Demystifying Music Theory

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April 19, 2013 by admin

Why Do Certain Chords Sound Somber While Others Sound Uplifting And Happy?

Are Chords And Scales connected?

Yes, It’s All Connected, And Music Theory Is The System Which Helps Explain How And Why.

WHAT IS A SCALE? - There are as many as 88 keys on some pianos, and a typical guitar has 6 strings spanning a fretboard of 22 or more frets.  How does someone best navigate this jungle of musical chaos?  Well, the first step is to take a deep breath and realize that there are only 12 distinct notes in our western system of music.  That’s it, just 12.  After that, the 88 keys on a piano are simply repeating the same 12 notes over and over again from lower to higher pitches known as octaves, which we’ll talk more about later.  

So we’ve been able to break through this jungle a bit and have carved out a very general path.  This 12 note path is called the chromatic scale.  A scale is basically a particular path which guides us through the 12 note system in different and interesting ways.  All other scales fall under the umbrella of the chromatic scale.  If you were to pick the open E string and then play each successive fret all the way up to the 12th fret then you have played the chromatic scale.  But, as you’ll notice, it sounds pretty bad. We have to carve out more specific paths through this jungle in order to manifest better sounding note arrangements.

The most important and well known path (the main tourist destination in this jungle) is the Major Scale.  So, this is where music theory begins…

INTERVALS - This is a simple numbering system which helps to identify the unique pattern of a scale.  Like any system, all of the different scales found in western music have to be compared back to one common reference point in order for the system to make sense.  This reference point is the Major Scale.

MAJOR SCALE INTERVALS - I’m sure you’ve heard the classic example of a vocalist singing do, re, mi, fa, sol, la, ti, do”.   Well, what a vocalist is actually singing is every note of the Major Scale.  It is a happy sounding scale made up of 7 notes which is best resolved when the 1st note is played again at the end of the sequence in a higher pitch (the octave I mentioned earlier).  This is why you hear the singer saying “do” at both the beginning and the end of the phrase.  All of the seven notes (plus the octave) in the major scale are simply numbered 1, 2, 3, 4, 5, 6, 7, and 8 is the octave (OCT = 8).  It is important to note that you’ll rarely (if ever) see the number 8 being notated in a musical context because the term ‘octave’ is more widely used.

MINOR SCALE INTERVALS - Another popular scale is the Minor Scale.  It can be thought of as the yin to the major scale’s yang.  If the major scale’s mood is described as ‘happy’ then the minor scale is ‘sad’.  In fact, this is the basic terminology used to describe the mood of most music.  If a piece is made up of a major progression then it generally has an optimistic character to it, while a minor progression is indicative of a more somber vibe.  So what differentiates the two?  The Minor Scale’s interval formula is 1, 2, b3, 4, 5, b6, b7, 8.  Wait, what’s the deal with the ‘b3′, ‘b6′, and ‘b7′?  This is simply a way of showing that the 3rd, 6th, and 7th notes in the Minor Scale are different from the Major Scale.  The other notes are the same.  Any scale that has intervals which differ from the major scale are labeled appropriately by a flat (b) or a sharp (#). In the case of the Minor Scale, the differing intervals are all flat (b), meaning each note is played 1 fret down from their original position (assuming the two scales are being played in parallel positions, meaning they both start from the same root or fret).  When you see b3, you’re literally just playing 1 fret down from the natural 3rd note in the Major Scale.  If you see a #4 in a scale formula, then you play 1 fret higher than the natural 4th note in the Major Scale.  

THE TONAL CENTER - An important part of all this is understanding the concept of a root note. This is the tonal center for any particular piece of music.  If you play through the major scale starting on the 5th fret of the low E string then you’ve played the scale in the key of A (‘A’ being the root).  Why?  For starters, the 5th fret on the low E string of a standard tuned guitar is the note of ‘A’ (just in case you didn’t know).  More importantly, that ‘A’ note is now the focal point of resolution for the entire scale (the 1 note of the interval formula).  If a vocalist started singing “do, re, mi, fa, sol, la, ti…” and then stopped abruptly before they sang the second “do” then the sequence would sound incomplete to our ears.  There would be a feeling of tension.  This is best resolved when the vocalist finishes the scale by returning to the root note.  There is almost a gravitational pull back to the tonal center of the scale.  Now, in some scenarios, there can be a difference between what the key is versus what the tonal center is in a certain piece.  However, we will steer clear of those other scenarios for now to avoid further confusion.

The intervalic system is applied irrespective of what particular notes you’re playing or what specific key you’re in at any given time.  For example, if we play the major scale starting from the 3rd fret of the low E string then we’re in the key of G major.  In this key, the note of F# is the 7th note (the last note) in the scale.  But if we jump to the key of D major then F# is now the 3rd note in the major scale.  What does matter, and what stays consistent, is the distance from the root note.  If you took a piece of measuring tape and measured a 6 inch distance on your kitchen wall and then also measured a 6 inch distance on your bathroom wall, what conclusions can be made?  The surface of the walls will look different, but the distance measured is still 6 inches, no matter what.  Similarly, you could imagine the key of G major being your kitchen wall and D major being the bathroom wall.  The notes (or the surface of the walls) will be different, but the distance of 6 inches (distance between the root and any given interval) will remain constant.

An alternative analogy could be that of a football team traveling from city to city during their season.  The distance from end zone to end zone (the interval formula) is always the same, but the particular stadium (the tonal center) of where the game is being played may change.

WHAT IS A CHORD? - Just like we carved specific paths (scales) out of the 12 note musical system, we can go a step further and find even more interesting patterns within scales.  There seems to be a very harmonious relationship between the 1st, 3rd, and 5th notes of any given scale which are the foundation for all chords.  This foundation is known as a triad.

TRIAD - This is the most basic Chord you’ll find (and the most common when it comes to Pop/Acoustic/Rock music).  Even when you’re strumming basic open chords (E Major for example) across all 6 strings on the guitar, there’s only 3 notes (Triad = 3) at play.  The reason it seems like more is because there are multiple octaves of those same 3 notes being played simultaneously.

TRIAD FORMULAS - Just like there is a major and minor scale which describes ‘happy’ and ‘sad’ moods of music, there is also a major and minor triad.  Additionally, there is also a diminished triad and an augmented triad.  The diminished triad is, essentially, a minor triad with the 5th note lowered by a half step (or 1 fret down) which gives it a tense and somewhat ‘classical’ sounding characteristic.  Conversely, the augmented triad is a major triad with the 5th note raised by a half step (or 1 fret up) which has an almost mystical sound that is utilized in classical as well as jazz music.  So now we can look at each type of Triad and identify them by their interval formula.

 

MAJOR TRIAD =          1, 3, 5 

AUGMENTED TRIAD =   1, 3, #5

MINOR TRIAD =          1, b3, 5 

DIMINISHED TRIAD =    1, b3, b5

 

CHORD PROGRESSIONS - A chord progression is the process of traveling from note to note within a given scale, but instead of single notes, you’re building a chord off of each note you play in that scale.

Just like there is a set formula with scale intervals, there’s also a set formula with building chords within a scale.  This is called the chord scale.  It is simply the ‘chord version’ of a particular scale.

MAJOR CHORD SCALE - How do you know when to play a Minor, Major, Augmented or Diminished chord in any given chord progression that you’re learning or writing on your own?  Sometimes you can do it by ear, but if you’re stuck, you can always refer to the chord scale.  The chord scale formula for the Major Scale is below:

 

1st chord = Major chord        (1,3,5)             

2nd chord= Minor chord          (1,b3,5)

3rd chord =Minor chord         (1,b3,5)                                                               

4th chord =Major chord         (1,3,5)                

5th chord = Major chord        (1,3,5)            

6th chord = Minor chord        (1,b3,5)                

7th chord = Diminished chord (1,b3,b5)        

 

You may have noticed by now that the 3rd note in any scale is CRUCIAL in determining the mood or quality of a triad.  If the 3rd note is natural to the Major Scale then that triad is ‘Major’ in nature.  If the 3rd is flat (b) it is ‘Minor’.  To the ear, the 3rd interval has a very strong characteristic and is the most obvious sign that a triad is ‘happy’ or ‘sad’ sounding.  The other intervals have their own characteristics but the 3rd is what really defines the ‘sound’ of a scale or chord.

 

MINOR CHORD SCALE - Here is the chord scale formula for a natural minor progression.

 

1st chord = Minor Chord         (1,b3,5)            

2nd chord= Diminished Chord   (1,b3,b5)             

3rd chord =Major Chord          (1,3,5)                                                            

4th chord =Minor Chord          (1,b3,5)                

5th chord =Minor Chord          (1,b3,5)                

6th chord = Major Chord        (1,3,5)            

7th chord = Major Chord        (1,3,5)

 

POWER CHORDS  - The 5th interval is a very stable sounding note (because it’s the same in both the Major and Minor scales).  This is why Power Chords are one of the first things beginners learn to play, because they only contain the 1st and 5th notes of a scale.  Power chords aren’t triads, they’re what is known as dyads (2).  So if you’re using all power chords in a song then you don’t even have to worry about the chord scale formula.  The only exception to this is the fact that the diminished chord occurs on the 7th triad in a major progression and the 2nd triad in a minor progression.  So in these two instances, a power chord wouldn’t sound very stable, and your best bet is to play either the diminished triad or a diminished power chord (1,b5).  However, some still feel comfortable playing a standard (1,5) power chord in these two instances which is simply a matter of taste and all depends on what sounds best to your ears.

COMPOUND INTERVALS - This topic goes a little beyond the introductory level of music theory, but I wanted to address it anyway.  Mainly because you’ll eventually hear of complicated sounding chords like 9th, 11th, or 13th chords.  ‘What’s this all about?!  I thought the basic system of intervals goes up to the number 8 (which is the octave) and just repeats again.  And what’s with the 13th chord?  I thought all of western music contained just 12 notes?  Is there an extra note that I’m not aware of?’

Well, no.  There is not a ‘mysterious 13th note’ floating around somewhere in the musical landscape.  This is merely a case of semantics and the idea that chord construction should follow a consistent set of guidelines.

As I mentioned earlier, the function of a triad is to stack the 1st, 3rd, and 5th notes of a scale on top of each other which are then played simultaneously to produce a chord.  The main thing you will notice is that the 2nd and 4th notes in a given scale are skipped in the triad formula.  The reason for this is that notes need a certain amount of separation in order to avoid a ‘clashing’ effect.

If you played the 1st, 2nd, 3rd, 4th, and 5th notes of the major scale, you won’t hear a great sounding chord.  This may seem counterintuitive because, after all, you’re playing all the notes of the major scale, right?  But, if too many notes are played simultaneously within the same pitch radius then things start to get muddy real fast.  There’s only so much frequency information our ears can handle, and if you’re playing 4 or 5 low pitched notes at the same time, your ears won’t like it.

This is where octaves can play a helpful role in offering even more separation between notes in order to build more complex chords.  Just like the 8th note in the major scale is the octave (or higher pitch version) of the root note, the 9th note is the octave of the 2nd note.  If you want to add the 2nd note to a major triad then try adding the higher pitch version of that 2nd note (the 9th) and you’ll realize it has a much more pleasing sound to our ears (this would be an ‘Add 9′ chord).

For the sake of consistency, notes added to the original triad are done so by continuing the concept of stacking odd numbered intervals.  So there are 7th chords (1,3,5,7) which do not include a compound interval (because the 7th note is still unique within the first octave of the scale).  However, any additional note that is ‘stacked’ after the 7th is usually referred to by applying this ‘odd number’ terminology (when discussing chord construction).

Therefore, the 9th note is the same as the 2nd note, except an octave higher.  The 11th note is the same as the 4th note, and the 13th note is the same as the 6th note.

The “7 & 7 rule” (as I like to call it) can be applied to remember these intervals.  Basically, any interval above 7 in all commonly found scales can be subtracted by 7 to ascertain the actual interval (9-7=2,  11-7=4,  13-7=6)

This is a quick explanation of what compound intervals are and how they’re applied to chord construction.  Just remember, there are no actual 9th, 11th, or 13th notes apart from the original 7 notes found in most scales.

So this about wraps it up for a basic introduction to music theory.  I have left out some topics (namely The Circle of 5ths, Modes, Sus and dominant chords) which I will address in a future post.  But I didn’t want to throw it all at you in one shot as the information presented here is more than enough to get your feet wet.


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