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It is widely known that music "wants" to be resolved on the tonic. But does it mean that I can end with the tonic, let's say, one/two octaves higher or lower than the whole melody that is being played? Or does it have to be in the "borders" of the whole piece? Can you, for example, resolve a Gmaj chord with Cmaj, but going up in pitch? It seems to me that it always go down in the pitch when resolving.

Also, can you build tension going down in pitch, instead of up?

There is no rule about in which octave should the melody or harmony progress or shift throughout the song, let alone rest at the end. It's common though to end with a lower pitch root note as lower frequencies give a more surround feeling than their upper octave counterparts, however the decision to use one or another is highly subjective.

Theory dictates that Gmaj will resolve at Cmaj, but it doesn't say that has to be a lower Cmaj. The functions of these chord progressions are maintained independently of their position over octaves.

An example of building tension when going down is C, Bdim, Am, when Am is acting as tonic on minor key.

An alternative to shifting an entire chord up or down over an octave is the use of inversions, which might produce a similar effect without actually moving all the chord notes.

All Cs are C, no matter the octave, this is called octave equivalency and it's derived from the base that all notes that are one octave apart are musically equivalent. If from B you add 1 half step or rest 11 half steps, you will reach C and in either way the tension will release. The only difference is that it will be higher or lower in pitch, but regarding tension both will work in the same manner.

This is why you can play 5 different notes in different octaves (like C3, C4, E4, G4, E5) and the chord is still called C, because the musically different notes accross octaves are still C E G.

I think I understand. V>I is the most common cadence, called the perfect cadence. It works theoretically because (in key C) the B takes the shortest route to the tonic C - one semitone. So, if you used the second inversion of G, using D G B in that ascending order, the B would be happy going directly to the tonic root, C.

However, if instead, you used the root version of G, G B D, then the D would be happy moving not much further, a tone, down to the C on top of a root C.

As a newbie, you may not be aware of oft-used mantras on this site - there are no rules to be followed, and listen to what you think may work - if it does, it's o.k. so that's always a first move. Give it a try!

I have noticed in people's speech patterns, especially with professionals such as radio announcers, that pitch is a very important part of their speech, and the borders are most certainly used for a purpose.

It seems that higher pitches work sort of like indentation in technical writing (i.e. with multilevel bulleted lists) to separate subclauses or parentheticals from main clauses... and a person's lowest comfortable pitch is used for punctuation or communicating the end of a thought.

Therefore, I posit that in composition, based on the listener's ever-present analogy to speech, it will sound more final if you finish on the bottom tonic or even on a tonic with more bass than at first.