#1
Numerical Notation / "Jianpu"
What it is and why it's useful


Introduction

Numerical notation, also known by the Chinese term jianpu, is a way of representing a scale or chord in reference to the Major scale. Since everyone knows the Major scale in and out, this notation will provide one with a simple way to illustrate interval relationships. It is also extremely popular on this forum, making its knowledge essential in properly communicating musical ideas with us. The notation sometimes goes as far as to manifest rhythm and octave. This is not necessary in our purposes, and is very outdated.

Before reading this post, you should already know about the Major scale, and be capable of constructing Major scale for any root. Similar knowledge of the Minor scale and chord construction would be appreciated, but no further knowledge is required. I hope it's an easy read. If you have any question, please feel free to post.

The Basics

This is what the Major scale looks like in numerical notation:
1 2 3 4 5 6 7

The number 1 represents the 1st note of the Major scale. The number 2 represents the 2nd note of the Major scale, and so on until the 7th and last note. In C Major, 1 would represent C, 2 would represent D, etc. This can be shown visually very simply.
1 2 3 4 5 6 7 <-- Numerical Notation
C D E F G A B <-- C Major scale


The Minor Scale (A New Perspective)

The Minor scale can be represented with this notation by using familiar symbols to modify the notes in the Major scale. Here's what it looks like:
1 2 b3 4 5 b6 b7

The best way to understand this is with an example. First, note that the E Major scale is E F# G# A B C# D#, and and the E Minor scale is E F# G A B C D. The notation says to take the 3rd note, the 6th note, and 7th note, and flatten them a half step, as instructed by the flat symbol (b) in front of each of those notes.
1 2 b3 4 5 b6 b7
    ^      ^  ^
    |      |  |

The result of the process, when performed on the E Major scale, is E F# G A B C D, the E Minor scale! Thus, one can use the numerical notation for the Minor scale to convert a Major scale into its parallel minor. This diagram represents this process with the E Major scale, and the familiar product:
E  F# G# A  B  C# D# <-- E Major
|  |  |  |  |  |  |
1  2  3  4  5  6  7  <-- Numerical Notation for the Major scale
|  |  |  |  |  |  |
1  2 b3  4  5 b6 b7  <-- Numerical Notation for the Minor scale
|  |  |  |  |  |  |
E  F# G  A  B  C  D  <-- E Minor


Those of the Harmonic and Melodic Flavors

The Harmonic Minor scale is the Minor scale with a raised seventh. In numerical notation, the 7th of the Minor Scale is a b7. When one raises it, it becomes just a regular 7 again. Therefore, the formula for the Harmonic Minor scale looks like this:
1 2 b3 4 5 b6 7

One could say (and it is often said) that the 7th of the Harmonic Minor scale is borrowed from the Major scale. By using this notation, it becomes apparent that they do in fact share a 7th.

The Melodic Minor scale is the Minor scale with a raised sixth and a raised seventh. By the same logic, its formula is as follows:
1 2 b3 4 5 6 7

It can now be seen that the Melodic Minor scale and the Major scale differ by only one note. That is the 3rd.

Numerical notation allows one to put all things in a common perspective, as seen by the above two examples.

Triads

This section assumes the reader's knowledge of chord construction.

The basic triads have an intuitive representation in numerical representation. Recall that all of the the four basic triads (Major, Minor, Diminished, and Augmented) contain the root, a third, and a fifth. In numerical notation, they also must contain the root (1), some 3, and some 5, be it natural, sharp, or flat.

The Major triad is the most straight forward. I believe it to need no explanation:
1 3 5

If you wanted to find the notes of the A Major triad, simply pick out the 1, 3, and 5 of the A Major scale: A, C#, and E.

The Minor triad is similar:
1 b3 5

If you wanted to find the notes of the A Minor triad, pick out the 1, 3, and 5 of the A Major scale, and lower the 3 by one semitone, as the notation says. It's easy to see that the Minor triad is the root triad of the Minor scale in this notation:
1 2 b3 4 5 b6 b7 <-- The Minor scale
|    |   |
1   b3   5       <-- The Minor triad


As a matter of fact, a scale is "minor" if and only if it contains a b3. Similarly, it is "major" if and only if it contains a natural 3.

The formulas for the Augmented Triad and the Diminished Triad are not hard to follow either. The Augmented Triad does introduce a sharp into the mix, however.
1 b3 b5  <-- Diminished Triad
1  3 #5  <-- Augmented Triad


Conclusion

The purpose of this post was to explain the notation. Obviously the depth is in its applications, not the notation itself. If you read around the forums here in MT, you'll notice Numerical Notation everywhere. I wrote this so that I could link to it in the event that someone does not understand the notation when I'm trying to explain a concept to them. Again, if you have any questions or comments, you are free to post.

-Eastwinn
i don't know why i feel so dry
#2
Nice post!

I like the idea of universal-key notations instead of describing everything as it relates to the C major scale.

Here's a notation that's similar in that it's universal-key, yet it goes further in that it's not based in particular on the major scale. Noteheads are not used for timing and are empty or solid depending on if the interval from the tonic is quartal (based on ascending fourths) which is solid, or quintal (comprised of ascending fifths) which is empty. The tonic notehead is empty if the tonic triad is major (major key) and solid if it's minor. It repeats every octave, with lines at the 1, 4 and 5 positions (the 4 and 5 lines are spaced half a notehead's thickness apart to achieve an octave-periodic staff for easier reading).


#3
^ Interesting and effective, but a little much to get used too. Things would be a whole lot better if a notation was used in the first place that was independent of key.

If you're working with twelve-tone technique, there's always the so called "integer notation" where the notes are numbered 1-11, starting with whatever you want it to start on. It's certainly a lot less confusing when you write your tone row done to use numbers instead of #'s or b's and what have you.
i don't know why i feel so dry
#4
Right, for non-tonal music, it's easier to use a numbered chromatic notation instead of trying to hammer everything into heptatonic terms.
#6
Quote by griffRG7321
Or suck it up and use standard notation


And deal with its C major bias, increasingly hairy key signatures, transpositional complications, lack of octave-equivalent uniformity, and needless clefs instead of orientational ease? Thank you much, but I'll pass.
#7
Quote by Dodeka
And deal with its C major bias, increasingly hairy key signatures, transpositional complications, lack of octave-equivalent uniformity, and needless clefs instead of orientational ease? Thank you much, but I'll pass.

I have to ask, with your hate of standard notation... what do you NORMALLY use? Or is it like having an abusive boyfriend that you hate but can't leave?
#8
Quote by DiminishedFifth
I have to ask, with your hate of standard notation... what do you NORMALLY use? Or is it like having an abusive boyfriend that you hate but can't leave?


I probably spend more time playing around with alternative notations than standard, though it's pretty difficult for anyone to get out of the "abusive" ( ) relationship with standard notation when it's, well, standard. Pretty much all (non guitar-specific) music literature uses it, so there's little escape.
#9
Quote by DiminishedFifth
I have to ask, with your hate of standard notation... what do you NORMALLY use? Or is it like having an abusive boyfriend that you hate but can't leave?




"haters gunna hate standard notation"
Gear:
- Ibanez RGR465M
- Ibanez S770FM
- PRS SE Custom
- Blackstar HT-5 Mini Stack
#10
Quote by Dodeka
And deal with its C major bias, increasingly hairy key signatures, transpositional complications, lack of octave-equivalent uniformity, and needless clefs instead of orientational ease? Thank you much, but I'll pass.


The more you read music the easier all those things become. It's not the end of the world because the notes don't repeat on the same line/space in octaves. It takes a few weeks of reading music to get past that.
#11
Quote by griffRG7321
The more you read music the easier all those things become. It's not the end of the world because the notes don't repeat on the same line/space in octaves. It takes a few weeks of reading music to get past that.


I'd rather keep the need for a mithridatic learning approach to a minimum.
#12
Quote by Dodeka
Nice post!

I like the idea of universal-key notations instead of describing everything as it relates to the C major scale.

Here's a notation that's similar in that it's universal-key, yet it goes further in that it's not based in particular on the major scale. Noteheads are not used for timing and are empty or solid depending on if the interval from the tonic is quartal (based on ascending fourths) which is solid, or quintal (comprised of ascending fifths) which is empty. The tonic notehead is empty if the tonic triad is major (major key) and solid if it's minor. It repeats every octave, with lines at the 1, 4 and 5 positions (the 4 and 5 lines are spaced half a notehead's thickness apart to achieve an octave-periodic staff for easier reading).





I really like that.
Quote by Night
wtf is a selfie? is that like, touching yourself or something?
#13
I really don't see either of those other methods as a viable alternative to standard notation, though.
Although it is worth noting that numerical notation is used alongside standard notation in the form of figured bass.
#14
Quote by Dodeka
I'd rather keep the need for a mithridatic learning approach to a minimum.


It's hardly a poison though, and the more you direct hatred towards standard notation the less inclined you are to see the better side of it.
Gear:
- Ibanez RGR465M
- Ibanez S770FM
- PRS SE Custom
- Blackstar HT-5 Mini Stack
#15
Quote by ArpeggiateTHIS
It's hardly a poison though, and the more you direct hatred towards standard notation the less inclined you are to see the better side of it.


Hey! I've already made huge concessions in that I used to be 100% in favor of chromatic notations. It took me a while to realize the importance of a heptatonic notation given the huge amount of music that uses that sort of structure (it'd be silly to have to use a top-heavy chromatic notation for tonal music). All I did was dispense with the bits of standard notation I didn't like.
#16
Numerical notation is not necessarily an alternative to standard, it's just useful for expressing intervals over ASCII text. I can't be bothered to use an image editing program every time I want to post something on here, and being specific with notes sometimes isn't appropriate.

Numerical notation is for general forms. There are tons of different ways you can have a major chord on standard, but one in numerical, 1 3 5. So when someone asks what a Minor b6/9 is, I can say 1 b3 5 b6 9 instead of saying "oh well a Cmb6/9 chord is C D Eb G Ab" or "A minor triad with a minor sixth and a major second added." Both are different ways of saying the same thing, and each way has its own benefits.
i don't know why i feel so dry