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Mixing Flash with Ambient
Setting the shutter speed in the light meter
When using a Sekonic L-358 light meter to read a flash exposure (the same applies to other models, I am simply not familiar with them), one of the nice features it has is its ability to indicate which percentage of the total exposure came from the flash — the rest of the exposure being from the ambient light available in the location where the metering was done.
Here is a figure taken from the L-358's user manual:

Metering flash exposure
As you can see in this example, 70% — "Percentage of flash in total exposure" — means that the flash was responsible for 70% of the total light, while 30% came from the ambient light available. The total amount of light ended up requiring an aperture of f/5.6 and 3/10th (let's call this f/6.3).
If 30% of the total light gathered by the light meter during a reading comes from the ambient light, if you change the shutter speed (without changing the flash power), you should expect that percentage to change: the longer you expose, the more the ambient light will have an impact on the total light, since you will gather more of it (while still gathering the same amount of flash). On the other hand, if you expose for a very brief moment, you will gather very little of the ambient light (while still gathering the same amount of flash), so the ambient light won't have much of an impact in the total light.
You might very well end up in a situation where the flash is only responsible for a small fraction of the total light (say, 10%) or, at the other extreme, end up in a situation where the ambient light has no influence on the exposure (which would give a 100% flash exposure). For example, when working in a studio environment, we usually don't mind leaving the modeling lights on when shooting, because we know that the light they produce is insignificant in the total exposure compared to the flash power (we get a 100% flash exposure all the time regardless).
Now, coming back to a location shoot where we mix some ambient light with flash, we should often expect situations where the percentage of the flash in the total exposure will not be 100%. In the situation of the figure above, where 70% of the total light came from the flash, suppose we were to expose for 1/30 instead of 1/125 — that is two stops more ambient, giving us a brighter background. In this case, the flash would now only account for ~40% of the total exposure. What's more, since we're adding ambient light to the previous exposure (flash remained the same), we now have more light overall, so we must use a smaller aperture — we go from f/6.3 to ~f/9.
This makes the shutter speed a crucial parameter to provide to the light meter, otherwise the obtained value will be wrong.
The only situation in which we could ignore the shutter speed would be in a pitch-black room where the only light is the flash — in this case, the ambient light (or lack thereof) would have no impact in the reading whatsoever.
Changing our perception of flash color gels
If you're mixing flash with ambient light, you know that you can (must?) correct the color of the flash so that its light color is well harmonized with the ambient light color, lest you get a quirky result.
But you can also use color gels not necessarily because you want to make the two light sources the same, but because you want to add an effect, such as warming up the subject so that it contrasts more with a colder background, for example.
In the image below, both the foreground and the background lights are of the same neutral color:

Foreground and background light have same color
Using a CTO gel (orange) on the flash aimed at the subject, you can warm up the subject, which will further isolate it from the background (which will now be of a relatively colder color than subject, even if it is the same as in the first shot):

Foreground light is warmer than background light (note: a strong color was used to make the illustration obvious)
Indeed, while the background remained the same, it can be said that the subject is warmer.
You will notice that I also (conveniently) included a gray card in the frame. If we take the picture above (the same exact file), but that we color correct using the gray card, here's what we get:

Image above, but white balance corrected with the gray card
You will notice that the subject is now perfectly neutral — exactly back to what we had in the first frame — but that the background turned blue (colder)! In this case, can it be said that the subject is warmer than in the first shot? Absolutely not — in fact, they are exactly the same, after correction, even if a "warming" gel was used.
If you're going to include a gray card (or GretagMacbeth chart) in your frame, you might want to do it while you're not using a gel on the subject, otherwise, balancing the color with a neutral reference will remove any color you might have thrown on the subject and, rather, affect the background. If you're going to include a gray card in your frame while you are using a gel, the way you should look at it is that you are in fact changing the color of the background in the opposite direction than that of the color gel (e.g.: if you're using a warming color on the subject, you're actually not changing the subject, but rendering the background colder!)
The fact that we are using a "warming" gel has no bearing on the final look of the image, because it depends on the white balance selected. A "warming" gel might therefore be more meaningfully seen as a "gel that makes the background colder"! That is why, when you work indoors under tungsten lights, you use a warming gel: not to warm up the subject (you still want it neutral), but rather to make the background colder.