[robbrown451]

Yes that is true and is a common mistake. The keys at the back of the keyboard should all be about equal width to one another, regardless of whether they are black or white.

There is an interesting "fudging" that has to happen, though, because 5/12 is not exactly equal to 3/7 (each of which should be the width of CDE relative to CDEFGAB.... 5 keys out of 12, or 3 white keys out of 7 white keys)

I actually discuss it in detail here (and all the weird ways people mess this up): https://youtu.be/xwKlKcymfDs?t=33

Here is some JavaScript code for calculating where each key should go. You can paste in the final numbers at bottom if that's easier. They start at the left of C (zero) and assume each white key is width of 1:

  var firstFiveWidth = 3/7; // c-e, 3 white keys
  var lastSevenWidth = 4/7; // f-b, 4 white keys

  // assume each of the 5 is equal width at back
  var cSharpMiddle = firstFiveWidth * (3/10);
  var dSharpMiddle = firstFiveWidth * (7/10);

  // assume each of the 7 is equal width at back
  var fSharpMiddle = firstFiveWidth + lastSevenWidth * (3/14);
  var gSharpMiddle = firstFiveWidth + lastSevenWidth * (7/14);
  var aSharpMiddle = firstFiveWidth + lastSevenWidth * (11/14);

  // average width of what a key in first five and a
  // key in last seven should be (then halve it)
  var halfBlackKeyWidth = (((firstFiveWidth/5) + (lastSevenWidth/7))/2)/2;

  var keys = [
    0,
    cSharpMiddle - halfBlackKeyWidth,
    1/7,
    dSharpMiddle - halfBlackKeyWidth,
    2/7,
    3/7,
    fSharpMiddle - halfBlackKeyWidth,
    4/7,
    gSharpMiddle - halfBlackKeyWidth,
    5/7,
    aSharpMiddle - halfBlackKeyWidth,
    6/7
  ]
  console.log("black key width: " + (halfBlackKeyWidth*2*7))
  console.log(keys.map(function(item){ return item *7}))

And here are the numbers I got: ( C to B)

  black key width: 0.5857142857142857
  [
   0,
   0.607142857142857,
   1,
   1.807142857142857,
   2,
   3,
   3.564285714285714,
   4,
   4.707142857142857,
   5,
   5.85,
   6
  ]