[elsherbini]

I've experimented a lot with different isomorphic tunings on the guitar - that is where each string is in the same interval. The obvious one to try is perfect 4ths, E A D G C F. This one is great because the same shape works everywhere, drop 2 chords for instance have three sets of shapes you need to learn on standard guitar but only one on perfect 4ths. However, I hate giving up the open B and E strings. You can fix this by adding an extra fret on the highest two strings (or just using a capo on the lowest 4 strings) [1].

My favorite isomorphic tuning though is minor thirds tuning, where each fret becomes a diminished chord. This allows you to explore Barry Harris' harmonic concepts really easily, which describes major and minor 4 note chords as combinations of two diminished chords. I made a video showing how this works. [2]

[1] https://www.youtube.com/watch?v=fFX5AQRg8Ko

[2] https://www.youtube.com/watch?v=1Kg1m5KqaoQ

[contravariant]

I have to say the phrase 'isomorphic tunings' is very confusing if you have a mathematical background. It apparently doesn't refer to tunings which are effectively the same (not entirely what this would mean, I suppose you could swap a few strings).

[mrob]

Wikipedia calls them "regular tunings", which I think is clearer.

https://en.wikipedia.org/wiki/Regular_tuning

[elsherbini]

Totally, my mistake. The correct term is regular tunings, which yield an isomorphic layout on the guitar (well, it would if you had infinite strings). In plain english, the same shape always corresponds to the same intervals no matter what strings you are playing.

[Analog24]

Perhaps isometric would be a better description? We're probably getting into the pedantic weeds here though :-)

[osrec]

Well, this is HN, afterall :p

[dwringer]

It means they are effectively the same as you shift rightwards or leftwards on the neck. So you can play a G major chord, move the same exact shape "down one string" and now it's a C major chord. This is not a feature of standard guitar tuning.

[Sharlin]

I guess isomorphic tunings are isomorphic in the sense that you can move a fingering not only up and down the fretboard, but also from one set of strings to another, and the chord remains the same, just transposed.

[smilekzs]

The minor thirds tuning is incidentally the same setup as chromatic button accordions (a.k.a. Bayan's)!

https://en.wikipedia.org/wiki/Bayan_(accordion)

[gleep]

Major thirds tuning, on the other hand, gives you a consecutive chromatic scale in any given position without stretching or changing the position. It's great for single note soloing.

[kazinator]

If all strings use the same interval, you have less variety in fingering; everything is the same everywhere.

The M3 interval between the G and B string is useful; you can allocate fingerings between those two strings to play certain things that don't work for a pair of strings that are a P4 apart.

[elsherbini]

Totally agree, I think regular tunings are cool and easier for learning in a lot of ways, but the ergonomics of standard tuning or other non-regular tunings make somethings easy that are really beautiful. I think making whatever you consider to be desirable on your instrument also be idiomatic and easy to do is good.

[toolslive]

Bass players use "regular" tuning. Fe, 6 String Basses: B E A D G C