Most ukuleles and five-string banjos, including many of those found in the Gretsch Roots Collection, use a form of tuning called reentrant tuning. Fair bet that you’re unfamiliar with the term, but you’re probably familiar with the concept if you play those instruments.
On a stringed instrument with reentrant tuning, the strings are not tuned in an ascending or descending order of pitches. That is, they’re not tuned in a succession of pitches that is strictly low to high or high to low (like, for example, most guitars). In reentrant tuning, there are one or more strings tuned to a pitch that breaks an otherwise linear order of pitches.
Take the ukulele, for example. Of the several ways to tune ukes of various sizes, a common tuning widely regarded as standard is gCEA.
See that lowercase g in front of the uppercase C, E and A? That’s not a typo. Rather, it indicates that this is a reentrant tuning in which that first string is not the G below the second string (C) by a perfect fourth, but a G tuned one octave higher than that, so that its pitch falls between that of the third string (E) and the fourth string (A).
This reentrant tuning is a standard tuning commonly used on tenor, concert and soprano ukuleles. Non-reentrant tuning can also be used for ukes, and indeed baritone ukuleles are often tuned DGBE in non-reentrant fashion (low to high, like the four highest strings of a guitar).
Most reentrant tunings only have one break in the order of string pitches; this break is called a reentry. The gCEA uke tuning described above illustrates this—the single reentry is the G that falls between the third (E) and fourth (A) strings.
Five-string banjos are another good example of reentrant tuning. Again, there is only a single reentry. The fifth string on these banjos is five frets shorter than the other four and is tuned higher than them, thus creating a reentrant tuning. Four-string banjos don’t have this shorter string and hence typically use non-reentrant tuning.
The most common five-string banjo tuning is gDGBD, an open-G tuning in which that first lowercase G represents the high shorter string, which is tuned an octave above the third-string G. Other five-string banjo tunings include aEAC#E, gCGCD, aDADE, gDGCD and aEADE, all of which are reentrant.
Other stringed instruments that typically use reentrant tuning include baroque and tenor guitars, the sitar, most lutes, the cuatro (a small Latin American guitar-like instrument), the Mexican vihuela (a small, deep-bodied rhythm guitar often used in mariachi groups), the charango (a tiny Andean member of the lute family) and the Ainu tonkori of northern Japan. The standard E9 tuning on a pedal steel guitar is reentrant; the instrument’s standard C6 tuning is not.
What about 12-string guitars—would that be an example of reentrant tuning? Actually, normal tuning on a 12-string guitar is generally not considered reentrant, as the matching octave strings for the standard G, D, A and low E strings are considered secondary rather than reentrant.