Yes, I am familiar with Behr's palette. I am a paint snob but I'm also an INTJ (Briggs-Myers personality type) which means rational and practical can trump snobbery. Behr is easily accessible and practical for many people and that is not lost on me. :-) A few shades darker than Manchester Tan would be Bleeker Beige HC-80. Of course, whenever you go darker that means other characteristics of hue will change. But these two are so close, I doubt you'll see a hue shift. It's just going to look darker. But the light is boss so you need to test in the space an see what happens. Can see Bleeker harmonizing nicely with Antique White. Bleeker is darker than Manchester and lighter than Lenox.

Is there something above that would tell me if it leans gray. You are correct. Chroma tells you how close to a neutral white, gray or black (the grayscale) a color is. It's called the whiteness, grayness or blackness characteristic of a color. MT's Chroma is 1.48 and Jute is 1.42. So Jute is just a snidge more grayed than MT. Or you could reverse it and say MT is just a snidge more colorful than Jute. Sometimes when people perceive a characteristic of grayness they'll call it a "gray undertone". When they perceive a characteristic of whiteness, they'll sometimes call it "chalky". Whiteness, grayness, blackness is not only technically correct, I think it's a lot more specific and simpler. As far as warm and cool, every color in context of its color system can be categorized as inherently warm or cool. In the example above, once you get to the 5Y mark in the yellow hue family, the colors start to shift to the cool side. Every color in a color system has a warm side and a cool side. With color temperature, odds are the inherent color temperature of a color will hold true. But context matters, the light matters. In situ with other contents of a room, a color that's warm in context of its color system could take on a cool role - or vice versa a color that's inherently cool could take on a warm role. Here's the Colorography for Manchester Tan. Puts the color in context of its hue family and illustrates chroma; maybe makes the whiteness, grayness, blackness scale I'm talking about easier to see/understand.

I agree Todd about them side to side. But the travertine is definitely a yellow tint (with New Venetian Gold granite) so probably calls for a yellow based color. The bathroom is its own room so I'm not sure if the paints in both areas have to flow or be the same/complimentary?

@mark_rachel, I changed to cedar key. I bought it to go with the new marble tile I picked for the fireplace. There is a lot of natural light in the room. It might be a little pinker than bleecker beige, but I don't really see the pink when I don't look at them together. To me it is a very very soft latte. In the store it felt more gray. On some adjacent walls, I have collectors item. It is a creamy color, seems like a very light version of the yellows I had before. It works with cedar key. I did not want to be surrounded by taupe or gray, which is why I chose to contrast with cream. My living area pallete right now is BM white, cedar key, and collector's item. The paint consultant picked out the latter two when I brought in my samples. I told her bleecker beige (taupe) was my least favorite color (sometimes you can't avoid things that work so well), and that I loved gray but didn't want to be surrounded by it. I lived with bleecker beige for several years. Visitors loved it. I think I was ready to tone down all the yellows on the walls and floor, so I am happy going with cooler hues. BM has a free 2016 color of the year booklet that features varying shades of white. I picked one up at my BM paint store.