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From what I understand, the 0-5-7 triad is a sus4 and 0-4-7 a major. So if I have C-F-G and descend a semitone from F to E into a C major chord what would be the technical term for it? I like to use this but with the root in the middle; G-C-F to G-C-E.

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You would just describe it as resolving the suspension. That is all there is to this and the chord technically isn't really changing.

Since we build chords in thirds and we define the basic quality of a triad with the third, the suspension makes that quality ambiguous. By going from the sus to the major quality you resolve this ambiguity, and this is used a lot to obtain a chord progression without switching chords as you really aren't changing what chords you're playing.

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  • To be pedantic, it isn't a suspension unless the F also occurred in the preceding chord. The "sus 4" is just a convenient name for the chord, regardless of how it is used. A context-free description would be "resolving the non-harmonic tone F". There are several more specific names for different usages of non-harmonic (or non-chord) tones here: en.wikipedia.org/wiki/Nonchord_tone – user19146 Mar 12 '16 at 6:29
  • The term "unprepared suspension" is often used. So I guess it must mean something. – Laurence Payne Mar 12 '16 at 11:06
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Resolution. Following suspension. By leaving out the 3rd, the chord is neither major nor minor. In your case, the F is masking that fact, only to reveal it when the F drops to E - the maj. 3rd. It could easily have gone - and sometimes does - to Eb, revealing a C minor chord. Incidentally, the first note is usually named no.1, rather than zero, and the subsequent numbers relate to the notes usually found in the relevant key. Thus C-F-G is known as 1-4-5 and C-E-G as 1-3-5.

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