Are some patterns that tend to get neglected in practice? Is that a good thing or a bad thing?
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8 out of 11 of those tetrachords are used for constructing scales or modes, as many as 8 X 8 = 64(?!), most of them do not have proper names.
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In my own "unpublished textbook" I label positions by semitone:
Half(=lo1st), 1st, lo2nd, 2nd, hi2nd(=lo3rd), hi3rd(=lo4th), 4th,
hi4th(=lo5th), etc....
I think Dounis may have actually discovered and systematized this, but I haven't read it. I reverse-engineered it myself while learning fingered thirds in C Major.
E (1 on d string, first position) - F- G- A - I call this "low" frame or L
Now if you assume you're in A Major, the same 1-2-3-4 on D string is in what I call "high" hand frame, or E-F#-G#-A
These two frames are super useful because you can use them to play one octave in fingered thirds starting with 3 on the lower string on the major tonic - Low pair of double stops, then high, then low, then high. This works for fingered thirds in any key, any string, as long as you start with the 3 on the major-equivalent tonic. I learned this using C major, starting on the D and G string in first position. Dont op 35 #8 is useful for this, but the raw scale is 100x easier.
Single-stopped, you can play a one octave major scale with just the high hand frame. (1-2-3-4-1-2-3-4).
There are two others, I call "middle", like on the A string in first position, B-C#-D-E. (The middle is bcause C and D are close., and what I call "wide" meaning all fingers are far apart. This is, for sintance, B flat -C -D- E natural on the A string.
If you start playing a very long scale (four octaves), you'll cycle through all four hand frames in a very simple plattern:
H - H -M -M (at this point you have run out of notes in first position on the E string and have to start shifting) - L - L - w (and then the pattern repeates but you are also out of string and hitting the bow with your left hand).
For a two octave scale in fingered thirds, the pattenr is L -H L H W - M - W , then it repeats (the third octave would be L again).
I find two octave fingered thirds scales to be a very useful exercise. If you understand this pattern, you can play any fingered thirds in any key, once you just figure out where in the sequence you are.
Maybe there are more patterns mathematically, but the only other one I have found to actually occur (Dont #8 hits this too) is the "harmonic minor" pattern, i.e. on A first position, B -C natural - D# - E, and of course pure chromatics (all 4 on top of each other).
For me, and my students, the basic four suffice with the knowledge that accidentals will appear from time to time but they are just calling for variations on the four basic locations of the half-steps.
Of course, we Doflein folks call the Patterns "Attitudes" and that leads to my favorite teacher joke which is to tell my students that when somebody says: "You have an attitude" they can respond with "I'm a violinist and I have four."
Approaching 50 years of playing I still rely on the basic four noted by Doflein augmented by responding to the accidentals when necessary. Over time it becomes automatic and outside the realm of conscious thought.
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I suppose it gets more complicated if you want to think about moving across two different strings.
EDIT: Curse my earlier math lapse!