High helmet or Tall Helmet are often used to describe helmet types, higher and taller, with a more vaulted helmet bell in comparison to more round types such as the Steel Cap ,Karma, leather cap or Orc helmet.
The well known elvish and numenorean winged- , spiked- and Crested helm designs were variants of this type. The sindarian Tholon type also had a somewhat lower helmet bell and was more similar to early dwarven helmets, yet it was still considered the archetypical "High-helmet" even if designs such as the Mountain-crown and morgul-mask , as well as some derived Haradron- and easterling helmet types, were much more bulbous and pompuous.
It is unsure what type of helmet Jrrt had on his mind while describing the elven and Dunadan armor. His illustrations of the gondorian crown seem to recall the egyptian hedjet crown while other sketches and illustrations of his call to mind spangenhelm, iranian, sogdian, sarmatian and phrygian helmets, and early celtic, bronze age or goldhat designs.Sometimes he might have had a morion or burgonet on his mind.Some of his "not high or tall" helmet designs look appear similar to ironhat, carolingian, kettle hat or steel-cap types.