Machining arcs in the Z axis

I am trying to cut an arc for the radius on a guitar fingerboard and I cannot figure out a way to use the only tool i remember how to use i.e. NativeCAM, I had to walk away form my cnc for the last 18 months so I am way rusty.
Is there any way to cut a 12" radius in the Z axis along the X axis? (I hope I am explaining the correctly), I thought maybe start cutting ever decreasing rectangles form the outer edges and just step up the Z axis gradually until I arrived at the peak but this involves math that I don't know. Is there an easier way to do this?

I have a parameter routine for my A Axis, calculating tool contact point of ballnose cutter, making spheric profiles. As a passionate guitarbuilder, I modified it for your needs. The screenshot shows the offsets. If it doesn´t fit as programmed, you can try to uncomment at the top, G10 L2 P1 R270, to rotate by 90 or 270 degree to swap x and y. and bring it back to standard after. I use normally a 8mm ballnose cutter for that.
The routine starts in the middle of fretboard at highest point, machining the X+ side first, when y going up, a z offset can be applied, on return the real z.
Then the X positions get inverted and the X- part is machined. Living in the metric world, G43 G21 G54 is in the routine.
Test carefully first, if you can use this.

WOW. Thanks, I'm going to try it this weekend on some foam first and hopefully go to wood. I really appreciate the help from both replies. I'm just now getting back to using my machine and this is the first project in a long time

That program worked great, I cant thank you enough I have only used NativeCam and never anything with G code. I had to change to SAE measurements and rotate 270 deg. as per your instructions and it came out perfect. I did get some errors? but no stoppages, I'm not sure what they mean, it didn't effect anything that I can see but here they are if you are interested. I'm using Axis, I'm right at the feed rate limit with my machine and my steppers seem to freeze at higher speeds until warm so I'm thinking that might be where these come from.
They have a bubble with an "i" which does nothing when clicked on and then an "X" box to close.
-0.021103 Step 46.00000
-0.022051 Step 47.00000
-0.023020 Step 48.00000
-0.024009 Step 49.00000
etc.....to step 55

I used debug to show calculated Z and testcounter as info. I deleted that now and i modified the routine and replaced it, now the arc XZ or YZ can be set by parameter, and no more need to rotate. If there is need to make a compound fretboard, like 10-16, i can try to modify, but that will take some time.