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In chord progressions, can a chord move to any other chord or is there any strictly rule? Can chords freely for to other chords?

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This question is too broad since the answer lies in what kind of music you are talking about. Baroque and Classical-era music has some pretty strict rules for chord movement, but the rules got a lot looser the music moved to chromaticism. Schoenberg made a pretty good case for why any chord can justifiably follow any chord, but that doesn't mean every progression sounds good. The short answer is "not really", but it is extremely subjective and dependent on style/era.

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    I agree about the Classical-era (a better name in this context would be common-practice harmony) but for most of the Baroque era the concept of "a chord" was quite different from the modern notion ("C major", "D dim 7", etc, etc) and in fact harmonic progressions (in the modern sense of the word) were much more adventurous than in the classical era - because baroque composers weren't really thinking about "chord progressions" at all! – user19146 Jun 8 '18 at 20:37
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    … for example, that the idea that C-E-G, E-G-C, and G-C-E were different "inversions" of the same (C major) chord, which is now universal, was more or less unknown in the Baroque era - it did not appear in any textbook until Rameau's dated 1744 - i.e. near the end of the baroque era, and at the time that book was not considered to be "mainstream thinking" about music theory. – user19146 Jun 8 '18 at 20:42
  • @alephzero, good to know. I know that the Baroque composers were thinking more linearly than chordally, but my teacher drove home tonic and dominant when I was doing all my fugues and chord progression was discussed when writing canon, so I guess I just assumed that was part of the thinking of the time. – Heather S. Jun 9 '18 at 2:09
  • @HeatherS. and to add to this, pre-baroque renaissance music can sound almost modern in its harmonic adventurousness sometimes youtu.be/5lRCpwmHdZg youtu.be/puJvWNi2PKA – Some_Guy Jun 15 '18 at 2:16
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If you're talking about 'music in general', then any chord can move to any other chord. Whatever you try, the universe won't end, and some people might like any given chord progression; even if they don't like it in one arrangement, they might like it in a different arrangement.

However, as Heather says, what chords and motions are 'allowed' (or expected) is an important aspect of what defines a style. Most compositions aim to fit (to some degree) into the expectations of one or more pre-existing musical styles, to allow tensions and resolutions to be created with reference to the common harmonic 'vocabulary' of that style. If you don't aim to fit at all into an existing style, then there's nothing to limit what harmonic (or rhythmic, melodic, timbral...) choices you make, but you may have to work harder to find an audience to enjoy your composition; most listeners are looking for music that they can relate to what they are already familiar with.

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In music produced now, yes, any chord can follow any other chord. In music there are 'rules', but they're more guidelines than anything else - this sounds better when you play this/that/the other.

The main criteria are going to be the listener's ears (and brain!) What sounds good generally is good, so take a few chords, play them in sequence, and listen carefully. Or watch the listener's reaction.

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