In this section I assume that you are already familiar with elementary concepts such as that there are basically only twelve different tones (in various octaves), that there is a certain interval between any two notes (for example that between C and E is the interval of major third, that is, the interval of four half steps, but you don’t have to remember particular intervals; I only assume that you are familiar with the concept), and that there are various scales (it is enough to be acquainted with C major and A minor).

Suppose somebody told you that should create a scale that would produce nicely sounding melodies. How would you go about it? There are two natural conditions for such a scale:

• You don’t want clusters of two or more half steps in a row (Like A, A# and B), because they are “too close”, they blend too much together
• You don’t want gaps, i.e. a jump of 3 ore more half steps (like between A and C), because you would loose continuity

Those two conditions are actually very restrictive and there are only four possible scales that meet them, the major / natural minor scale, the minor melodic scale, the whole tone scale and the double diminished scale. If you impose the following natural criterion, there will be only two remaining possibilities, the major/natural minor scale and the melodic minor scale:

• You don’t want the scale to sound the same all the way around, i.e. after playing some notes of the scale, you should be able to recognize what scale it is. In other words, the fact, that a piece in the key of C doesn’t start with the note C shouldn’t mean that there is no other way to recognize that the piece is in C.

If you consider the whole tone scale, for example, it sounds the same whatever tone you start with, and is therefore too “vague” to create understandable melodies.

The diatonic scale

The most consonant, purest interval after the octave is the perfect fifth. If you play an interval of perfect fifth (say, C and G), the impression is almost as of one tone. The perfect fifth (e.g. G) only supports the base tone (i.e. C), it doesn’t add any tension or mood. The reason for this is that the frequencies of tones that establish the perfect fifth are closely related; their ratio is 3:2 = 1.5, or at least approximately – in the equal tempered tuning (which is prevalent today), the ratio is just very close to 1.5. For example, the standard middle C has frequency approximately 261.626 Hz, the G above it has frequency 391.995 Hz and their ratio is 391.995/261.626 = 1.498 (almost exactly 1.5).

If we start with F and add perfect fifths, we get C, G, D, E, A, B (the next fifth would be F#), or, written alphabetically, A B C D E F G. In other words – you can produce the whole diatonic (that is, major or natural minor) scale just by adding consecutive fifths from some tone. You can now probably understand the diagram on the right. It shows the tones of the C major (or A minor) scale. We start with F and add perfect fifths, obtaining C, G, D, A, E, B, and then we stop. That is, all black lines represent the perfect fifth. The red line is actually not the perfect fifth; it is the diminished fifth, or what is called a tritone (because it is exactly the interval of three consecutive whole tones).

A little interlude about the minor and the major scale is in order here. What you see on the right actually reveals the structure of these two scales. The A minor scale contains with A two fifths above it (E and B) and four fifths below it (D, G, C, and F) and this is what matters. Every minor scale “around” some tone (called root) contains two fifths above it and four fifths below it. Similarly, every major scale contains one fifth below the root (F in the case of C major) and five fifths above it (G D A E B in C major).

Now, I would give you a task. You should write the tones of the major scale around G. How would you achieve that? You just have to rotate the heptagon one step to the right, so that there be actually only one fifth below G and 5 fifths above G. Simply raise F by a half step to F#. This causes two things. The tritone between B and F extends to the perfect fifth whereas the perfect fifth between F and C shrinks to the tritone. And that’s exactly what we wanted – by rising the upper note of the tritone, the red line (the tritone) moves clockwise and we get exactly the major scale structure around G (one fifth down, five up) or the minor scale structure around E (two fifths up, four down), respectively. The next step shouldn’t be surprising:

You should now be able to name all the scales in the image above; remember the major scale structure – one fifth below, five fifths above. What is the third one? That’s exactly D major (one fifth below – G, five above – A, E, B, F#, C#). What is the fourth one? Well, it isn’t very surprising. It’s A major.

As you can see, be adding sharps we “move” the heptagon clockwise. Can we go in the opposite direction? Consider again the C major scale. If we flatten B, the tritone again extends to the perfect fifth, but the new tritone appears between B (flat) and E. By adding flats, we move counterclockwise:

Well, if you have ever been wondering where does the order F#, C#, G#, D#, … and Bb, Eb, Ab, Db, … come from, you don’t have to wonder any longer. Again, you should quickly see the names of the major and minor scales – the second one is F major, the third one Bb major and the fourth one Eb major.

Structure of the major and the minor scale

(to be continued)