Top plate graduations
Graduations together with arching have a great influence on the resulting tone of the violin.
Graduation patterns
Before you start removing material, you should have an idea what graduation pattern you will choose.
a) membrane - uniform in thickness all over the plate
b) common - the most used system with the central part thicker
c) reverse - thinner in the center
d) spine - thicker along the center line
Each of these patterns has its acoustical qualities, which ideally are matched to the correct arching. It all depends on what sound you want from the violin.
In our violin we will use the common pattern which is also the pattern Stradivari used in many of his violins. This pattern is also best if you need to get the M5 frequency as high as possible.
Measuring variables
During graduation you will have to measure the following criteria:
a) Area thickness You will use the thicknessing caliper to measure the thickness in the area you are working on. See the [[Tools|Tools]] section for a description of the thicknessing caliper.
b) Mode frequencies These depend on the stiffness of the plate. The M5 frequency is the most important. Refer to the section on plate tuning to learn how to measure these frequencies.
330-360 Hz here is the accepted range for the common pattern. It shouldn't be more than the M5 in the back plate.
Look at Fig. 1 which describes how areas on a plate affect the mode frequencies. Therefore, for example, removing material in the central section number 1 lowers both the M5 and M2 frequency.
c) Weight Plate weight influences the ease with which the plate gets excited by the bow. 60-70 grams range for a finished plate with bassbar often considered is ideal. Too heavy a plate doesn't resonate freely enough.
d) Flexing Apart from measuring using instruments, you should also get a feel for how the plate feels in your hands. Flex the upper and lower bouts, twist the plate along its axis, flex the small areas in the bouts.
e) The stiffness index One of the numbers which describe the stiffness, weight and arching is the stiffness index. It really combines the a) and b) into a formula. The formula is (M5 frequency squared) * weight = stiffness index.
The ideal number for the common pattern is 8 000 000 for the front and 14 000 000 for the back {bulls eye}.
For our finished plate it is (333 squared) * 68 = 7 540 452.
Generally, the goal is to create a plate that is as lightweight as possible, while retaining as much stiffness as possible.
Thicknesses
In Fig. 2 you see the averages for 48 Stradivari top plates. The thickness maps are here for reference only so that you have some idea of the real thicknesses. Bear in mind that Stradivari used first rate wood which allowed him to graduate the plates thinner than you probably will be able to.
Graduating
Now you know what to check for, so you can start removing material.
- Put the plate on something soft so that you don't dent the outside surface.
- Use a small thumb plane. Make sure you don't remove too much wood in one place. Make the transitions between areas of different thickness as smooth as possible. Avoid overthining spots.
- Keep checking the variables mentioned at the top of the page. First thickness, then frequencies, flexing, weight.
- Create a table for your measurements, like the one below, to mark your progress.
| Mode 1 | Mode 2 | Mode 5 | Plate weight |
|---|---|---|---|
| 117 Hz | 208 Hz | 401 Hz | 85 gr |
Finishing
- When you start getting close to finished, switch to your scraper and finish the surface smooth.
- Measure again all variables and make a record.
| Mode 1 | Mode 2 | Mode 5 | Plate weight |
|---|---|---|---|
| 94 Hz | 175 Hz | 353 Hz | 72 gr |
The plate is finished for now. The numbers will still change after you have cut out the f-holes and after the bass bar has been added but not by too much. You can now proceed to the Cutting the f-holes.
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