Guitar Fingering For Music Performance (Page 3 of 4) in pdf

index - middle

results in different measures depending on the strings in-

volved.

Locality is deﬁned as follows: given two positions p

and q in input, locality

= α (

), where

fret

α is a factor that depends on the technical skills of the

performer and the height of the strings over the ﬁnger-

-6

-5

-4

-3 -2 -1

0 1

3 4 5

delta fret

board. A suitable value we have found after preliminary

test of the implemented model is α = 0.25, so locality

index - ring

ranges over [0, 8.5] (8.5 = 0.25 (17 + 17)). The local-

ity factor accounts for the fact that playing at higher frets

is itself harder than near the head of the ﬁngerboard: go-

ing from the 1 to the 17

fret, strings are progressively

more raised from the ﬁngerboard, the which increases the

-6

-5

-4

-3 -2 -1

0 1

3 4 5

related difﬁculty deriving from pressing higher fretted po-

delta fret

sitions. E.g., pressing a string raised 0.2 centimeters from

Figure 4. Example of the contribute of Fret Stretch to

the ﬁngerboard, at the 12

fret, is harder than if the same

the WEIGH function for the ﬁnger pairs index-middle and

string is raised 0.05 centimeters, at the 5

fret: the local-

index-ring.

ity factor is also motivated by the pedagogical literature

which usually prescribes beginners to start playing at the

ﬁrst frets, because they are considered more comfortable

, which assumes negative and positive val-

fret

and less tiring. Moreover, for less skilled musicians, fa-

ues, according whether the movement goes towards the

miliarity with the ﬁngerboard notes decreases while going

body of the instrument or the head of the ﬁngerboard. It

away from the head of the ﬁngerboard.

is important that this distance is directed, because reposi-

ACROSS difﬁculties. Across difﬁculties depend on

tioning the hand in the direction of higher frets is easier

only one factor, which measures the difﬁculty deriving

than the opposite: so the easier direction provides positive

from the vertical distance between ﬁngered positions. Gi-

differences, while the hardest direction provides negative

ven two positions p and q, deltastring =

string

differences. Fret stretch is a function of delta fret, in that

is the difference in terms of intervening strings between

it measures the difﬁculty for a given delta fret and ﬁn-

two positions. Vertical stretch is the measure of the dif-

ger pair. In Figure 4 we show two simpliﬁed fret stretch

ﬁculty due to a given delta string for each ﬁnger pair.

measures for the pairs

and

index-middle

index-ring

Also for vertical stretches we deﬁned a comfortable span.

Both diagrams are restricted to the signiﬁcant part of the

Given the lesser contribution of vertical distance to the

delta fret (complete diagrams would go from -17 to +17).

overall difﬁculty, we have assigned ACROSS difﬁculty a

Also, the two diagrams exhibit the same shape, by show-

range in [0.25, 0.5]. We assign 0.25 points in the case the

ing a predictable minimum (0.5) which is a low positive

delta string is a comfortable span, 0.5 otherwise. We have

measure that is assigned when the distance between the

a comfortable span between close ﬁngers (e.g.,

index-

two ﬁngers is the comfortable span. The comfortable span

) when delta string is 0 or 1; between not adjacent

middle

is the distance at which two ﬁngers can press their re-

ﬁngers (e.g.,

) when delta string is 0 or 3, and

index-ring

spective positions with a minimum effort: such transitions

for the pair

when delta string is 0 or 4.

index-little

are thus encouraged by the assignment of a low weight.

Simultaneous positions. WEIGHT accounts for the

The Figure 4 (case

) shows that we have a

index-middle

difﬁculty of playing simultaneous positions in a chord as

comfortable span between close ﬁngers working on close

well as the difﬁculty of playing notes in succession. For

frets, while the comfortable span between

index-ring

example, the ﬁngerings for the C Major chord displayed in

is reached when ring ﬁnger presses a position two frets

Figure 3 may be composed by the ﬁngered positions in the

higher than index, thus delta fret being 2. Instead, if the

Table below, so that the weight of each different ﬁngering

comfortable span is exceeded, a larger effort is required

is the sum of the weight between each two positions, i.e.,

to perform the transition between p and q: this is the case

(C3,G3), (C3,C4), (C3,E4), (G3,C4), (G3, E4), (C4,E4).

of delta fret wider than 1 for

, and delta

index-middle

fret wider than 2 for

; in both these cases the

index-ring

note: C3

note: G3

note: C4

note: E4

fret stretch measure is 2. The two diagrams also show

<5, 3,3>

<3, 0,0>

<2, 1,1>

<1, 0,0>

the higher difﬁculty for the negative directions. Finally,

<6, 8,1>

<5,10,3>

<4,10,4>

<3, 9,2>

the two diagrams are simpliﬁed in the sense that the fret

<6, 8,1>

<3, 0,0>

<4,10,3>

<1, 0,0>

stretch also takes into account the direction over strings:

when the two ﬁngered positions are on the same fret, it

Respectively, the three ﬁngerings listed (each row depicts

expresses the preference for higher ﬁngers to press lower

a possible ﬁngering for the chord displayed in Figure 3)

strings

, which is the relaxed formulation for a binary

yield the overall weights 7.5, 34.25, 17.75: each one con-

constraint enforced during the chords ﬁngering [7]. This

stitutes the weight of a vertex in the graph, and is then used

to compute the difﬁculty to reach the next graph entry, be

Recall that we start numbering ﬁngers from index, and strings from

it a chord or a single position.

E treble.

Guitar Fingering For Music Performance Page 3

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