Understanding the Number System

[T-Block]

Hey LGMers, ya boy T-Block is back at it again. Even though I've been stressing the importance of the number system for a long time, there is still some of you out there who don't quite get it. I understand your frustration, and I think I've found a way to finally shed some better light on this concept known as the Number System.

There is a certain scenario that I keep seeing from some posters who are trying to learn theory and apply it to their playing, but something doesn't quite make sense. That scenario goes a little something like this:

random poster: "How come I see musicians playing notes outside the key, but are still in key?"

my response: "Even though those musicians are playing notes outside the major scale, they are still playing in key."

random poster: "Oh, I see. That makes sense."

But do they really get it? I've wondered this so many times. If this scenario sounds like something you've done, raise your hand? LOL, just kidding, but really I never really went into detail and explained how and why playing those notes outside the major scale still keep you in the key.

Well, I believe the Holy Spirit has revealed a way for me to explain this in a way that should make sense and give you that "light bulb" moment on your way to understanding the number system.

O.K., now most of you out there have seen my post(s) on basic music theory. In those posts, I told you about the musical zip code: 3-6-2-5-1. In other posts, I've also extended this zip code to include all the scale degrees of the major scale: (7)-3-6-2-5-1-(4)

If you can recall, I also made a series of posts called Explaining Progressions. In one of those posts, EP #3, I sort of explained the scale degrees that were in-between the scale degrees. I called them "tweeners". These are the scale degrees like #4, b7, #2, etc. What I've failed to do was connect the two ideas together. Well, hopefully this post is gonna bridge that gap. Let's get it started!!!

[T-Block]

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.

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, these are just the basic names for these intervals. They get more specific when you alter the second note in an interval. That's where you get stuff like major 3rd, minor 6th, diminished 7th etc. Here is the link to more info on intervals: http://www.learngospelmusic.com/forums/index.php/topic,30189.0.html

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

[T-Block]

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 so u can compare: http://www.learngospelmusic.com/forums/index.php/topic,34778.0.html

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".

[T-Block]

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. Here is the link: http://www.learngospelmusic.com/forums/index.php/topic,33036.0.html

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.

[T-Block]

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:


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!!!

[SisterCM]

Wow!    Thank you this is just awesome and really breaks the number system down to a level were everyone should understand it.  Again thank you for all your help. 

[asley]

Thanks for writing in such a simple way. I will try it and think it will help me out.I was looking for such simle tutorial and now I get it here. Thanks once again.

[christopher77]

I like this music.

[allonesound]

this is really good! thanks

[rayjohnson83]

Man, I wanna be like you when I grow up..

[Bronzee]

Me too...!   

[doorway]

Love it! If I'm understanding correctly, you just keep going thru the musical zip code until you get to the right chord.

[T-Block]

Love it! If I'm understanding correctly, you just keep going thru the musical zip code until you get to the right chord.

That's the basic gist of it. Once u find certain progression that you like, just memorize them and use them whenever you want.

[pilotprogram]

T-Block

Yeah, you cleared up a matter that I had a couple of months back in regard to the famous 1-6-2-5-1 progression.  Still new with progressions I was wondering why the 1 was followed by the 6 but not the 4, 7, and 3 then the 6,  2, 5 and to the 1.  I now see you can skip the 4 to the 7  to the 3 of your MUSICAL zip code to get to the 6 from the 1.  You can treat the skipped parts as passing chords to one's discretion.  My own light bulb moment.

Thanks.  This is truly a masterpiece.

 

[T-Block]

That's it sir, you got it.

[floaded27]

I totally get ur explanation, as there are many different ways to present this. In a nutshell, any diatonic chord can follow any other diatonic chord (chords composed only of notes within the key sig). Its good to know the cycle of fourths (zip code) and presents opportunities to fill in passing chords, but it can be a bit confusing to think of every simple progression as some jump around that.

Going from the 1 to the 2 should be just that, not 1-4-7-3-6-2, but leave all the middle out. It should be the other way around. the zip code should show u what u can stuff in there, not what was left out. Kinda defeats the purpose of a simple progression.

I think the tricky part comes when trying to explain things outside the key signature, basically how do we play complex chords with notes outside the key sig, as well as chords with a root outside the signature, and what KIND (quality) of chords are they??

And here's where i think ur on the money. You gave an excellent starting point.

Here's another. You can also use different modes of a key, and borrow chords from that, since it has the same key center. The most common one being the Aeolian mode......which is, yes you guessed it, the natural Minor scale.

So using our example of the key of C
1 (C maj)
2 (D min)
3 (E min)
4 (F maj)
5 (G maj)
6 (A min)
7 (B dim)

We can also call upon our friend the C minor and borrow chords from there.
1 (C min)  - changed chord quality
2 (D dim)  - changed chord quality
b3 (Eb maj) - new chord
4 (F min)  - changed chord quality
5 (G min) - changed chord quality
b6 (Ab maj) - new chord
b7 (Bb maj) - new chord

Now since we are BORROWING these chords, you shouldnt go OVERBOARD with them, but it can be the case that they can be permanent parts of the song progression rather than just simple passing chords (for those writing songs) we encounter many songs that do just that with that b7 chord.

Now in theory we can do this with the 5 other modes (we already just showed Aeolian (minor) and start out with Ionian (major)), but dont do too much otherwise you'll sound a mess, kinda like the guy that tries to shove in like fifteen passing chords between every progression. there is a thing as too much!!!

I'll stop here as not to overwhelm, but leave open for additions, comments, questions, etc.

[T-Block]

Going from the 1 to the 2 should be just that, not 1-4-7-3-6-2, but leave all the middle out. It should be the other way around. the zip code should show u what u can stuff in there, not what was left out. Kinda defeats the purpose of a simple progression.

If u do it that way, then you're not following a "system" anymore. A system should be something you can use everytime to show or explain something. That's why I did it this way, more so u can get a visual. I totally get what ur saying tho.

[floaded27]

If u do it that way, then you're not following a "system" anymore. A system should be something you can use everytime to show or explain something. That's why I did it this way, more so u can get a visual. I totally get what ur saying tho.

i thought the number "system" was the fact that each interval in  the scale can be assigned a number, and each had certain properties (and thats the part we use every time to show and explain) not that it had to "follow" a specific order or pattern. But like i said there's so many different ways to explain it. I've read different books, visited different sites and talked to different people, and almost all had a different spin on it. I guess its whatever way makes more sense to you. There are many nuances that many view differently, which i think also influences style of play as well.

[T-Block]

Well, at least as I understand it, it's a system for tonicization. The whole idea of coming up with numbers in the first place in the classical days centered around getting back to one using the chords that had the strongest pull. Nowadays, it's pretty much whatever u want it to be. I'm just attacking it as it originally was developed and implemented.

I could be wrong as well. If anyone can correct me, feel free.

[floaded27]

Your right in that certain chords have a stronger pull to particular chords/roots than others and they settle better. That was the original idea. But with the progression of musical styles, that doesnt quite hold in its strictest form. The idea back then was to pick chords that created the greatest sense of resolution and least tension. The thing is, sometimes u WANT that tension (remember at one time diminished chords were TABOO because they did just that, create tension).

But i guess as one gets advanced, they'll learn how to build and release tension with the chords they choose. of course there's an art to it (weird because art and music are separate subjects in school. lol). Personally my views and conceptualization of the whole system evolves and adjusts as i continue to move beyond the basics, and attempt to explain within the realm of the system the  "out of the box" stuff i encounter. (Often time the abstract players have NO music theory, so they cant explain it, so ur forced to do so to the best of your ability)

Yes its all about the tonic. And we know that the strongest pull is to the 4th, with the second strongest to the 5th. But sometimes we dont want the strongest, sometimes we want to avoid the 1. However u do that, or experience it done may shape ur musical concepts.

By no means am i saying ur wrong or trying to diminish (no pun intended) what you have posted. I actually expanded on my theory with ur method and have additional ways to present concepts which is always a great thing. This stuff can be simple and so deep all at the same time.