Without yellow, a range of greens or oranges cannot be mixed. A yellow that is close to the primary yellow is essential. In fact, there is no true primary color when it comes to pigments, as impurities will be present, no matter how small. Check many yellow pigments and a few will have a "bias" of one kind or another. This could be a "golden yellow", possessing a little brown or orange, or a lemon yellow, which leans slightly towards green, as it has a sharp acidic quality.
Looking at oil paints, there are several different types of cadmium yellows. There is cadmium yellow (dark), which is almost red in tone; simple cadmium yellow, which looks almost orange, and then cadmium yellow (light), which is a rich yellow hue. You can also find Lemon Cadmium, which is a sharp bright yellow. I find Cadmium Yellow (Dark) to be redundant for an artistic palette and I prefer Cadmium Yellow (Light). This color has a sharp and rich quality that is very close to the primary yellow.
Lemon Yellow is also a very useful color, as this yellow is more acidic in quality and is perfect for mixing greens. Cadmium yellow (pale) is the ideal color for rendering bright sunlight and golden lining in clouds. When mixed with small amounts of burnt sienna and white, an effect approximating Neapolitan yellow can be achieved. Lemon Yellow is the ideal color for showing sunlit lawns and unripe fruit. Both of these yellows cover the yellow spectrum, from warm to cool yellows.
Daffodils contain a lot of lemon yellow, as do the leaves of immature apples and saplings. Cadmium yellow (pale) can be found in the heads of dandelions, clay pots and sunlit paths.
Since both yellows possess different characteristics, each behaves differently when mixed with other colors. When lemon yellow is applied as a thin glaze, it has little effect on the color underneath unless applied to a pale surface. For this reason, lemon yellow is ideal for glazing techniques. Cadmium yellow (pale) is more concentrated, so you need to add a little linseed oil to create a thin glaze.
Artists may find many other yellows when looking through paints that I personally find redundant. These are: yellow ochre, a dirty yellow-brown; Neapolitan yellow, a creamy tan; and bismuth yellow, a pale greenish-yellow.
A more useful yellow that might be worth exploring is South Sand Yellow, a bright pure yellow and lemon cadmium. Some other yellows that might be worth trying if one wishes to expand the palette are Indian Yellow, a rich, bright yellow, and Chrome Yellow, a slightly cooler but still rich yellow.
Lemon Yellow is more transparent in nature than Cadmium Yellow (dark), so it needs a little white to give it coverage. Cadmium Yellow (light) is heavier in consistency and therefore has better coverage intensity. Since it is slightly orange, it is not the best yellow counterpart for clean green blends. However, it is well suited for warm greens and oranges. Adding cadmium yellow (pale) to Cadmium Red or Big Red Lake produces a rich orange-red color. Adding a little burnt Sienna to this yellow produces a golden yellow.