What are the common ways in which students are introduced to tenths? Are there certain etudes or technical exercises (or pieces even) that teachers commonly use?
Thanks in advance!
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What Jeewon is saying is that to place a tenth, you can first start with a sixth on 2-3. (That's why it's important to make sure that you can reliably place in-tune sixths.)
Then you hold the 2-3 in place and place the 1st and 4th fingers so you have 2-4 and 1-3 fingered octaves. The two fingered octaves will be a third apart. And the 1-4 will form a tenth.
Be really careful stretching for tenths. You need to build the strength up over weeks.
1. Stretch from pinky to 1st finger (as mentioned above). This is not always possible in a real piece, but it's a good safety step for beginners.
2. Practise scales in 10ths, but try and press the left fingers down with as little pressure as possible to make a good sound.
3. Vibrate as widely as you can! If you can vibrate 10ths, then you have a very 10ths solid technique. Of course this is much easier to do in the higher positions.
Get the Spohr No. 2 concerto. It's a lovely piece and there are just a few tenths. Also those tenths are not in first position so they're less of a stretch, so it's a good starting point, for the reasons Raymond mentioned.
Once you can do fingered tenths then you'll be read for "The Last Rose of Summer."
10ths are the beginning of Wieniaski 1, provided the soloist doesn't shred the orchestra tutti as a warmup (looking at you, Ray Chen). But nailing those 10ths are very different than working up to them as a teaching exercise.
I think it takes experience and practice to understand this next point, but sometimes I reach up for tenths, sometimes I reach down, it depends on the context and where you are on the instrument, and frankly, your hand and wrist natural shape (after a certain point on the instrument, I am forced into 2-4 octaves and even tenths).
Bruch was my first encounter with 10ths, and I never did any exercises until I played that piece. Fingered octaves I encountered later.
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It's can be hard to get a good tone from the side of the 1st finger.