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For my new year's resolution, I decided to play octave scales. I didn't make any particular speed goal, because I don't know if I can achieve that, but I do know I can achieve playing through them first thing when I wake up in the morning.

What fingering should I use? I started looking through Hanon and Cortot technique books, but neither offered any real guidance on what fingering I should use on the scales.

Does anyone have any idea where I should look to find this out?

1 and 5.

Are you asking because you're trying for legato?
Then, it's a different story.
But in a Dohnanyi book I have, the exercises that include octaves (which sometimes are scales, sometimes are arpeggios, etc.), there are generally two manners in which to practice:
1) 1+5 on white keys and 1+4 on black keys
2) all 1+5

That's just what is given on those exercises in that one book, but they are not legato scales, and are more for developing relaxation when playing octaves.
Hope that helps a little bit!

I used to always play 1-5, until my last teacher asked me to try 1-4 for black octaves.

I haven't looked back since........

I'm trying to be as legato as possible, but I accept any answers and all advice

I've seen two points of view on how to strike the notes. Some teachers say to flap your wrist, others say to use you whole arm. The sound is different so I'd experiment with both.

1-4 is tough with small hands which makes legato is even harder. In that case, the pedal has to bridge the notes. It also helps to stay very close to the keys.

Actually, it depends on your hands. If you reach more than an octave comfortably (e.g. a 9th or more) then 1-4 on blacks is better. 1-4 typically reaches as far or further than 1-5 because 4 is longer than 5.

If your hand is quite large (10th or more) and flexible, you can even use 1-3 at times, for example ascending RH F#,G#,A# octaves.

Some caveats... don't bother with legato at first. It's easy to strain yourself that way. Also, get used to noticing the angle of your forearm to your hand. Try to keep it so your forearm joins your hand so a center line through your forearm would extend out through your middle finger. There will be a temptation to swivel your hands away from the center of your body (called ulnar deviation) This is a very advanced technique and can cause trouble so stay away from it at the beginning. Last, yes it is OK to have very high wrists when playing octave scales, if it helps.

For scales I do them all 1-5 in these three ways

- p half notes with a dead-weight drop into the keys and complete relaxation
- f eighth notes with elbow staccato (straight wrist)
- mf triplets and 16ths with wrist staccato
always trying to avoid ulnar deviation, to keep the wrist down, and to play close to the tips of the black keys.

Legato is useful in repertoire, requiring 14 and sometimes 13 on octaves (and the occasional ulnar deviation) but I don't play enough pieces with long legato scale passages to make it worthwhile as exercises.

"The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low, and achieving our mark" - Michelangelo (disputed)

My favorite option too.

Yes, I think this is worth repeating.
Also, using the pedal for legato is a sensible option, especially if you have small hands.

I used to use 1-5 on white, 1-4 on black, but in my old age my left-hand (non-dominant) 5th finger is noticeably weaker, and I seem to be more accurate with 1-4 on white and black, especially when forte (fore)arm touch is required, for the left hand only. Alternating 4th and 5th fingers seems best for scales with the right hand, and with chromatic scales, best for both hands. And unless you are raising the roof, wrist touch.

Fine, then my goal is to play octaves like Cziffra.

Definitely you should learn Chopin Op. 25 No. 10 if you haven't already. Try doing 1-5 in the outer sections and 1-5, 1-4, and even 1-3 in the super-legato middle section. It's a great piece!!

This is dependent on hand size and stretch. I can reach a tenth. Even though I can reach 1-3 comfortably, I find in pieces it puts far too much tension. Even 1-4 if it is really fast, I find it to be awfully stretchy.

That is the spirit, go for it!

Most rapid octave passages in real music are played staccato, so this is the best way to play the scales as well.

If you find difficulty in stretching the octave, first practise over a 6th.

I like to use 4 on black, 5 on white because it makes the fingering much easier to memorize when learning octave passages in pieces.

Keep the hand fairly loose and floppy. Tension causes the octaves to be much more tiring. It doesn't matter if the other fingers tap on the surface of the black keys while the octaves are being played.

The wrist staccato is slightly more rapid than the full arm staccato, but leads more rapidly to fatigue. The full arm staccato actually looks like a wrist staccato, but in fact the hand movement is being driven not by the wrist but by the upper arm and forearm, as follows: The forearm moves rapidly forwards (towards the piano) then immediately backwards (as when punching someone!). This causes the hand to be passively thrown up, then down. It is on the backward movement of the forearm (i.e. the downward movement of the hand) that the octave is struck.

May I suggest you learn the scales in octaves first legato. The reason I suggest this is because when you play the octaves legato you are placing your 4th and 5th on the keys exactly where they should be for playing them very fast non legato. I learned this late in life when I bought The School of Octave Playing by either Kullak or Phillip. I can't remember which. I think it is Kullak. Studying his school of exercises taught me exactly where on the keys to place my fingers. Fingers 1 and 5 should be played very close to the black keys so there won't be much movement in getting to the black keys. On the other hand (no pun intended) fingers 1 and 4 should played very near the fronts of the black keys so not much movement is required to transition to the white keys. I had never thought of this, but it made perfect sense to me. It revolutionized my scales in octaves. I can play them very fast now. Hope this is of some value to you.

I really did not expect so much good advice about playing octaves. Thank you everyone who has posted, I feel like a better person already

One thing I noticed already, that I didn't expect, is my technique of moving my hands from the back to the front of the keyboard has improved. I didn't know it needed improvement, but playing octaves you have to deal with that so much, that you start getting good at it.

OK, with the exception of Liszt (Hungarian Rhapsodies, Campanella, Eb Concerto, etc.), I would disagree. Lots of octaves are written to be legato. I'd include almost every octave that Chopin ever wrote. Rachmaninov also. Balakirev (sorry!). Beethoven. Despite what someone said, I still think you should learn Chopin's Op. 25 No. 10. After that, you will know how to play legato octaves and the staccato ones will then just play themselves.

ok, I will try

I use 13, 14 and 15 also for staccato.

Particularly when going down and on black keys, 13 is a good option. Makes better connection with the keys than if you have to jump all the time. The upper fingers make the legato line, the thumb always jumps.