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I'll tell you - I'm glad you've started this topic because I've refined my positions just yesterday...
i say refine because my finger placement interval has gotten shorter ... Shorter gaps between notes. You should also consider tones; attention to pitch - because you will begin to hear sounds that aren't the note your looking for, especially in higher positions. Recognizing these things are often : what advancing in violin is about (refinement).
for example last week I was playing a D and this week I've realized that D is actually more of an E/F. Thus my finger grouping has shuffled closer to the scroll across the entire fingerboard in order to refine the tones and resolve those inaccurate fluctuations between string crossings.
I tell you these things to shed light on potential encumbrances that you may be dealing with.
as for figuring the correct pitch for yourself you can play a double stopped octave (first finger on the lower string with your fourth finger on the higher string) but even still with that technique, it may prove difficult to imitate the actually octave without great ears. I think that when it comes down to it, and you're practicing scales; you WILL hear the inconsistencies so you CAN fix them there - on the fly.
Alveraz20 said .......................Any advice on knowing how far apart the other notes are in these positions?
First practice and listen carefully, then when you've done that, practice and listen some more. Finally, practice and listen. Repeat over and over.
I've learnt all the notes in 3rd position recently, and I'm playing plenty of tunes in third but I still can't produce as good intonation as I can in first. I'm just starting to play some tunes where there are shifts between 1st and 3rd and back in the middle, and I'm finding that actually helps to ground the pitch.
The higher up the fretboard the close the notes are together to the point of having to move one finger before you can put the next one down and be in tune. An exercise I am doing to help intonation is to pick a verse or phrase of a song that you can play on one string, in the position your learning and play it on every string until you have the intonenation down for that phrase on that string the go to the next string till your comfortable on all 4 strings then change keys and start over again.
Master the Frog and you have mastered the bow.
Just my two cents
Use your thumb. It is usually a helpful method. Instead of just trying to hit the correct note with a certain finger, you gradually learn to memorise the location of the thumb in each position, and its particular moves between every shift.
(I would practise shifts from 1st to 3rd position and backwards and watch and feel my thumb. Let's say in the A string, and use your 1st finger that you already have mastered to check if the thumb-and hand- position is the proper one)
That way, you not only move your whole hand into position, and every finger should feel home and ready to play