Approaching diminished 7ths on the violin
December 02, 2017
The AMEB requires violin students to play diminished 7th arpeggios in various forms from grade 3 onwards. These appear initially in technical exercises, and then from grade 4 are grouped in sequences alongside dominant 7th arpeggios and chromatic scales.
The most important thing is to begin with a solid foundation and understanding of what we are trying to play. If you haven’t already read my post about diminished 7th fundamentals, it would be a good idea to do that now before you continue reading.
The critical takeaway from that post, is that every interval in a diminished 7th arpeggio is a minor 3rd, and this fact leads us to a surprising realisation: if we learn how to play minor 3rds on the violin, then by definition, we learn how to play diminished 7th arpeggios. In any key! 🎉
This touches on a super important point about efficiency of learning and practise. Why spend hours teaching diminished arpeggios “by rote” in every key, when you can equip your students with such a simple skill that enables them to immediately construct literally any diminished 7th arpeggio? Unfortunately it appears that the AMEB technical syllabus is not optimised for this style of learning, but nevertheless, approaching it in this way can drastically improve the speed at which your students pick up new keys, as well as the reliability of their knowledge into the future.
So, if the real challenge is playing minor 3rds on the violin, then how do we teach that? If for simplicity’s sake we limit ourselves to first position, then there are actually only 7 possible pairs of fingers that produce minor 3rd distances. Here is a table summarising those combinations, which can be played on any string/pair of strings. They are all ascending intervals, so the last 3 (e.g., ↑2 ➡ 0 require crossing to the next string).
Minor 3rd finger combinations in 1st position on the violin
| Lower finger | Upper finger |
|---|---|
| 0 | ↓2 |
| ↓1 | ↑2 (↓3) |
| 1 | 3 |
| ↓2 | ↓4 (↑3) |
| ↑2 (↓3) | 0 |
| 3 | ↓1 |
| ↓4 (↑3) | 1 |
This table is a fantastic reference for a student to have on hand. But don’t just hand them a copy! It’s works so well to have them create it for themselves. After doing a bit of exploration on the instrument to actually discover some minor 3rds for themselves, I will usually write out the left hand column of the table (which covers all possible first-position fingerings on a single string), and then ask the student to work out what finger creates a minor 3rd above each one, filling in the table as we go.
Since we now have a reference for how to play any minor 3rd in first position, and we also know that diminished 7th arpeggios are made exclusively of minor 3rds, we are ready to to try and play one! Remember, don’t reach for the sheet music at this point! The whole idea is to arrive at the notes from the understanding we have built. In this case, we can simply string intervals from the table together, starting from any note we like! For example…
Let’s start from open G (yep, play it 🎻).
The table shows us that a minor 3rd above an open string is a ↓2. That’s the next note to play!
To continue, the student just needs to now understand that the ↓2 they are currently playing is the new lower finger of the next interval. This means we need to find the ↓2 back in the left hand column of the table, and read off the new upper note, ↓4!
We can continue up the violin in this way, as far as first position will take us.
I recommend students practise traversing the table as it is written above, but for the sake of clarity, here it is written out in the order I’ve just described, starting from an open string (like G in our example):
| Lower finger | Upper finger |
|---|---|
| 0 | ↓2 |
| ↓2 | ↓4 (↑3) |
| ↓4 (↑3) | 1 |
| 1 | 3 |
| 3 | ↓1 |
| ↓1 | ↑2 (↓3) |
| ↑2 (↓3) | 0 |
| 0 | ↓2 |
| ↓2 | ↓4 (↑3) |
You can see here that the fingering described in this table produces a G diminished 7th arpeggio! Here’s what it sounds like:
It’s true that beyond 1st position you’ll need to come up with a new plan for fingering, but by that point playing diminished 7ths in 1st position should have prepared your students’ ears very well for tackling the higher positions. If this approach works, you can effectively reduce the workload of learning (for memory) every possible diminished 7th arpeggio in 1st position to the memorisation of that single, 7-row table.