January 26, 2012

The Only Theory Lesson You’ll Ever Need, Part 2

Math professor

In Part 1 of The Only Theory Lesson You’ll Ever Need, we covered the foundational elements of music theory: the musical alphabet, the concepts of whole steps and half steps, and the use of accidentals (sharps and flats) to fill in the blanks between natural notes.

In Part 2, we’ll use that information to take the next step forward: constructing major scales and understanding keys.

Major scale construction is one of the most important things you could ever learn in music theory, since EVERYTHING else is built upon this foundational concept. And gaining insight into scales and keys teaches us how notes are related within a musical “family”, and what notes tend to complement each other in melodies, riffs and solos. Let’s get it on!




Building the Big Kahuna

The major scale is the single most important element of music theory. It’s the granddaddy of all musical concepts, the Big Kahuna. Call it what you will – all other musical concepts flow from the major scale, so it’s critical that we learn to construct it correctly.

A major scale is a sequence of seven notes (plus the octave note) that sounds like the familiar do-re-mi-fa-so-la-ti-do. It can be built from any starting pitch, and that pitch gives the scale its name. For example, if we build the scale from the starting pitch C, we would get a C major scale. Makes sense, huh?

Constructing the scale correctly is simply a matter of picking a starting note and then applying the major scale formula of whole steps and half steps:

WHOLE – WHOLE – half – WHOLE – WHOLE – WHOLE – half

You might also remember it as, “two wholes and a half, three wholes and a half”.

It’s because all major scales follow the same formula of whole steps and half steps that we can achieve the same do-re-mi sound off of any starting pitch. As long as we follow the formula accurately, we’re able to maintain consistent relationships between the notes, which ensures that all of our major scales – no matter the starting pitch – sound like do-re-mi.

Following the Formula

Let’s build a major scale from scratch. Using our previous example of C as our starting pitch, we’ll apply the major scale formula as follows:

Starting pitch = C
C + whole step = D
D + whole step = E
E + half step = F
F + whole step = G
G + whole step = A
A + whole step = B
B + half step = C

The C major scale, then, consists of the notes C-D-E-F-G-A-B-C, and when played, sounds like do-re-mi. You may also note that the C scale is constructed from natural notes only, as it needs no accidentals (sharps or flats) to fulfill the formula. Since all major scales are unique, the C scale is the only one with no accidentals; every other scale has its own number of sharps or flats.

Once you’ve learned how to construct a scale, it’s good practice to also think of the notes in terms of their number, or scale degree. For instance, in the C major scale, C is the “1″ (or root note), D is the “2″, E is the “3″, etc. This will come in handy later, when learning to build chords and transpose to other keys.

Using Sharps

Before we move on, there are two special rules to follow regarding major scale construction:

1 – All letters must be represented once and only once.
2 – We use either sharps or flats to complete the formula, never both.

Keeping this in mind, let’s try another scale from a different starting pitch: G.

Starting pitch = G
G + whole step = A
A + whole step = B
B + half step = C
C + whole step = D
D + whole step = E
E + whole step = F#
F# + half step = G

The G major scale, then, consists of the notes G-A-B-C-D-E-F#-G.

Why F#? Remember that E/F are natural half steps. However, in order to fulfill the formula, we need a WHOLE step above E, so we would travel a half step to F and another half step to F#.

Picking the note F# rather than Gb, its enharmonic equivalent, is important because it follows the “each letter is represented once” rule. It also creates the concluding half step to G – perfect!

Using Flats

For a final example, let’s construct the major scale starting from F so we can see accidentals from a different perspective.

Starting pitch = F
F + whole step = G
G + whole step = A
A + half step = Bb
Bb + whole step = C
C + whole step = D
D + whole step = E
E + half step = F

The F major scale, then, consists of the notes F-G-A-Bb-C-D-E-F.

Why Bb? Remember that A and B are a whole step apart. In order to fulfill the formula, though, we need a HALF step above A. Since we’ve already used the note A, we would not call the target note A#, but rather by its enharmonic equivalent, Bb. The pitch Bb is a whole step from C, so it fulfills the formula moving forward as well.

I would recommend that you practice writing out some of the more common scales. Having major scale construction at your fingertips is a great foundation for learning about chord construction, one of the major elements of guitar theory. The scales I usually recommend – besides C, G and F – are: D, A, E and Bb. As a challenge, try writing them out now following the above process and I’ll put the answers at the end of this lesson post. Feel free to download and use the handy-dandy Major Scale Worksheet I’ve put together.

Major Scale Worksheet (PDF)

The Key

Of course, the major scale is what a musician is referring to when he/she says, “This song is in the key of ____.”

The key is simply the family of notes – the major scale – that makes up the sound of your song. The central note, or key center, of your song will be the root note of your major scale. So if the song is in the key of G, then the root note G will be the main note of your song, and all other notes relate to it.

key of GMusic Reading Alert!: The key can also be determined by looking at the far left of the staff on traditional music notation. The accidentals in the key of the song will be represented on their respective lines of the staff in what is called the key signature. So a song in the key of G, for example, would have one sharp (F#) located on the top line of the staff, which is where the F note is positioned. This indicates to the musician that all F notes are to be sharp throughout the song, keeping us nicely in the key of G.

The notes that occur naturally in any key – that is, the notes that we derive by using the major scale formula – are called diatonic notes. They are “of the key”. Most of the notes of a typical pop song will be diatonic. However, if all songs contained only diatonic notes, then all songs would sort of sound the same. To add a little spice to your musical gumbo, many songwriters will sprinkle in a few notes that do NOT occur naturally in the key. These “outside” notes are called non-diatonic.

Now before any theory nerds beat me to the punch, songs do not only have to be in major keys, with major scales as their basis. Some songs are in minor keys, or even use modes (variations on the major scale, which we’ll save for a future lesson). But minor keys and modes flow from the major scale concept, so for this lesson, let’s just stick with the major scales/keys to avoid unnecessary confusion.

In Part 3 of this series, we’ll explore the final piece of the theory puzzle: harmonizing the major scale with chords and learning to transpose to other keys. Stay tuned!

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Answer Key

D Major Scale = D-E-F#-G-A-B-C#-D
A Major Scale = A-B-C#-D-E-F#-G#-A
E Major Scale = E-F#-G#-A-B-C#-D#-E
Bb Major Scale = Bb-C-D-Eb-F-G-A-Bb

How’d you do?

5 Comments »

  1. Gary Lacey says:

    “This song is in the key of ____.”
    This reminds me of something I’d like to tell you about. I’ll try and keep it short.

    I know someone who plays guitar and he claims he is completely self taught.

    What he really means is that he’s learnt by downloading the tabs to songs off the internet. He buys guitar magazines too.

    He’s never bothered to learn any chords, scales, or notes on his guitar.

    He was invited to play bass in a group by one of his friends who plays lead guitar. They practised regularly once a week until his friend, the lead guitarist left.

    They then decided to audition a new guitarist. I said to my friend “The first thing he’s going to ask is What key is this song in. What are you going to say?”

    His reply was “I’ll show him where we’re playing it.”

    I asked him the next day if he asked what key they were playing in. He did and he said he went over to him and showed him on his guitar where they played it.

    The guitarist was good but be he didn’t join the group and they split up shortly after.

    Perhaps a good case for learning a little theory like chords, scales, and notes. I know it’s hard to believe that someone could play guitar without learning any of this but it’s a true story.

  2. jim says:

    Interesting story. It’s a little sad to me, honestly, that some musicians have zero desire to learn to communicate with their fellow musicians in a “musical” way. Instead they would rather point to a fret and say, “Just put your finger there.” I’m going to assume that it is just rampant laziness.

    And although playing comes first and theory comes second, just knowing the basics of your instrument and the fundamentals of music theory instantly makes you a more powerful musician. What could possibly be bad about that?

  3. [...] you have already gone through the process of writing out some of the more common major scales in Part 2 of this theory lesson (you have, haven’t you?), you should take it a step further now and [...]

  4. [...] you have already gone through the process of writing out some of the more common major scales in Part 2 of this theory lesson (you have, haven’t you?), you should take it a step further now and [...]

  5. Dave says:

    I can’t tell you enough how important this stuff is. Years ago when I started teaching myself theory lights started to come on instantly. when I play with other musicians who also understand it I give them the key and can call out chord progressions by number and they know exactly what to play. In addition understanding the formula’s for the scales allows you to figure out for yourself where the scales are all over the fretboard instead of just using or reading and memorizing patterns. great for fretboard knowledge which I work on all the time. so I review this stuff often.

Jim Bowley is a well-known Bel Air, Maryland based guitar instructor. Jim is respected throughout Harford County, and the MD/DC/PA region, for his guitar teaching technique of tailoring instruction for each student’s skill level — he gives lessons to beginner, intermediate and advanced adults and children.

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