I’m starting to think that the major scale is a product of nature more than of man.
So a few years ago I had a guitar lesson with an adult beginner and I was showing her how to play a G major scale. After I was done she asked, “Why?”
I asked “why what?’
“Why those notes in that order.”
I answered her question in a word salad that had something to do with Bach thinking it was a good idea so we just stuck with it. It was totally a guess. The question she had was a very valid, simple one that I should have been able to answer. I had never asked myself this question, my professors at Cal State Fullerton never told me the answer to this, maybe because I didn’t ask. At any rate, I really didn’t know “why those notes in that order.” (It’s a good question!)
You see, when you live in the fish tank of music you don’t often see your environment the way a non-musician does. It sometimes takes the perspective of someone outside of your domain of competence to see where you really need to shore up your understanding.
Arnold Schoenberg taught me why we have a major scale. Last year. That’s how long it took me to find the answer. In Schoenberg’s “Theory of Harmony” chapter 4 he states “Our major scale, the series of tones c,d,e,f,g,a,b, the tones that also provided the basis for the Greek and church modes, we can explain as having been found through imitation in nature.” Intriguing.
The overtone series is a naturally occuring phenomenon in music. When a frequency is played, other frequencies are along for the ride. When we play natural harmonics on an open string we expose these overtones in isolation. Here’s the first one.
C-C
12th fret harmonic, on the same location of the fretted octave,
7th fret, Harmonic G note, same location as the Perfect 5th.
5th fret harmonic, same location as the perfect 4th but this time sounding a C two octaves above the fundamental.
4th fret harmonic, the same location of the Major 3rd and sounding the E two octaves above the fundamental.
There are more overtones, but let’s just stop here because these are the first four overtones above the fundamental pitch.
Did you notice that they spell a chord? C,C,G,C,E. It’s a C chord. That means that every frequency has a major triad stowed away within it.
This works for the piano as well. If I depress a key without sounding it, the string won’t have a damper on it, and therefore the fundamental should expose the harmonic once it’s frequency activates the string, let’s try it.
By the way, if we do this on a stringed instrument, we can get the same harmonics moving towards the bridge, check it out.
I found that out, like, last week. Try it out yourself.
So, since every tone has a major triad along for the ride, how does that get us a major scale? Well, remember how in the last lesson we explained that Perfect 5th was the first true diad? We can logically conclude that the process can be repeated from the 5th, which we call the dominant tone from C. So we gather the overtones from a G fundamental. We get a G major triad.
Now we have a C triad and a G triad.
Now, remember how 5ths are 4ths and 4ths are 5ths? That means that C has a 5th below it that we ought to consider a sort of dominant. We might even call it the SUB dominant, which we do. So let’s repeat this process from the 5th below C, F.
We now have an F major triad added to the mix. So, let’s hear Schoenberg take it away.
“Now if C is taken as a midpoint, then it’s situation can be described by reference to two forces, one of which pulls downward, toward F, the other upward, toward G.
These tones pull towards each other. G wants to go the C, as C wants to go to F. This is a snapshot of the tonal relationship surrounding a harmonic gravitational center known as C.
If you add up the first 4 overtones of the pitches C, G and F you would get a collection like this:
C,E,G. G,B,D. F, A,C
Add up the these tones and then put them in order from C to the nearest octave C.
You would get C, D, E, F, G, A, B, C. Our major scale. That’s why many songs are only three chords. You can harmonize any diatonic tone in the major scale with only three chords. Why? all that you are using are the chord tones belonging to the tonic, dominant and subdominant chords.
Move the center of tonal gravity over to G and then you have to account for the dominant of G, which would be D. The D note has the 4th overtone of F# so therefore you would have to add an F# to the equation for the key of G major.
Move the tonal center to F. F has a subdominant tone Bb, so you would have to add Bb to the equation for yield an F major scale.
So there you have it. The next time a student asks me the question of “why these notes in this order?” I will have an answer for them. Or at least a youtube link.
Thanks for watching, in the next lesson we dive into Triads and Taoism so that should get weird. Thanks and be safe.