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The modern Ten-string guitar

To put it succinctly, the addition to the guitar of four strings tuned a specific way (C, A♯, G♯, F♯) is to this instrument as the invention of the various pedals is to the piano. To appreciate the analogy, three concepts first need to be understood. These are that: there exists a phenomenon called resonance; a string has certain resonant frequencies corresponding to its overtones or harmonics; the guitar's fingerboard is normally tempered so that, of the pitches produced by the left hand on the fingerboard, really only the octaves of the open strings, and to a large extent their fifths, are 'in tune' with the strings' resonant frequencies. As a consequence of the above, the fact of the matter is that the (normal) guitar as an instrument has an inherent inconsistency between those sounds produced on the fingerboard that are effectively enforced and sustained by so-called sympathetic resonance (that is E, B, A, and D) and those other eight tones of the chromatic octave, each of which lacks the same support from a sympathetic string, in other words, from a string whose strongest resonant frequencies (that is, fundamental, octaves or fifths) include a resonant frequency that corresponds to the pitch produced on the fingerboard. This inconsistency has been corrected by the introduction of the modern 10-string guitar.

Conceived in 1963 by Narciso Yepes, the concept of the modern 10-string guitar follows a strict musical and scientific logic. Yepes discovered that, by adding four strings tuned to four very specific pitches, string resonance would be available for all 12 tones of the chromatic octave, without introducing any redundant resonances (more of E, B, A, and D) that would serve only to perpetuate, or worse, augment the inconsistency. In other words, the invention of Yepes was the addition of the strings C, A♯, G♯, F♯, which vibrate when pitches corresponding to their resonant frequencies are initiated on adjacent strings. Thus (to consider only one of these tuned resonators, the 10th string, or F♯): if F♯ is played (on the 6th string), the 10th string will resonate in unison. Likewise, it will produce the higher octaves f♯, or f♯' when these pitches are played on higher strings. In addition, this same F♯-string will resonate when its fifth is played, producing the tones of c♯ or c♯'. In the same manner each of the twelve tones of the chromatic octave is now supported by a string resonator, and (should the performer so wish) any tone can be sustained beyond the moment when the left-hand finger has let go of (or shifted position on) the string upon which the sound was initiated. The analogy to the pedals of the piano should now be evident. It should also be noted that (correctly understood) the idea of the modern 10-string guitar is, in a sense, exactly contrary to what is in the popular opinion considered to be the 'obvious' reasons for adding extra strings, that is to say extended bass range as open strings and/or simplification of left-hand technique through the avoidance of barrés and stretches. While the modern 10-string guitar does offer the extended bass range (scordatura of the 7th, or lowest, string is possible down to Helmholtz A1), it is contrary to other so-called 'multi-string' guitars, including ones that arbitrarily also have ten strings, in the sense that these make no attempt to resolve the resonance issue and, indeed, even augment it when additional B, A, or D strings (and their resonances) are introduced. Nevertheless, for better or worse, the popular opinion seems to prefer (as far as methods of stringing and tuning go) the 19th century concept of a 10-string guitar (extra basses for the sake of extra basses) rather than the nuanced interpretative possibilities that the modern instrument has to offer.

[http://en.wikipedia.org/wiki/Guitar]