Power Up the Triad with Natural Tuning
For readers of thrillers and action novels, triad power derives from a mysterious and dangerous Chinese gang. For us musicians, triad power comes from the chord that is the working result of the three notes that form a triad. I would like to explore the origen of the triad in the overtone series to show how natural western music was and is by developing the triad in music.
Before plunging in to the whole harmonic development of natural sound, I can’t resist referring to Tesla’s declaration that 3, 6 and 9 were the key to understanding the physical universe. We will be dealing with the numbers 2, 3 and 5. I hope to arrive at my favorite tuning 432 Hz.
And yet, I could do this from Tesla’s numbers. His 3, 6 and 9 begin a Fibonacci sequence that arrives at 432. Whaddaya think about that? Here’s the series: 3-6-9-15-24-39-63-102-165-267-432. Pa-da-boom!
If you have no great objection I would like to start with the most natural rhythm we may agree on, the daily rotation of the earth. It’s called the diurnal rhythm. It’s very slow compared to the speed at which we move around. If you were a being that lives millions of years, you may be able to hear the sound made by this repeating cycle.
Doing the Math
Multiplying one rotation of diurnal motion by 24 we get an hour. One hour is 24 times as fast as one day. The factors are 3 and 2 to the 3rd power, (3x2x2x2). When you triple a frequency you get the fifth above that frequency, plus an octave. In a simplistic reduction, the tone of an hour is a fifth above the tone of a day.
The expansion to a minute will require 5, 3 and 2. A cycle 60 times as fast as an hour would easily be calculated as 1 x 5 x 3 x 2 x 2.
We could think of an hour as the base frequency. Five times that frequency yields the 3rd in interval expression. And 3 times that gives us the 5th higher than the third. This would sound like a major 7th.
Seconds are derived exactly the same way. A second would sound as a major 7th to the minute. We can start with the second and work backwards to the day to find what is the frequency of diurnal motion.
Recall that in Bach’s time middle C was declared to be 256Hz. That’s a power of 2. You can divide by 2 until you get 1. Therefore, one second can be thought of as a very slowly vibrating C.
Here we go: C, one second is the major 7th of Db, the minute, and Db is the major 7th of D, the hour. D is the 5th of the day, the hour being an octave of 3. That means our planet turns on the note of G. Maybe that’s why Masons have a ring with a big G on it.
Now for the A432Hz
Starting with C, let’s go by 3’s. C times 3 is G. G times 3 is D. D times 3 is A. Or 3x3x3 = 27 for a very low A. Now, taking the octave ascension, starting with 27: 2x = 54,
2x = 108, 2x = 216, 2x = 432. I told you so.
This is not the way music physicists think. Maybe they could shoot down this whole idea. I don’t know. What I do know is that this system yields notes that sound right, when sounded by a frequency generator.
Getting Back to the Triad and its Power
The Triad…no I haven’t forgotten about the triad. The notes of the triad can be produced from any base note by the multiples of 3 and 5. The funny thing, for me, is that 3x produces the 5th and 5x produces the 3rd. Clever, don’t you think?
There are music traditions that don’t use the triad. Not as a chord. But the Western world has used the chord for centuries. We’re really into chords.
One number I may have neglected is 7. Multiplying a frequency by seven gives you the…minor seventh, or very close to it. Close enough for fiddle music.
The notes of the C scale all have whole number frequencies when you start with 256Hz. After some time you might just recall that D on the violin is going to be 288Hz.
That’s double the 144Hz note playable on a 5 string violin. (heh-heh) And 144 is one of those interesting numbers.
The 5 string violin and the viola also get to play the 128Hz C. And I have a tuning fork that gives this frequency when struck. It’s from science surplus. Science has been using 256Hz for middle C a very long time. Since the time of Bach.
Science and Nature Agree on A 432Hz
And it was a mathematician who came up with 256Hz for middle C. Although at the time Hz was not a thing. Was this scientifically derived from actual practice of how instruments were tuned? Probably not. Somebody made a decision and it turned out to be a fortunate guess.
Science has followed this standard since then.Maybe we can, too. And while it’s easy enough to use a C 256Hz tuning fork for a viola or 5 string violin, for most purposes, A 432Hz is a good choice to arrive at natural tuning. And it’s scientific, too. Does it get any more reasonable than that?