Hey Friend,
We’ve come full circle with the major scale. The Perfect Octave interval brings us back to the root note of the scale, the same as the tonic except that the pitch is higher.
As I’ve said before, the perfect octave sound wave has a value in Hertz (the frequency) of double what the tonic frequency is.
Did you catch the correlation between “sound wave” and “Hertz?” It just struck me that “frequency” is "the number of times" a sound wave occurs within one second.
You know, “how often” = “frequency."
Dang, am I slow or what?!
I wanted to clarify what I said before about the octave (at the twelfth fret) “cutting the string in half.” That phrase might give you the idea that the number of Hertz should also be divided by two, not doubled.
But remember, when you play an open string, the sound is created by the vibration along the entire length of the string between the nut and the bridge of your guitar.
When you put a finger on a string, your finger effectively becomes the nut, so it shortens the length of string that can vibrate and produce sound waves. The shorter a string becomes, the more it vibrates over that shortened distance.
With a higher frequency of sound waves, the pitch of the note gets higher.
So when you play a note at the twelfth fret, you’re halving the length of the string between the nut and bridge. And that gives you the pitch of the perfect octave.
Not to get too mathematical, but each one of these intervals is a ratio. Where the tonic is a 1:1 ratio (one to one), the perfect octave is a 2:1 ratio (two to one). The frequency is doubled over the tonic.
A perfect fifth has a ratio of 3:2. I think of it this way…
If I take the entire string length between the nut and bridge and split it into three equal parts, each of those parts will give me a perfect fifth pitch. That also means I’d have two places on the fingerboard to place my finger in order to produce the perfect fifth pitches.
"3" equal lengths, "2" places to put your finger to create those equal lengths.
Try it yourself if you have an electric guitar. Pick a string. Then place a finger on the seventh fret. This is a perfect fifth interval.
The next perfect fifth would be on the nineteenth fret. If you were to measure the distance between the nut and seventh fret, you would find that it’s the same distance as between the seventh and nineteenth, and the nineteenth and the bridge.
Make sense?
Whew! Math and Physics, yo!
Here’s our interval chart again:
Tonic - we call this the root note most of the time; it’s the first note of the scale. In the key of C major, this note would be C.
Major Second - this is one whole step (tone) above the tonic. In the key of C major, this note would be D.
Major Third - two hole steps above the tonic. In the key of C major, this note would be E.
Perfect Fourth - five half-steps above the tonic. In the key of C major, this note would be F.
Perfect Fifth - seven half-steps above the tonic. In the key of C major, this note would be G.
Major Sixth - nine half-steps above the tonic. In the key of C major, this note would be A.
Major Seventh - eleven half-steps above the tonic. In the key of C major, this note would be B.
Perfect Octave - six whole steps above the tonic. In the key of C major, this note would be C.
In the key of C major, that is the shift from C to C. When we look at the scale pattern, we see it’s six whole steps (tones), the full twelve frets on the fingerboard.
1 2 3 4 5 6 7 (8)
C D E F G A B (C)
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W W H W W W H
I know your head might be spinning right now, and I get it. It took me a few stabs at this stuff for it to start making any sense, but once it did, it opened a new understanding to me about how notes are formed and work in conjunction with other notes.
Try out the examples:
On the examples, I’m sure you recognize “My Sharona,” by The Knack. The other two are definitely older references. The second is from “Gone With The Wind” and the last is a song recorded by Nat King Cole.
Alright, have a great day - it’s Friday Eve. Hope it goes smooth for you!
Peace~
Dave
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