The one consistent feature of successful colour schemes is balance. They may be high intensity, or soothingly quiet - but in their own way, for their own purposes, they are balanced. I suspect it is this phenonemon that leads to the proliferation of dogmatic colour rules: "It will Never Work Unless you include a bit of something complementary / light / dark / warm / saturated etc." Within a particular personal colour esthetic, such a rule may give consistently satisfying results, but it can also be limiting. Balance is as complex and subtle as the colours themselves, and I find it most useful to understand the underlying attributes of a colourway and play with the parameters until something clicks. Equally enlightening is the practice of collecting and analyzing existing instances of pleasurable colour, especially from the natural world. The whole process is about training the eye and the intuition to see deeply, and be open to new possibilities.
This will be a rather theory-heavy installment, but I felt it would be sensible to give a very basic introduction to some of the concepts that form a basis for experimentation and play. This is by no means a comprehensive treatise on colour, and there are excellent books out there that expound on the subject in great detail, my favorite being Deb Menz's "Colorworks".
1) The Colour Wheel. It is well worth your while to procure a high quality printed version for reference, as it is an incredibly useful tool.
The wheel places colours in a natural progression, orienting the coolest directly opposite the warmest. The cool shades fall above the horizontal line, the warm below it, and the primary colours (red, blue and yellow) form an equadistant triad.
Colourways tend to fall into two main categories:
Analagous colours lie adjacent to one another on the wheel eg. blue-green, yellow-orange-red. There are rules and conventions about how much of the wheel should be used, but the main point is that the colours relate by being close, by flowing into one another, and therefore have low tension in their relationship. Analagous colourways are easy to succeed with, though their exclusive use can be boring.
The second group of colourways relates through geometric symmetry at points around the circle, including arrangements such as complementary (directly opposite), split complementary (a triangle between a colour and the hues on either side of its direct complement), hexad (six evenly spaced colours) etc. I think of these as high tension relationships, with the highest tension occuring between direct complements, particularly where the cool/warm disparity is greatest. The tension creates energy and excitement, but also necessitates careful balance, which is where the colour wheel becomes a very useful problem solving tool. Try plotting your colourways on the wheel and playing with the resulting geometric proportions. Often (though by no means always), adding a colour that completes a symmetrically balanced shape (or subtracting one that is skewing it) is just the thing to pull a combination into harmony.
Ideas: If a direct complement is overwhelming, try turning the tension down a bit by using the hues on either side of it. Spice up a bland analagous set by adding a wee dab of their direct complement. Keep in mind that the quantities of each colour do not have to be equal (in fact, it's generally a bit jarring if they are), nor do the qualities (saturation, value). As the number of widely spaced colours increases, so does the sense of busyness.
Having said all that, none of this is absolute. Nature makes some perfectly lovely colourways that are not analagous, neither do they form a symmetrical triangle or polygon on the colour wheel. I think of the wheel primarily as a tool for seeing, playing, and sometimes getting unstuck.
2) Value refers to the lightness/darkness of the colour as it compares to the grey scale. For example:
In PhotoFiltre, clicking the big colour block at the top of the vertical menu on the right will open a small window with detailed parameters of the chosen colour. (Ignore the red/blue/green for now - see the disclaimer below.) Playing with the "Lum" number will adjust the value.
3) Saturation refers to the relative brightness and purity of a colour. Saturation is decreased by adding something: white (which will also lighten the value), same-value grey (maintains the value), black (darkens the value), or another colour, often its complement, which dulls the colour but adds complexity. Here's an example of decreasing saturation while maintaining the value:

In PhotoFiltre, playing with the "Sat" parameter will allow you to adjust the saturation while keeping other parameters constant. (Since this offers only one of the myriad of desaturating possibilities it is somewhat limited, but it is quite interesting to plug in a given colour and see where it falls on the scale).
Overall, warm colours tend to dominate cool, lighter stand out against darker, high saturation dominates low. Varying these parameters may create intriguingly subtle illusions and effects; for example, warm colours are perceived as being lighter than cool colours with equivalent saturation and value. Balance and harmony depend on the complex interplay between all these factors (and more besides).
Putting it Together:
Before launching into a computer-generated example, I need to clear up a wee technicality. Your computer screen does not create colour in the same way that pigments and dyes do. I have chosen to ignore this fact for the simple reason that this series is about combining existing coloured objects (ie. yarn and textiles) in harmonious ways, not creating the colours in the first place. (Though I do salivate at the thought of taking a course in dyeing theory.....) Therefore, since the point of playing with colour on the computer is to approximate the qualities of coloured objects in order to experiment with arranging them, the technicalities of arriving at that approximation are (mostly) irrelevent. Enough said.
Here's an example from the colour archive:
One could see this as a rich purple melting into blue, with a tiny splash of the direct complement, orange. You will also note that the purples and blues range considerably in value and saturation, while the orange is very saturated.
If you leave out the blues, choose the redder of the purples and let in the green of the leaves, a perfect triad emerges.
Now to choose a finite textile colourway. My personal reaction to the photo is to reject the crocus at the lower right - it looks faded, anemic - what drew me to this cluster was the deep velvety purple one at the upper left, with the tiny orange jewel at its heart. But would it have the same appeal without the surrounding leaves?

The crocus alone is rich and sophisticated; the leaves add an element of softness and whimsy. Either one could work beautifully, but I think I'm going to go with the leaves this time.
Going back to the original photo and pulling a palette within the chosen range:

I have pulled up the photoeditor's numerical assignments for each colour, noting the (S)aturation and (V)alue. I don't want to overemphasize the significance of the numbers, given the aforementioned technical limitations of the software, but they do give a nice rough guide to the colour parameters.
Purple: The predominant purples are of very similar hue, dark and moderately saturated, with small variations in value and saturation creating the subtle streaking. The petal tips reflect the light, creating high value highlights within the same hue and saturation range.
Orange: This is an interesting effect - the second, lighter colour is closer to what the eye reads and expects, but the first is what I actually pulled from the photo. The hue and saturation are the same - only the value differs, likely due to the lack of light on the area. In combination, the high temperature disparity between warm (orange) and cool (purple) provides plenty of tension and contrast. The high value orange could be too much, even garish, while the darker version keeps the tension in check. (This is what I mean about learning from nature - it is a clear demonstration of the illusion of warm colours appearing lighter than their actual value.)
Green: The greens cover a value range similar to the purples, but on the whole are much less saturated, which keeps them quietly in the background, not competing with the main event.
Lessons learned: From a colour wheel perspective, this was a high tension colourway - a triad with maximal disparity between warm and cool. Strategies for bringing it under control included: desaturating one or more of the hues, and keeping the values similar. Since the optically dominant hue (orange) is not the main feature of the picture, it was further kept in check by restricting it to a very tiny area.
And that's how I pull apart a colourway. I don't always check the numerical parameters, but they can be very useful in training the eye to pick up subtleties and illusions that a quick glance will miss.
Translating that into a pattern, and then a textile brings up other fascinating topics such as optical mixing, undertones, neutrals, and the various forms of contrast. Next time!