...The best written instructions on the topic I have seen are that the plates tones should be even all over the plate and that the back plate should be somewhat higher in frequency (tap tone) than the top plate (belly).
...The acceptable range is at least 1/2 tone (one half of a full tone difference) and no more than a full tone difference. Anything more or less and the instrument will never be successful (no matter how long you wait!)
...After seven years of learning, building, testing and research... I believe that the following is good solid proved-by-experience advice. A reasonalble goal is thus:
..."When the plates are fully mature (have stopped changing frequency) the back plate should be 3/4 of a full tone higher than the top plate".
... For example, if the top plate is D4 (295HZ) then the back should be 318HZ, that is more than D#4 and less than E4.
...A reasonable survey of both the evenness of the plate tone and the separation between top and back plates can be done with taps from the fleshy tip of your finger (with a lot of practice of course).
... I had reached this conclusion before the VSA (Violin Society of America) national convention held in Portland, Oregon in November 2004. Part of the every two year contest is a tone competetion. About 100 violins were entered by makers from all over the world. Ten instruments were awarded either silver medals (the highest tone award) or certificates of merit for tone. I examined all these winnning insturments and they all had this evenness of the plate tap tones and about this half to a full tone plate seraration. {the same was true for the viola and cello competetion winners too.)
...Just think about this: the best violins entered by the best makers in the world, and only 10% are judged to have a 'good' or excellent tone! Perhaps you would agree with me that there just has to be a way to bring more consistent results than this.}
...Next I examined the appearance winners that did not also earn an award for tone, and they did not have this agreeable plate tuning; so I think that proper plate tuning is an important indicator for a pleasing tone.
...Earlier this year Wade Hassell (owner of Memphis Violins) came be to visit and he shared an interesting book by author Dieter Ennemoser. Dieter has written a book entitled "The Character of Sound" {ISBN 3-907073-32-0} (c) 1990. In this book he reveals (as I understand it) his theory that because our brain hears sounds transmitted through small carbon based bones in our inner ear, sounds that have a symphahetic frequency with the element Carbon at body temperature will be preceived as being more pleasing.
...For instance, he says that among the resonate frequencies of carbon at body temperature are the frequencies of 213.5HZ, 232.5, 242.5, 262, 285, 300, 322, 353.5, 376, and 396.75HZ.
...Now to get parings that are about 1 1/2 semi-tones apart we are left with the frequencies: 213. 5 / 232.5HZ; 262/ 285HZ; 322/ 353.5 HZ for the (Top Plate / Back Plate) combinations.
..Other acceptable pairings would be 188/199HZ; 242/ 262 HZ; and 300/ 322HZ.
The first three parings for plate frequencies, I would suggest, are the most ideal for violins. I did a survey of instruments I had made(of my first 16 violins) as I knew some of the major component frequencies. I also knew which violins played the best and had been purchased for orchestra playing. It was surprising to me how close the above information fitted the real-world results of my own experience. My own instruments that had been particularly successful had close frequency correlations to the frequencies listed above.
...My conclusion is that Mr. Ennemoser is on to something! I recommend that you try to exactly produce these frequencies in as many parts of your violin as possible.to achieve the best results of tone and color.
...With acoustics, the best effect is achieved by exact matching... but close is next best.
...For instance, one of my most successful violins had plate frequencies of 256 top and 280 back. (notice close match to 262/285HZ above). The last violin I made, I achieved 320/352HZ for the plates, 320HZ for the bridge, and 353HZ for the fingerboard and tailpiece. This violin was heard by 70 people in an introductory concert by violinist Ron Kilde and a number of qualified listeners praised the tone they heard. I am persuaded that the plate frequencies of 322 top and 353.5HZ back are ideal, with the 262 top and 285 back frequency a good match too.
...I suggest that the fingerboard and tailpiece match each other exactly and that they should be at one of the above Ennemoser frequencies mentioned, and preferably, also the same as the back plate frequency. The top area of the bridge should match the top plate frequency. ( the fingerboard and tailpiece should match the tap tone of the center of the back plate..)
... I hope this information is helpful. Please feel invited to share your experiences in this area, or ask questions by e-mail.
...For most of the fittings on a violin, the back plate fundamental tap tone seems to be the best goal frequency for a fine sounding instrument. {I try to use 353HZ for the back plate when I can.}