In the exercises of thirds instead of playing it 1/3 2/4 3/5 can I play it 1/3 2/4 1/5 or it's not advisable? It's really hard for me to raise the fourth finger when going to play 3/5; are there exercises for that part to make you easily move from 2/4 to 3/5 smoothly and legato?
I'm new to piano, so I apologize if this is a silly question.
You didn't mention if the question is about playing diatonic or chromatic thirds, but I assume you mean diatonic. Also you didn't mention if your just asking about a kind of sort of 5 finger short passage of continuous movement through all the octaves. I'll cover the continuous movement as that will give you the technical fingering to cover just about all fingerings for thirds.
As many have already said, there are no absolute correct fingerings. Standard fingerings work for most applications, but should be adapted to either fit the hand or fit the fingering requirements in the surrounding musical context.
Having said that I think there is a general principle to keep in mind: be aware of the transitional fingering for continuous motion in thirds while avoiding the thumb on black keys. That's my own wording - I don't know of a standard wording to use. It best illustrated with examples:
Diatonic thirds:
The basic pattern is...
345 123
...basically third played with every other finger in a kind of fixed 5-finger position.
...but notice that the thumb is repeated...
23 11
...to shift the hand position to allow the basic pattern to fit the keys such that you can continue up and repeat at each octave. (Really its to avoid having the thumb on the black key G# at the top of the scale.)
To me that is the essence of playing diatonic thirds: a 5-finger position shifted by the repeated thumb transition, and the even more general principle of avoiding the thumb on black keys for scale playing. This applies to all keys.
Chromatic thirds:
...the basic pattern is...
34 12
...where the basic idea is to not use the thumb on the black keys.
When the lower tones of the third pass through B C C# or E F F# - or the enharmonic equivalents - the pattern is extended to...
345 123
...so that finger 3 plays the black keys instead of the thumb.
The essence is an alternating two-finger pair extended to fingers 3 and 5 when avoiding the thumb on the black keys. This applies regardless of the starting position in the chromatic scale.
If you need to use alternate fingers for thirds - for any reason - you can keep these transitional fingerings in mind along with the understanding their purpose is to avoid the thumb on black keys.
About your fourth finger:
That's just basic hand anatomy. The fourth finger is less independent that the others.
Unless there is something unusual about your hand the fourth finger problem is a matter of training to gain finger independence.
All of the teaching materials I have seen put 5 finger independence exercises before playing double notes. Make sure you have devoted enough time to finger independence exercises. Don't let your ego get in the way and consider this to be beginner stuff. If your fingers don't move independently, you have to train them.
From my experience it especially important to play such exercises slowly, because slow execution seems to demonstrate smooth control with a relaxed hand. Playing too fast might disguise a kind of 'twichy' motion that disguises a lack of total control.
Don't use 'alternate' fingerings just to avoid poorly trained fingers.
All fingering is flexible!
BUT, in a passage of 3rds, confined to the '5-finger position' you need a pretty good reason NOT to use 1-3, 2-4, 3-5. And 'I'm a beginner, and I find it hard to lift my 4th finger' isn't a good reason!
It sounds as if you're playing an exercise that covers that problem already! Stick with it. Check with your teacher that your arm, hand and finger positions are correct.
Fingerings are suggestions, but in exercises they might be the whole point
When you learn a piece and you can do better with another fingering than the one on the piece, feel free to change it. Those are only suggestions.
With an exercise, on the other hand, the point is to learn how to do things that are hard. Of course, if you play it with a different fingering, you're still playing the same tune, and might even be playing it better (i.e. it sounds nicer), but the point of an exercise is not to sound good, but to help you learn. You might totally miss the point of the exercise by changing the fingering. Of course it also depends on the exercise itself - if the point isn't to teach you fingerings but legato/staccato or whatever, it might be harmless to change from the fingering.
Use the fingering as given in this exercise
In this particular case especially, I'd advise you to use the one that is given:
"It's really hard for me to raise the fourth finger when going to play 3/5; are there exercises for that part to make you easily move from 2/4 to 3/5 smoothly and legato?"
The anser is yes, it's the exercise you're doing right now, and it will only help you learn it with the fingering as written.
Whatever you are playing on piano, it is important to plan out the fingering so that you get the articulation you want and are able to get to what follows easily. The exact fingering is going to be dependent on the context of the piece, in combination with what works for your hand. It is advisable to try out different fingering options to decide what is best.
Take a look here as an example - Chopin, Etude #6 gis-moll. This is just a reference, there are a couple of ways, I think Liszt had his own way. As another reference, you can take a look at Czerny's 'The Art of Finger Dexterity', op 740 #10
A very long time ago, I took piano lessons briefly.
I collect memory gadgets. The piano teacher knew this, and she gave me one: NARF. Notes, Articulation, Rhythm, Fingering. You want to think about ALL of these.
This sounds like a practice exercise, as opposed to a piece. It is designed to get you to the point that you can finger what you need, when you need it, how you need it. As such, it is worth the effort to work on it, as written, 1-3, 2-4, 3-5 and all.
The point in training particular fingering systems is to have a repertoire of standard fingerings working well together that can be applied without thinking. That does not mean that they will result in the unambiguously anatomically best total way to play any piece, merely that they will quite likely result in a feasible way to play it and will be well-suited to avoid "painting you into a corner" when sight-reading.
When you are training for a marathon and your trainer gives you a route, there is little point in finding shortcuts for that route. Even though for most real-life routes there may be corners you can cut, sometimes you will not have the time for finding those corners on a particular route, and being able to go the full distance will make the difference.
Fingerings marked in scores are editorial marks - they've almost always been added by someone other than the composer (with a few exceptions for etudes). Even in conservatory juries you're not going to lose points for using an alternative fingering.
But I do have a rule for my students: if they use an alternate fingering they have to be able to explain why they made that choice. "It's easier" isn't a good reason. "Crossing with 4 instead of the 3 that's marked places my third finger in a better position for the chord that follows" shows they've put some thought into it.
You don’t have to follow the rules. Rules are to break and not like laws. Carl Philip Emanuel Bach offers different fingersettings and if he didn’t ... I would! The purpose to be able to play a piece in a comfortable way and enjoy playing is as important as to train the independence of each finger. Not every piano player has the aim to become a professional pianist. The joy of making music should be in a positive balance with finger training.
