I think the following codes may work well:

ContourPlot[f[m1, m2], {m1, 100, 1150}, {m2, 100, 920}, ContourLabels -> All,

Axes -> False, Frame -> True,

FrameLabel -> {"\!\(\*SubscriptBox[\(m\), \(\(1\)\(+\)\)]\)(GeV)",

"\!\(\*SubscriptBox[\(m\), \(\(2\)\(+\)\)]\)(GeV)"},

ColorFunction ->ColorData["GrayTones"],

(*ColorFunctionScaling->False,*)

PlotRange -> {Full, Full, Full},

Contours -> {0.55, 0.65, 0.75, 0.8, 0.85},

BaseStyle -> {FontFamily -> "Times", FontSize -> 24},

ImageSize -> {500, 500}]

Richard's suggestion is a nice suggestion. Here is another take by creating your own color function that makes use of "GrayTones".

myColorFunc[x_] :=

colorRange[3.33333 x - 1.8333] /.

colorRange -> ColorData["GrayTones"]

ContourPlot[(2 + Cos[x^2 + y^2]) 0.85/3, {x, 0, .9}, {y, 0, .9},

ColorFunction -> (myColorFunc[#1] &), ColorFunctionScaling -> False]

I created a function that has a max around 0.85 and a min around 0.55. over the plotting range.

Thanks for the answers ..

But, both of you are suggesting that I should include 0.55 and 0.85 into my plots ... but I do not want that ... the range of my function might be 0.6 to 0.8 ... I just need to change the range of the inbuilt color functions from [0,1] to [0.55,0.85]

Change the ColorFunctionScaling to True, this scales your plot colors values from 0 to 1.

Furthermore ColorFunctionScaling should be automatically set to True when you use ColorFunction so Brian's suggestion should work just fine!

Usually I directly include ColorFunction->(ColorData["colorset"][a+b#]&) in the plot options.

where a and b are set in order to obtain the desired rescaling of the color range. With the same system you can make the color scale non-linear by using different functions. Take care that for # varying between 0 ad 1 the function stays between 0 and 1 too.

I think you can just include this in the options:

ColorFunction -> (ColorData[{"ThermometerColors", {0.55,

0.85}}]), ColorFunctionScaling -> False