Rethinking the Guitar as a cross-set.

 

While I am not a guitar player, I have nevertheless observed how the instrument is played and used as most of us who are non players. It has struck me that at one possibility has been over looked which i will explain here and provide one example, not to be definitive tuning but as an good example of  what i see as a fruitful direction for the instrument. 

The tuning of a guitar can be thought of as a cross-set between the open strings and the where the frets are placed. Traditionally this has resulted in the same notes of the scale but has been useful with exploring the spacing of chords as well as range. With JI or subsets of larger ETs interesting variations occur as a result. While this has been a concern those working with any type of inequality, it has advantages that open up musical possibilities. 

If we look at how the instrument is often used we see guitar players often using the upper fret area in points of  excitement. traditionally the timbre of the instrument becomes more inharmonic due to the shorter length of the string coupled with the side to side motion of the string.  and it seem that tuning systems could be designed to explore intervals that might have more of the nature of the music played. It is easier to conceive the guitar as a cross-set when we still preserve having frets that run all the way across. While it is possible to retune the open strings that have individual frets it potentially become complex .

 Conceptually this idea would be to have more restful intervals in the lower range with more bright or most even dissonant intervals above. Since it takes very few changes in a scale to change to over all character, It could be just the change in a few ratios ( or say scale steps if using an ET. A conservative example might be having more 5 limit ratios in the lower range with their pythagorean counterparts in the upper range.  For myself it would be useful also in my vacillation between my Centaur and Centaura tunings. Here is a diagram showing one fretting possibilities (not to scale) .

Hopefully this will provide some further ideas. Various high number ETs such a 31 and especially 41 could choose subsets that covered all the 41 tones just in different ranges for their different tension and expression.

Andreya Ek Frisk has been kind enough to forward this accurate fretting of the tuning discussed.