Just Intonation and Locating Pitches

Okay, I had a copy of this Post, and thought I'd re-post it, as so many were lost. Plus, there seemed to be some interest the first time.

Here it is:

Ever notice how Barber Shop Quartets and really great Choirs sound so "Harmonious"?

This is because the Naturally Occuring Pitches of the Overtone Series ring so well together. They Blend so smoothly.

If there is no Piano or other Equal Temperment Instrument around to screw them up, these Vocalists will usually go straight to the more Harmonious "Justly Intonated" Pitches.

Not that Equal Temperment is bad. Far from it. But, the Resonance created by Justly Intonated Pitches is just so compelling and full sounding, that they are hard to escape.

Anyway, if you want to hear these for yourself, they are easily accessed right on your Guitar's Strings!

Here's a good way to do just that:

On an A String, the 12th. Fret Harmonic will give you an Octave of the Open A Note. This could be expressed as a 2:1 Ratio.

What about splitting the String into 1/3s?

This is basically playing the Harmonic at the 7th. Fret.

And this Pitch (3:1) is the Perfect 5th. of A. An E Note.

See how this Pitch appears so strongly? This helps to explain WHY a Perfect 5th. is so fundamentally important.

Power Chords anyone?

Split the String into 1/4s and you get another Octave of the Fundamental (4:1). Or, 2 Octaves above the Fundamental.

This is right over the 5th. Fret.

Split the String by 1/5s, (5:1 Ratio) and you'll arrive at a new Pitch. This is the Major 3rd., or C#.

You can find this Pitch right behind the 4th. Fret. Not directly over the 4th. Fret, but slightly behind it. A little closer to the Nut.

Now you have the Building Blocks of the Major Triad.
In this Example, it was the A Major Triad, spelled A E C#

When you use Octave Reduction to bring all of these Pitches into Intervallic Space, you end up with what looks like Stacked 3rds.:

A C# E

And this is as far as it goes with most Western Music Theory.
It's called "5 Limit" Tonality, as it goes as far as the 5th. Partial (5:1 Ratio).

*Now, listen to that JI (Justly Intonated) Major 3rd.
Compare it to the Fretted Major 3rd. on the G String, 6th. Fret.

Hear how Sharp the Fretted (ET, or Equal Temperment) 3rd. sounds in comparison?

Ever wonder why there is such a strong desire to "slightly Bend/Tweak" that "Minor 3rd" C Note, whenever playing those "5th. Fret Pentatonic Minor Blues Box Licks"?

So, if this all looks like mumbo-jumbo, try just playing these Harmonics and listening to them. Then, try playing a plain old A Chord, and compare the sound with the sound of the Harmonics.

Here's the Harmonics we're talking about:

All on the A String:

12th. Fret, 7th. Fret, 5th. Fret, behind the 4th. Fret and just a little towards the Nut.