+ or #5?

Chords, scales, harmony, melody, etc.
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For a chord with notes going from low to high: G, C, D# (P4, A2), should I call it a G+sus 4 or a G#5sus4? I realize that it is usually construed as a Cm chord in second inversion (with D# being the enharmonic equivalent of Eb), but there is a reason I am wanting for G to be interpreted as the root of the chord.

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Sure it's D#, not Eb?

When I read G sharp something, then my root will be Ab. So that's not the way to write a Cm/G.
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+ and aug tend to be used on chords that match with the augmented scale (G A B C# D# F), #5 is more likely to be used for chords that correspond to other scales that have a #5 degree: Gmaj7#5 (matching with the G A B C# D# E F# scale) and G7#9#5 (equivalent to Galt7 and matching with the G Ab Bb B C# D# F scale).

Also, #5 is usually written at the end of chord names because otherwise it looks kinda ambiguous: Is it G #5sus4 (G C D#) or G# 5sus4 (G# D# C#)? A less ambiguous spelling could be Gsus4#5.

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G5+

the C in the middle is irrelevant. G5 is a powerchord. two notes, but the 5th is augmented. that is all.
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As Bert says, it's a standard C minor chord. The notes are C Eb and G. There is no D# and it's not augmented in any way.

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