
X-height is simply the height of the lowercase x in a given alphabet. Many regard that relative x-height of a given typeface as a factor in readability, believing that a larger x-height better accentuates the distinguishing characteristics of the lowercase letters simply because the main body of the letter is larger.
For this reason it is a commonly held notion that smaller x-heights are better reserved for display type where an enlarged size compensates for diminished readability.
X-height is also related to the readability and economy in type design. With a larger x-height, you will generally get higher legibility at smaller sizes. However, from what I’ve learned so far the x-height is only one of a number of interrelated factors, and that in fact determining what is the best ‘value’ in terms of the combination of readability and economy is quite complex.
If you normalize two faces so that their x-heights are the same on the paper, you will find the following make a difference to the readability-economy issue.
1. Set width
The length of a lower case alphabet in different fonts will be very different, even when their x-height is made the same. Example: Baskerville is wider than Times New Roman. The narrower font would be more economical, other things being equal (which they never are).
2. Ascenders and Descenders
If you use a less leading font, you can get more letters on the page. The length of the ascenders and descenders will limit how tightly you can lead, as Stephen notes above. However there are other factors that also affect how tightly you can lead with good readability so this may not in fact be an advantage.
3. Darkness of the typeface.
I just learned this from Mitchell & Wightman’s ‘Book Typography’. They compare Quadraat, a dark face with a relatively large x-height and Spectrum, a light face with a relatively smaller x-height. Quadraat requires more leading to look not excessively dark on the page, and Spectrum needs to be relatively tightly leaded not to look too light. In their illustration 11/15 Quadraat and 12/14 Spectrum are about equally readable, and Spectrum ends up being more economical, even though it has a smaller-x-height.
4. Optical Size
What makes this issue particularly tricky is that the trade-offs are different at different optical sizes. For example, if you go down to 9 point, probably Spectrum will be not very readable, and Quadraat will shine.
Improper or too-short x-heights drastically affect reading speed, particularly for those with vision problems (cataracts, etc can cause dramatic vision loss in the center of focus, so they will only see the tops/bottoms and ascenders/descenders of letters).

This is particularly true for large text or text intended to be read at distances. It is also why the US Government is moving away from ALL CAPITALS on road signs as changing them over to proper upper and lower case lettering. The human eye recognizes the shape much faster than it can parse individual letters and assemble the world.
In general, my conclusion is that at smaller text sizes, large x-height becomes a distinct advantage, but at larger text sizes, it can be even a disadvantage. Then at display sizes it can even reverse again so in fact this issue is really complicated.
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