Here is an exercise that builds on a fragment from John Coltrane’s solo on Giant Steps that gets you through all the major triads (4 3) and half diminished arpeggios (3 3 4). In the original context the half diminished is actually a dominant ninth without its tonic. It contains a diminished triad (3 3) and a minor triad (3 4) magically combined.
The numbers add up to +1, which means it rises gently up in semitones.
On the violin, this is a fantastic exercise if you play it in first (or half) position using open strings whenever possible, as each iteration of the pattern requires different fingerings. The logic is all in your ear, but not on the fingerboard.
But once you are onto the top two strings something else happens. You start repeating the same fingering, but a half-step higher each time. The logic is now under your fingers too. Of course, if your violin technique was up to scratch, you could have done what a guitarist would do, and played it that way from the outset, staying on the G and D strings, shifting effortlessly chinwards in half steps.
The reverse can sometimes happen. Something that goes all over the place on a guitar can be neat on the violin.
Some time last year I proposed this exercise that gets you through all thirty-six major, minor and diminished triads in the twinkling of an eye. It was inspired by the chord sequence of the song There’s a kind of Hush (written for Herman’s Hermits, I was surprised to discover, by my friend’s dad).
As you can see, the numbers add up to -7 which means that it descends in fifths; and also means you will have to substitute a +3 move for the -9 every so often to bump it up the octave. But, that aside, the finger patterns you discover on the top two strings will repeat as you go down. The logic is under your fingers.
I like to combine these two exercises, slipping between them, using the major or the diminished triad as a hook. One leads you up and one leads you down, so you never have to run out of space.
They are of course easy-peasy on the wholetone panpipe or double-wholetone-row xylophone, but that may not be your instrument of predilection. I have road tested them on saxophone and flute and they become strangely automatic after a while. It probably makes you a better sax player.
So what does this all mean? My takeaway is that using such “cross-platform” exercises on different instruments can offer you insights into the intervallic logic of what you are playing better what you would get from just one instrument. That is bound to strengthen you as a musician.
And check this out: learning two unrelated instruments will keep you from getting into those dreaded ruts that you get into if you stay on one horn the whole time. That is sure to enrich you as a musician. Stronger and richer: that can’t be bad.