11 String Guitar in Conventional Tuning by Heikki Rousu, 2019
In the case of my primary guitar, the first 6 strings are as on a normal guitar and the extra bass strings descend diatonically from the E 6th string, as in the Romantic tuning of a 10 string guitar. Strings are usually tuned (1-11) E, B, G, D, A, E, D, C, B, A, G but the extra basses are altered chromatically depending on key. 11 string guitars can alternatively have all strings of the same length and on the fretboard, in which case special strings are needed which gradually increase in thickness.
On my guitar the highest sounding 8 strings are frettable & of the same length (approximately 650 mm scale length). Strings 9-11 operate like diatonic harp strings, played open, and increase incrementally in length. The left hand stretch beyond 8 fretted strings is rarely needed in lute music so having a fretboard under strings 1-8 only, makes the neck less heavy. Having strings 9-11 as unfrettable, gradually increasing in length, means normal E 6th strings can be used, ensuring an even tone and easy availability. Strings 7 & 8 are respectively high and extra high tension E strings.
The advantages of my guitar compared to 6 string guitar are:
more sympathetic resonance
wider range in the low register
ability to play directly from Renaissance lute tablature (with 3=F# tuning)
more faithful transcriptions of Baroque lute music, Bach's music and better arrangements of the music of other instruments
somewhat easier left hand fingering (as more bass notes are available as open strings).
The potential disadvantages are:
frequent and more complex damping of the bass notes is needed to avoid a sustain pedal effect when not wanted
right hand disorientation due to the unfamiliarity of the position of the extra basses, necessitating much practice, time and effort to use them effectively and accurately.
The best known 11 string guitarist is probably Moran Wasser: https://youtu.be/abbSA08CBP0