Time to discuss something quite abstract that confuses a lot of people who aren’t very theory literate.
Finding them confusing or not understand the "why" of the is understandable; if you've learned the Fretboard of the Keyboard and you know all the notes of the 12 Tone Equal Temprament Scale, these exotic little buggers can leave you scratching you head wondering if you've made a mistake somewhere...
You haven't. 👍🏽
Some of the tables in this post have a lot of data in them and on mobile/cell phones they're going to look a bit super-squashed so this one might be best viewed on a Desktop or Tablet for the extra screen realestate.
Notes that are Enharmonically Equivalent are notes that have the same PITCH but different NAMES based on how they're used and where they appear.
Each version of the note serves a very specific purpose and HAS to be what it is for the internal logic of a Scale or Key to function correctly.
We encounter these things all the time in Scales and Keys and generally no-one seems to care; for example, the notes G# and A♭ are Enharmonic Equivalents; they both sound the same and occupy the same location on the Fretboard or the Keyboard but because they are a what could be considered “everyday accidentals”, ones that occur between other “non-accidentals” like G or A, we all accept that in a Flat Key it’s A♭ and in a Sharp Key it’s G#.
However, to really understand what’s happening we need to review how the Major Scale is built to really get to the root of why these things exist.
Scales are made up of 7 NON-REPEATING (this is important) notes that use the letters A-G; this collection of 7 is drawn from the 12 Tone Equal Temperament Scale (often called the Chromatic Scale).
This Scale contains all the notes including the “Accidentals”.
The distances between notes in the Scale are called Intervals. They come in Whole-step (W) and Half-step (H) forms.
If the movement between notes requires you to “step over” another note, that is a Whole-step (W) movement. If the movement is from one note to the next with NO note between, this is a Half-step (H) movement.
If we start with C Major (because it has no Accidentals) we have the notes C-D-E-F-G-A-B, a collection of 7 NON-REPEATING letters.
If we take this Scale and look at it in the context of the 12 Tone Equal Temperament Scale we can see the interval pattern formed to create it.
(I’m going to concentrate on the Sharp Keys for the sake of time and space, but the concepts hold true for the Flat ones too).
On the bass Fretboard, that looks like this:
Hitting all the notes C-D-E-F-G-A-B-C (incidentally all the White Keys on the Piano from C to C) gives us the pattern: W-W-H-W-W-W-H.
We have to "step over" some notes to get from one note in the Scale to the next and for others, we don't. This pattern is the same for ALL Major Scales. Learn it once and you can build any Major Scale from any note.
If we move our way up the 12 Tone Scale and apply this pattern/formula at every note we'll eventually get ALL the Major Scales.
For example, here’s same table with E♭ Major in it.
On the bass Fretboard, that looks like this (notice that the fingering pattern is exactly the same; learn this shape and you know ALL the Major Scales 👍🏽):
If we move our way up the 12 Tone Scale and apply this pattern/formula at every note we'll eventually get ALL the Major Scales. However, just doing this gives us a really ugly, not very useful table of Scales/Keys (you have been warned...).
Told you it was ugly...
If we take a deep breath and look for the notes in the Green boxes we can see that these Scales have different amounts of Sharps or Flats in them.
Using this information we can build out a new table with each Scale/Key rising by one Sharp at a time until we get something much tidier and useable.
Here are just the Sharp Keys:
Let’s remove all the notes we don’t need for the Scales to be right and we get this (incidentally this is the foundation of the Circle of Fifths that you’ve probably heard of):
This table is much better but now it has a couple of notes in it that are what cause people the problems… We have encountered our more “exotic” Enharmonic Equivalents…
Remember: the Major Scale MUST have 7 NON-REPEATING note names in it and it MUST follow the W-W-H-W-W-W-H pattern.
By meeting these conditions we have no choice but to include the notes E# and B# and herein lies the confusion for most people.
On the Fretboard and the Keyboard the notes E# and B# occupy the same places as F♮ and C♮ respectively. They sound the same too so what’s the deal?
If you don’t understand how and why Major Scales work the way they do then this will be a head scratching moment for you and you may come to believe it's all arse.
If we take the Key of C# Major from the table above it MUST have 7 NON-REPEATING notes in it so we have the notes C-D-E-F-G-A-B notes.
However, since we’ve been moving along the 12 Tone Scale collecting the Keys in order as the Sharps increase by 1 each time, we’ve arrived at a point where we have these 7 NON-REPEATING notes but they ALL have Sharps and that gives us: C#-D#-E#-F#-G#-A#-B# and NOT C#-D#-F♮-G#-A#-C♮-C#...
I know, it's not "really" simple...
When you understand how a Major Scale is built these “exotic” Enharmonic Equivalents make perfect sense.
The same logic used here applies to the Flat Keys. When you get up to Keys like C♭ Major you encounter notes like C♭ and F♭. This is just the Flat version of what we’ve seen above.
For the Scale to be mechanically sound, ie: following the W-W-H-W-W-W-H pattern and containing 7 NON-REPEATING note names, you MUST use C♭ and F♭ in them even though when played they sound like B and E and share those positions on the Fretboard and Keyboard.
In short, the Key of C♭ Major is Enharmonically Identical to the Key of B Major, a Sharp Key with 5 Sharps in it: B-C#-D#-E-F#-G#-A# and a hell of a lot easier to conceptualise and play!
I hope that helps.
It’s a bit of an esoteric, deep nerd subject and I’m sure people have written entire books and doctoral theses on this subject but this is just a high-level look at what they are, why they are and how they work.
