Note: this is a rather technical post, it will probably be interesting only for people who also use pencils professionally. But feel free to read on.
I often get asked what boxes of pencils I use. The answer is "mostly Caran d'Ache" but not in a box.
I do have the remnants of a very old box I got as a teenager. But based on my drawing habits and experience I now use my own "box" mixed from all the colours I know will work for me.
The comment about light point to the fact that I used my two lamps, one with cold, one with warm light, this of course affects colours in a photo, I use both to try and get the colours as right as possible.
I would recommend to everyone, even seasoned artists to buy James Gurney's excellent book "Color and Light"
It offers the best of tools to understand, or to revise all the notions of colour theory, in a way that won't seem boring or too complex. You can also find the information on his blog, but the book is handy to have at hand.
Now the "problem" for me is that in the book all the colour schemes and tools are based on oil painting mixtures. I mostly work with pencils, inks, and some other similar mediums, but none that can be premixed on such a level.
You can of course make a palette of pencils based on a specific gamut, but you will bump into a problem if you need to tone down a colour. You can't mix a grey colour adapted to the gamut. Your only option with pencils is to mix things on the paper.
As James Gurney explains very well, the ideal mix of greys, will be the ones you obtain with the primaries of your chosen gamut. This is something you can't do with pencils, there is a variety of greys (I've shown a few on the photo above), but it will be hard to match them.
To tone down you colours, you're better off trying to layer complementaries, or as I often do use watercolours.
Here too I apply the choices I am explaining here. In both cases the "exception" are the browns, I rarely use them but it can be handy.
Now the main thing I want to explain here is why I find it better to discard two types of pencils. The ones I call "pure colours" (primaries in the larger "YURMBY" sense) and the ones I call "pre-mixed colours"
If you refer back to James Gurney's system, the "YURMBY" wheel, the "pure" colours are the ones that are on the outside of the wheel, before they are toned down.
The "pre-mixed" colours would be the ones that are very much toned down and usually give a very muddy result when used in layers. One example would be the "olive" crayon, it's a pre-mix. It's fine for kids who just want a lot of different colours, but if you need this it's best to mix it yourself
In short, it’s best to use colours that will fit in the intermediary layers of the YURMBY wheel, not too close to the edge or you’ll have to mix too much, and not too much towards the center or you’ll loose the choice to guide your colour where you want it to go.
As pointed out there are exceptions, I use browns sometimes, but not often. Brown as such isn't even a colour, in a drawing you will have to use a mix of greys and light colours to give the impression of a brown colour. It's hard to explain but it's a sort of illusion a trick for the eyes.
With pencils you have to consider the number of layers. My rule is usually under four layers you won't get a good enough result, but there is also a maximum, that will depend on cases, but after 5 or 6 layers, things will often start to go really wrong.
I will end this here, if I get the time and if there is some interest I might go further into the use of layers.