Having spent the best part of a year with the usual 4ths melody & 5th bass tuning & still not feeling any thing like at home with 5ths, after I had the good fortune to land a bamboo 12 string Grand my thoughts started to turn to what some refer (I hope jokingly!) to as the Dark Side of the Fourths...
I was particularly take by what Rob Martino & Jayesskerr have written on the topic (this post
viewtopic.php?p=118103#p118103 especially). I was reminded of how I came to choose 'All Fourths' tuning (EADGCF) as what I use on all my guitars.
To dip my toes (or rather fingers!) in Mirrored 4ths, I I started with a simple experiment that essentially reversed what Emmett did all those years ago when he to started with fifths. He raised a string by a tone, left the next lower string un-changed, then dropped the next lower by a tone. I did the opposite with the 3 lowest RMR bass strings so E2 A1 D1 became D2 A1 E1. Only 3 strings to work with, but enough to feel that I liked the idea & wanted to take the experiment futher.
While waiting on a set of Mirrored 4th strings from SE, I decided to see what I could achieve on my Graphite 10 string (then set up for Full Baritone) using strings I already had to hand.
My first try involved switching the Baritone melody strings from the melody side to the bass then tuning them down a semitone, and re-fitting the Classic 10 melody strings that had been on the Stick when it arrived then tuning them up a semitone.
That gave a 'Mirrored 4ths' arrangement, i.e. octave inlay correspondence over 5 frets (e.g. bass 2 to melody 7), and lowest melody as a 'virtual' extension of the bass 4ths.
Code:
G#3 D#3 A#2 F2 C2 G2 C3 F3 A#3 D#4
That worked but didn't feel quite right, so I retuned all strings down semitone so that the melody side was unadjusted 'Classic 10', and the bass side was a whole tone below the melody side of Baritone melody. That made the arrangement equivalent to 'Mirrored 4ths', but a 5th higher.
Code:
G3 D3 A2 E2 B1 F#2 B2 E3 A3 D4
I really liked that. The mirrored fourths arrangement immediately felt more natural to my hands and my brain.

I'm sure someone must have done that tuning before, but if so I've not found it, so in the absence of another name I called it 'Baritone Mirrored 4ths 10' (hence the first attempt became 'High Baritone Mirrored 4ths 10').
I know that people say that Mirrored 4ths really needs 12 strings, but to me the 'Baritone Mirrored 4ths 10' arrangement gives a very usable range of possibilities in the guitar range of tones & I was planning on leaving the Graphite in that tuning.
Once the 'proper' Mirrored 4ths for the Grand arrived, I fitted them and set making it my 'home'.
The absence of the lower bass end of Classic (C1) & RMR (D1) was a pity, but I had in mind that maybe when, in due course, my 'built to order' Grand arrives from SE (it could easily be another 6 months) I might try a dropping all strings a 4th on the older Grand (I've not seen a name for that arrangement, so maybe 'Deep Mirrored 4ths 12'?), but other than that I had no plans for change...
After a month or two with normal Mirrored 4ths I felt that I wasn't getting a lot of use out of the low melody string, especally so at the lower end, so I started musing on the possibilities.
Around that time I happened to revisit Rob's video about his custom 7 bass & 5 melody Mirrored 4ths Stick, & was reminded that limited use of string 6 was part of his reason for ordering the 7 + 5 Stick. However I didn't see a 5+7 as where I wanted to go (even it was possible & practical). Options for widening the interval between low bass & low melody seemed like a good subject for study.
An early thought was to put an extra 4th between the two sides. Dropping the bass side by inserting a B0 that could be either a 'Classic' or MR low bass dropped a whole tone, or a Dual Bass Reciprocal low bass, gives
Code:
C3 G2 D2 A1 E1 B0 B1 E2 A2 D3 G3 C4
i.e. a straight 'reflection' but with an octave between the two low strings. If that arrangement doesn't already have a name, how about 'Matched Mirrored 4ths 12'?
'Matched Mirrored 4ths 12' doesn't give any useful full inlay correspondences, but it does include a 5 string octave inlay correspondence over 5 frets, e.g. bass fret 2 (8-12) to melody fret 7 (6-2). Spotting that 5 string correspondence gave me an idea...
If the interval between low bass & low melody is increased by a whole tone to a 9th by putting Classic 12 melody on the melody side and 'Matched Mirrored 4ths 12' bass on the bass side it gives
Code:
C3 G2 D2 A1 E1 B0 C#2 F#2 B2 E3 A3 D4
That arrangement had several features that appeared interesting to me.
a) Double octave inlay correspondence over 10 frets, e.g. bass fret 2 to melody fret 12
b) 5 string octave inlay correspondence over 5 frets, e.g. bass fret 2 (7-11) to melody fret 7 (5-1)
c) String 6 (the 'extra' melody string that isn't part of the 5 string octave inlay correspondence over 5 frets) is the 'low 5' of string 5. So with a bass root on the bass low string and a harmonising octave block an inlay away on strings 5-1, string 6 allows easy access to the 'low 5' & 'low 6' of the octave, notes which feature in countless melodies.
d) The overall range of the tuning is comparable to that of 'normal' 4ths/5ths Stick tunings, albeit with less overlap.
e) Since low melody is the 9th of low bass, it provides alternative access to an octave for a 1 5 octave power chord, or a 10 for a different 1 5 10 open triad. I'm not sure how useful that might be in pracctice, so probably minor, but the scope is there.
f) The melody side is back to good old Classic 12 / RMR 12.

In the absence of another name I call this arrangement 'Wide Mirrored 4ths 12'.
Once again I started my experiment with my Graphite 10 string. Instead of making that just the inner 10 of the ablve, I found I could ge a 4th higher 10 string equivalent by leaving the melody side as it already was (Classic 10 melody) and using the lowest 5 bass strings from my spare 'Mirrored 4ths' set on the bass side, giving
Code:
C3 G2 D2 A1 E1 F#2 B2 E3 A3 D4
and calling it 'Baritone Wide Mirrored 4ths 10'.
I liked what I found. It gives me (pretty much) the range of a normal 4 string bass & 6 string guitar on a single 10 string instrument, with most of the 'Wide Mirrored 4ths 12' benefits listed above. I think it has enough difference & appeal that it will still get played even with the 12 string version available.
I'm now converting the #5826 bamboo Grand to 'Wide Mirrored 4ths 12'. I've done the re-stringing and intonation. Next thing is to work on the action. Then I need to get back to learning to play...
I have 'fretboard map' illustrations of all the above tunings (i.e. the 'thought experiments' as well as the actual trials) if anyone is interested?
I've attached the 'Wide Mirrored 4ths 12' map.
Attachment:
Wide Mirrored 4ths 12.pdf
Edited to correct a typo.