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Copyright © 2018 by Wayne Stegall
Created March 15, 2018. See Document History at end for
details.
Table
1:
Equal-temperament
error
for
common
intervals |
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
(1) |
Δnut-average = |
Δnut-string(1) + Δnut-string(2)
+ Δnut-string(3) + Δnut-string(4) + Δnut-string(5)
+ Δnut-string(6)
6 |
String Name |
|
String Number |
|
Δnut-optimal (mm) |
|
Δnut-average (mm) |
|
εnut (mm) |
|
εnut (cents) |
E | 1 | 0.3 | 0.583333 | 0.283333 | 0.754476 | |||||
B | 2 | 0.7 | 0.583333 | –0.116667 | –0.310762 | |||||
G | 3 | 1 | 0.583333 | –0.416667 | –1.110121 | |||||
D | 4 | 0.5 | 0.583333 | 0.083333 | 0.221939 | |||||
A | 5 | 0.5 | 0.583333 | 0.083333 | 0.221939 | |||||
E | 6 | 0.5 | 0.583333 | 0.083333 | 0.221939 |
Figure
1:
Fully
compensated
nut |
Figure 2: Average compensated nut |
(2) |
compensationsaddle =
0.148571 × numstring + 1.58 |
String Name |
|
String Number |
|
Δsaddle-optimal (mm) |
|
Δsaddle-average (mm) |
|
εsaddle (mm) |
|
εsaddle (cents)s |
E | 1 | 1.3 | 1.728571 | 0.428571 | 1.141096 | |||||
B | 2 | 2.1 | 1.877142 | –0.222858 | –0.593670 | |||||
G | 3 | 3.1 | 2.025713 | –1.074287 | –2.863663 | |||||
D | 4 | 1.5 | 2.174284 | 0.674284 | 1.794982 | |||||
A | 5 | 1.7 | 2.322855 | 0.622855 | 1.658141 | |||||
E | 6 | 2.9 | 2.471426 | –0.428574 | –1.141856 |
Figure
3:
Linear
regression
plots
average
saddle
line
through
ideal
points. |
(3) |
compensationsaddle =
0.186047 × numstring + 1.23023 |
String Name |
|
String Number |
|
Δsaddle-optimal (mm) |
|
Δsaddle-average (mm) |
|
εsaddle (mm) |
|
εsaddle (cents) |
E | 1 | 1.3 | 1.416277 | 0.116277 | 0.309669 | |||||
B | 2 | 2.1 | 1.602324 | –0.497676 | –1.326036 | |||||
G | 3 | 3.1 | 3.100000 | 0 | 0 | |||||
D | 4 | 1.5 | 1.974418 | 0.474418 | 1.263122 | |||||
A | 5 | 1.7 | 2.160465 | 0.460465 | 1.225985 | |||||
E | 6 | 2.9 | 2.346512 | –0.553488 | –1.474808 |
Figure 4: Linear regression plots average saddle line through all points except G. |
Figure
5:
Custom
saddle
intonation
shows
little
additional
compensation
for
the
A
and
D strings. |
() |
compensationsaddle =
0.755812 × numstring + 1.23023 |
String Name |
|
String Number |
|
Δsaddle-optimal (mm) |
|
Δsaddle-average (mm) |
|
εsaddle (mm) |
|
εsaddle (cents) |
E | 1 | 1.3 | 0.941859 | –0.358141 | –0.954149 | |||||
B | 2 | 2.1 | 1.127906 | –0.972094 | –2.591049 | |||||
G | 3 | 3.1 | 2.625582 |
–0.474418 |
–1.264044 |
|||||
D | 4 | 1.5 | 1.500000 | 0.000000 | 0.000000 | |||||
A | 5 | 1.7 | 1.686047 | –0.013953 | –0.037163 | |||||
E | 6 | 2.9 | 1.872094 | –1.027906 | –2.739930 |
Figure
6:
Factory
compensation
in
error
by
≈
–0.5mm. |
|
1See related article: Custom Intonation.
Document History
March 15, 2018 Created.