The last colour study gave me an idea.  But before I can try it, I need a selection of browns and greys I can use.  Because previous studies have focused on over-dyeing, I needed to do some colour mixing.  

I looked at previous studies, both those done with thickened dye and in the bucket, and selected nine different ratios of red : yellow : blue that showed the potential to result in a neutral.  I knew that different combinations of primaries would give different kinds of neutrals.  I also knew that some ratios would be more likely to result in a neutral than others.  

Once I started, I also became fascinated by the effect of changing the relative strength of the dye concentrates themselves.  This is something I've experimented with before but this was an opportunity to explore it more thoroughly.  Sometimes this could make the difference in whether I achieved any neutrals at all.  

Above is an example of what I mean.  These three sets all used the same primaries (scarlet, golden yellow, royal blue in this case).  In the one on the left the relative strength of the dyes was 1:2:3 (weak red, strong blue); the middle set is 2:2:3 (strong blue); and on the right, 2:3:2 (strong yellow).  Not in this picture, I also did a set of 1:1:1 (equal strength) for each set of primaries.  The same dyes, the same mixing ratio in each row, different relative dye strengths.  Once I'd finished, I found that the ratio of dye strength most likely to give neutrals, for any combination of primaries, was either 1:1:1 or 2:3:2.  

In the picture above, each row represents a different mixing ratio of red : yellow : blue.  In this case, the primaries were scarlet, lemon yellow and royal blue.  I started with nine different ratios but gradually eliminated those that rarely resulted in a good neutral so that by the end I was using just six.  In the best cases, any of these six could give a neutral.  But across all the combinations of primaries I tried (six in all), the most reliable mixing ratios proved to be 3:2:1,  2:3:1 or 3:3:2 - i.e. the third, fifth and seventh rows in the picture above.  

And the best combination of primaries?  Scarlet / Golden Yellow / Royal Blue produced warm neutrals and has a bias towards green.  Or Scarlet / Lemon Yellow / Royal Blue, which gives much cooler neutrals and has a bias towards blue.  Magenta or Scarlet / Golden Yellow / Turquoise were also good, but only if you strengthened the yellow so that it could stand up to the turquoise. 

Unsurprisingly, the worst combination from this point of view was Magenta / Lemon Yellow and either Turquoise or Royal Blue - which both yielded a lovely range of violet (above).  So the next time someone tells you that mixing all three primaries together will result in "mud", challenge them to try it with those three.  And if they challenge you, strengthen the yellow and mix in a ratio of either 2:3:1 or 3:3:2 and it's possible to get a grey - a blue-grey but still grey.