In this article you are about to discover a different approach to the tonal music theory which will make learning musical principles about 50 times easier. I claim that what would take you weeks or months using the traditional approach will reduce to mere hours using my system. By using my method, you will be able to play any chord progression in any key with only very little need of actual learning. This may sound impertinent, but you can very easily verify that yourself, since this wouldn’t take you much time. I don’t suppose any preliminary knowledge, except that you are familiar with the names of intervals (such as perfect fifth or major third), most common scales (such as major and minor) and that there is something called “chord progressions”.

If you are used to call notes A, B, C, …, G, you can easily fall into the illusion that classical (and most of the modern) western music is based on whole steps and half steps, i.e. that you build scales (such as a major scale) by successively adding whole steps or half steps. It is not quite so; in fact, western music is based on perfect fifths. Let’s start with the note F; what note is the perfect fifth above it? It’s C. And above it? G. And so on… By stacking fifths, you get the following sequence:

Did you notice anything interesting? By starting at F and adding perfect fifths, we got all the notes of the C major (or A minor) scale. This is not a coincidence. Any major scale can be built so that you take one fifth below the tonal center (F below C in this case) and five fifths above the tonal center (G D A E B in this case).

So, to form a G scale, we would simply start with G and include one fifth below it and five above. However, until now, we haven’t given any name to the perfect fifth above B, so lets extend our “vocabulary” first. The traditional approach is to start anew and call it F again, but with a sharp sign. The next is called again C, but again with a sharp sign, and so on:

What should we do with the left side? Let’s call the perfect fifth below F B♭, then E♭ and so on (we now repeat the same sequence from the right):

The names we’ve chosen (using sharps and flats) may seem a little ad hoc, but the logic behind this naming will be explained later. If you don’t believe me that these all are indeed fifths, you can convince yourself by playing the notes on your instrument. What should come after B♯ and before F♭? Another copy of F C G D A E B with something called a double sharp sign (x) and a double flat sign (♭♭):

So, we know how to call the notes, but what is this all good for? As I have said, a major scale can be formed by taking one fifth below to tonal center (by “tonal center” I mean the “base” note of the scale, i.e. C in C major) and five fifths above it. So what happens if we start with G as our tonal center? By looking at the line above, you see that one fifth below it is C, five fifths above it are the notes D A E B F♯. Put together, the G major scale consists of

Similarly, if we start with, say, A, we obtain

Now, if I tell you to tell me the notes of A♭ major, you shouldn’t hesitate; just look at the line and read seven notes starting with the one on the left of A♭:

This itself may be quite useful, but we still did not get to the real purpose, namely that chord progressions are determined by their relative position to the tonal center in the line of fifths. For example, C – F – G is what would traditionally be called the I – IV – V progression (or tonic, subdominant, dominant, and this is the most common progression in western classical music). Notice that F is on the left of C, G on the right. The same pattern applies to any other key; for example, in the key of G the same progression would be G – C – D (by “the same” I mean it would sound completely the same, just a little higher or lower). In the key of A♭? The same! One left, one right, or A♭ – D♭ – E♭ (just look at the line; the segment above suffices).

What about the I – vi – ii – V – I progression (also one of the most common chord progressions)? In C major, this is

(m denotes that the chord is minor, since the chords at the vi and ii degrees of a major scale are minor). By looking at the line you can see that at first you actually jump three letters to the right and then return “stepwise” back to C. This has to be the same in all keys, so in G, this leads to

(Remember, you start with G in the line and jump three times to the right and then return “letterwise” back). In A♭:

Cool, we know how to find these chord progressions in any key when we look at the line of fifths. The problem is… Usually when we play there’s no line of fifths to look at. How to solve this problem? Rename the notes.

The ultimate solution

This may sound harsh, but what I actually want to do now is to rename the notes (that is, to write different symbols instead of A, B, …, G). In fact, it isn’t such a big deal; it took me about half an hour to learn to name all the piano keys using the new names with certainty. So the rule is:

C = –2 in the new notation. What are the notes of C major?

And what about, say, B = 3 major?

Naming notes of any key becomes trivial. But in fact, it is not the notes in a key what matters, the important thing is what is their function. Every note is determined its relative position to the tonal center. I shall denote this position by +n or –n, for example, 1 is +1 of 0, 5 is +2 of 3, –3 is –1 of –2 and so on. The tonal center itself will be denoted by +0. What does it mean in terms of chord progressions? For example, the progression I – IV – V can be written as +0 –1 +1. In 0-major this means 0 –1 1, in 3 major this means 3 2 4, in 7 major this means 7 6 8 etc. Minor chords and other types of chords can be indicated using m or another traditional symbols. For example, we can write

for the usual I – vi – ii – V⁷ – I progression.

The point is that once you learn how to play chords using this naming system on your instrument, you know how to play any chord progression in any key. For example if you know how to play chords –10 major, –9 major, and so on, –10 minor, –9 minor and so on, on the piano (its actually quite simple; it took me only one evening to learn how to play chords from –10 to 10 (both major and minor) on piano instantly (although I am a guitarist and I hadn’t known the fingerings until that evening; if you are a pianist, you just have to remember where are the notes in this naming system)). For example, just after one evening of training with no previous knowledge, I was able to play the I – vi – ii – V progression (i.e. +0 +3m +2m +1) in all keys, because it’s trivial. Want to start in 2 major (E major)? Just play the chords 2 5 4 3 2 (or more precisely 2 5m 4m 3 2). In 4 major (F♯ major)? Play 4 7 6 5 4. In –6 major (A♭ major)? Play –6 –3 –4 –5 –6. How long would it take take to you to learn these progressions using the traditional letters? Just compare:

If you don’t already remember them, the letters appear completely random. This is exactly the reason why many musicians are able to play well in one key and are completely lost in another key. Using numbers… there’s nothing to remember. Everyone can count to ten.

Melody and chromaticism (where are the sharps and flats?)

You may now say “Well, that’s all nice, harmonies are simple, but what about melodies? They must become utterly complicated to think about.” This, in fact, is not really the case. Lets start by explanation, what the flats and sharps really are: ♯ simply means +7, ♭ means –7. For example, F = –3, so F♯ = –3 + 7 = 4. Similarly, B = 3, so B♭ = 3 – 7 = –4. This explains the traditional notation. We can just write any value using A, B, …, G (that is, the values from –3 to 3) with enough sevens added or subtracted (notice that x (double sharp) is just +7+7, i.e. +14).

This explains also the staff notation. We chose the lines and spaces to denote notes from –3 to 3 in melodically ascending order. If we want to denote a note outside this range, we simply do that by adding or subtracting seven from a note (we write a sharp or flat sign in front of it). Luckily, this note is melodically always in the place where it should be, that is, F♯ lies between E and G. So, when you know the numbers of the notes on the staff, reading sharps and flats shouldn’t be a problem, –3♯ is just a way to write 4, –2♯ = 5 etc.

Have you ever been taught that flats tend to “move down” and sharps tend to “move up”? This has a deeper reason. There’s a rule that applies very often:

Finally, return to the problem of melodies. How does, for example, A major look like written melodically? It’s

This is not really that hard if you know the whole/half-tone structure of major scales, namely that it is WWHWWWH. Whole tone up is +2, half tone up is (inside a scale) is –5. You can therefore read the scale as +2 +2 –5 +2 +2 +2 –5. This applies to any scale. If we choose C major, we get

This isn’t really harder than to learn A B C♯ D E F♯ G♯ A or C D E F G A B C.

Other types of scales

When you denote non-diatonic scales such as the whole tone scale, double-diminished scale and other exotic scales, the notation gets messy because it is based on the diatonic scale. However, it is only the notation that’s problematic, the line of fifths has no problem with such scales. For example, the whole tone scale is created by stacking whole steps, that is, +2. So C = –2 whole tone scale would be –2 0 2 4 6 8 (that is, C D E F♯ G♯ A♯). Similarly, double diminished scale is created by alternating whole steps and half steps. Half steps in the context of a scale are the closest possible, i.e. –5. For example D = 0 double diminished scale would be 0 2 –3 –1 –6 –4 –9 –7 (D E F G A♭ B♭ C♭ D♭). Notice that the letter D appears twice, but no such irregularity occurs in numbers.

We also haven’t discussed the minor scale until now, but it is also quite simply. By looking at the A minor scale, we can see that a minor scale is created by taking four fifths below the tonal center and two above, so, for example, G = –1 minor scale is –5 –4 –3 –2 –1 0 1 (i.e. E♭ B♭ F C G D A). Harmonic and melodic minor are exactly what is denoted in the traditional notation. For example, A melodic minor is A natural minor (i.e. –3 –2 –1 0 1 2 3) with F = –3 and G = –1 raised to F♯ = 4 and G♯ = 6, that is, the whole scale is –2 0 1 2 3 4 6. You can see that this scale has “gaps”; it doesn’t contain 1 and 5. The effect of these gaps is that this scale is not stable, it tends to return to the A natural minor scale.