scale. This kind of name is often used in music theory. These names are as follows:

1. tonic
2. supertonic
3. mediant
4. subdominant
5. dominant
6. submediant
7. subtonic (if tone 7 is a M2 below the tonic)
   leading tone (if tone 7 is a m2 below the tonic)
8. tonic

The first degree (or step) is called the tonic, because it the tone that gives the key its name. A scale that starts on C is said to be in the key of C; a scale that starts on F is an F scale; and so forth. The fifth degree is called the dominant of the key because of the important role it plays. The fourth degree also plays an important role, though less so than the fifth degree, and the fourth is called the subdominant. The fourth is also a fifth below tonic (P4 inverts to P5), so it is the "sub"-dominant, because it is the "dominant" below tonic. When the seventh degree is a half-step (or m2) below the tonic, the seventh degree is called the leading tone, because one of its basic functions is to lead to the tonic.

The terms "scale" and "key" are almost synonymous. Music written using the C major scale predominantly is said to be in the key of C major. If you know what key you are using, then you know what scale(s) and chords you can use to start with. We'll return in greater depth to this topic in the keys section.

The major scale is arguably the most important scale in all western music. From it, one can derive virtually every other scale used in all western tonal music. The major scale is arranged as follows:

Major Scale

1      2      3      4      5      6      7      8 (=1)
 \    / \    / \    / \    / \    / \    / \    /
   M2     M2     m2     M2     M2     M2     m2
 (whole (whole (half  (whole (whole (whole (half
  step)  step)  step)  step)  step)  step)  step)

• C major: C, D, E, F, G, A, B, C
• A major: A, B, C, D, E, F, G, A
  
• B major: B, C, D, E, F, G, A, B
  
• B major: B, C, D, E, F, G, A, B
  

A minor scale is said to have three forms, natural, melodic, and harmonic. In fact, these forms are theoretical constructions. In real minor key music, specific phrases or chord progressions draw on all three forms, as needed. The key of the music is just called minor; there is really no such thing as music in a melodic or harmonic minor key.

A natural minor scale can be derived from a major scale as follows. If you take a major scale and play it starting and ending on the sixth degree, you get a natural minor scale that is called the relative minor of that major scale. For example, if you use the notes of the C major scale, but instead of starting and stopping on C, you start and stop on A, you are playing an A minor scale; and A minor is the relative minor of C major. This idea is represented in the following chart:

Natural Minor Scale

major steps:  6      7      1      2      3      4      5      6
minor steps:  1      2      3      4      5      6      7      8 (=1)
               \    / \    / \    / \    / \    / \    / \    /
                 M2     m2     M2     M2     m2     M2     M2
               (whole (half  (whole (whole (half  (whole (whole
                step)  step)  step)  step)  step)  step)  step)

The melodic and harmonic minor scales are variants on the natural. The melodic minor scale has two forms: one for going up the scale (ascending), and another for coming down (descending). These forms reflect the fact that, in practice, melodies in minor keys often raise the sixth and seventh degrees a half-step each when the melody ascends through them to the tonic. But when a minor key melody descends through the seventh and sixth degrees, they are usually not altered. The melodic minor scale is thus called melodic, because it is derived from concerns that arise from melodies. The ascending melodic minor scale's interval relationships are as follows:

Ascending Melodic Minor

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  M2   m2   M2   M2   M2   M2   m2

Similarly, the harmonic minor is called harmonic, because it is derived from concerns that arise from harmonies (two or more notes played together). In this case, the seventh degree is raised one half-step (so it becomes a leading tone, instead of being a subtonic; I'll cover why in the discussion of chords). The sixth degree is unaltered, and the harmonic minor is the same ascending and descending. The resulting scale has a characteristic sort of "eastern" sound to it, because of the A2 between steps six and seven. The interval relationships in the harmonic minor scale are as follows:

Harmonic Minor Scale

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  M2   m2   M2   M2   m2   A2   m2

For example, if you play the C major scale from D to D, you are playing the D Dorian scale (since D is the second degree of C major, and Dorian is the mode on two). If you play it from F to F, you have the F Lydian mode (F is degree four of C major, and Lydian is the mode on four). If you play the E major scale from B to B, you get the B Mixolydian scale (B is the fifth degree of E major, and the mode on five is Mixolydian).

The modes are sometimes grouped according to whether they have a major or a minor kind of sound. To be either a major or minor scale, the interval from the tonic (1) to the dominant (5) must be a P5. Recall that a P5 can be thought of as being made up of M3+m3 or m3+M3. Scales that have a M3 between the tonic (1) and mediant (3) have a major sound; those with a m3 between tonic and mediant have a minor sound. I will return to this concept in the discussion of chords. Lydian (the mode on four) and Mixolydian (the mode on five) are considered major modes. Dorian (2), Phrygian (3), and Aeolian (6) are considered minor. Locrian (7) is neither (its interval from tonic to dominant is a tritone, not a P5) and is much less used than any of the other modes. Here are the interval relationships for the modes.

1. Ionian (= major)

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  M2   M2   m2   M2   M2   M2   m2

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  M2   m2   M2   M2   M2   m2   M2

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  m2   M2   M2   M2   m2   M2   M2

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  M2   M2   M2   m2   M2   M2   m2

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  M2   M2   m2   M2   M2   m2   M2

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  M2   m2   M2   M2   m2   M2   M2

1    2    3    4    5    6    7    8 (=1)
 \  / \  / \  / \  / \  / \  / \  /
  m2   M2   M2   m2   M2   M2   M2

Rock music, folk music, blues, and other kinds of popular music often use the pentatonic scale and/or the blues scale. Both of these scales are used primarily for melodies, improvisations, and so forth. The chords used in music with pentatonic and blues scales are the same as those in major and minor scale music. The pentatonic scale is as close as there is to a universal scale. It is used in classical/traditional musics of China, India, Japan, and many other cultures.

The pentatonic scale, which is a variant of the major scale, gets its name from the fact that it has only five different notes ("penta" means five). The five notes are degrees 1, 2, 3, 5, and 6 of the major scale. To play a pentatonic scale in a given key, just play a major scale of that key, but omit degrees 4 and 7. For example, an A pentatonic scale would be A, B, C, E, and F (degrees 1, 2, 3, 5, and 6 of the A major scale).

Pentatonic

1    2    3    4    5    6 (=1)
 \  / \  / \  / \  / \  /
  M2   M2   m3   M2   m3

The blues scale can be thought of as a relative minor variant of the pentatonic. A pentatonic's 5th degree is the same as a major scale's 6th degree, which, you may recall, is the basis for the relative minor of that major scale. The point is that if you play a pentatonic from 5 to 5, you have the basis for the blues scale, and that the blues scale is a kind of relative minor of the pentatonic. For example, A minor is the relative minor of C major. Similarly, A blues is the "relative" blues of C pentatonic. To complete the blues scale, you add in the half-step between degrees 3 and 4 (= degrees 2 and 3 of the pentatonic). I should also note that sometimes this half-step is thrown in when playing pentatonics, too. If this is all clear as mud, I hope the following chart will clear things up:

Blues Scale

pentatonic steps:  5      1      2    2/3    3      4      5
blues steps:       1      2      3    3/4    4      5      6 (=1)
                    \    / \    / \    / \    / \    / \    /
                      m3     M2     m2     m2     m3     M2

Some examples:

• A blues: A, C, D, D/E, E, G, A
• E blues: E, G, A, A/B, B, D, E

20th century classical music introduced new scales and whole new ways of thinking about music theory. There is 12-tone music, whole tone and octatonic scales, music written without notes, etc., etc. I am just going to cover the whole tone and octatonic scales here.

The whole tone and octatonic scales cannot be derived from a major scale, and they have very distinctive sounds. The whole tone scale gets its name from the fact that it is composed entirely of whole tones (aka whole steps). There are only six different notes in a whole tone scale, as opposed to the seven in majors, minors, and the modes. For example, if you start a whole tone scale on C, it will be: C, D, E, F, G, A, C. Here are the intervals in a whole tone scale:

Whole Tone

1    2    3    4    5    6    7 (=1)
 \  / \  / \  / \  / \  / \  /
  M2   M2   M2   M2   M2   M2

The octatonic scale gets its name from the fact that it has eight different notes. It is arranged by alternating whole steps and half-steps, and it is sometimes called the whole step/half-step scale. It is also called a diminished scale, because all of its triads are diminished (for more on triads, see the section on chords).

There are two versions of the octatonic scale for each "tonic": one where the first interval is m2, and another where the first interval is M2. Here are the interval relationships for the octatonic scales:

Octatonic Scales

1    2    3    4    5    6    7    8    9 (=1)
 \  / \  / \  / \  / \  / \  / \  / \  /
  M2   m2   M2   m2   M2   m2   M2   m2

1    2    3    4    5    6    7    8    9 (=1)
 \  / \  / \  / \  / \  / \  / \  / \  /
  m2   M2   m2   M2   m2   M2   m2   M2

Though the whole tone and octatonic scales may seem somewhat artificial (and they are sometimes referred to as "artificial scales"), they are perfectly valid scales, and you can make some wonderful music with them.

Introduction | Steps | Intervals | Scales | Chords | Keys

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