In my case, since becoming active on this forum early in 2018, my take away has been the higher the better, so I'm cutting at max height for my mower at 4". I'm also not using any sort of fungal control practices at this point and I don't have any irrigation.
This is the from the lawn maintenance guide in the articles area:
Always mow high at 3 inches or higher on a regular basis. Mowing high permits proper photosynthesis. That means the grass needs sunlight to grow. The shorter the blades of grass, the more you impede the photosynthesis process. Photosynthesis takes place at just about the middle of the grass blade. Ever notice the grass is yellowish closest to the soil? The reason is that as the grass utilizes sunlight to manufacture its own food, chlorophyll is produced to give the grass its green color. It is very important to remember you should never remove more than one third of the grass blade at a time or you shut down the food factory, which causes stress. You may wish to mow once a week or 2-3 times a week, depending on how fast the grass grows. Either is fine just so long as no more than one third is cut off at once.
Infrequent deep watering and frequently mowing high are the two crucial points of lawn care. Anything else you do is secondary to these cultural practices. Proper watering and proper mowing are what encourage a healthy growing environment for a lush green lawn that is able to crowd out weeds.