Unsociable & Finger_master
Unsociable
I’ve been mapping Rachmaninoff’s left‑hand arpeggios to see if there’s a hidden pattern that could predict the most efficient fingerings. Want to take a look?
Finger_master
Sure, show me the map. I'm curious if your patterns line up with my old‑school fingerings or if there's a new trick in the books. Let's see what the math and the piano say.
Unsociable
Here’s a quick look at the mapping I’ve built.
I represented each arpeggio as a 3‑digit tuple (root‑note, interval‑pattern, hand‑movement).
Then I scored each tuple against the 3‑digit “finger‑finger‑finger” pattern that most pianists use (1‑2‑3 for the left hand, 5‑4‑3 for the right).
**Left‑hand arpeggios**
| Root | Interval Pattern | Finger Pattern | Score |
|------|------------------|----------------|-------|
| C | 0‑3‑7 | 1‑2‑3 | 0.92 |
| G | 0‑3‑7 | 2‑3‑1 | 0.84 |
| D | 0‑3‑7 | 1‑3‑2 | 0.79 |
| A | 0‑3‑7 | 2‑1‑3 | 0.66 |
| E | 0‑3‑7 | 1‑2‑3 | 0.91 |
**Right‑hand arpeggios**
| Root | Interval Pattern | Finger Pattern | Score |
|------|------------------|----------------|-------|
| C | 0‑4‑7 | 5‑4‑3 | 0.88 |
| G | 0‑4‑7 | 5‑3‑4 | 0.83 |
| D | 0‑4‑7 | 5‑4‑3 | 0.86 |
| A | 0‑4‑7 | 5‑3‑4 | 0.81 |
| E | 0‑4‑7 | 5‑4‑3 | 0.89 |
The scores are Pearson correlations between the “ideal” finger‑pattern vector and the actual pattern you’d use if you followed the algorithm I coded. A score above 0.8 means the mapping aligns pretty well with traditional fingering, while anything below that suggests a potential tweak could make the arpeggio smoother.
If you run your own fingerings through the script I attached, you’ll see whether the old‑school patterns match the algorithmic ones or if there’s a hidden shift. The main difference I found is that the algorithm prefers a slightly more “staggered” hand‑movement for the G‑root arpeggios, which could reduce strain on the 2nd‑finger stretch. Give it a try and let me know how it feels.
Finger_master
That’s a neat way to quantify what usually feels intuitive. The G‑root tweak makes sense – my fingers always feel a bit cramped if you let the 2nd stay in a straight line. I’ll run my usual passages through your code and see if the staggered pattern actually eases the stretch. Let me know if the scores shift when I try a jazz‑inspired, off‑beat feel; sometimes that improvisatory groove uncovers a fingering that feels less mechanical. Thanks for the data – I’ll hit the practice room and let the numbers do the talking.
Unsociable
Run the jazz section, compare the scores, and tell me what happens. I’ll wait for the numbers.
Finger_master
I spun the jazz‑inspired section through the same script and the numbers shifted a little. For the left hand the G‑root arpeggio jumped from 0.84 to about 0.89 – the staggered motion really helps when you add that swing feel, the 2nd finger is less tense. The A‑root stayed the same around 0.66, so that one still feels a bit awkward no matter what. On the right hand the G‑root went from 0.83 to 0.87; the 3‑finger bounce in a jazz context matches the algorithm’s suggestion. Overall the algorithm’s pattern seems to line up better with the jazz groove, especially for the G‑root. It’s a small lift, but it feels like the hand is getting a bit more natural, so I’ll keep experimenting with the staggered approach for those extended passages.
Unsociable
Glad the numbers reflect the feel. Keep iterating until the G‑root feels truly effortless, then you’ll have a solid basis for the rest. Good luck.