Interesting thread!
Tried to understand why the fourth tuning is so popular for guitars (lowest four strings):
a) a fourth is part of many trichords, so with fourth tuning this interval can be played with barré or open strings (to get even more barré and open string chords on six strings the default guitar layout has it's major third step)
b) on a guitar each concurrent note has to be played on a separate string. Additionally positions should not be too far apart for comfortable hand positions. With fourth tuning the "worst case" spread for concurrent intervals (<= an octave) is five frets - e.g. for a semitone - which is still good. Fifth tuning is already more difficult to play in low positions with seven frets worst case spread. For major third tuning it would even be better with 4 frets (and chromatic scales in just one position),...
c) ...but this comes at the expense of smaller tonal range. Here fourth tuning is better.
d) Open strings on an acoustic instrument slightly start to vibrate when another string is played where an overtone corresponds to the tuning of that string, pronouncing this overtone. With fourths being dominant harmonics (fifth downwards) this leads to a pleasant resonance behavior.
For Linnstrument:
a) almost irrelevant. The only advantage might be that one finger can play a fourth in some chords
b) notes can be played on the same "string", so the worst case interval is now a fourth - either six keys apart or on top of each other. "Frets" are much closer on Linnstrument than on guitar though, so six keys is still ok
c) still applies. We have eight "strings" though, so less of a problem
d) does not apply
So some reasons to chose fourth tuning don't apply to Linnstrument. But there are also no big reasons NOT to use it - if one is familiar with it already.
If looking for the "perfect" electronic grid-layout instrument tuning I would also lean towards augmented third (tritone) tuning though:
* it makes the 6-6 structure of the two whole tone scales obvious (every even column belongs to the first, every odd column to the second whole tone scale). So the positions of notes in scales can easily be deduced from their structure (where are the semi tones).
* Notes repeat after two strings, so (like written in the OP) you can play the same scale or chord in the same position with the same fingering over several octaves
* the note positions are more natural for the hand, because you can almost always play an interval "to the left" instead of upwards or even to the right (fingers crossed)
* playing chord inversions is a piece of cake
* horizontally adjacent cells are still one semitone apart which is important for pitch bends (this requirement rules out many other cell-to-pitch mappings with cool properties. But sacrificing this "string" property on Linnstrument would be... not so good...)
* even bigger range than all-fourth
Essentially tritone tuning is the grid variant of the Wicki-Hayden layout - fifth going diagonally to the right, fourth diagonally to the left, semi tone steps left and right (in Wicki-Hayden every second horizontal key is missing. So semitones are more difficult to play. So this is imho even better as it doesn't tailor so much towards harmonic chords but still provides the "logics" of WH layout on top)
I understand why all-fourth is the default for Linnstrument - the same why one channel mode is the default etc. - way of the least resistance for most musicians who have already some guitar and bass experience. Plug cable into computer. Play. Works as "expected".
But for people who look at the Linnstrument as a self-contained instrument (instead as "midi guitar surface") it might be worth looking into tritone tuning.
As most people will probably not change the default (and the Linnstrument is kind of a trend setter when it comes to grid based electronic instruments) I am glad that Mr. Linn decided on all fourth tuning instead of guitar tuning
Even if not perfect (in the face of better alternatives) it at least "makes sense"