Circle of fifths, enharmonics?

Why are the flats or sharps named the way they are? I have ideas, but pretend like I know nothing. (Not much of a stretch.)

For example the left, flat side. Why is B flat not called A sharp?

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A major scale consists of 7 tones and has a particular structure of 2 whole tones – 1 halftone – 3 whole tones – 1 halftone.

Suppose we have C major scale (all white keys). The key is C major, and the tonic is C.

Let’s now move our tonic C down the fifth. We get F. But if we play a scale from F using only white keys, we can see and hear that a major scale structure isn’t respected, and the “wrong note” is 4th degree of the F scale – B natural. Note that the A sounds fine, it’s the B we need to lower.

So, in order to conform with the structure of major scale we need to lower that B, so we get Bb. Thus, we get a key of F major, with F as a tonic, and one flat sign – Bb – in key signature. B flat isn’t called an A sharp here because we already have the A note in this key, and it’s not sharp, it’s natural.

Then we can repeat this procedure and move further down the circle of fifth. The tonic of the next key will be Bb, and the note we’ll have to lower will be E. Thus we get the key of Bb major with two flats (Bb and Eb) in key signature. And so on.

We can choose to move not down the circle (getting more and more flats), but up, getting sharps. We’ll add sharps to notes in order to maintain major scale structure. And if we move far enough, we’ll start getting double sharps and at some point we’ll get keys, for example, of B# major or E# major. E# major enharmonically equals F major (in equal temperament), but the names of scale degrees are different – they are like in E major, (with appropriate sharps/double sharps), and the sound of E# major is identical to F major.


I think the most important line of @alexander 's response is the first line. A huge chunk of musical theory emerges from the fact that the diatonic scale traverses the octave in a characteristic sequence of intervals that repeats itself. One way of looking at that pattern is the major scale, in which case those intervals are layed out as follows: W-W-H-W-W-W-H. The minor scale is W-H-W-W-H-W-W, which is just looking at the same repeating sequence of intervals from a different starting point.

 ^             ^             ^

     ^             ^             ^

C major and A minor are the only diatonic scales where the interval pattern falls in such a way that all the tones line up with the “Natural” note names of the staff (strictly speaking, the other 5 “modes” of C major also line up with the natural note names, e.g. D Dorian, E Phrygian, F Lydian, G Mixolydian, B Locrian).

Per @Ian 's excellent post in another thread, as keyboard instruments developed, they came to adopt the convention of placing those naturally named notes on the “white keys”, and placing the remaining 5 notes of the chromatic scale on the “black keys”.

Because we can see that our musical system has 12 notes in any octave (with an equal intervalic distance between any two adjacent notes), It should be intuitively obvious that regardless of note names or “white keys versus black keys”, we can construct a 12 tone chromatic scale using any note as the starting point. The interval pattern for this would be H-H-H-H-H-H-H-H-H-H-H-H. The chromatic scale can be thought of as a sequence of intervals that gets you from your starting note to the note one octave highter. There’s no reason we can’t use an artbitrary note as a starting point, and rather than ascend through the pattern of the chromatic scale, ascend through the pattern of the major scale (or any diatonic scale). So in the case of the major scale: W-W-H-W-W-W-H. If we do this with the major scale using any note other than C natural as the starting point, our pattern will end up falling onto some notes that have “non-natural” names (i.e. “the black keys” on the piano). As @alexander 's post mentions, we assign names to these “non-natural” notes BASED ON THE CONTEXT IN WHICH THEY ARE PLAYED, avoiding using the “letter” part of the note name more than once within the same scale.

So for a scale that includes E natural, for example, if the same scale includes the note one half-step below E natural, we will avoid calling that note “E flat” to prevent having two “Es” in the scale, and will instead call it “D sharp”. In contrast, for a scale that includes D natural and the note one half-step above D natural, we will avoid calling that note “D sharp”, and will instead call it “E flat”.

And regarding the circle of fifths in general, check out this video by Michael New:


I’ll take a whack at a concise answer.

We generally can organize any piece of music to be based on some common 7 note scale - a key center, often a major or minor scale.

To make reading music (or even discussing the notes) simpler we want the pitch collection (the scale, the key center) to have

  1. only one of each letter (A, B, C, D, E, F, G)
  2. as few ‘double sharps’ or ‘double flats’ as possible
  3. As few instances of E#, Fb, B#, or Cb, as possible

If we try out alternate spellings of the scales as was pointed out, we’ll often get something that ‘breaks’ the guidelines

key of Eb major as example

Eb F G Ab Bb C D >

could be spelled

D# E# F## G# A# B# C## but yikes

or D# F G G# A# C D but we have two types of Ds and two types of G. not even possible to have a key signature for it.

See here,
All the TAB is the same, but on the staff the first and last measures make the most sense. The second measure at least shows the notes in order, going up in steps, but we have some odd enharmonics. The third measure is just downright kooky!


Really cool ways of explaining this!

I’ll add my two cents:

In addition to the necessity of making senseable scales there is another aspect to the question of

That aspect is the function of the Note, which depends on the harmonic context.

Now bear in mind:

In a C7 Chord you would call that note a Bb, because it is the seventh note up from the root note of the Chord:

1 - 2 - 3 - 4 - 5 - 6 - 7
c - d - e - f - g - a - b

So the Bb’s function is that of a 7th in that C7-chord.

In an F#-chord on the other hand, you would write it as A#, because it functions as the major third:

1 - 2 - 3 - 4 - 5 - 6

f#- g#- a#-b-c#-d#

That way more complex context like #9 becomes explainable:

E7#9 chord:

1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9

e - () - g# () - b - () - d - () - fx

(an “x” commonly indicates ##)

There already is a major third, “g#”, so the “fx” is not called “g”, because it doesn’t function as third in that chord. This complicates the note reading a bit - fx instead of a simple g - but it displays the harmonic information contained in that chord more accurately.


well put! My first exposure to this was Willam Leavitt’s “Advanced sight reading for guitar” book which had a lot of reading exercises in harmonic minor. So in, say G# harmonic minor, the natural 7th is Fx. And it seems weird to people who are new to it, but it really does make it all cleaner.


This sounds a little contradictory to me. Natural minor has natural 7th, and harmonic minor has raised 7th. So I guess it is more correct to say that in G# harmonic minor the 7th is Fx, while the natural 7th is F#.

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I know some people use the terminology like that, but I think it’s way more confusing. In fairness, it’s less ambiguous if I say “the major seventh” rather than “the natural 7th”

“natural” being more ambiguous than “major” or “minor”

Even if some conventions teach otherwise, I do stand by this because when you’re dealing with music that changes modes it’s way less confusing, but to each their own and I’m sure what’s best could vary with context.


I see. You consider harmonic minor as a scale of its own, rather than natural minor with some degrees altered.

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Sort of - I see the major scale as being “the intervals” and spell everything in relation to that.

For example:

I say the natural minor/aeolian scale is 1 2 b3 4 5 b6 b7

the harmonic minor is 1 2 b3 4 5 b6 7

lydian dominant is 1 2 3 #4 5 6 b7

a minor seventh chord is 1 b3 5 b7

‘fur elise’ starts 5, #4, 5, #4, 5, 2, 4, b3, 1

if someone asked me what the difference is between aeolian and dorian (just in terms of the pitches, not the use or application) I’d say “dorian has a major sixth and aeolian has a minor/flat sixth.” Actually before this exchange I probably would also say that dorian has a natural sixth but I see now that could be a little ambiguous…so thanks!

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Would it be correct to say the reason is to make it easier to read on the staff?

I’m still wrapping my head around it, thanks for all the explanations.

That’s definitely a huge, if not the biggest, part of it.

But also when we are considering different harmonies it also makes things cleaner.

For example, for a minor 7th chord:

it’s 1 b3 5 b7

well, a #4 and a b5 are enharmonically the same.

but minor 7th with a b5 vs with a #4 are two different things

the b5 means that “the fifth is flat” - there is no perfect/natural fifth in the chord, but it doesn’t say anything about the 4

the #4 means there is a sharp 4th in the chord, but it doesn’t say anything about the 5th.

So a #4 over a minor 7th chord would typically be a m7 with a natural fifth and a #4

a m7b5 is a different chord entirely (and much more common) - different function in most progressions, different harmony, you improvised over it differently, etc.

hope that helps…

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You know, adding just a super practical thing that I think it’s easier to understand things like:

5 #5 6 than it is to write 5 b6 6. Just a small detail but in the latter you might have to stop for a second and go “wait, is the second occurance of the 6th also flat?” And in the former it is clearer.

So similarly when spelling a scale or chord kind of confusing to say something like 1 b3 3 b5 5 7 rather than 1 #2 3 #4 5 7

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Wouldn’t it be so much better to recreate all these names with no sharps n flats, though that’s off topic… I really feel it could be so much simpler if each note had a name.

It would wipe out all the confusion.
Am I incorrect?

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There actually ARE notational systems that do this, typically for much more ‘modern’ music and modern approaches.

It is extremely relevant that something like, 1 3 5 7 maintains a similar quality of sound whether it is 1 3 5 b7, 1 b3 5 b7, 1 b3 5 b7, etc etc, and the same holds true for other instances where the letters/numbers may be the same but the flats and sharps change. They definitely sound different but there is a certain type of consistency when compared to something like 1 2 3 4 or 1 3 4 5 (any b/#)

I could kind of babble about this for a while but I think if you’re new to theory you’ll find the more you study chords, scales, intervals, and analyze music and progressions, you’ll see this consistency and the usefulness of it.

The 12 tone systems that I referenced aren’t as useful for ‘normal’ tonal music with common harmonic conventions

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That’s one reason. But I like to think that every note in a scale has a function, at least when looking at chords. Using that logic every step in the scale gets it’s own note, no repeating of note names/numbers because that would make the note’s function confusing.

Ignoring upper extensions for this discussion the main notes are 1 = root, 3 = major/minor, 5 = provides stability, 7 = leading tone. The 2, 4, and 6 are replacement tones. The 2 and 4 replace the 3 and create suspension, the 6 replaces the 7. The 2 and 4 can be added to a major or minor triad but that’s a whole other discussion of whether it’s a ninth chord, an add 2, add 9, blah blah blah crazy-hair naming convention theory black hole waste of time.:exploding_head:

Think of the scale degrees as a convertible car. The 1 is the car brand, 3 is open/closed top, 5 is the frame, 7 is automatic steering. The 2 and 4 are replacement hard or soft tops, 6 manual steering. Upper extensions are custom paint jobs. Chord progressions are a road trip.

A minor chord is spelled with a b3 instead of a #2 because the 3 determines major or minor. A diminished chord is spelled with bb7 because that note is functioning as a type of leading tone (7) note. The #4 (augmented fourth) and the b5 (diminished fifth) notes are the same enharmonically but they have different chord functions. #4 is a custom hard top, b5 is a bent car frame.

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Not sure if this is slightly OT, but there are historical reasons behind all this stuff. The Western tradition of writing music goes back to the Middle Ages when neumes were used for writing plainchant tones in monasteries. Originally they just indicated whether a syllable was rising or falling in relative pitch, with some refinements to show ornamentation in pitch and meter. As things got more complex, “graduated neumes” were invented, basically the origin of the staff lines.

Thing is, the dominant template for plainchant was the A minor scale. So A was the center of the organization of the 7 diatonic tones. Hence A B C D E F G. But as other kinds of music needed to be transcribed, particularly as music in the major modes came to dominate, the center moved to the relative major of A minor, namely C. Hence our screwy thing of starting our alphabetical arrangement two steps in from the beginning: C D E F G A B.

As regards sharps and flats, the usual account I’ve read is that the diatonic scale always has a tritone interval (between the 4th and 7th in the ionian mode), which was considered ugly (the “devil’s note”) and to be avoided. You could do that by flatting the 7th, though of course then you get a tritone between the 7th and the 3rd, so you flat the 3rd… and before you know it you have a complete set of black keys.

Relating the modes to each other in terms of a single note change is something I was taught by the inimitable Boston area guitar teacher, Sam Davis, who uses it to conceptualize not just how the ionian template modes relate to each other but also how the whole modal system, which includes the modes of the 3 altered scales (yup, they have modes too–what, you thought there were just seven?), relates between the templates as well as within them. I loved his term for this system (Sam being brilliant at inventing his own terminology): absolutistic modal flatitude. Sam’s guitar lesson flyers are worthy of devoted study in their own right (the “Channeling Mel Bay” one prompted a phone call from the esteemed Mr Bay, then still extant, pointing out that he wasn’t in fact dead yet, to which Sam replied “That doesn’t mean I can’t channel you.”)


Just to close the circle: Sam’s method in the Ionian template actually starts with the Lydian mode, because it’s the most upwardly inflected, or “most major” as he put it, in that it not only has the major 3rd but also a “major” 4th. So you flat the 4 to get Ionian; you flat the 7 of Ionian to get Mixolydian, flat the Mixo 3rd to get Dorian, the Dorian 6th to get Aolian, and so on until you have everything flatted that can be flatted and still be in the template. Hence “flatitude.” Once I got it, I found it a faster way to access the modes mentally than the standard thing of “phrygian shifts the root to the 3rd of the major scale etc,” which was how I was first taught it back in the dark backward and abysm of time—always seemed an impossibly slow and cumbersome algorithm to load in the midst of an improvisational situation.

Though I have to admit I never mastered the whole Music Molecule in all its majesty. He has a physical model of it he built using one of those molecular model kits with the rods and spheres you see in high school science classrooms.


As a guy who’s an atrocious sight-reader…

…enharmonic naming conventions DO make sight-reading infinitely easier. Since each scale degree is it’s own line or space, then if you know what key you’re in (from the key signature) then you basically can just follow the melodic contour of the line rather than thinking about note names while you’re playing, and just stick within the appropriate scale. Most notes are going to be notated without sharps or flats (since that’s already captured in the key signature) so if you see a sharp or flat notated on the staff you know you just need to be a half step higher or lower than the “correct” scale pitch.

This is a big part of the reason why it matters to notate something as Bb rather than A# in, for example, the key of F - it keeps the 5th degree on its own ledger line, whereas in F you would otherwise have both an Ab and an A#, and while the pitches would technically sound correctly, distinguishing between the two as written would be an effing nightmare while trying to read on the staff. :rofl:

Honestly, it’s really a pretty elegant solution. To your point, would it be easier to try to use a 12-note system with full chromatic naming, rather than a diatonic system with seven pitches and sharp/flat modifications…? In standard western music, I think that would honestly be more confusing simply because the very fact that standard notation sort of “pre-defines” a universe of 7 pitches when you indicate a key signature and only gives you special indications as to when you’re deviating from that universe radically simplifies the process of reading music, by a factor of nearly two.


This is tangential, but came across it recently and might be of interest…

1  b2  #2   3  b5  #5  b7   --  How I think of the altered scale.
1  b2  b3  b4  b5  b6  b7   --  How I saw someone introduce it recently.

…and I’m fond of the former because it nailed home the importance of 1, 3, and b7 better than the enharmonic, literal view.