Enharmonic Equivalents are one of those music terms that sound complex but aren’t actually complex at all. Basically enharmonic equivalents are where the one note can have more than one name.
Sometimes when I am explaining this to a piano student of mine and they have a puzzled look on their face, I use the analogy of a person. Take myself for instance, to you the reader you might not even be aware of my name that appears with every single article, so to you I might be known as just ‘the author’, but to my piano students I am Jen. When I am doing relief teaching in a school, I am known as Mrs Crabb. To my own kids I am Mum and to my nieces and nephews I am Aunty Jen. All these different names I have are still just the one person – me! The difference though, is that it is me in different contexts.
It is reasonable to question why enharmonic equivalents exist and the simple answer is that it depends on the context of the note. For instance if you are playing a piece of music where the key signature is sharps, then you will have notes that are referred to as being sharp, such as D sharp. If the key signature of the piece of music is using flats, then D sharp will not be played, but the exact same note will be referred to as E flat. Are D sharp and E flat exactly the same note? Absolutely yes, they are the same note, just in the different contexts of one being a key using sharps and the other being a key using flats.
Using the example of the enharmonic equivalents of E flat and D sharp, E flat is found in almost every flat key that is major, except for F major (which has only one flat – B flat) and C major (which has neither sharps or flats, so it is often at the beginning of a list of both sharp keys and flat keys). Now looking at the same note, D sharp, this can be found in E major, B major, F sharp major and C sharp major. As a result of finding E flat in more major keys (a total of 6 major scales) than a D sharp (there are 4 major scales), you are much more likely to play E flat than you are a D sharp, even though they are exactly the same note.
It should be noted that C flat major does technically exist (although I have never seen it used in a piece of music), because C flat major is exactly the same notes and therefore the enharmonic equivalent of B major (which has 5 sharps).
There are two things to be aware of, the first is that in major keys, if the notes are not the natural note, they are either sharp or flat. You do not get a mixing of sharps and flats in the same major key. The second point is that enharmonic equivalents are sometimes used to minimize the number of sharps or flats. Most piano players would agree with me that it is easier to read five sharps rather than seven flats, as in the case of B major/C flat major.
So enharmonic equivalents sound like a difficult concept, but they aren’t because they are merely different names for the same note just used in different contexts.