This Is So Cool- How We "Get" Our 12 Notes

TSJMajesty

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I know that chords are naturally derived from physics:

Divide a string in 2 equal parts, play that harmonic and you get the octave interval. Ok, easy enough.
Divide a string into 3 parts, play either of those harmonics and you get the fifth.
4 parts, you get the next octave on the 1/4 and 3/4 nodes,
And 5 parts, you get the major 3rd.

So "nature" gives us, via simple physics, a root-3rd-5th-octave major chord.

Beyond that, I used to think someone came up with a formula to generate the remaining notes (the 12th root of 2, btw), so they would "fit correctly" between those first couple of harmonics. But not exactly.

Yes, we use that formula to create this thing called equal temperament, but the 12 notes continue to originate from physics.

Go back to the 2nd harmonic which gives us the 5th. Start on any note.

So starting with C, gives us a G (G is the 5th of C, which comes from the harmonic.) Now continue...

G as the root, the 5th is D
D gives us A
A gives us E
E-B
B-F#
F#-C#
C#-G#
G#-D#
D#-A#
A#-F
F-C
And that's gives us all 12 notes!

Major "lightbulb moment!"
 
The One Where Estelle Dies Episode 15 GIF by Friends
 
Counting the notes on the fretboard gives me 12 notes too.. ¯\_(ツ)_/¯

Lol all jokes aside, I see it! :) Also another little trick below:

If you wanna know what what relative minor / major is to the scale you're playing (incase no one knows this)

If you're in A minor, it's the 3rd note of that scale that makes the relative major aka "C".

If you're in A major, it's the 6th note of that scale that makes the relative minor aka "F#".

or

If a major wants to find his minor, go down 3 steps
If a minor wants to find his major, go up 3 steps
 
Oh, and btw, I posted this before I watched the entire video, but he goes on to point out that if you use only the first 5 notes of that series (or any other series, that starts with a different note), you get the Pentatonic scale.

So look at it: CGDAE, or in order: ACDEG is the A Pentatonic scale. Kewl!!
 
I know that chords are naturally derived from physics:

Divide a string in 2 equal parts, play that harmonic and you get the octave interval. Ok, easy enough.
Divide a string into 3 parts, play either of those harmonics and you get the fifth.
4 parts, you get the next octave on the 1/4 and 3/4 nodes,
And 5 parts, you get the major 3rd.
The pitches you get from that exercise are chord tones based on just intonation. It is important to note that those are not the pitches on which western music is now based. There are several reasons for that.

So starting with C, gives us a G (G is the 5th of C, which comes from the harmonic.) Now continue...

G as the root, the 5th is D
D gives us A
A gives us E
E-B
B-F#
F#-C#
C#-G#
G#-D#
D#-A#
A#-F
F-C
And that's gives us all 12 notes!
The final pitch - the second one you've called "C" - is not an octave multiple of the original C. There's a mathematical fact that gets in the way: just-intonation fifths are based on the ratio of 3:2. If C is one, then G is 3/2, D is (3/2)^2, A is (3/2)^3, etc., etc. The problem is that cycle of JI fifths doesn't yield another C. That's because octaves are powers of 2, whereas fifths are powers of 3. No power of 2 equals any power of three. The difference between the second "C" in your sequence and an actual octave relative of the original is called the Pythagorean comma.

Major "lightbulb moment!"
That's the first of several lightbulbs that will come on if you pursue this a bit further.

Just intonation was used for centuries. Among the problems with that system is the fact that it only works well in a very small number of closely-related keys. Another temperament was called well temperament. Bach wrote a number of pieces for well tempered clavier. There's more information here: Just intonation.
 
I know that chords are naturally derived from physics:

Divide a string in 2 equal parts, play that harmonic and you get the octave interval. Ok, easy enough.
Divide a string into 3 parts, play either of those harmonics and you get the fifth.
4 parts, you get the next octave on the 1/4 and 3/4 nodes,
And 5 parts, you get the major 3rd.

So "nature" gives us, via simple physics, a root-3rd-5th-octave major chord.

Beyond that, I used to think someone came up with a formula to generate the remaining notes (the 12th root of 2, btw), so they would "fit correctly" between those first couple of harmonics. But not exactly.

Yes, we use that formula to create this thing called equal temperament, but the 12 notes continue to originate from physics.

Go back to the 2nd harmonic which gives us the 5th. Start on any note.

So starting with C, gives us a G (G is the 5th of C, which comes from the harmonic.) Now continue...

G as the root, the 5th is D
D gives us A
A gives us E
E-B
B-F#
F#-C#
C#-G#
G#-D#
D#-A#
A#-F
F-C
And that's gives us all 12 notes!

Major "lightbulb moment!"

So basically the circle of fifths? That's neat! I'll have to watch the Kiko video.
 
Also can we add Kiko Loureiro to the "guitar YouTubers who are actually rock stars" list? He has over 600k subs!
 
So basically the circle of fifths? That's neat! I'll have to watch the Kiko video.
The circle in just intonation except once you get back to the first pitch 12 5th up it ain’t in tune as Jay pointed out. It’ll be 21.5 cent sharp since I’m guessing most here don’t do comma
 
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