Perhaps you've already learned the good old-fashioned "Pentatonic scale" (major or minor versions, it doesn't matter). Perhaps you know you can learn some of "the modes" (of the Major Scale) by adding two extra notes to one of the modes of this scale. If so, you know how quick and easy that is. Which other seven-note scales can we learn by adding two notes to the Common Pentatonic?

I'll assume you know how to find the modes of a scale, so that we don't care about answers that are different only because they're modes of each other. We'd like to know which genuinely different seven-note scales we can get in this way. The answer is related the the subject of my forthcoming book, Spectral Analysis of Scales, which will of course appear on this blog when it's ready.

The analysis in that book suggests that the answer is the "7-spectrum" of the Common Pentatonic, which consists of the following ten scale groups:

I've tidied this up a bit compared with the version in the book, which is generated by an algorithm that doesn't always "interpret" things in the way I'd like (unfortunately there's no way to fix this that I can see without a lot of error-prone manual messing-about). In particular, I've selected what I think is the easiest scale in the group to recognise, not the one the algorithm gives me or necessarily the one that contains the Common Major Pentatonic in root position.

This is quite the collection of scales. Only two are in common use in the West. The scales in the rest of these groups include a large number of Carnatic melakatas plus a lot of very rare and exotic scales indeed. Each one can be approached by adding just two notes to the Common Pentatonic fingerings you already know; they cannot be mastered that way, but this is a good way to start experimenting with exotic scale sounds to see what catches your ear.

Spellings, analysis and CAGED fingerings of all these scales can, of course, be found in Scale and Arpeggio Resources

The Scales in More Detail

Two of these -- the Major and Melodic Minor -- are well-known and need no further introduction.

A further two are what I call the "double blues scales". If we think of the 3, b5 and 7 as the three "blues notes" that are commonly added to the Minor Pentatonic, these shapes involve adding two of these notes together:

• Adding the 3 and 7 to the Minor Pentatonic shapes gives the Chalanata shapes
• Adding the b5 and 7 to the Minor Pentatonic shapes gives the Kamavardani shapes

These might seem unpromising on paper, since they just contain very common blues sounds. Yet many of their modes offer extraordinary combinations of notes and they are, after all, very easy to learn.

Let's look at the remaining ones, re-ordered to bring out some similarities. Here we're looking at adding notes to the Common Minor Pentatonic fingerings, following the same idea as the double blues scales:

• Ionian b5: b2 and b5
• Vanaspati b4: b2 and 3
• Varunapriya #5: b5 and 6
• Ionian #6 (Naganandini): 3 and 6
• Melodic Minor b4: b6 and 7
• Harmonic Minor #6 (Varunapriya): 2 and 7

Considering the b2 to be a fourth "blues note" -- which I suppose it isn't really, but it's certainly an easy note to find and sounds good, used with care, in a blues context -- makes Ionian b5 and Vanaspati b4 very easy to learn.

Learning the location of the 6 then makes the next two (Varunapriya #5 and Ionian #6) straightforward, since the other note is just a familiar blues note in each case. The last two may require a bit more thought, but I would again treat them as a pair, sharing the 7, and I imagine this would make learning them no harder than the others.

These are not all the possibilities: I have excluded scales that contain a long run of three or more consecutive semitones, since they tend to be less interesting to work with. But even given that, we have 70 distinct scales that can probably be learned in a couple of months.