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All the above is complex.
Try the following much simpler rules for violin plates. I hope this will particularly help those making their first couple of violins. [Note: Completely updated 14th-30th March 2011]
The basics of good violin plate tuning comes down to this.
The violin plates measured here have low moisture content at about 6%, which is normal for wood in a heated workshop in winter. All Mode 5 frequencies should be set 15 Hz lower with 12% moisture content (MC) when plates are tuned in summer:
(1) The Mode 5 ring tones of both front and back plates are by far the most important characteristics of the violin plates as far as defining what the violin will sound like and how playable it is.
The dynamics of the violin are from the belly of the violin, and power comes from the back1, in each case how much the plate ‘rings’ and what frequency it is at.
(2) The Mode 5 ring tones of back and front then both need to be between 300 and 370 Hz. If they are not in this range then you will have to start again. The back should have a ring tone equal to or greater than the front.
However, under some circumstances, when you know what you are doing, the back may be up to a semitone (+ 6% in frequency) higher than the front, but there is a risk that the strings will ‘saturate’, the tone be too aggressive and some notes may be unplayable.
This is just what Carleen M. Hutchins recommended 30 years ago, and more modern measurements and work have shown her conclusions were sound.
(3) To get a violin that will sound and play superbly then the picture or figure right will help 1: click on it.
What this shows is that if you want to make a ‘Solo’ toned violin you will need to make plates with ring tones matched in the range 340 to 365 Hz.
For an ‘Orchestral’ tone you need to match them between 330 Hz and 340 Hz.
For a ‘Student’ toned violin you will need to have a back at about 335 Hz, and and a belly plate at about 320 Hz - it will be easy to bow and a delight for chamber and pub music. Note that a (quite ‘poor’) belly with a low Mode 5 can be matched to a back with a higher Mode 5 to make a very good (student tone) violin.
On the figure/picture given above the Mode 5 ring tones of back (frequency read off along the bottom ‘X’ scale) and the Mode 5 ring tone of the front or belly (read off on the vertical scale) need to fall within the green / brown / purple ‘box’.
The 3 diagonal lines from top right to bottom left are the points where back and belly plates have an exactly equal Mode 5, or differ by a semitone.
Outstanding ‘Solo’ instruments’ have plates with Mode 5’s falling in the upper purple area.
The figure/picture applies to finished, varnished plates with ff-holes and bassbar in place.
Making pates from scratch
Cutting the f-holes on a belly reduces the Mode 5 by about 2 semitones (2 x 6%, about 38 Hz), but the original Mode 5 frequency is then restored to the same (or to a slightly higher frequency) by installing the bassbar.
The belly plate Mode 5 frequency then increases when it is varnished, but note the back increases hardly at all. For a belly, both Modes 2 and 5 go up by about 5 to 8 Hz as the varnish hardens, so just make them a little low on the Mode 5 ring tone when hollowing out the belly before you cut your f-holes.
(4) The Mode 2 frequency of each violin plate should also be at or just below half the Mode 5 or ‘Ring tone’ frequency. Having Mode 2 any higher than this serves no purpose and increases its weight. A low plate weight is a VERY GOOD THING.
If you want to compensate for poor wood pieces with too low a Mode 2 (i.e stiffness across the plate) then you can be brave and put 5 spruce ‘straps’ across the belly from side to side 1 to 3 mm high, 6 mm wide. For a back plate put a maple patch ~3 mm thick (which can be layers of veneer) right across the central area and then thin it to set Mode 2.
Mode 2 is not nearly as important to a violin’s tone as Mode 5, so just set it at half of Mode 5 using the techniques I show on the arching and thicknesses page. Unfortunately Dr. Nigel Harris’ work gives too much importance to Mode 2: just set it to half Mode 5 and forget it.
(5) You can compensate for any heavy plate (and most amateur plates are too heavy!) by treating it as if it has a higher Mode 5 than that measured: just add on 5 Hz for each 10 grams it is too heavy!
So say a finished belly has a tap tone of 330 Hz but weighs 80 grams: it is 15 grams heavier than we would like (see Table 2 below for standard reference weights for plates). So it behaves in the violin as if it has a tap tone of 330 + 1.5 x 5 Hz = 337.5 Hz. The same is true for heavy backs.
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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You will need to look at the plate stiffness page for the figures if you are making or modifying violas or small violins.
........... And that’s it!
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1 Footnote: This model is derived from Alonso Moral’s paper of 1984, which links the plate Mode 5 frequencies directly to the main body resonances, and also to the data published on Patrick Kreit’s website that gives the ‘deltas’ between these (A0), A1, B1-, B1+ body resonance’s we should look for in a first rate violin. You will need to get Patrick Kreit’s book to get more details.
2. Contact me for the diagrams for other A1 body mode frequencies.
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 "Viable violin plates locus, A1 = 467 Hz, smll2")
