This is a complex question with a simple answer and requires a slight disclaimer. I believe the finish can change the sound of a saxophone so the answer is yes! But, the different color of lacquer makes no difference. I need to say that the following thoughts are the writer's, and there are some that might disagree.
(A good example of different finishes can be found on the Yamaha YAS-82Z)
With that said, let's start with the most common finish – lacquer. Lacquer is a liquid substance that dries hard, protecting the metal of the sax and maintaining its beautiful appearance. Most saxophones are made primarily of brass, and then lacquered. There are saxophones available that do not have lacquer on them known as un-lacquered instruments. The difference between the same model with and without lacquer can be significant.
The raw brass models tend to be louder, have more spread, are free blowing and often referred to as 'jazz horns' due to their sound. The standard lacquered sax will have a more compact, centered sound, with a little more resistance and won't play as loud. Un-lacquered instruments will discolor and lose their initial shine pretty quickly. Many players like the look of a vintage, older sax, and choose this option for the visual appearance, but I do need to caution you that raw brass will oxidize and discolor.
Most lacquer has color added, even on gold-toned brass saxophones. Many manufacturers add darker gold color to the lacquer to increase the rich look and visual appeal of the instrument. The color has no effect on the sound but will increase the thickness of the lacquer needed to cover the brass. A black sax and a gold sax will sound the same if the lacquer is applied at the same thickness. My white lacquered Yamaha alto has a lot of lacquer on it, and the sound is darker and softer overall.
Plated finishes are always a great option to consider. Silver saxophones have a more complex sound, more extreme dynamic range and they blow with more freedom. The sound will be more spread and the tone tends to have more dark qualities at softer dynamics, and then sound brighter when played louder.
Silver will tarnish over time and care of a silver saxophone is more involved. Some people just like the look of the silver and there are manufacturers that add lacquer over the silver to maintain the shine, but you will lose some of the character that silver plating adds to the sound with lacquer over the silver.
Gold plated saxophones are very different. The process involves a coat of silver plating over brass, and then gold is plated over the silver. The combination has an interesting effect on the sound. Dark, big, full, centered but not as spread as silver plated, more resonate yet very free blowing. One minor tradeoff is the extended range known as Altissimo notes. There is something about the gold that seems to focus the sound on the fundamental overtones and limits the high overtones a bit. I have found that even a gold plated neck impacted how high I could play above the written range of the saxophone. There are always tradeoffs. I love the sound and vibration on gold-plated saxophones, but prefer other finish options for more contemporary playing styles and greater access those really high notes.
The same basic attributes apply to the finish on saxophone necks, but to a lesser degree. For instance, I have silver necks on a black lacquered alto and tenor sax. I felt like the all silver sax was too bright for me, but loved the silver plated neck, because it seemed to add a little edge and volume when I played loud.
Another topic altogether is the base metals used, and how that affects the tone, response, volume, and overtones. There are brass, cooper, bronze, nickel-silver and sterling-silver saxophones available.
I hope this helps you understand a little bit about the different instrument finishes. Red and blue may sound the same, but gold-plated and un-lacquered finishes can have a huge difference in the sound of your saxophone.
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Los Angeles based freelance saxophonist Greg Vail is among the most versatile woodwind players on the west coast. His work in jazz, pop and contemporary gospel music spans over 30-years. Greg maintains an active digital presence at www.gregvail.com.