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> Intervals, Chords, Triads And Harmonies, Part 4 - Triads
Andrew Cockburn
post Mar 29 2007, 10:50 PM
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Intervals, Chords, Triads and Harmonies


Part 4 - Triads


Hi all, if you have been following along so far, you now know about the degrees of the scale and intervals. We're now going to start putting this to work for us in part 3 of the series - triads.

First of all, what is a triad? Well, its the simplest type of chord, one consisting of 3 distinct notes. Another way to look at it is as 2 intervals stacked on top of each other, sharing the middle note of the three. Basic chords such as C, F, G, E etc all qualify as triads, because although you may be able to play them on all 6 strings in some cases, there are only 3 distinct notes, some of which may be repeated. As the simplest of chords, triads are probably among the first chords you learnt as a beginner. In fact, triads are very versatile, and you can go a long way with them. They come in four different flavours. The first two are very common, the last two you may not have heard of before.

Major Triad

The major triad is probably the most common chord type you will encounter. We all know major chords - C,F,G,E,D,A,etc - these are all triads. Using the techniques we learnt in the last lesson (which is here if you missed it), we describe triads using intervals counting from the base note. A major triad consists of:

Root note
Major third
Perfect 5th

Using that recipe and varying root notes, you can create any major triad in the diatonic scale system - 12 in total.

What was that ? What is the diatonic scale system? I threw that in just to check you were listening; Diatonic is a term that refers to the types of scales almost exclusively used in western music, that consist of a mixture of half tones and whole tones - exactly the type of scales we have been using until now, with our T and S formulae - T T S T T T S for major for instance. The opposite of a diatonic scale would be a chromatic scale which is constructed entirely of half tones.

OK, back to major triads - lets try one out! In the key of G, the notes in the major scale are G,A,B,C,D,E,F#,G. Using our major triad formula, we pick out G,B and D - the notes in a G major triad. Check that against the G major chord you know - you should find that each note you play is one of those three.

You can finger the chord of G like this:

Attached Image

Minor Triad

Ok, next up is the minor triad - just like your standard minor chords, like Am, or Dm. The minor triad differs from the major triad in that the first interval is a minor 3rd rather than a major 3rd - form our interval lesson we know that this means the 3rd note is flattened a semitone. Lets look at the triad of A minor. If we were trying for a major triad, we would look at the scale of A major - A, B, C#, D, E, F#, G#, A, and the major triad would be A, C#, E. But for the minor triad we would flatten the 3rd, to get A,C,E - which is consistent with the scale of A minor A,B,C,D,E,F,G,A. Notice that as we discussed in the previous lesson we can see that the minor scale is the same as the major scale with a flattened 3rd, 6th and 7th - the key of A shows this particularly clearly, as the notes we flatten to go from major to minor are all sharpened in the A major scale. We can remove the sharps (which is equivalent to moving the note down a semitone) to get the notes of the minor scale.

We could finger our Am triad like this:

Attached Image

Diminished Triad

The first two triad types, Major and Minor have changed the 3rd interval. The next two change the 5th interval instead of or as well as changing the 3rd. First the diminished chord. The rule for a diminished chord is that we use the root note, a minor 3rd, and a diminished 5th - no prizes for guessing why we call these diminished chords!

Our example for diminished chords will be Ddim. The scale of D is D,E,F#,G,A,B,C#,D. The root is D, the minor 3rd is an F, (one semitone down from F#), and our diminished 5th is Ab, or G#, again, one semitone down from our perfect 5th.

You could finger it like this:

Attached Image

In the guitar world at least, diminished triads are pretty uncommon - players prefer to use the diminished 7th chord which adds an extra note and makes the chord sound a little better. Its quite an odd sound, but very distinctive. Accomplished shredders very often will use diminished chords as the basis for arpeggios and sweeps to get a particular sound, very different from major or minors. They are often used to create tension which is resolved by a change to another chord, often the root.

Augmented Triad

Finally, our last type is the Augmented triad. We get an augmented triad by using the root note, a major 3rd, and an augmented 5th. In this example we'll construct a C augmented triad. Using the scale of C - C,D,E,F,G,A,B,C, the root is C, the 3rd is E, and the augmented 5th would be a G# or Ab. You could finger it as below.

Attached Image

A very typical use for an augmented chord is as a bridge from the dominant to the tonic - remember those names from the lesson on degrees of the scale? We tend to use them occasionally when we are talking about chord functions. The tonic in the key of C is C itself, and the dominant is G. So what I said above translated to the key of C is that we can use an augmented chord to lead us from the dominant ( G ) back to the tonic ( C ). In this case, the chord sequence we would use would be:

G -> Gaug -> C

Why does this work so well? Its because of the way the individual notes move within the chords. The differing notes between a G and a Gaug is that 5th - it moves from a perfect 5th to an augmented 5th. In the chord of G that means moving from a D to a D#. The chord of C that we are resolving to happens to have an E note in it (it is the major 3rd), so we get a nice little sub-melody when we play those 3 chords - D, D#, E - which seems to lead us very pleasantly from the G chord to the C chord. This kind of movement within chord function accounts for a lot of the effects that different chord sequences have on the ear within the context of a particular song, and the cool thing is that in the first two lessons we covered the language and concepts to understand that kind of analysis - if nothing else, you can impress your fellow band members!

Other Triads

Now that we have covered the four types of triad you are probably wondering why there are only 4 types of triad - why can't we have a C triad with a minor 3rd with an augmented 5th for example? Well, there are no rules in music, all we are trying to do is explain something that at times can be pretty indefinable. The pragmatic answer to the question is that yes, of course you can do that. Its just that the results might not be too musical, and on the whole people avoid certain combinations of notes. However, it might well be the perfect chord to finish off your killer riff with, and if that is the case, be my guest and do it - in the next lesson we'll have a look at how we might go about naming some of the more esoteric chords like that, and you can figure its name out for yourself! (OK, since you asked, a C triad with a minor 3rd and an augmented 5th might be called Cm#5, but don't quote me on that!)

Final Words

Now that we have looked at the 4 types of triads, you have the ability to figure out the notes of any one of 48 different chords! That's 4 individual types for each of 12 keys. In the next lesson, we'll start to look at some more complex chords and pretty soon you'll be able to work out hundreds of chords just by memorizing a few simple rules!

As ever, feedback and questions are welcome.

This post has been edited by Andrew Cockburn: Apr 29 2007, 03:05 PM


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radarlove1984
post Mar 30 2007, 04:27 AM
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Great lesson. I'm finally learning enough to ask questions cool.gif

Could you clarify something about the Augmented triad? Let's use the notes for your example.

C would be the root note, and E would be the major 3rd, right? The part that I'm confused about is the Augmented 5th. I'm pretty sure G is the Perfect 5th, and you say that G# is the Augmented 5th.

Could the augmented 5th also be referred to as the minor 6th? Are they the same notes, but the chord is called Augmented, or am I getting my terms mixed up?

This post has been edited by radarlove1984: Mar 30 2007, 04:28 AM
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Andrew Cockburn
post Mar 30 2007, 01:31 PM
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QUOTE (radarlove1984 @ Mar 29 2007, 11:27 PM) *
Great lesson. I'm finally learning enough to ask questions cool.gif

Could you clarify something about the Augmented triad? Let's use the notes for your example.

C would be the root note, and E would be the major 3rd, right? The part that I'm confused about is the Augmented 5th. I'm pretty sure G is the Perfect 5th, and you say that G# is the Augmented 5th.

Could the augmented 5th also be referred to as the minor 6th? Are they the same notes, but the chord is called Augmented, or am I getting my terms mixed up?


No, that's right - some intervals overlap as you pointed out. Since the 6th is an A, a minor 6th would be an Ab or a G#, so yes they are the same. At this point it comes down to convention how we refer to the individual notes. 5ths are pretty much always important parts of most if not all chords so we try and keep some sort of 5th reference in there, so Aug 5th is preffered over Min 6th even though they are the same. Also, since we are talking about an augmented 5th (by convention) we name the chord that way.

One thing you'll find with music theory is that although it is basically logical, a lot of things are done by convention, and are probably the result of decisions made hundreds of years ago. And at the bottom of it all, musical theory is an attempt to explain why certain notes make us feel the way they do - a very difficult thinig to tie down!

This post has been edited by Andrew Cockburn: Mar 30 2007, 05:53 PM


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radarlove1984
post Mar 30 2007, 06:23 PM
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Thanks for clarifying that. It makes sense.
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Rockwouldbe
post Jun 7 2007, 10:28 AM
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Stratman58
post Jun 15 2007, 12:48 AM
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I learned very much from this lesson Andrew thank you. It helps so much more to sit down with your lessons with a guitar, and take it piece by piece. I feel as if I just cleared another mountain after this one.


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Andrew Cockburn
post Jun 15 2007, 03:10 AM
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QUOTE (Stratman58 @ Jun 14 2007, 07:48 PM) *
I learned very much from this lesson Andrew thank you. It helps so much more to sit down with your lessons with a guitar, and take it piece by piece. I feel as if I just cleared another mountain after this one.


Cool - there's more on the way - really must write part 5 of this - thst is where it gets really interesteing smile.gif

Tonight I've been working on a Circle of Fifths lesson - will post it in the next 30 minutes.


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eddiecat
post Sep 23 2007, 02:55 PM
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Good morning Andrew!
This is an awesome lesson!
Now, to maj, min, aug, dim chords:
If I'm not mistaken, in relation to your previous lesson,
we could also write a formula in semitones for these chords:

Maj chords= 4+3 semitones
min chords= 3+4
aug chords= 4+4
dim chords=3+3


Hope I'm right. huh.gif
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Muris Varajic
post Sep 23 2007, 07:37 PM
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You're more than right Eddie! smile.gif

Andrew is going to slap me for this,so I'll run like hell now !! cool.gif


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Andrew Cockburn
post Sep 23 2007, 11:57 PM
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QUOTE (muris @ Sep 23 2007, 02:37 PM) *
You're more than right Eddie! smile.gif

Andrew is going to slap me for this,so I'll run like hell now !! cool.gif


* slap * !!!

Eddie you are right - and it means more coming from me than Muris ok ???

(Just kidding, thanks for helping out Muris you are always welcome in any of my lessons)


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FretDancer69
post Jan 13 2008, 06:20 AM
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great lesson Andrew, this well help me create awesome minor, major, augmented and diminished Sweep arpeggios!! cool.gif


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tarzan
post Feb 4 2008, 10:45 PM
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QUOTE (Andrew Cockburn @ Mar 30 2007, 07:31 AM) *
No, that's right - some intervals overlap as you pointed out. Since the 6th is an A, a minor 6th would be an Ab or a G#, so yes they are the same. At this point it comes down to convention how we refer to the individual notes. 5ths are pretty much always important parts of most if not all chords so we try and keep some sort of 5th reference in there, so Aug 5th is preffered over Min 6th even though they are the same. Also, since we are talking about an augmented 5th (by convention) we name the chord that way.

One thing you'll find with music theory is that although it is basically logical, a lot of things are done by convention, and are probably the result of decisions made hundreds of years ago. And at the bottom of it all, musical theory is an attempt to explain why certain notes make us feel the way they do - a very difficult thinig to tie down!


Andrew's explanation is perfect, but if anyone is still confused here's how i finally figured out for myself whats the difference between these inharmonic equivalents (G# and Ab):

they both sound the same but they're written differently. that's all!
G# is a fifth and Ab is a sixth, so they are different.

the same thing applies to words:
"sea" and "see" are both pronounced the same, but are written differently and mean different things.

simple!

great job Andrew! :-D
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Nemanja Filipovi...
post Feb 4 2008, 11:42 PM
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...considering inharmonic equivalence...does the G# exist as a scale(teoreticly) sundly he does...but in the scales "scale"...are C G D A E H F# C#..... he is there soundly but not teoreticly.... does he exist?

This post has been edited by Nemanja: Feb 4 2008, 11:52 PM


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FretDancer69
post Feb 9 2008, 07:39 AM
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Hey there Andrew, a quick question here.

In the Am Triad:



why is E on the open 6th string muted? it is an E and it belongs to the notes of a Minor Triad. We have 2 other E's ringing (2nd fret g string, open 1st string), but why do we mute the open 6th string?


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Andrew Cockburn
post Feb 9 2008, 08:04 PM
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Hi Fret - it all revolves around voicing the vhord and making it sound good.

When playing a chord, one of the most importasnt notes is the root note - it gives the chord its identity so we usually make an effort to have that be the lowest note in the chord. You are right that the E belongs there, but look what happens if we play that as the root - we get:

E A C E

Now, that has all the notes for A minor, but it vould be interpreted with E as the root in the following way:

E root
A 4th
C 6th

Now thats a wierd chord - could be somthring like E sus +6 maybe, the point is it doens;t sound like an A minor when the root is E. Changing the root or adding a new note as the root can change the identity of a chord - and there will be a lesson on this soon smile.gif


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post Feb 9 2008, 08:18 PM
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QUOTE (Andrew Cockburn @ Feb 9 2008, 01:04 PM) *
Hi Fret - it all revolves around voicing the vhord and making it sound good.

When playing a chord, one of the most importasnt notes is the root note - it gives the chord its identity so we usually make an effort to have that be the lowest note in the chord. You are right that the E belongs there, but look what happens if we play that as the root - we get:

E A C E

Now, that has all the notes for A minor, but it vould be interpreted with E as the root in the following way:

E root
A 4th
C 6th

Now thats a wierd chord - could be somthring like E sus +6 maybe, the point is it doens;t sound like an A minor when the root is E. Changing the root or adding a new note as the root can change the identity of a chord - and there will be a lesson on this soon smile.gif


thanks Andrew, i understand a little more now. Ill wait for your lesson smile.gif


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post Apr 3 2008, 07:55 PM
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Just wanted to add to the praise for Andrew's terrific lessons on theory and those who've contributed. When I was young and began to play, I wasn't very cooperative with my guitar instructor when it came to learning theory. Well, after about 10 years of playing regularly, I became bored, sold everything, and took a ten year break. I know I became bored because my progression and understanding of music had stopped. Now, after that 10 year break, I know I enjoy playing more now than I did before because of lessons like Andrew's and this site. It's become invaluable for me.

I spend about 1 hour, 3-4x a week going through the lessons in "Andrew's theory lessons" and loving every minute of it. I noticed that a good majority of the information was posted within the past 6 months. Don't stop! Please! smile.gif The outline of all the lessons covered is terrific and I want to be able to go through each one.

I hope it gives the instructors here a sense of accomplishment to know that a 2nd timer like me is finding the guitar even more enjoyable now due to the efforts of those that contribute content to this site.
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Andrew Cockburn
post Apr 3 2008, 08:13 PM
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Thanks! Its great to get some good feedback like this, makes it very worthwhile!

I have to admit I have been making less lessons recently as Kris has me busy working on the WIki, Competitrions, Moderation and all sorts of other stuff, but I will continue to make lessons as I get time, I still have some good ones left in me to write!


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post Apr 15 2008, 05:43 AM
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It's about time that I've bothered with a couple more of your lessons , Andrew. And I've been )*!@#(*(#$(#*$ about how chords are formed, today I quickly went through some of your earlier lessons and this one to get the picture, and I will surely come back to them to cement that idea in. Finally I understand these things << thanks man I'm very grateful >> . Actually as a beginner - if you are told bits and pieces of this by people, and some of the advice is also wrong, you end up totally frustrated trying to understand this stuff. Everyone at GMC should send you flowers and praises for slapping these VERY easy to understand musical theory lesson at us biggrin.gif THANKS AGAIN ANDREW
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post Apr 30 2008, 11:44 AM
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Hi Andrew, me again, just a quick question. In your lesson you losely describe where you would typically use a diminished chord:

QUOTE (Andrew Cockburn @ Mar 29 2007, 09:50 PM) *
Diminished Triad

They are often used to create tension which is resolved by a change to another chord, often the root.


I just want to clarify this to see if im thinking along the right lines.

In your example, if the chord was Ddim would, would the key be Em therefore using the Dmin chord to get to the Em chord.

Or is it that a Ddim is usually used to get to a D chord (the root of the chord)?


Thanks in advance, your lessons are more helpful than a polish man on salary laugh.gif
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