Angel is a name* proposed by Mason Green for the temperament that tempers out 81:80 (thus, it is a meantone system), and has a period that is a flattened 3:2, four of which make a pentave (5:1), while its generator is an octave. This temperament is very closely related to quarter-comma meantone (which was the standard for most Western classical music); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead).
If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a 31edo temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another.
More specifically, the term angel may refer to various MOSes and MODMOSes that are derived from this temperament. There are MOSes with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the pentatonic, diatonic, chromatic, and enharmonic scales respectively.
Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.
In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.
Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in all-fifths, since the period is a fifth.
* Because this temperament almost seems too good to be true.