# Scales

'But wait, I thought this was a tutorial on chord charts!' Patience—we'll get there. We must lay some groundwork first. Chords are based on scales. So to accurately name and understand chord symbols, we must first grasp the underlying scales and intervals.

# Intervals

An interval is simply the distance between two notes. One of the most basic intervals in music is the octave, the distance beween two notes of the same name—for example, between two Cs on the piano. The octave is a natural phenomenon whereby doubling the frequency of a note results in a higher pitch that we perceive as the same note, or the same 'kind' of note. Sometimes when trying to match a pitch, we may even sing the note in a different octave and not notice because of the similarity in sound.

Within the interval of an octave, individual pitches or notes can be determined in different ways. In Western music, the octave is divided into 12 equidistant notes. We can see this on the piano keyboard by counting the notes (both black and white) between two Cs. When we've reached note 13, we've come to another C (an octave higher) and the same 12-note pattern starts again. This series of notes is called a chromatic scale and the distance, or interval, between each note is called a a half-step. An interval of two half-steps makes a whole-step. (In classical theory, these are also called a semitone and a tone, respectively.)

## Chromatic Scale

Let's step away from the piano for a moment, and think a little more abstractly. We can plot these chromatic notes along a line representing pitch, left to right, low to high:

As you can see, the pitches are equally spaced along the line and every interval is a half-step. If you listen to these pitches played in succession—say, starting with C and then playing consecutive notes, ascending to the next C—your ears and brain perceive that the pitches rise by equal steps, which in fact they do:

Now let's consider the major scale. The seven notes of the Western major scale are a subset of the chromatic scale as shown here:

The major scale intervals are not all the same—there are half-steps and whole-steps. The numbers from one to seven are generally referred to as scale degrees. Using 'W' for whole-step and 'H' for half-step, we can condense the major scale pattern to:

But here's the interesting thing. When we hear the major scale, we tend to perceive a consistent step-wise change of pitch, just like the chromatic scale. The sound is so familiar that we don't really distinguish between the whole-steps and half-steps:

This perception of equal intervals in the major scale is reinforced visually by the piano keyboard's layout. The C major scale is played on seven consecutive, equally spaced white notes. But even though the notes are equally spaced in size, they are not equally spaced in pitch—evidenced by the irregular placement of the black chromatic notes between white notes.

## C Major

### Diversions

As with many topics in this tutorial, this explanation of intervals and scales may leave you with more questions than answers. Why 'tone' and 'semitone'? Why start with C and not A? Who came up with the piano design anyway? I'm afraid following these rabbit holes would quickly derail us from the central topic so I must leave them for you to explore.

# Major Scales

The major scale is the basis for understanding and speaking about chords and progressions. For instance, if I mention a 'G chord with a sharp five', the 'five' refers to the fifth note of the G major scale, which is a D. And if I speak of a 'two-five-one' progression, again, those numbers refer to degrees of the major scale.

As we saw above, the C major scale is easily visualized on the piano since it is all white keys. Every other key or scale also has its own distinct visual and tactile form. I like to think of each key as a landscape on the keyboard, with different areas that are 'home' or 'away'. (More on this in the Progressions section.) The more you practice and become familiar with the major scales/keys, the more they will become familiar landscapes for you. And to really understand what's going on behind chords and progressions, learning and practicing the major scales in all 12 keys is crucial. It lays the foundation for the freedom of creating music from symbols on a page. The goal is to become a seasoned traveler in all of these various landscapes.

Use the example below to see the major scale landscape in all keys. In C, the whole-step/half-step pattern is most clearly seen by the absence of a black note between E and F (3 and 4) and between B and C (7 and root). By changing the key of the example, you can see how the whole-step/half-step pattern remains consistent.

## C Major

Since the major scale uses seven notes out of the twelve available, there are five notes that fall outside of the scale. Again, with C major this is easily seen because the five black notes are the 'outside' notes. To name these outside notes we use sharps and flats to denote their deviation from major (e.g. 'b3' or '#5'). Generally, the term diatonic is used to refer to the notes within the scale, while chromatic is used for the outside notes. (The term diatonic is one of those slippery, classical terms that can have several other meanings—but I use it to mean 'within the scale' or 'derived from the scale'.)

## C Major

Diatonic notes
Chromatic notes

The above example is quite crowded but it gives a sense of the landscape created by both diatonic and chromatic notes of a given key. Chord symbols will reference all of these notes in many different ways. The degree numbers can extend into the second octave as well. The next example shows all of the degrees and alterations commonly used in chord symbols. (We will return to this in the Chords section.)

## C Major

Diatonic notes
Chromatic notes

All of the degrees and alterations within the first octave have alternate names as well:

Degree Other Names
1 root, tonic
b2 minor 2nd
2 major 2nd
#2 augmented 2nd
b3 minor 3rd
3 major 3rd
4 perfect 4th
#4 augmented 4th, tritone
Degree Other Names
b5 diminished 5th, tritone
5 perfect 5th
#5 augmented 5th
b6 minor 6th
6 major 6th
bb7 diminshed 7th
b7 minor 7th
7 major 7th

As mentioned above, the major scale has a particular pattern of whole-steps and half-steps that gives it its sound:

A mode of a scale simply means starting at a different point in the pattern, resulting in a different sequence of intervals. You'll notice that with the major scale pattern, we can start at any other point and get a distinctly different pattern—for a total of 6 other modes. These modes were codified and explored by the Greeks in ancient times and retain their Greek names.

The graphic below starts with the Ionian mode (the major scale itself) and then shows how the whole-step/half-step pattern is shifted to form each mode.

Thinking of the modes as interval patterns is not very intuitive, however. It is much easier to consider how the scale degrees of each mode deviate from a major scale (a.k.a. the Ionian mode):

 Dorian 1 2 b3 4 5 6 b7 1 Phrygian 1 b2 b3 4 5 b6 b7 1 Lydian 1 2 3 #4 5 6 7 1 Mixolydian 1 2 3 4 5 6 b7 1 Aeolian 1 2 b3 4 5 b6 b7 1 Locrian 1 b2 b3 4 b5 b6 b7 1

One clarification should be made regarding modes. If someone speaks of, say, the C Dorian key or scale, it may seem logical to first think of the major key of C and then surmise that the Dorian mode of C starts on the second degree which is D—but this is not what is meant by 'C Dorian'. Instead, it means to take the degree pattern for Dorian (as seen above, having a b3 and a b7) and apply this to C major. In other words, play a C major scale but with a flat 3rd and a flat 7th.

# Fingering Patterns

Most fingering for major scales can be intuitively figured out—basically, whatever is comfortable for your hands. However, there are standard, common-practice fingerings, explained below. (For notation of piano fingerings, the thumb is 1, the index finger 2, the middle finger 3, etc.)

We can divide the major scales into two groups based on their fingering patterns.

## Group 1

Group 1 includes all of the major scales that start on a white note and have sharps. For all of these (with the exception of the left hand for B major), the left- and right-hand fingering patterns are the same.

 R.H. 1 2 3 1 2 3 4 5 (1) C C D E F G A B C G G A B C D E F# G D D E F# G A B C# D A A B C# D E F# G# A E E F# G# A B C# D# E B * B C# D# E F# G# A# B L.H. 5 4 3 2 1 3 2 1

* The left hand for B major is different: 4 3 2 1 4 3 2 1

### Practice Tips for Group 1

• For coordinating both hands, notice that the third fingers of both hands always hit together on the 3rd and 6th degrees of the scale, as shown by the dark dots with white text in the example above.

## Group 2

Group 2 contains the scales with flats. Except for F major, they all start on a black note. These are trickier because each scale's finger pattern is different; however, there are underlying patterns to help.

## Right Hand

For the right hand, think of 2 clusters of notes: C-D-E and F-G-A-B. These will always be fingered as 1-2-3 and 1-2-3-4 respectively. So the same note names will always be struck with the same finger (the thumb is always on C, 2 is always on D or Db, etc.)

 R.H. 2 3 1 2 3 4 1 2 3 1 2 3 4 F F G A Bb C D E F Bb Bb C D Eb F G A Bb Eb Eb F G Ab Bb C D Eb Ab Ab Bb C Db Eb F G Ab Db Db Eb F Gb Ab Bb C Db Gb Gb Ab Bb Cb Db Eb F Gb

## Left Hand

For the left hand, an ascending move from a white note to a black note necessitates a cross over, where the fingers cross over the thumb to strike the next note. In four of the scales, this occurs when moving from the 3rd to the 4th and from the 7th to the root. (F major and Gb major differ.)

 L.H. 3 2 1 4 3 2 1 3 Bb Bb C D Eb F G A Bb Eb Eb F G Ab Bb C D Eb Ab Ab Bb C Db Eb F G Ab Db Db Eb F Gb Ab Bb C Db
 L.H. 5 4 3 2 1 3 2 1 F F G A Bb C D E F
 L.H. 4 3 2 1 3 2 1 4 Gb Gb Ab Bb Cb Db Eb F Gb

### Practice Tips for Group 2

• As with Group 1, take note of when the same fingers on both hands strike the same degree. Usually, the thumbs are together.
• The scales with the most flats, Db and Gb, are actually the easiest to play because of the way the landscape naturally fits the hand with the thumbs always playing the white notes.

# Practicing Scales

Diligent practice of scales solidifies each key landscape both aurally and visually. In addition, scales are a great way to improve dexterity, technique, and coordination. Here are some suggestions for your practice routine:

• Start with hands separately to get a feel for fingering patterns.
• Coordinate both hands together. This can be challenging but hopefully the patterns and tips given above will help.
• A common exercise for hands together (using a metronome clicking on the quarter-note):
• One octave, half-notes, up and down
• Two octaves, quarter-notes, up and down
• Three octaves, quarter-note-triplets, up and down
• Four octaves, eighth-notes, up and down
• Intervals: Play hands together but start right-hand on the third, so hands will be a tenth apart.
• Contrary motion: Play hands together, one ascending and the other descending.
• Three-against-two: Play left-hand two octaves in quarter-notes while simultaneously playing right-hand three octaves in quarter-note triplets. The hands start and end together but are playing at different rates.

# Minor Scales

Minor scales can be a bit confusing because there is not a single type of minor scale. There are actually several variations, and the categorization and naming of them varies. I consider four scales that can all be considered 'minor'. They each have the same interval pattern for the first five notes (the same as major but with a flat 3rd) and the variations come about by how the 6th and 7th degrees are handled.

## Harmonic Minor

If you've taken classical lessons, you probably learned the harmonic minor scale. Here, the 6th is flatted but the 7th remains unaltered so that it retains the half-step resolution of leading tone to root. It has a distinctive sound because of the extra-wide interval between the 6th and 7th.

## Dorian Minor

The Dorian minor scale pattern comes from the 2nd mode of the major scale (see inset above). In contrast to the harmonic minor, the Dorian has the 7th flatted but the 6th remaining unaltered. To better understand the modal relationship, change the key of the example below so that it displays D Dorian minor. You will see that it contains all of the notes of C major scale, but going from D to D.

## Aeolian/Natural Minor

The Aeolian minor is also a mode of the major scale (see inset above). As you probably know, each major key has a relative minor which shares the same key signature. The relative minor is the 6th of a major key, i.e. the relative minor of C major is A minor, F major's relative minor is D minor, etc. Therefore, this scale is also called the natural minor or relative minor scale. In this scale pattern, both the 6th and 7th are flatted.

Again, use the example below to see the modal relationship, for example how A Aeolian relates to C major.

## Melodic Minor

The melodic minor is a unique scale in that it has both an ascending form and a descending form. Ascending, the 6th and 7th are unaltered, allowing the typical resolution of leading tone to the root. Descending, the 6th and 7th are both flatted, making it identical to the Aeolian or natural minor scale (compare with example above). Therefore, the ascending melodic minor scale is the distinct fourth type of minor scale. It is identical to a major scale except for the flat 3rd.

# Other Scales

There are certainly many other types of scales to explore and learn. To stay in scope for this tutorial, I will only mention some here for further study:

• diminished - a symmetrical scale, alternating whole-steps and half-steps (3 distinct forms)

• whole tone - a symmetrical scale, all whole-steps (2 distinct forms)

• pentatonic - five-note scale with major and minor types

• blues scale - general form is , but there are several variations