A reentrant tuning is a tuning of a stringed instrument where the strings (or more properly the courses on coursed instruments) are not ordered from the lowest pitch to the highest pitch (or vice versa).
A break in an otherwise ascending (or descending) order of string pitches is known as a reentry. Most common reentrant tunings have only one reentry; In the case of the soprano ukulele, for example, the reentry is between the third and fourth strings, while in the case of the Venezuelan cuatro it is between the first and second strings.
Instruments often tuned in this way include:
The tunings of coursed instruments such as the twelve-string guitar and twelve-string bass are not considered reentrant provided that the principal string of each course is ordered from lowest to highest.
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The soprano ukulele is the most common instrument normally tuned in reentrant fashion. All ukuleles other than the baritone are most commonly tuned in reentrant fashion. These conventional reentrant tunings are sometimes known as high-4th tunings.
Non-reentrant tunings, also known as low-4th tunings, exist for these instruments.
In general, the smaller the ukulele the more likely it is to be tuned to high-4th tuning, with the soprano almost always tuned in high-4th, and the baritone almost always low-4th.
The ten-string extended-range classical guitar was originally designed for a specific reentrant tuning invented by Narciso Yepes, now called the Modern tuning. Both this and other reentrant tunings, such as the Marlow tunings, are now used, as well as non-reentrant tunings such as the Baroque.
All of these tunings may also be used on derivative instruments, such as ten-string electric and jazz guitars.
The Venezuelan cuatro is a small member of the guitar family with four nylon strings, and is very similar in size and construction to the ukulele. It is one of several South American instruments by the name of cuatro, which is Spanish for four, and not all of which have four strings.
The traditional tuning is reentrant, but with the reentry between the first and second strings, rather than between third and fourth as in the ukulele. The results are very different in tone.
More modern tunings of the Venezuluelan quatro are non-reentrant.
An enormous variety of tunings are used for the four-string tenor guitar, including a relatively small number of reentrant tunings. One example of a reentrant tuning for tenor guitar is strings 1-3 E-B-G as for the normal 6-string guitar, but string 4 tuned to D an octave above the 4th string of the 6-string guitar.[1]
The fifth string on the five-string banjo, called the thumb string, also called the "drone string", is five frets shorter than the other four and is normally tuned higher than any of the other four, so technically this is a reentrant tuning, albeit not in the more usual sense of the term. The five-string banjo is particularly used in bluegrass music and old-time music.
The four-string tenor banjo, more often used in jazz, lacks this shorter string, and is rarely if ever tuned in reentrant fashion.