Tip: Are you a non-native English speaker? I have just finished creating a 
Web AppSince I have written a post on quick interval naming, the name of this post may suggest some redundancy. However, in this post, we shall explore a completely different approach (that I have developed). The point is to memorize the following three orders of the letters A, B, …, G:
| Second [horizontal] order | Third [vertical] order | Fourth [diagonal] order | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| … G A B C D E F G A … | … A F D B G E C A F … |
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By memorizing, I mean being able to tell the letter before and after every letter in each sequence. The visualization above makes it easier because you just have to memorize what lies in the → ←, ↑ ↓, and ↗ ↙ directions from a particular letter. This visualization is also ‘consistent’ in the sense that going ↑ and → is the same as going ↗.
The point now is to know how many flat or sharps the scale you are in has. Although you may not have realized it, if you memorized the three orders, you already know the order of sharps and flats; it is exactly the same as the fourth order: Bb, Eb, Ab, Db, … . For sharps, we just go from the other side: F#, C#, G#, E#, … .
Once we know how many flats or sharps the scale we are in has, we just have to remember this information when using the orders. The A major scale, for example, has three sharps, i.e. F#, C#, and G#. So when we are in A major, above A would be C#, on the right of F# would be G# etc.
Harmonic progressions
Once you remember each order and the sharps or flats of each scale, it is trivial to name any degree in any scale because they correspond to the following positions:
| III | IV | |
| VII | I | II |
| V | VI |
In other words, II is →, III ↑, IV ↗, V ↙, VI ↓, and VII ←. For example, A major has 3 sharps: F#, C#, G#. From the three orders, it is easy to fill in the following table:
| C# | D | |
| G# | A | B |
| E | F# |
However, this is not the main thing this approach is good for. The most important application are the relative motions. Every one of the six directions has a certain feeling associated with it. For example, when I moves to VI (e.g. C to Am), the impression is very similar to IV moving to II (F to Dm) or IV moving to IV (Am to F) because it’s always ↓ (we will not consider seventh chords, voicings etc. in this post to keep things simple).
Of course, the feeling depends on many other factors, including voicings and the actual scale degrees, but the main, underlying feel stays very similar. Below, I try to describe the feel of every motion; nevertheless, it is not possible to really describe the feel—you have to learn it through listening.
| ↗ | Very strong, direct, full of motion. |
| ↙ | Very strong, direct, somewhat opposite of ↗ |
| ↑ | Very weak, almost melancholic, in some voicings not perceived as a harmonic motion at all. |
| ↓ | Stronger than ↑, naturally flowing into the next chord. |
| → | Quite direct, but somewhat dull when used twice or more in a row. Weaker than ↗. |
| ← | Somewhat dull, not usable in many situations. |
If you write sheet music, this is really all you need (when it comes to knowing the chord names in your harmonic progression), because if you write a triad from a particular note, the quality of the triad is already determined by the key signature.
However, if you play the chords on an instrument (such as a guitar or a piano), you also have to know the quality of the chord (whether it is major, minor or diminished). Of course, it would be possible to derive some rules for that, even if you don’t know at which scale degree you are, but I strongly recommend that you learn how the scale degrees are related to each other, e.g. that ↓ from IV leads to II, so that you always know “where you are”. It is not, however, necessary to memorize it; if you improvize, you will naturally start “feeling” the scale degrees and their relations after a while.
