Non-musical scales X.

Fingering scales by Sápi III.

 

This section contains Sápi fingering scales that have a range of three strings.

 

 

The three strings give a total number of 81 variations (34). Combining these with the standard fingering 24 combinations will have a result of 81 x 24 = 1944. However, the variations that only involve one or two strings will be deducted from this number (we have 3 one-string variation, and 3 x 14 = 42 two-string variations), so to get the final number we will use the following formula: 81 - (3 + 42) = 36.

36 variations where all three strings are used, combined with the standard 24 fingering combinations, and the result is 36 x 24 = 864.

 

Let's see what we've got so far:

I have copied here how Zoli Sápi calculates the number of variations. Although it is a very much different calculation, the end result is still the same.

 

...The four notes can only be distributed on the three strings in a way where there will always be a string that has two notes on it. To calculate the number of these occasions, we need to use the following formula:

 

 

where

  • n = 4

  • k = 2

Thus 4! / 2! * (4 - 2)!) x 3 =18. And since the remaining two fingers on the other two strings can be interchanged, we need to double it: 18 x 2 = 36. This is the number of variations for four fingers placed on three strings, on consecutive frets.

This 36 variations need to be multiplied by the 24 fingering combinations, that is 36 x 24 = 864. In the below charts, the same colors mean same picking technique in a given scale group. All scales are played with alternate picking...

 

2-1-1 scales

 

2210

 

2120

 

2102

 

1220

 

1202

 

1022

 

2201

 

2021

 

2012

 

0221

 

0212

 

0122

 

1-2-1 scales

 

1120

 

1210

 

1201

 

2110

 

2101

 

2011

 

1102

 

1012

 

1021

 

0112

 

0121

 

0211

 

1-1-2 scales

 

0021

 

0201

 

0210

 

2001

 

2010

 

2100

 

0012

 

0102

 

0120

 

1002

 

1020

 

1200

 

What's the next exercise? The 4-string fingering scales!

www.music-instrument-guitar.com - Non-musical scales X. - Fingering scales by Sápi III.

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