**
Non-musical scales VIII.**

**
Fingering scales by Sápi I.**

My student and friend Zoltán Sápi came up with this scale idea, which fits so well among the non-musical scale exercises that it proves that fact I have always had in mind; Pénzes Metholodogy gives constant inspiration to others to explore and come up with new things in music.

So his brilliant is simple; since non-musical scales is generally for finger independence and mastering alternate picking, the best way to achieve this is generate scales along a logical pattern, and make sure they fingering and string changes. So he came up with the basic idea as well as put a lot of effort in literally creating the scale exercise system. Zoltán, thank you for your work!

I consider the Sápi fingering scales so important that I have included them in Pénzes Methodology (as part of the complex music theory and the non-musical scales sections)

Note!

Unlike in the common language, there is a distinction between combination and variation in mathematics. To always stay clear, I will use the common language expressions.

Given this simple fingering combination...

**1-2-3-4**

...which can be illustrated in other ways, like this

or this (digits):

**0000**

This basic fingering combination can be played on any desired position on the fretboard, at any desired speed. Here comes the question to this; What is the maximal number of variations to these four notes (1, 2, 3 and 4)? Mathematically, the answer is 4! = 24 (permutation without repetition).

You can see whole set of combinations below:

Counting the different combinations, it is really 24 different ways of combining these notes! 24 scale combinations that help with finger independence, at any fret position!

Let's take a look at the concept owner himself playing a combination of 1-2-4-3. He started off at the third fret of the E1 string (but as I mention, you could basically play the combinations at any fret position).

What's the next exercise? The 2-string fingering scales!