I've seen fanned frets on some extended-ranged classical and electric guitars. What are the benefits of guitars with fanned frets? Are there any drawbacks?
The idea of fanned frets is, in essence, to combine the baritone or bass guitar with the regular guitar in one instrument. Fanned frets enable strengthening the tone of the lower strings by giving them a longer speaking string length. They can also enable a high string that can be tuned higher than is possible on a conventional guitar by giving it a shorter vibrating length, enabling a higher-tuned string that won't break under the tension.
In the modern era the technique was first used on an 8-string guitar designed by classical guitarist Paul Galbraith and built by luthier David Rubio. Galbraith wanted an instrument where he could play notes one 5th lower than on a standard 6-string, and one 4th higher as well, adding a full extra octave to the instrument. He called his design the "Brahms guitar" because he found he could play convincing arrangements of Brahms solo piano repertoire on his instrument. He then built up his own repertoire of arrangements where he plays solo classical guitar with lower bass parts and a fuller sound.
Bartolex 8-string fanned-fret classical guitar
Low "A" to high "a"
Next up came Charlie Hunter, who worked with luthier Ralph Novak to create an 8-string electric guitar that has the range of the regular 6-string but also adds a full octave lower. (This design has a longer scale length enabling the extra bass range, but doesn't enable any higher notes). Charlie Hunter plays in a style where he covers the range of both the bass guitar and the electric guitar all by himself (Ralph Novak's slogan is "Fire you bass player"). Hunter usually performs with just himself and a drummer.
Novax Charlie Hunter 8-string fanned-fret jazz guitar
Low "E" to high "e"
Strandberg Misha Mansoor 7-string fanned-fret guitar
Low "B" to high "e"
Here are some luthiers that build 8-string fanned-fret classical guitars.
Here are some luthiers that build 8-string fanned-fret jazz guitars.
A well-known company that makes more hard-rock oriented guitars
Six-string guitars and bass guitars that use fanned frets
The technique of fanned frets has also been applied to the conventional 6-string guitar and the conventional 4, 5 and 6-string bass guitar. The theory here is that the lowest strings and the lowest notes make a stronger, fuller sound by giving them extra vibrating length, and the upper strings get a brighter, clearer sound by giving them a shorter vibrating length.
The best example is Dingwall bass guitars, whose low "B" string has a scale length of 37 inches (940 mm), while a conventional bass guitar with a low "B" string has a scale length of 34 or 35 inches (864 mm or 889 mm)
Dingwall Leland Sklar signature 5-string fanned-fret bass guitar
Low "B" to high "G"
As luthier Chris Larkin explains for this 9 string bass monster - To get suitable tension on the huge variation of string sizes it required different scale lengths for each string and so needed fan frets.