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If all the above is too complex for you, then the following simple rules for violin plates may help a lot: I’m sorry this is a bit ‘teacher’, but it seems appropriate ......
Violin plate tuning
The basics of plate tuning for good violins comes down to the following: the ring tones of both front and back plates of a violin need to be :-
i). matched to each other for a good instrument as follows in Table 1a. This is with the belly, raw, i.e. that is before the ff holes are cut, the bassbar added, and before varnishing :-
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Violin plate
Ring tone (Mode 5)
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Table 1a: belly raw plate
scale note
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Tone characteristics of instrument
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315 Hz
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E flat + 4 Hz
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Student or chamber tone for easy bowing
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335 Hz
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E natural + 5 Hz
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Orchestral tone
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355 Hz
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F natural + 5 Hz
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Soloist’s tone
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and in Table 1b for back plates (and for finished bellies with ff’s cut, bassbar fitted and shaped, and varnished) :-
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Violin plate
Ring tone (Mode 5)
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Table 1b: back plate
scale note
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Tone characteristics of instrument
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330 Hz
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E natural
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Student or chamber tone for easy bowing
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350 Hz
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F natural
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Orchestral tone
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370 Hz
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F #
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Soloist’s tone
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There are no surprises here! The violin’s belly’s ring tone (Mode 5), when first thicknessed should be nearly a semitone below the back plate if plate weights are ‘normal’, which ties up exactly with ‘normal’ violin making practice.
You will need to look at the plate stiffness page for the figures if you are making or modifying violas or small violins.
ii). Then ideally the Mode 2 frequency of each violin plate should also be half the Ring tone or half the frequency of Mode 5. It is quite acceptable to ignore Mode 2 (people have for years!), but if you want to compensate for non-optimal wood pieces then you can use the “effective” Mode 5 of a plate, which takes into account non-ideal values of the Mode 2 frequency of a plate too. If you can, you should try and get Mode 2 to half of Mode 5 frequency, but if you can’t than the following method works well:
For every 9 Hz the Mode 2 is low - relative to Mode 2 being 1/2 of Mode 5 - then the “effective” Mode 5 should be taken as correspondingly low by 6 Hz*.
Example: Question: If a violin belly has a Ring Tone (or Mode 5) of 370 Hz and a Mode 2 of 160 Hz (ideally it should be 185 Hz) what is the equivalent “effective” Ring tone or Mode 5 of this plate?
Ans: To compensate for the low Mode 2: then we know Mode 2 is low by 185 - 160 = 25Hz, so the “effective” Mode 5 of the belly plate is 2/3 x 25 = 17 Hz lower that that actually measured, or 370 - 17 = 353 Hz. This is because if Mode 2 is lower that it should be, then the “effective” Mode 5 is lower too.
iii) . The ‘reference’ weight of each plate is as follows in Table 2: This includes the standard or reference weight of violin, viola and 4/4 ‘cello plates.
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Plate Reference Weights: violin & viola Table 2 modified 20 May ‘10
belly uses relationship: linear dimension (length) ^ 2.53, back (length) ^ 2.31 rel. to 4/4 violin.
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Back Length mm
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Back Length ins.
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Ref. Front or Belly wt. (gms.)
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Ref. Back wt (gms.)
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300 mm (1/2 size)
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11.8”
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41.7
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73.1
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328 mm (3/4 size)
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12.9”
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53.1
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91.1
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357 mm (4/4 size)
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14”
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64.7
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109.3
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387 mm viola
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15 1/4”
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79.4
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131.7
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394 mm viola
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15 1/2”
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83.1
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137.3
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407 mm viola
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16”
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89.6
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147.2
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419 mm viola
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16 1/2”
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97.1
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158.3
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4/4 ‘Cello
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~ 30” (760 mm.)
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438.2
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627.8
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Now, when you have tuned a violin plate to the chosen frequency of Table 1a and 1b, then where a plate’s weight differs from that in the table (as it almost always will), then decrease the Ring Tone or Mode 5 by a semitone for every 24 grams the plate is too heavy relative to the reference weight in Table 2 above.
This is the same as decreasing the Ring Tone or Mode 5 by 0.8 to 0.9 Hz for every gram the plate is too heavy once you are at the ring tone of Table 1. This applies to both the violin front (belly) and the back plates. Or if you were to take “1 Hz for every gram” you would not be far off!
Example: Question: If a full size (4/4) violin belly has a Ring Tone (or Mode 5) of 370 Hz and a weight of 80 grams, how much should I reduce the tap tone by to make it suitable for an “Orchestral” toned 4/4 violin?
Ans: The belly is 80 - 64.7 = 15.3 grams too heavy , relative to the Reference plate weight. So I need to get the ring tone down by 15.3 x 0.8 = 13 Hz, to 370 -13 = 357 Hz. So I need to reduce the thickness of the belly plate (or reduce the height of the bassbar a little if you have to) to get a tap tone (Ring or Mode 5) of 357 Hz **.
The same calculation applies to the back plate: it too should have a ring tone suited for an Orchestral-toned violin.
........... And that’s it!
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* This is the result of Dr. Harris’ work.
** The effect of reducing both Mode 2 and the decrease in plate weight has been taken into account here too.
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