Understanding the Number System

[admin]

What I’m gonna do first is fully explain how and why the number system works. Even in those times when it seems like the you’re not following the number system, trust me you are. All examples will be in the key of C.
Credit Goes to T-block

In order to start understanding the number system, you need to have a basic understanding of intervals. An interval is the distance between 2 scale degrees. The interval is supposed to be measured starting with the first scale degree to the second scale degree, not the other way around. To illustrate this, here are all the scale degrees that are used in music:

1 2 3 4 5 6 7 8 9 (10) 11 (12) 13 (14)
C D E F G A B C D E F G A B

Now, to get an interval, you start with 1 and match it with any of the other numbers. Depending on the number you match it with, you get a different interval. Let’s start with the first interval, which is 1-1.

1-1 = this interval is called a unison
C-C

When you move from 1 to 1, you don’t really move anywhere, but you do have to play the note a second time in order to establish an interval. So the name unison reflects this non-moving movement. The next interval is 1-2.

1-2 = this interval is called a second (2nd)
C-D

When you move from 1 to 2, it really is a physical movement. However, what you've really done is added a second number. So, the name second reflects this. Here are some others:

1-3 = this interval is called a third (3rd)
C-E

1-4 = this interval is called a fourth (4th)
C-F

1-5 = this interval is called a fifth (5th)
C-G

1-6 = this interval is called a sixth (6th)
C-A

1-7 = this interval is called a seventh (7th)
C-B

The next interval, 1-8, is a unique interval. I bet some of you out there would call this interval an 8th because it follows the pattern set by the previous intervals right? Well, you could call it that if u want, but it has a special name:

1-8 = this interval is called the octave
C-C

The reason why this interval has to have a different name is so that it gets distinguished from a unison. Here are the last few intervals:

1-9 = this interval is called a ninth (9th)
C-D

1-11 = this interval is called a eleventh (11th)
C-F

1-13 = this interval is called a thirtienth (13th)
C-A

*The intervals 10th, 12th, and 14th are not used



Now that you have a basic understanding about intervals, let's look at the number system.

[admin]

You start with the musical zip code (my version):

7 - 3 - 6 - 2 - 5 - 1 - 4
B - E - A - D - G - C - F

Now, the numbers in this zip code are all the same distance apart, meaning that movement from any one number to the very next number is the same distance. The movement here is by 4ths. So, going from 7 to 3 (B-E) is a 4th movement, from 3 to 6 (E-A) is a 4th movement, from 6 to 2 (A-D) is a 4th movement, etc. This is also the way the Circle of 4ths move. So, if you really think about it, this zip code is a numerical representation of the Circle of 4ths. Hopefully, that is a light bulb moment, lol. Here is the link to the circle of 5ths/4ths

The overall purpose of a musical progression is to get back home. Home in music is the 1. This means that each chord keeps moving through the zip code until it eventually finds its resting place at 1. So, for example let's say that you're in the key of C and you play a chord with E in the bass. What comes next? Just check the zip code. In the key of C, E is a 3. What comes after 3? If you said 6 you answered correctly. It would look something like this:

E / D-G-B (3)
A / E-G-C (6)

Those 2 chords sound nice and logically follows the zip code. Pretty simple so far right? Now, let's complicate things a little. Using the example above, let's say instead of going to 6, you go to 4:

E / D-G-B (3)
F / F-A-C (4)

Now, after hearing these 2 chords back to back, your ears will tell you that sounds good. However, the theoretical part of your brain may be thinking "Whoa, wait a minute, RED FLAG. You can't do that cuz it doesn't follow the zip code." So, the question now becomes how can something that sounds so good not follow the zip code? The answer is, it sounds good because it does indeed follow the zip code. Well, how is that? Let me explain:

What happened here is you merely by-passed a few of the scale degrees and played the chord that you wanted to play. In this case, when you played the 3, you by-passed 6, 2, 5, & 1 and went directly to 4. So, here's the illustration:

E / D-G-B (3)
skip 6
skip 2
skip 5
skip 1
F / F-A-C (4)

Did you see that? Even though u didn't follow the zip code, the end result gave you the same feeling as if you did follow it. So, in reality, you did follow it, just not step by step. This is one reason why you don't have to play every chord explicitly like it's supposed to be according to the order of the zip code, but it still works and sounds good.

So, no matter what chord you play, you just keep circling the zip code, land on the chord you want, then you're off again. You keep doing this until you get home, which is 1. I like to use the analogy of taking a road trip. Following the zip code to the letter is like driving a car to your destination. This is the 3-6 example above. However, not following the zip code to the letter is like taking a plane. Instead of going from one to the next, to the next, to the next, etc. until you reach your destination, you just fly right to it. This is the 3-4 example above. Hopefully this is another light bulb moment, lol.

So, even if you play something like 1-5-6-4, you're still following the zip code. Let me show you:

C / G-C-E (1)
skip 4
skip 7
skip 3
skip 6
skip 2
G / G-B-D (5)
skip 1
skip 4
skip 7
skip 3
A / A-C-E (6)
skip 2
skip 5
skip 1
F / F-A-C (4)

This progression should sound familiar. If it doesn't, this is the progression used in the song "He's Able" by Deitrick Haddon and Voices of Unity feat. Darwin Hobbs. It's also used in countless pop/rock songs, R&B songs, and even other gospel songs. Is it all starting to sink in now? I hope so. Now it's time to bridge the gap and add in those "tweeners".

[admin]

If you haven't viewed my post talking about the degrees in-between the scale degrees, then you should at least take a look at it before moving on.
I guess I should start this off with an example:

E / E-G-C
F / F-A-C
F# / F#-A-D
G / G-B-D

O.K., we got this progression here that sounds pretty good. All of those chords have notes in the bass that most people would say are in the key of C, except for one, the F# / F#-A-D. Well, I beg to differ. I say that all of those chords are in the key of C, including the F# / F#-A-D.

But T-Block, how can you say that when F# isn't in the key of C? I'm glad you asked that question. Let's take a look at that odd chord:

F# / F#-A-D

First of all, what kind of chord is it? It's a major chord. Next, what is the root of the chord? It's D. So, this is an inverted D major chord. Now, what chord comes after it? That's right, a G major chord. In the key of C, a G major chord is a 5 chord. If we look back at the musical zip code, what precedes a 5? Yup, a 2. In the key of C, what note is a 2? That's it, D.

Hmmm, let's think about this for a moment. In the zip code, a 2 comes before a 5. In the key of C, that would be a D coming before a G. In the example, the root of the chord with F# in the bass is a D, which is a 2 in the key of C, which goes to a G major chord, which is 5 in the key of C. Are you making a connection yet? Let's keep going.

Since the root of the chord F# / F#-A-D is D, and D is 2 in the key of C, and the next chord is a G major chord, which is 5 in the key of C, what you really have here is a 2-5 progression. Now comes the challenge: How do we fit F# into the number system?

Let's look at the note F#. If you split this note up, you have F and #. Now separately, we know what each of these mean. F is a white note on the keyboard. # means to raise a note 1/2 step. In the key of C, what scale degree is the note F? Correct, it's a 4. So, now what we have to do is make the sides equal:

F# = 4?

The rules of mathematics say what you do to one side, you gotta do to the other side. So, the 4 becomes a #4. We know from our progression that the D major chord with F# in the bass went to a G major chord, a 5. So, what I'm gonna do is add this to the zip code:

7 - 3 - 6 - 2 - #4 - 5 - 1 - 4

Did you see that? Now that it's a part of the zip code, the movement makes sense not only to the ears, but also in theory. Another light bulb moment, lol. I'm gonna add in more later, but let me explain something else that you may have missed here. The D major chord with F# in the bass, has the root D. The note D is definitely in the key of C. So, even though the F# isn't in the key of C, it's root is in the key of C. So, by association, the note F# is temporarily in the key of C.

What I'm saying is this, all of the chords that I call "tweeners" have their root in one of the 7 true scale degrees. So, by association, every note is a part of every key. You don't believe me? Let's look at some more examples:

C / G-C-E
C# / A-C#-E
D / A-D-F

O.K., the first and last chords are clear cut. That middle chord however, poses a problem. Or does it? Just like we did with the D major chord in the previous example, let's analyze this chord and try to make sense of it.

C# / A-C#-E = A major chord

What comes after it? A D, which is 2 in the key of C. In the zip code, what comes before 2? A 6. And in the key of C, what note is 6? That's right, it's an A. So, the last two chords constitute a 6-2 progression. How do we account for the C#? The same way we did for the F#. C is a 1 in the key of C. So, we gotta balance the equation:

C# = 1?

It's a #1. So, let’s add this to the zip code:

7 - 3 - 6 - #1 - 2 - #4 - 5 - 1 - 4

Is it starting to make more sense now? I really hope so. Take a deep breath (WHEW), now let's go on to the final component and cap this whole thing off.

[admin]

Here is a zip code that I've compiled that encompasses every scale degree. I thought about every song, every chord movement, every progression I've ever played in my life and the order that I played the chords in. And hopefully, this zip code will show that no matter what progression you play, it can be explained using the number system. I'm showing it in two ways. You can pick which way you like the best, but they both say essentially the same thing:
Credit Goes To T-Block

Illustration #1

7 - (#2/b3) - 3 - (#5/b6) - 6 - (#1/b2) - 2 - (#4/b5/b6) - 5 - 1 - (#4/b5) - 4 - (b7)
B D#/Eb E G#/Ab A C#/Db D F#/Gb/Ab G C F#/Gb F Bb

This illustration recognizes those scale degrees outside of the major scale as being part of the key. They are almost given as much weight and importance as the regular scale degree chords.


Illustration #2

D#/Eb G#/Ab C#/Db F#/Gb/Ab F#/Gb Bb
(#2/b3) (#5/b6) (#1/b2) (#4/b5/b6) (#4/b5) (b7)
7 - 3 - 6 - 2 - 5 - 1 - 4 -
B E A D G C F

This illustration recognizes those scale degrees outside of the major scale as well, but treats them as temporary breaks, or passing chords as some of you out there are more familiar with.


This is why you can play chords that seem like they are outside of the key, but they sound like they fit. In fact, they do fit because they are tied into the number system. Anytime you go outside the zip code (so you think), you get sucked back in by playing one of the true scale degrees, thus allowing you to stay in key. So, no matter what you play, it's in the number system. Any questions?

I thank God for giving me this idea and for allowing me to share it with you all. Even if you still don't 100% get it, trust me if you stick with it and keep studying and practicing, it will click for you. There are still things I don't understand, so don't feel bad. We are all in the same boat, trying to become better musicians for God, ourselves, and our world. God bless!!!