Interesting Pentatonic Discovery

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Delving into music theory over the last couple of years has not only been greatly beneficial for my guitar development, but I find it an absolutely fascinating subject in its own right.
I’ve been delving into pentatonics a great deal in the last few months, and last night I had a random thought.

" How many diatonic chords can I build from the pentatonic scales, given the absence of 2 of the 7 notes from the parent scales? And can what I find tell me anything useful?

As a first ballpark guess, I thought, probably 3, maybe 4. Certainly from the root note, and likely 2-3 others, given I was only missing 2 notes. What I discovered was not only surprising, but intriguing.

Using the Keys of A/Am as a working example, I thought well, OK, heres the pentatonic scales, lets see what happens.

A Major Pentatonic

A B C# E F#

To my surprise, I could only build 2 chords.

  • One from the root - A Major ( A,C#E),
  • One from the 6th - F#m (F#,A,C#).

Mmm, OK I thought, lets see what happens with the Minor Pentatonic.

A Minor Pentatonic

A C D E G

Again, I could only build 2 chords

  • One from the root - Am (A,C,E)
  • One from the 3rd - C (CEG).

Well, that certainly surprised me, given you take only 2 notes from 7, and end up with 2 chords from 7. Then I saw it - the little gem inside both. The only other chord I can build in either pentatonic scale is the relative major/ minor pair of the key.

For A Major pentatonic, the only other chord is F#m, the relative minor of A major.

For A minor pentatonic, the only other chord is C major, the relative major of A minor.

Now this has really got me thinking. " Why does this occur".

Now, this intellectual wandering probably isnt going to help me nail the solo from ACDCs, You Shook Me All Night Long that I’ve been working on lately, but its fascinating nonetheless, and one to add to the mind files, which may provide some fruit somewhere down the line.

I’d be very interested in any input from the more experienced here. ( "Cue, Richard - @Richard_close2u ).

Cheers, Shane

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Wow, Shane, great discoveries.
I love this stuff.
I have never thought along these lines or viewed things this way before.
New perspectives!
:slight_smile:

From the Circle of Fifths topic, Part 4 … do you recall how we could find a seven-note major scale, identify the location of its root note, use a pair of perpendicular arrows to identify the relative minor root, and find both major and minor pentatonic scale notes by cutting off the two notes from either end?

The C major scale and the relative A minor scale

C ionian 1
C ionian 1722×726 40.2 KB

C Major scale
C, D, E, F, G, A, B

A minor scale
A, B, C, D, E, F, G

C major pentatonic ← → A minor pentatonic

circle5ths 4 07

Here are three views of the seven note cluster. In each I have greyed out the same two notes (F and B respectively) as they are the two notes we will eliminate to arrive at the major and minor pentatonic scales.

  • The seven notes in the order they appear on the Circle of Fifths
  • The same seven notes shown as the C major scale
  • The same seven notes shown as the A minor scale

a1

a2

a3

Now harmonising the C major scale. Note that this gives chords which match exactly the harmonised A minor scale so we will not repeat the process.

  • I = C major = 1, 3, 5 = C, E, G

  • ii = Dm = 2, 4, 6 = D, F, A

  • iii = Em = 3, 5, 7 = E, G, B

  • IV = F = 4, 6, 1 = F, A, C

  • V = G = 5, 7, 2 = G, B, D

  • vi = Am = 6, 1, 3 = A, C, E

  • vii = Bdim = 7, 2, 4 = B, D, F

Notice that anywhere a chord contain either the 4th or the 7th scale degree, it will not be a chord that can be made from the five pentatonic notes. Each occurs in three of the seven chords (with one instance of them both occuring - the diminished chord). A total of five chords are therefore impossible to make with the pentatonic notes. And the sequencing pattern ensures that the two chords that do remain are the C major and the A minor, the relative major and minor chords.
Is this pre-ordained?
Is this divine creation?
Is this the glory of nature?
Is this another mathematical equation with a great big formula?

Whatever it is, I get a little WOW from it.
And the urge to wonder if there are more parts to explore.

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Shane,
I’m not sure whether this is the answer you’re looking for, but if you write out the seven triads and delete any that contain the 4th or 7th notes of the relevant scale, there are only two left. So in the key of A, delete all triads that contain a D or G.

ACE
BDF
CEG
DFA
EGB
FAC
GBD

Hopefully that wasn’t a load of bollocks.

Edit: Richard beat me to it. And included pretty pictures.

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Thanks for the reply Richard, detailed as ever. I knew I wouldnt be waiting long :rofl:.
Yep certainly fascinating, and these are the things I think about often.
The initial thought was borne out of my current practice on basic chord tone targeting while utilising pentatonic shapes, and what arpeggio and triad notes of certain diatonic chords intersect with the scale, and which do not.
I’m trying to learn more effectively how to “see” particular arpeggios/ triads and the surrounding scale pattern/notes/ intervals at the same time. In isolation, I’m going along OK with both, but seeing them as one multilayer unit is an entirely different ballgame. Im under no illusion that this is a difficult task to master, and is a multi year endeavour, but I’m on my way :crazy_face:
Thanks again Richard,

Cheers, Shane

I suppose this thought exercise was like a little exploration and self test. Something like " Shane, give us your best guess on how many diatonic chords in a pentatonic scale, based on what you think you know so far. You’ve got 5 seconds. Then lets see what we find".
Once I worked through it on paper , the actual logic became apparent, but the fascination remained at what the logic revealed. Why does the logic reveal this? And more importantly, how can it help me when playing?

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You lost me at this point!! :slight_smile:

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:exploding_head:

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Great discovery Shane. I was wondering what this one was going to be about. All very interesting and equally well proven by Mr C. Is there more to this than meets the eye ? Will knowing this fact make a difference to how you’ll approach lead play/impros ? Keep us posted if anything develops.

Cheers

Toby
:sunglasses:

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@sclay, play something for us. My eyes glaze over on this stuff to be honest. Whatcha got?