British cities, even London have many areas which are "low" density, in that there are often 2 storey houses with a garden at the front and back. Skyscrapers are a rarity except in very central areas.
Birmingham as an example has 1 million people with a density of around 4,000 per km2. It has no skyscrapers (buildings 40-50 floors or higher) unless you include the relatively short 40 floor Holloway Circus, but this is the only one close. Would you consider a city with no skyscrapers as high density? 4000people per km2 is not low density.
As a comparison Atlanta (someone cited above) has a population density of 3,000per km2, but does have many skyscrapers. Going on cities with comparable population like San Jose or (at the upper range of comparable) Dallas their population densities are both 2000per km2 or lower. I admit, there are physically larger cities, but they have skyscrapers.
The point of what I was trying to say (I think) is that density is a bit relative. What I would consider "high" density does not include skyscrapers as I live in the UK. Skyscrapers are a rarity here, but we still have high density of population. But someone in the USA or Hong Kong would always think of skyscrapers! When deciding to put down high density zone, I just do what I want. I let it flow and come out organically and just what looks and feels right. High density would normally arise in areas which have demand but no space. Think a central district or the like.
