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I am new to music theory and I was wondering what the difference is between harmony and consonance/dissonance. What are the reasons behind these terms and how can you apply it in practice if, for example, you'd like to compose a song?

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Harmony is a noun that means "simultaneous sounds." Consonant and dissonant are adjectives that describe harmony; think of dissonance as "tension" and consonance as "stability/release."

In terms of composing a song, you'll often want your harmonies to match what's happening in the lyrics. If a song ends "happily ever after," it doesn't make much sense for it to end with a dissonant (=full of tension) harmony, does it? Similarly, if the song ends with a major disruption in the lyrics, it might be nice to end with a slightly dissonant chord. If your song is a story of turmoil moving to triumph, you could tell that story with the harmonies by progressively moving from dissonance to consonance. These examples are pretty one-dimensional, and the best music is much more nuanced than this, but they give you a decent starting point.

Lastly: Colloquially, "harmonious" has come to mean something like "consonant," and every once in a while someone (typically a non-musician) will say "harmony" and mean "consonance." Just be aware that sometimes people use these terms interchangeably, even if they're incorrect.

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    Dissonance is often used to push music forward because it pulls the ear toward wanting a consonant resolution. Consonance and dissonance can be used to match music to the lyrics, but it can also be used ironically if you want the lyrics to say one thing but the music to say another. – Heather S. Mar 21 '18 at 14:03
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Harmony is a general term relating to the putting-together of differently-pitched sounds (possibly of different timbres) to create subjectively interesting effects.

Consonance and dissonance are more specific words - Consonance ⇔ Dissonance is a spectrum along which different harmonies can be classified as sounding 'smoother' (consonant) or 'rougher' (dissonant). Note that it's not possible to fully understand harmony by measuring it along this axis alone - you also need to consider aspects like voice leading, and the emotions that tend to be subjectively associated with different types of chord.

Sometimes people (speaking more 'informally', from a musical perspective) use the word 'a harmony' to mean 'a consonance', and 'harmonious' to mean 'consonant'.

  • Consonance ⇔ Dissonance is a spectrum along which different harmonies can be classified... We also refer to intervals as consonant and/or dissonant, not only harmonies. – Stinkfoot Mar 20 '18 at 23:10
  • @Stinkfoot to my mind, that's a question of talking about the harmonic characteristics of the interval... – topo morto Mar 20 '18 at 23:25
  • I don't want to belabor the point. But I took a theory course from a well respected instructor who spent two lectures talking about consonant vs dissonant intervals and never played any harmonies - just illustrated by playing a perfect 5th - C then G - and contrasting it with the sound of a tritone: C then F#, etc, etc. So I think it's applicable without harmony at all - the sound of two pitches in sequence can be consonant or dissonant. – Stinkfoot Mar 20 '18 at 23:53

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