Margaret,
I suppose it depends a lot on the surface and type of black fabric it is, the kind of light it is in, as well as what other colors might be around it.
Some fabrics are shiny, others very flat. A black cotton T-shirt is a very soft surface and does not reflect much, compared to black satin, which is shiny and very reflective. Also, is the light warm or cool? Not all blacks are the same in color, either. Some blacks are bluish, others are made from a deep red. (That is why some black fabrics get pinkish if bleached or as they fade.) Sometimes this underlying local color shows, other times not.
So you must try to see the colors in the black. Coming from me, it may sound strange but if you are having a problem seeing anything but black and grays, try scanning a photo and in Photoshop (or the image editor of your choice) boost the saturation to the maximum; you will then exaggerate the colors. You might start to see violets or reds in the black, or depending on the lighting, maybe blues or even greens. Now of course, if you are working from life, you will have to just look hard. You can always count on other strong colors to reflect their color onto others.
When painting from life, another trick I use is to look at the flesh tones as a guide for the colors of my painting. I look in the reflected light on the skin under the chin: is it warm or cool? Also, look at the highlight on the skin: is it bluish or yellowish? I simplify it like this: if the highlight is yellowish, my shadows will lean toward purples. (Complement of yellow.) And if my highlights are cool or bluish (as they are in north light most of the time), then my shadows will be warm. (Orange is the complement of blue.) It is easier to see these colors on white or the light skin tone than on the black, but if you use this as a guide when painting the black, it will help. If the highlight on the skin is bluish then you can't go too wrong to paint all the highlights bluish. If the shadows are warm, then paint all the shadows warm. Now this is simplified, since any number of things can affect the light and shadows to make this completely wrong, but it is a start. Also I could also give you a bunch of formulas (mix this and that to make blacks), but that would not cover all situations; in fact it would only cover one situation at best.
Another piece of advice, or rule, I was given once (and soon disposed of) was never use a black at all and mix all your darks from other colors. Now it is true that you can get black from mixing dark reds and blues, or dark greens and red. But I figure if Sargent could use Ivory black, I can too, and I just mix colors with it to further warm it or cool it as needed.( Ivory black is already a cool black.) I hope I helped, but really there is no secret that covers all cases and all types of black fabric.
Just as a guide, I try to give you the most common case I run into. Since the lighting in my studio is a cool light, many times I encounter the same situation, so I mix blacks the same a lot. (Of course this is a starting point, since as I said, all fabrics are not the same.) I use Alizarin, Ivory Black and maybe some Viridian in the darkest areas; of course the mix varies. In the highlights, I use Cerulean Blue or Ultramarine - again, it depends on the fabric. Again, I use the colors in my skin tones as a guide. I might neutralize the colors on soft fabrics with a mix of Burnt Umber and white added to this mix to make a warm gray. Sometimes, I find I just cannot get the color I want in a single application of paint. Sometimes, if the black is very deep, I start with a deep complement to the final color, then glaze the final color over it. This is true of other dark colors as well. For a dark burgundy I may start with a dark brown in the darkest areas, and then use the local color over that. I may even use Raw Umber in place of Ivory black, depending on the black.
I don't know why, but I always set out to answer these questions yet end up with a very long post and never really feel I have covered it, or even answered the question. I think Nelson Shanks said it best when asked what colors he uses in flesh tones. He answered, "Do you have 2 years? I will tell you." Meaning that no two flesh tones were the same so you can't mix them using a formula. I think that is true of anything. You can try, as Helen Van Wyk did, to come up with color recipes and these can help as a starting point. But in the end, they fail to cover every situation, and it does not take long before you find you are not happy with the results. Maybe someone else has a better answer. I need to go back and study this more
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