Chopin's Fantaisie Impromptu
Learning Chopin's Fantaisie Impromptu Op 66 #
Following the guidance of Chopin’s Fantaisie-Impromptu, Op. 66, Fast Play Degradation (FPD) This is definitely something I struggle with, so I am doing it!
Shortly upon waking the realisation of what (n+k-1)! came to me, it is incredible. I figured out what 3 choose 3 meant in playing three notes on the guitar. Playing CEG simultaneously, as a chord, is a 3C3 pattern. Recalling this pattern in my mind, as I play the three notes on the guitar, I tried to think of what it meant for allowing for more of the same notes to be in the chord. Changing the pitch of C would mean bringing in a distinct element, perhaps an octave higher. In order to pick the same C twice, at the same time, we need another string, of the same width! Or another guitar. If I allow three of the elements to be the same, eg CCC, then I need three strings. Two of the strings are already occupied with E, and G, and I can only produce the same C on the same type of string, so I need two more strings to create two more C notes. The -1 means the C that I already have in "CEG".
In summary, n is the number of different notes I can play, eg len("CEG"), or three notes. k is how many notes I play at the same time, for example, playing 3 notes at the same time. n+k in 3+3 means three strings for the three distinct notes, plus three for the repeating notes. In n+k-1 we subtract one string, because we one of it we already dedicated to one of the distinct elements. 🎸
I find it a wonderful, but odd feeling, of finally seeing the solution, and insight into problems I struggled to understand.
Is there topology of combinations of notes on the guitar, and combinations of outcomes throwing dice?
Yes. How to start learning this piece? Why, using 20/80 principle, growth mindset, and other learning how to learn awesomeness I know very well! Perhaps it would help if I brought a cup of coffee first. Drinking coffee is probably not an actionable lead measure, but reading textbooks on piano play, and making effort to learn piano pieces are.
The guide suggests reading Selected Topics in Piano Practice, before learning the piece. I think I read this section before, but I will spend some time reading it, as an atomic habit.
"Producing a good tone" involves learning the basic components of the basic stroke: the downstroke, the hold, and the lift. It is also useful to do the Tai Chi walk, alternating the yang, and the ying principle while placing the weight from one leg to the other. One leg supports our weight, the other one relaxes, and senses the place for the next step. While transitioning the weight to the sensing leg, both legs will support the weight at the same time. AB will intersect, two notes will be held at the same time, from 2C1 we move to $V^i_{2,2}$. That would mean we can also move to not supporting the weight, or levitate, in other words. ['01', '10', '11'] seems to resemble $C^i_{n,k}$ for "ab", where $C^i_{2,2}$ is ['aa','ab','bb']. aa is weight on one leg, bb weight on the other leg, ab weight on both.
In karate kata we step similarly to the tai chi walk, and it is interesting to find these connections. I never thought I could "stand" with my fingers on the piano keys, but believed that I was to 'levitate' my hands over the keyboard.
I am using a metronome, timer and pie charts, as suggested by Nahre Sol.