ranjit wrote While I agree that principles are the way to go when learning to play scales and can result in quicker memorization, there are multiple possible scale fingerings and the reason why we have standard fingerings is largely because of convention and not because they are the logically most efficient way to play them. That is, someone not exposed to standard fingerings will not necessarily come up with them independently.
There are essentially seven alternatives once we accept the premise that there are seven tones in a scale, the 4th finger is only used once per octave so work out where that one goes (or can go) and you're good to go.
It only takes seven tries to find out which versions are workable, which are not, which are best and which are reasonable alternatives. Once the principle has been learnt you can always work out a scale fingering in a few seconds. Chopin's idea is that the long fingers go on the short keys and vice versa. In this way the 4th finger, RH, "belongs" on Bb and in the LH it belongs on F#. This is the easiest way of passing the thumb under the fourth, the trickiest part of each scale.
Liszt advocated, as an exercise, scale playing with C Major fingering for ALL keys. My teacher gave me the principles and assigned working out the fingering as homework but I wasn't a beginner.
If you were to work out and practise all seven variations each day I think you’d quickly settle on a preference.
Well of course he does! It puts the 4th finger on the only black key in the scale in each hand. That's the essence of the scale fingering principle introduced by Chopin instead of the standard, which I believe goes back to CPE Bach's Versuch.
ranjit wroteLikewise, why wouldn't you play a C major scale 12341234? After all, it's likely quicker that way.
In practise it should indeed be one of the seven versions to try. The reason for using 4 on the seventh (RH) or second (LH) is that the scale can finish using the fifth finger at the outer ends for those that like to do that. Some teachers advocate scale practise without using the 5th finger at all. There is no reason not to use all seven variations for C Major since there are no black keys.
ranjit wroteYou could also play a C chromatic scale 123412345123
While other fingerings are possible (and that might be explored at some stage) there are three main fingerings for chromatics (rising from E in RH, descending from C in LH): French (123 13 13 123 13), English (123 1234 123 13) and Liszt's, which you've given, (123 1234 12345 1).
The reasons for them are that more thumb crossings give greater clarity and fewer give greater speed. When these have been learned they can be applied easily starting on any key. Is there really a need for writing all these out for someone ready to start on chromatic scales?
