If the instrument is tuned in fifths then, indeed, a diatonic scale pattern that proceeds perpendicularly across the finger board at the same position has four notes on each string.
However, these four notes are sometimes spaced differently: different patterns of tones and semitones.
When an instruent is tuned in fourths, scales use three notes. There are ways to conform to many of the string-to-string pattern variations by leaving out fingers:
a - b c' # index ring pinky
e f - g # index middle pinky
- c - d
It seems that the fifths tuning is quite tyrannical in this regard.
Now when it comes to the major scale, that scale is actually a stack of two identical tetrachords, which are a fifth apart. These tetrachords have identical fingerings:
# tuning in fifths now:
g - a - b c
c - d - e f
So now if you have your fingers spread out in the right way to play the C-F tetrachord, all you have to do is preserve that when going to the next string.
I suspect violinists must be exploiting this sort of relationship; favoring fingerings that show tetrachord symmetries.
The Dorian mode (D to D mode of C major) also has two identical, stacked tetrachords, so if we slide one position down that pattern, we are still good:
g - a - b c - d
c - d - e f - g
[ Dorian box ]
[ Ionian box ]
But, having observed that, these fingering patterns are not easy even in isolation, regardless of whether there is a change in the pattern going to another string.
Excellent information here! For something a little more unusual, you can see guitar players in the experimental realm (think John Coltrane, not Thurston Moore) use four finger per string technique in standard/fourths tuning via the work of Ollie Halsall and Allan Holdsworth. Highly nimble and skilled, these guys were the 60s/70s inspiration for later shred-monsters like Eddie Van Halen (who worked to get Holdsworth a record deal). Something must have been in the water around Cambridge during the late 60's for two completely different oddballs to emerge with nearly identical techniques, especially considering that they both played in the same band for a brief moment. (Allan Holdsworth played with Tony Williams, Jean Luc Ponty, and Soft Machine. Ollie Halsall played in Patto, a band that Queen opened for and Led Zeppelin could barely keep up with, along with gigs with Brian Eno and Kevin Ayers. Rumor has it Ron Wood was the next choice after Ollie during the Rolling Stones' mid 70s lineup change).
It should be noted that Holdsworth actually played a bit of violin (you can hear it on Temporary Fault off I.O.U.; Karzie Key off the infamous Velvet Darkness album; and recordings of Tempest, Soft Machine, w/ Gordon Beck, and Gong).
Holdsworth even experimented with fifths tuning on his SynthAxe (since you could just do that in software), most notably for the song Non Brewed Condiment[1] off Atavachron, and the solo in In the Mystery, I believe, and had a separately tuned guitar for the live performance of the aforementioned song[2].
There's an interview from the 90s where he talks about his thoughts on fourths vs fifths[3].
He later said at a clinic (in the 2000s) that if he were to relearn the guitar, he would've used all-fourths tuning[4].
To some extent they should have some similar properties since a fourth is basically the inverse of a fifth (modulo an octave). In theory you should also be able to shift a tetrachord on an instrument tuned in fourths you'll just go the other way and be off by an octave.
Being off by an octave is pretty important for melodic lines, which is usually how the violin is used… so while you can translate chords from tuning in fifths to fourths or vice versa, in my experience, you need to relearn to play if you're doing melodies.
However, these four notes are sometimes spaced differently: different patterns of tones and semitones.
When an instruent is tuned in fourths, scales use three notes. There are ways to conform to many of the string-to-string pattern variations by leaving out fingers:
It seems that the fifths tuning is quite tyrannical in this regard.Now when it comes to the major scale, that scale is actually a stack of two identical tetrachords, which are a fifth apart. These tetrachords have identical fingerings:
So now if you have your fingers spread out in the right way to play the C-F tetrachord, all you have to do is preserve that when going to the next string.I suspect violinists must be exploiting this sort of relationship; favoring fingerings that show tetrachord symmetries.
The Dorian mode (D to D mode of C major) also has two identical, stacked tetrachords, so if we slide one position down that pattern, we are still good:
But, having observed that, these fingering patterns are not easy even in isolation, regardless of whether there is a change in the pattern going to another string.