Why the Same Chord Can Have Different Names
Notes
Learning to find and understand chords in a piece of music is a difficult task because chords often don't simply appear as a stack of notes on top of each other in an obvious formation. A lot of the time, chords have their notes arpeggiated, jumbled up, and with a melody woven in between, making it hard to see which notes belong to the chord and which notes don't.
This is where prediction comes into play. If we are playing a piece of music in the key of C major, which uses the notes C, D, E, F, G, A, and B, then there are also certain chords that we expect to see and this can help us parse the notes that are on the page. The most common chords to see in a piece of music are chords I, IV, and V. In the key of C major, chord I is a C chord (C, E, G). Chord IV is an F chord (F, A, C), and chord V is a G chord (G, B, D).
This means that if we see lots of Gs, Bs, and Ds, even if there are some extraneous notes also there (from a melody or moving bass line, etc.), we can confidently predict that this is probably chord V, which is a G chord (G, B, D).
Having said this, often, notes by themselves may not be enough information to determine the chord's name or function. Meaning that you may see another situation where there are Gs, Bs, and Ds in a bar, but it may not be acting as a G major chord. For example, if an E is snuck into the melody several times as a chord note that the melody is working around, this may actually be better labelled as an Em7 chord (E, G, B, D). An Em7 chord contains the same notes that a G major chord contains, except it also has an E.
There are even some examples where no new notes need to be added in order for the chord to be relabelled based on the context in which we find it. For example, if we had the notes E, G, and Bb, in isolation this would typically be considered an E diminished chord. However, if we are in the key of F major and this chord is followed by an F major chord (F, A, C), then this would change how we perceive this chord, and instead we would consider this to be a C7 chord, but with a missing C (C, E, G, Bb). The reason for that is because of its function within the piece of music. Typically, at the end of a phrase, we expect to see chord V moving to chord I, and in F major, that would be a C major chord (C, E, G) to an F major chord (F, A, C). However, sometimes that C chord is something called a dominant seventh instead, which is, in the key of F major, a C chord with a seventh on top (C, E, G, Bb). So, what we perceive the chord to be can change based on the context as well as just the notes that we see.
Context
A more easy-to-understand example of this is if we see the same chord, but named enharmonically. The “enharmonic equivalent” in music is a fancy way of saying the same note, but with a different name. The enharmonic equivalent of Db is C# because both of these are the same key on the piano. They are just labelled differently.
So, a Db major chord (Db, F, Ab) is labelled so in one context, but in another context, we may see the exact same notes played on the piano, but it would be labelled a C# major chord (C#, E#, G#).
Enharmonic equivalents are used depending on the key of the piece of music that we're playing in. If we are playing a piece of music that is using sharps, then we're much more likely to see C# major, whereas if we're reading a piece of music that is using flats, we're much more likely to see Db major, as these are the chords that will show up in those particular scales.
Interestingly, enharmonic equivalents are a good way of composers pivoting to different scales very easily. For example, if they're using a scale where a Db major chord is used, they could then relabel that chord as C# major and access all of the scales where C# major is possible.
This tells us something very important about music; chords are not labelled strictly because of the notes that they contain, because often you will find chords where not all of the notes are used. We find the label that is the most accurate for the function of the chord. We may label a chord as one thing in one situation because that's the most appropriate label for that context, but in another situation it may be referred to as something different.
Function
Ultimately, chord names are supposed to tell us something about the harmony, its relationship to the key and other chords, and what the piece of music is trying to do. It is often the case that there are many labels that we can use for a particular chord, but the label itself is meaningless if it doesn't tell us something more about the music.
For example, the notes A, C, E, and G form an Am7 chord. However, we could just as easily refer to this as a C6 chord (C, E, G, A), as it's exactly the same notes. So why would we refer to that chord as one over the other?
Well, it depends on its function and the purpose that it's serving within the piece of music as to which is the best label for it. A C6 chord feels like a C major chord with an additional note. If we arrive at this chord by lifting a B up to a C so that a C feels like the root of the chord, then C6 may be a more appropriate label for the chord than Am7. However, in a different context, Am7 may feel like a more appropriate label because of its minor quality of sound, particularly if we're in the key of A minor, for example.
The purpose of chords is to tell us more information, to give us an idea as to the sentiment, the character, and where we are within the piece of music. What's important is that we build up a strong prediction machine in order to give us a sense of which chords we're likely to see in any given situation. That way, when it comes to moments where chords are ambiguous and there are multiple possibilities as to what a chord may be, you can more easily understand what the music's intention is and label it accordingly.
Matt