PT 1: “THE ORIGINAL NUMEROLOGY : HOW THE RATIOS NATURALLY OCCURRING IN NATURE HAVE AFFECTED THE WAY WE VIEW NUMBERS IN OUR CULTURE”
Have you ever wondered why certain numbers have such a special significance to our culture? WHY is “The Trinity” or “The number 3” linked to “God”? Why is 13 considered “Unlucky”? Why is “the number 6” equated with “The Devil/The Anti-Christ” ??
Also,why are there so many “12’s” in our culture?
Well, being a musician I notice the connection between “Numbers and Music” more than most of my non musical friends, and the connection seems to me to go far beyond just music!!
In my opinion, there is a case to be made that these simple numerical relationships that create these different pitches we hear could be linked to (or at least part of the reason) behind the “Symbolic Nature” we have given to those numbers in our culture thru out history.
Perhaps it all goes back to the relationship between music and the numerical ratios between different pitches that create those intervals/sounds.
To get to the bottom of this, we have to go back to around 400 B.C.(Perhaps earlier?) were there was a Greek named Pythagoras who noticed that there were numerical relationships in music/the way pitches are created thru simple mathematical ratios.
Here’s the gist of what he discovered:
You take any tone as a “starting point”.(In music, that tone is referred to as “One” or “The Tonic”.)
Now we all know the symbolism of “The number 1″ in our culture. In music, as all musicians know ,”1” is just “home base”———–BUT the number “1” is also the number of “God” of “Unity” —-and “here’s the rub”:
You can get the same “tone” or “tonal color” of the original pitch “1” pitch via divisions of that frequency by TWO.
If you double the speed of the frequency you have decided is “one”, you get the higher octave which is the same tone. If you double the speed of THAT tone, you will get the next higher octave,(also the same tone,but a higher pitched version)
So similar tones are created by “divisions of 2”
(2/1 or 4/1 or 8/1 create higher versions of the original pitch: 1/2 ,or 1/4 or 1/8 etc create lower ones.)
However, the first DIFFERENT “harmonic tone” created in the harmonic series from “The original pitch” is actually achieved from dividing the “Original frequency”(“One”) in THREES. When you do this,THEN you get the musical tone we call “The Perfect fifth”.
This continued “division by three” of each preceding new “Perfect fifth” can be done 12 TIMES. Thus all 12 tones actually come from divisions of tones by 3.
So right there you can see where the symbolism of the number 3 comes in
(The “Trinity God”, “God is “1” but “also 3” etc)
Also,we see the significance of the number 12!!
Think of the influence the number 12 has had in our culture!!
12 months in a year
12 disciples of Jesus
12 astrological signs
12 to a dozen
12 inches to a foot
12 notes in “The Western Scale”
12 Tribes of Israel
The “Alcoholics anonymous program is called “the 12 step program”
So we can see why the numbers 3 and 12 are such a big deal and how the #2,4 and 8 are just repetitions of the #1.
But what about the others?
Well, if we divide the original pitch(“1”) in 5’s we get “The Major Third” interval.
Divisions of 7? The “Flatted 7” interval.
BUT———- what about the #6?
Ahhhhhh—–the number 6. Think of the symbolism attached to that number!!
Mostly, the number 6 has long been equated with “The Devil”, and coincidentally,there is NO “harmonic tone” produced on the 6th division of any tone!!!
If you play guitar or any stringed instrument, you can check this yourself. Go to where you’re “perfect 5th harmonics” are created and divide that area in half—-you will not be able to produce any harmonic in that spot—and that represents the “6th division” of the original starting pitch.
Of all the single digit numbers,there is no ” Significant Harmonic” produced by dividing the “Original Pitch” in 6’s.You would think there would be, as its just the third division divided by 2. When we divide the octave by 2,we get the octave,so why is there no ‘harmonic” produced when we divide the perfect fifth by 2?
Well the fact is,we don’t know why—it’s just the way it is.
So lets look at this one more time:
Of all the single digit numbers, you can get different harmonic tones by dividing the original tone by single note ratios(#1-9) EXCEPT for number 6!!
1/2, 4, and 8=The original tonic and its octave(Same tone)
1/3 , 1/9=The perfect fifth, all 12 notes of the western scale
1/5=The major third
1/7=The dominant 7
This is significant because In western culture, the #6 is always referred to “the Devils Number” and as we all know, the Devil “Is removed from God”.
Also the 6th tone in the 12 tones of the western chromatic scale is the “Flatted fifth” —it is the furthest away from the original pitch on the circle of fifths. If you look at the circle of fifths, the “Flatted Fifth” is located at the “polar opposite of the tonic” on the “Circle”.
In other words, if you start with “C” at the “north pole of the circle of Fifths”, you get F# at the “south pole” of the circle.
It also takes 6 divisions of the “perfect fifth”(which is created by dividing the original pitch into 3) to get to “the Flatted Fifth”.
So you can see how the #6 plays out in nature in relation to musical pitches and tones.
There’s also one more reason “the Flatted Fifth” was connected to “the Devil” and called “The Devils note”:
The “spooky sound” of the interval!
In an age where most music that was written down was linked to the church, the “Flatted Fifth/Tritone” sounded “evil”. As it was based on “the 6th step” in the chromatic scale as well, they decided it must be “The Devil in music”. (They even called the flatted fifth interval “The Diabolicus im Musica”)
It was forbidden to sing this interval in church or compose music in Church that had that interval. (Something to think about when you hear people referring to The book of Revelation and the number “666”= “The Number of the Beast”)
So we can see one possibility of why the #6 has gotten “a bad rap” and is equated with “The Devil” and “Being apart from God” as it is the only single digit rational number that does not create harmonics when it is the divisor of the original pitch.
Now,last but not least,lets look at the #7:
In the west, the number 7 symbolizes “Completion”
(7 days in a week, God created the earth in 6 days/rested on the 7th—- when you’re happy you are in “7th Heaven” etc.)
So is it a coincidence that the last single digit “rational number” that creates a “new sound” is the number that represents “endings” and “completion”???
(Just to clarify—-The 8th division produces the same pitch as #1 and the #9 produces the same pitch as the #3—-so the #7 is the last single digit number to produce a different sound)
I would submit that there is no coincidence with any of these relationships,and that the “math” involved in music(which is embedded right into the fabric of nature itself) has affected our culture a lot more than we realize!!
Next to come in “PT 2”:
We will examine the connections between the emotions we feel when we listen to music and the numerical relationships in the music—namely how the numbers in music and the numerical relationships between different pitches and chords are connected to the emotions we feel when we hear a piece of music/a musical composition/song.