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Probably the most important reason that there are so many more 2 piece backs is that the lumber for the back is usually quarter sawn, i. e. the log is cut into pie shaped pieces lengthwise along the grain. Therefore you'll never have more than half the tree's width to work with. Most often quarter sawn boards are not wide enough to create a one piece back. Sometimes though the lumber is cut in slabs lengthwise and if the board is wider than a violin it can be used to to create a once piece back.
Some people say that the one piece backs sound deeper or darker, but I don't know if this is a valid generalization. I would think that the quality of the particular boards involved and the skill of the luthier contribute more to the way the violin will sound than whether the back is made of one or two pieces.
I can say that I have a FM Soloist and they have (or at least the one I have) a one piece back and I like the way it sounds -- usually. I do like the way a one piece back looks better than 2 piece backs though, because the flames run uninterrupted across the back.
A positive attitude may not solve all your problems, but it will annoy enough people to make it worth the effort. ~Herm Albright

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I am doing research to build my own mandolin. I am NOT an expert or authority. In Mandolins the tops are made from 2 book matched pieces of some kind of spruce. The reason for book matching is to have a uniform distribution of close grain at the center line and wider grain at the edges where flexibility is desirable because the belly has to vibrate to produce the sound. If you think about it, that is probably true for violins.
It would appear that a one piece back might have a non uniform distribution of grain widths that might emphasize either the treble or bass side of the instrument depending on grain distribution. A book matched back may well repeat in the back the even distribution of grain widths and provide a more neutral response across the range of sound produced in the instrument.
I am aware that in some mandolins the wood of the backs is often pieced to produce artistic patterns and this piecing may use different kinds of hardwood to produce the look. This doesnt answer your question but you might find the info interesting.
Octave Ray

Honorary tenured advisor
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Rob C said
I've wondered that myself. Some violins i've seen that say one piece back still have a seam in the middle and the grain doesn't seem to line up like it should. I would have thought that was 2 pieces?
If it has a seam and the grain doesn't match that's definitely a 2 piece back.
A positive attitude may not solve all your problems, but it will annoy enough people to make it worth the effort. ~Herm Albright

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What I have heard is that it takes a very skilled woodworker to make the flames match up. I wonder too if it takes more wood to make the match? It would take an older tree to get the width of wood a person needs to make a back from a single board.
Here is my Berty - notice that the flames line up towards the lower end but as they move up don't quite line up.
Violinist start date - May 2013
Fiddler start date - May 2014
FIDDLE- Gift from a dear friend. A 1930-40 german copy, of a french copy of a Stradivarius. BOW - $50 carbon fiber. Strings - Dominants with E Pirastro Gold string.

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Schaick said
What I have heard is that it takes a very skilled woodworker to make the flames match up. I wonder too if it takes more wood to make the match? It would take an older tree to get the width of wood a person needs to make a back from a single board.Here is my Berty - notice that the flames line up towards the lower end but as they move up don't quite line up.
It could be that it's the viewing/photograph angle. The chatoyance of the wood will vary by angle, so it takes looking at several different angles to get a feel for it. Also, one side's matching stripe may appear to go "in" while the other side's appears to come "up" even when they are perfectly aligned.
A violin's back is also carved, so the further the cut deviates from the central plain the more chance there is for mismatch. An ideal mismatch requires a very consistent piece of lumber where the flame has a regular periodicity.

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You guys are a wealth of information! Thank you everyone for the awesome responses. It's so fun to see the different opinions and experiences people have.
I'm really unable to hear a difference between the two, but that might be because my ear is still pretty untrained. As I've improved in my playing, I've gotten the chance to experiment with both types, and although some people really prefer one over the other, I imagine most of it is cosmetic preference.
I'm just starting to look into dipping my toes into the luthier world as well, and it's been very interesting to study that from a maker's perspective as well. Uzi, your information was super interesting from that angle.

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@Fiddlerman You are the first man - other than my husband to say those words to me!!!
Violinist start date - May 2013
Fiddler start date - May 2014
FIDDLE- Gift from a dear friend. A 1930-40 german copy, of a french copy of a Stradivarius. BOW - $50 carbon fiber. Strings - Dominants with E Pirastro Gold string.

Schaick said
What I have heard is that it takes a very skilled woodworker to make the flames match up. I wonder too if it takes more wood to make the match? It would take an older tree to get the width of wood a person needs to make a back from a single board.Here is my Berty - notice that the flames line up towards the lower end but as they move up don't quite line up.
It is very easy to get the grains to match up. The wedge of wood is cut through the middle and then folded out. This is called book matching.
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