How I work My final analysis ot this outline
ANALYSE OF A GUITAR OF ANTONIO STRADIVARI
Measurements in px
horizontal measurements
maximum width of the lower part LB
pp'
246
maximum width of the rose
aa'
70,7
maximum width upper part UB
qq'
194,7
minimum width of the middle part MB
ee'
157
vertical measurements
length body and saddle
PQ'
440,1
length of the body
PQ
402,1
length tangency
OQ
73
length tangency
PM
84,2
length tangency
PN
234,3
bridge
PMbr
80,1
length
NQ
167,9
length
NQ'
205,9
Surface relations
possible ratios for the relation between the width (pp’) and the length PQ and PQ’ (including the table saddle)
pp'/PQ
0,612
pp'/PQ'
0,559
The quotient 0,612 matchs the ratio 8/13= 0,615
The quotient 0,559 matchs the ratio 5/9 = 0,555
But a better relation can be found. Actually we notice that :
pp'+qq'
440,7
pp'+ee'
403
and we find these ratios even more relevant
pp'/pp'+ee'
0,610
pp'/pp'+qq'
0,558
it appears that the both length PQ an PQ’ equal the sum of the widh pp’+ ee’ and pp’+qq’
Other relations in the length
The bridge (distance PMbr) is set with a ratio ⅕ of PQ
PMbr/PQ
0,199
The waist (N) is set by a ratio 5/7= 0,714
NQ/PN
0,717
The ratio 5/7 sign the use of number (fig left) or the use of a square (fig right)
Relations in the width
The quotients 0,791 et 0,806 recall the ratio 4/5=0,8
and the quotient 0,287 matches the ratio 2/7= 0,285
qq'/pp'
0,791
éé'/qq'
0,806
aa'/pp'
0,287
the first idea is to retain a simple proportional serie
the width (pp’) minus ⅕ = the upper bout (qq’) minus ⅕ = the waist (ee’) In this case the measurements are:
pp'
qq'
ee'
real measurements
246
194,7
157
theoritical measurements
246
196,8
157,4
An other possibility worth to be study if we pay attention to the ratio 2/7 which give the measurement of the rose. In this case qq’ and ee’ simply result of the first ratio by a division two and five implying the ratio 1-1 and 2-3 (fig left)
pp'
qq'
ee'
real measurements
246
194,7
157
theoritical measurements
246
193,3
158,1
And the end, a division in 14 would allow to set all these measurements with the same unit part. (fig right)
This solution solution present the advantage to correspond to what we know of the rules of the “symmetria” as they are smartly illustrated by the Henri Arnault de Zwolle luth drawing of the XV° century.
The design give us the opportunity to underline one more time the role played by the serie of numbers of the harmonique section approximation (relation between the square and its diagonal). These ones corresponding to musical ratios of the harmony unisson, octave, fourth and fifth.