Hi Fred
I wouldn't suggest to any of my students that they play the octaves without pedal unless they are marked staccato.
The purpose of the sustaining pedal is actually to enhance the tone quality you produce; the fact that it also facilitates legato in situations where it would otherwise be impossible is a happy by-product.
Most of the octaves in this work are accompanied by some sort of broken chord figuration that also benefits from the pedal - bear in mind that Schubert was an early Romantic, so a Mozart-like clarity is not often required.
To avoid, or at least alleviate tiredness in the hand playing the octaves, remember not to carry on pressing once you have played one. At the piano, play any old octave and press hard for a few seconds, then lighten the weight to the point where you are only just holding the key down. You will feel the difference at once.
You can also use a combination of sustaining pedal to create the legate for you, and a freely flowing arm to loosen any tension that builds up - it is this tension that causes tiredness. Try this to get the idea: slowly play a rh octave scale; legato pedal each one so you can let go of the keys as soon as you have played them; support the weight of your arm from your shoulder and let your wrists and forearms be loose and flexible; you should be 'stroking' the keys as you play, rather than 'hitting' them.
General principles when playing Schubert:
* His favourite genre was song, so treat most pieces as a 'song without words' i.e. with a sweet singing tone and gentle accompaniment. Having said that, there is more to the accompaniment than is instantly obvious, so look for opportunities to counterpoint the melody.
* Shape the phrases as a singer would. The ends of the phrases sometimes benefit from a little extra space in the way a singer in a lyrical song will take extra time, although without actually stopping the sound as a singer would.
* Avoid sentimentality.
* Remember that Schubert composed for a piano with a poor sustaining pedal mechanism. Many of his articulation markings reflect this, we tend to play differently on a modern instrument. Listen to recordings and you will hear, for example, many pianists produce a beautiful tone in the opening of this piece by using the pedal and not detaching at all; others will combine both.
Hope all this helps
Steve