I've been teaching myself for 4/5 years. Somewhere along the line I came across these Alternate Scale Fingering
that seemed like a good idea.
I've been practicing them and I like them. They feel quite intuitive and logical. Recently I've taken a teacher for the first time and she is insisting I revert to traditional fingerings. I'm resisting!
1. Firstly does anyone else know this fingering and what are peoples opinion about the utility or otherwise of them?
2. Secondly, should I be a good student and stop resisting or is there a case, as I feel there is, to be made for sticking with these fingerings I've now learnt
I should add my main goal here in learning the piano is to be able to improvise (as opposed to learning repertoire)
Also, I think my teacher is really good!
These alternate fingerings for the most part are well known since several decades. They continue to use the 1231234 pattern only that the initial finger is different for some keys.
In Major the difference is for the 4 keys of G, D, A and F for the left hand. The changes are simply based on the fact that the left hand pattern for these keys is not quite as practical in the standard fingering as it is for the right hand.
Therefore the proposed fingering is the one used for the left hand pattern of the sharp/flat key that has the same number of accidentals (ie for D major, use the LH pattern of B flat major). I will pass over the rationale but it is based on symmetrical configuration. The resulting fingering is indeed slightly better, however you will only notice it in really fast tempos. For most ordinary tempo, the standard fingering is just fine.
For the minor scales, there is not a similar possibility, however some pianist have proposed slightly improved fingering. Typically Moszkowski in his scale book proposed a different fingering (again changing simply the order) for the left hand in harmonic minor scales of F, C, G, D and A which is reproduced here by T. Kelly.
Now the issue is that for the key of A minor for example, you have now 3 different LH fingering for the natural, harmonic and melodic minor. If the fingering of Moszkowsky is marginally better than the standard one for the harmonic minor, the one proposed by Kelly for the melodic one is no better and I think less efficient than the standard one. In fact using the same standard fingering for all 3 cases works quite well and there is really no need to go into such refinement for such a simple key. Similarly I do not find that the C minor harmonic fingering is any better than the standard one. In addition it has the disadvantage of changing the contrary motion symmetry that you benefit from in the standard fingering.
All in all, the few changes have also some drawbacks such as introducing more fingerings. These alternate fingerings are really usefull for pro/advanced musicians for challenging pieces in very fast tempos. You can certainly be aware they exists in case you would need them. I often times practice my scales with the C major finegring in any key to make sure that I do not rely on the standard fingering and to practice more difficult configuration (A flat major for example).
In real pieces sometimes you can not afford to start a scale with your preferred fingering and so you need the flexibility to execute an alternate fingering instead. But that would be for advanced players.
For your second question, I do not want to get into the relationships between you and your teachers; that is your decision. From a technical standpoint, my point of view is that the fingering proposed by T. Kelly for the minor keys is too complicated and brings marginal benefits (if any) for a beginner. For the major keys, I think it is a good practice to train yourself on the standard fingering which has some other side benefits such as keeping the symmetry in contrary motion. There are only 4 keys that are different and only for the LH.