How to calculate consistent shades of gray (gray-100 through gray-900) from custom color?

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I'm working with a template based on Bootstrap. The .scss variables for grays are as follows:

$white:    #fff;
$gray-100: #fafafa;
$gray-200: #f7f7f7;
$gray-300: #e8e8e9;
$gray-400: #aeaeb2;
$gray-600: #5d5d66;
$gray-700: #393944;
$gray-800: #23232f;
$gray-900: #171724;
$black:    #000;

The 'bootstrap' light and dark values are based off of these colors:

$light:     $gray-200;
$dark:      $gray-900;

I am changing the color scheme and would also like to change the light and dark values to different grays even though they're not TRUE grays. I'm assuming that in order to do this well I will want to change all of the shades of gray to shades of this color.

The dark color I would like to base this on is: #393E3C

What is the best way to go about calculating the new shades? Thanks!

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