In Hill's book about Stradivari's life and work, they mentioned 3 conditions which would lead to good sounding violins: 1. Varnish, 2. Dimensions and construction, 3. Wood. The varnish is the most important. Past research showed us that the main components of varnish were linseed oil and rosin with some suspension particles such as pigment and protein. Many resins commonly used in violin varnish such as rosin, fused amber, mastic, etc. are completely miscible with linseed oil. On one extreme we have a pure oil and on the other, a pure resin. In between the extremes, we have a continuous variation of oil to resin ratio. The long oil length varnish (say oil to resin ratio of 3 to 1), historically called “liquid resin” or vernice liquida, has a consistency of a heavy crème or marmite. Such varnish can be applied without solvent with a stiff brush or palm of your hand as shown by Koen Padding. The short oil length varnishes are solids at room temperature and therefore need to be dissolved in solvent for application. I use both types of varnishes, but prefer vernice liquida in winter to avoid breathing hazardous solvent fumes.
I have worked on many double basses.
Few modern instruments I have ordered white from top maker in China ,
I tuned them, string them and played them for few weeks and them varnished them.
After about one month instrument sounded this same. In my opinion proper vanish have very little effect on the sound.
Sorry for language mistakes – English is my second language
We now realize that the varnish coating which will affect the tone of violin is not the outer colored layer, rather it is under coating or ground coating. There are 2 things related to the "ground":, 1. the wood pore filler, 2. the substances which penetrate into the wood. Varnish will only affect the tone of violin and viola. For the larger instruments such as cello and double bass, varnish serves as an esthetic and protective coating only.