Does rules in 4-part harmony also apply to piano arrangements ?
Like for example no doubling the 3rd note of the chord, or moving in parallel 5, etc.
They don't fully apply, no. But it depends on what you're trying to do.
Remember that the voice-leading rules for four-part harmony are to mimic eighteenth-century chorale procedures. Piano arrangements are by default not in the eighteenth-century style, so by that logic there's little need to follow all of the voice-leading rules.
With that said, a few rules do still persist today, even in popular music. More than anything, I think the rule of resolving the chordal seventh down by step is the most-followed rule from the eighteenth century.
Forbidden parallels, however, happen all the time in music of the 20th century (and even earlier).
So depending on what you're arranging, you may find yourself breaking these rules all over the place. But that's okay, because if the piece you're arranging isn't in the eighteenth-century style, why arrange it like it is? (Unless you're trying to be hip with a different style arrangement!)
Lastly, I just wanted to note that doubling chordal thirds happens all the time. It's a rule that's been passed down, and it might be to prevent people from doubling the leading tone (which is the third of the V chord). But doubled thirds in tonic chords happen all the time, and they're a necessity (!) in some vi chords at a deceptive cadence.
No they don’t. They don’t apply to any music. Not even chorale music. Music has no rules. The fact that generation after generation of students come away from their study with this idea is more than grounds for scrapping 4 part harmony from pedagogy altogether. It obviously does far more harm than good.
I think with 4 part harmony the sight of the forest has very much been lost for the sight of the trees. There is no doubt that there are many more students who can write flawless 4 part harmony than can actually understand or explain what it is they’ve learnt, why they’ve learnt it and how it fits in to the larger goal of understanding of music.
4 part harmony is a tool that is supposed to help you “understand” harmony. Harmony can never be understood intellectually, we can use intellectual tools to help us get to an understanding, but they are only a stepping stone or ladder that we move on from. Harmony is only “understood” when it is felt. That is, you have to understand what a V – I cadence feels like, what the establishment of a tonal centre feels like, and what the ambiguity between tonal centres feels like.
This is why, as a paper exercise, 4 part harmony is worse than worthless, it’s dangerous. It should primarily be taught as an aural exercise with the written component as a tool to facilitate this.
4 part harmony was a solution to a problem. How do we go about teaching harmony? It is an intellectual abstraction that is famously modelled on Bach’s chorale works. (Bach obviously didn’t learn the model abstracted from his works, he worked with, intellectual abstraction of his own, no doubt, but primarily his “understanding” his feeling for harmony, counterpoint, music) This was chosen as it’s the point where (functional) harmony, as we know it today, emerged out of counterpoint. So it’s supposed to give you a sense of the contrapuntal genesis of harmony, how the tendencies that exist in certain melodic notes lead to the tendencies in the simultaneous, combined sounding of those notes.
The use of 4 voices obviously allows for use of the full triad with an extra voice to allow (minimal) experience of doubling (voicing), and the contrapuntal aspect is there to give you experience of counterpoint as well as being consistent with the aural environment within which harmony evolved.
It can’t be emphasised enough that 4 part harmony is an abstraction, and idealised model that is designed to allow you concentrate on the harmonic aspects of music, with everything else stripped out. It’s resemblance, in any way, to actual music should not be misunderstood.
4 part harmony should be a sandbox that is used for aural harmonic experimentation and discovery, that fact that it’s taught as a collections of dogmatic rules that should be learnt and applied in a rote fashion is just utterly criminal.
That all being said, if you look at a lot of music from around the CPP you will see a “resemblance” to 4 part harmony. This is a result of the conception and understanding of music of the composers, they wouldn’t have felt at any point they were restricted by “rules”, they only had tools and ideas with which to use and experiment with.
Another thing to bear in mind is that music is not always voices. It sometimes is an interweaving of interdependent melodic lines, and also sometimes just slabs of harmonic sound. And also, everything in between. Sometimes these things will be intentional, and sometimes incidental, but you will ultimate chose these things on how you think they sound, how they feel.
Ultimately you should feel free to experiment with music in any way you wish. All the things you have learned are just ways people have done so in the past, and you can use or discard these things at your whim, dependant on how they sound, they feel to you. Of course to make that decision it helps if you understand them, and to do that you have to understand how to feel them. 4 part harmony should be a vehicle for you to do this, but I suspect the way it’s taught it will achieve this goal for a very select few, if any at all.
In a piano arrangement, unlike in 4-part vocal writing, you don't normally have different voices. In a four-part Bach chorus, for example, or in a hymn, all the voices will be singing the same words and you'll have melodies and counter melodies going on.
On the other hand, most piano arrangements are one melody line being embellished and emphasized through creative use of harmony, style, and technique. You don't simply have multiple parts moving in similar rhythmic patterns like you do in vocal music. You may have counter melodies and such going on, but it is a very different style from vocal writing, for the simple reason that the piano is a totally different instrument than the voice.
For this reason, I'd say the rules aren't as applicable to piano arrangements.
The concept behind 4-part harmony excercises is to teach you the basics of voice leading. It is in reality completely unlike any real music you may find. All it really aims to do is teach you the basics. In actuall fact, real four part voice harmony does things like voices go over and under different each other, which is a real no-go for your excercises.
Also you may find octaves doubled in piano music that looks like the doubling which your are told to avoid but this is not a doubling of the harmonies perse but more just two of the same notes played to increase the sonority of a passage, those types of doubling are very piano-like.