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In a few pieces of music I have read through, I have come across double-sharps and flats.

To my understanding, they are two semitones above/below the note indicated. What is, then, the point of these notations? Why don't you just write the equivalent note and avoid these accidentals?

  • 1
    AFAIR its mainly a formal notation issue. You can augment notes in the scale, so if F# is a note in the scale, but G is not (say in the scale of A-major). And you want to emphasize the fact that you are augmenting F# up a half step (say in a triad/chord), you write F## , even though you could have just as easily but a natural in front of the G. But that is just my recollection - which is why this is a comment. – crasic May 13 '11 at 9:14
  • 4
    @Noldorin: You may not (yet) have come across double accidentals in piano music, but I assure you they exist in the piano/keyboard literature. Just off the top of my head, I know that I have encountered them in Bach and Beethoven at the very least. – Alex Basson Jun 4 '11 at 12:34
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    @Noldorin : See the first movement of Moonlight Sonata from Beethoven ; there is 2 or 3 double-sharps there. – Patrick Da Silva Mar 29 '12 at 20:52
  • 1
    @PatrickDaSilva: I already accepted they exist if you read up. :-) Actually, as AlexBasson rightly hinted, I have come across some in my own playing between then and now. Now too many, but from time to time... – Noldorin Mar 30 '12 at 3:22
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    @Noldorin : I was just giving you an explicit example ; I came across double sharps and asked a question here myself about them, this is why I found this question. – Patrick Da Silva Mar 30 '12 at 16:22

11 Answers 11

68

Often it has to do with altering notes in a key that are already sharpened or flattened, such as a harmonic minor in a key where the 7th is a sharp. Take G♯ minor: You could write F♯♯ (or F𝄪) as a G, but then your scale would have no F note in it but two different G's. Every time you put down an G note, you'd have to attach a sharp or natural to indicate which note is to be played. It's clearer to have an F𝄪 and a G than to have a G and a G. And some will insist that every scale should have one of each letter-note.

I also suspect than in just intonation there's a difference between a doubly-accidentaled note and what would be the equivalent note in equal temperament (i.e., F𝄪 is not actually the same sound/frequency as G). This answer to another question does a good job of explaining that.

  • 19
    For example: In the G# harmonic minor scale, what's the seventh note? G#, A#, B, C#, D#, E, and... well, it's got to be some kind of F, right? And it has to be a half-step below G#. So it must be an F##. – Alex Basson Apr 27 '11 at 0:39
  • 1
    The G# major scale has this too (6+2#): G# A# B# C# D# E# Fx, enharmonic of Ab major scale (5b) : Ab Bb C Db Eb F Gb. – ogerard May 16 '11 at 14:58
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    +1 for mentioning temperaments. But in any temperament whose perfect fifth is not 7/12 of an octave Fx & G have different pitches. Temperaments which (like just intonation) are not meantone have another issue besides, namely that the tone between do & re (e.g. G-A in G major) is unequal to the tone between re & mi (e.g. G-A in F major). – Rosie F Jun 20 '16 at 10:19
35

It's spelling. It's like "hear" vs. "here". You wouldn't write "Come over hear so I can here you better" even though it sounds the same.

A major triad is spelled as if the notes are a certain distance apart. On the staff the notes will be on three lines or three spaces. In the key of C sharp minor, the tonic chord is C sharp, E, G sharp. You write it as C E G without the sharps because the sharps are already in the key signature. To turn it into a major chord you write C , E sharp, G -- not C, F natural, G.

Now suppose you're in B major. The third note of the scale is D sharp. To build a minor chord on D sharp you write D, F, A (which you play as D sharp, F sharp, A sharp because of the key signature). Now to make it a major chord you write D, F double-sharp, A.

There are times when you might write D sharp, G natural, A sharp when the chord has a different meaning. It has the same notes but it's functioning as something other than a major triad because of the chords that come before and after it. Again, it's like "here" vs. "hear".

  • 2
    Yes, that's where the analogy breaks down. In two chords G#-B#-D# followed by A-C-E, if B# and C sound alike to you but have different meanings as the middle notes of a G# major chord and an A minor chord, they are homonyms. If they sound different to you because one is in a major chord and the other is in a minor chord but they mean the same because they are played on the same key, they are synonyms. (Off topic: I'm a Zappa fan too.) – Mark Lutton Jul 16 '17 at 23:54
  • I'm a Zappa fan, but I have some doubts. Recently listening to composers like Stravinsky and Schoenberg and I'm questioning Zappa. The way he combined elements of rock/RnB/pop with cutting edge compositional techniques is impressive, but I sense that his music lacks cohesion. IMO he was often more interested in shock value than pure musical expression (he did have to make a living). His fusion jazz isn't too impressive IMO-mostly imitating Weather Report, Tony Williams Lifetime, etc. (Some of his alumni have said as much.) Sleep Dirt, Burnt Weenie and Jazz from Hell are my favorites right now. – Stinkfoot Jul 17 '17 at 2:35
  • @Stinkfoot - there will be cases, such as played on continuously variable pitch instruments such as violins, where B# and C are not the same note or played at the same pitch. – Tim May 2 '18 at 7:17
  • @Stinkfoot "Here" and "hear" are homophones, no? I think the analogy is spot on: same sound, different spelling. – Richard May 2 '18 at 15:36
  • @Richard - you're a little late to the party - LOL : same sound, different spelling - but they represent two completely different values/words/definitions. Not really so with enharmonics - C# and Db have exactly the same value on the piano. But you could quibble and say that C# and Db are also entirely different values - they come from different scales and function differently. I wouldn't entirely object to that argument either... – Stinkfoot May 2 '18 at 20:12
22

The flat or sharp symbols (not yet considering double-sharps and double-flats, we'll get to that) are used for two purposes:

  1. to indicate how the diatonic notes of a key different from the notes in the key of C
  2. to indicate how chromatic notes differ from the diatonic notes

It's in the latter case you encounter double-sharps and double-flats.

Consider the case of D major: F♯ and C♯ are notes in the scale (the third degree and seventh degree respectively). This is an example of the first type. But if you augmented the 5th in D major, you'd write it A♯. This is an example of the second type. NOTE that you couldn't write an augmented 5th in D major as B♭ because the fifth is an A and you're raising that one semi-tone.

When you raise or lower a diatonic note, it keeps its letter name. Now say you were augmenting the third. The diatonic note is already marked with a sharp, so you have to use a double-sharp to indicate it's raised a semi-tone. Hence it becomes Double sharp (G would be incorrect as that would be a fourth in D major, not an augmented third; similarly a diminished fourth in D major would be G♭ not F♯)

In B major, with its diatonic notes: B C♯ D♯ E F♯ G♯ A♯, if you needed to augment the 2nd, 3rd, 5th, 6th or 7th degrees, you'd use a double sharp. NOTE if you need to augment the B or E you write them B♯ and E♯ and NOT C or F.

If the diatonic note is already flat; the diminishing by a semi-tone would require a double-flat.

If a diatonically sharp note is to be diminished or a diatonically flat note to be augmented, you typically explicitly use the natural symbol ♮.

For example, a diminished fifth degree in B major would be F♮.

8

It's all about conventions. It would sound pretty weird to say that the major key of G sharp has both natural G and G sharp, don't you think?

It's also done to make it obvious when there's a foreign note to the current scale (say, a natural B in a C sharp major key).

It might be used by composers to point out certain tonal (diatonic or chromatic) relationships. For example, C sharp is "closer" to E double-sharp than to F. That way, composers can make any modulation into E double-sharp and then, by enharmonic equivalency go to the "distant" F.

There's even some documented music theory about how to write the chromatic scale correctly based on the current key signature.

  • 1
    The G# major example is why most musicians prefer to plan in flat keys. Less to think about even though the notes are enharmonic. – Rein Henrichs Apr 28 '11 at 22:04
  • I always understood that it was to help wind players cope with key transitions in complex pieces - stay with the flats when the previous section was in a flat key, or stay with the sharps and add one etc. – Michael Hetton May 2 '11 at 0:54
4

The actual reason double accidentals were created was to complete music theory. An example of this would be in augmented and diminished notes.

The rules of music theory state that an augmented interval MUST be a raised semitone of the perfect interval:

In the key of B, your steps are: B, C#, D#, E, F#, G#, A#, B

Your perfect 5th is an F#. To diminish it, you HAVE to drop the pitch a semitone, and so your diminished 5th would be an F♮ instead of an E#. When augmenting, the same rules apply. To augment it, you HAVE to raise the pitch a semitone, so your augmented 5th would be an Fx instead of a G♮.

In the key of Db, your steps are: Db, Eb, F, Gb, Ab, Bb, C, Db

Your perfect 5th is an Ab. To augment it, you raise the pitch a semitone, so your augmented 5th would be an A♮. To diminish it, the same rules apply. You HAVE to drop the pitch a semitone to diminish the interval, so your diminished 5th would be an Abb instead of a G♮.

However... when composing music, accidentals are dealt with differently. The modern purpose is to use the least amount of accidentals as possible.

When doing this, you should try to make it so you have no written naturals since they are already understood. Only the notes that are not natural should have accidentals. You will find out that this is not always possible with just single accidentals.

Below is a blue scale run in the key of C, written 3 different ways. The one at the bottom is the one with the least amount of accidentals.

|C, Eb, F, Gb, G♮, Bb, B♮, C, B, Bb, G, Gb, F, Eb, C| 7 accidentals

|C, D#, E#, F#, G, A#, B, C, B, A#, G#, F#, E#, D#, C| 4 accidentals

|C, D#, F, Ex, G, A#, B, C, B, A#, G, Ex, F, D#, C| 3 accidentals

Using less accidentals makes it less complicated, of course... Reading an Ex after an F♮ is really wierd, but it makes sense because it uses less accidentals.

Triple accidentals also exist. They are rare though, because the only case you would use them is if you need a double accidental on G#/Ab. Try to guess why ;)

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    I'm not sure I can get on board with your last point -- the amount of ink in a double flat is the same as two accidentals, so those examples would be equivalent. Besides, ink is NOT that expensive. We would still write the second way because it is easier to read, however -- that's the reason. – NReilingh Oct 11 '13 at 16:08
  • Actually, it would save ink to write it as G, G#, A, G#, which only has one accidental. As NReilingh points out, that can't possibly be the reason. – Dan Hulme Oct 12 '13 at 9:50
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Say we have music in a certain minor scale where a particular note is sharp, according to the key signature.

For instance, the key of G# minor.

In G# minor, in the natural minor scale corresponding to the notes of B major, we have an F# note: it approaches the G# tonic from a tone below.

Now what happens if we want G# harmonic or melodic minor? We need to sharpen this note to make a leading tone. So F# is sharpened again: Fx (let the x symbol denote double sharp). Although this note is enharmonic to G, logically, it is a natural minor scale's sharpened note.

Trying to represent it as a natural G would be notationally awkward as well as confusing.

It would be notationally awkward because given phrase of music in the same bar could use both the G# and the Fx pitches. If the same note letter G is used for both, then there may have to be numerous transitions to G natural and back to G#, which might be verbose and hard to read.

There is a bigger problem than merely too many accidentals: namely that the G would be written on the "wrong" staff line. If we use G natural instead of Fx, and then write an ascending G# melodic minor scale, we will end up with two consecutive notes on the same line: the G natural and the G#. This would be unnecessarily confusing, visually: a half step looking like a repeated note (where you have to decipher some accidentals to see that it is not the case).

It would be confusing because the Fx note in the harmonic minor scale in the key of G# minor is in fact a sharpened F#. It is not a flattened G#. We know that the G# is not flattened because G# is still present in the altered scale (it is the root, after all). Flattening a note in a scale means that we remove that note and replace it with one which is one semitone down. In fact what is going on here that the F# has been removed, and was replaced by a G. The notation follows this understanding, and calls it an F double sharp.

So this is the purpose of a double sharp (and likewise a double flat). It occurs when we want to sharpen (or flatten) a note in a scale, but that note is already sharpened (or flattened) by the key signature.

  • 1
    This is obvious in the keys of G# minor and D# minor. Consider how to write a short trill on the raised 7th and 8th (tonic) notes. In G# minor, you could write a g with a natural sign, then a g with a sharp, then a g with a natural, and so on. Or, you could write g-fx-g-f-g-f-g. Only one accidental, whereas the other has to have an accidental on each note because the note keeps changing from natural to sharp. Now, that's "notationally awkward." :) – BobRodes Feb 20 '14 at 20:53
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In order to explain The Purpose of Double Sharps/Double Flats I want to start with some very simple (albeit not very brief!) rules I used as a kid, and still teach to this day, for 'naming' the notes of any Major Scale.

First a few things to keep in mind about major scales (other scales don't always follow these rules):

   - Only the C Major Scale has No Sharps and No Flats.
   - We NEVER mix flats and sharps in the same Major Scale.  
   - The name of the scale includes the ROOT of the scale.
    (So the root of the Bb Major scale is Bb.  The root of G Major is G)

On with the rules:

RULE #1 - We must end up with 8 notes. Which doesn't help us a ton, but it's a start. And for now we can think of it in a few different ways:

 x x x x x x x x   or   1 2 3 4 5 6 7 8    or   Do Re Mi Fa So La Ti Do

 (variables / degrees / solfege)

RULE #2 - We must Start and End on the same note - the root & it's octave. So the name of the scale gives us the first and last note! Let's start with D Major - and now we have:

  • D x x x x x x D

RULE #3 - Every other letter of the musical alphabet must be used exactly one time - in alphabetical order. (and this is really the answer to your question - but it will take a minute to be clear why)

The letters of the musical alphabet are A B C D E F G. We're not talking about notes right now - just letters. And each one of them must be in every major and minor scale exactly one time - except for the root - which we've covered - it appears twice. So now we know a bit more about the D Major Scale:

    • D E F G A B C D

    WARNING: although I know i haven't made a mistake because I'm following the rules - I also know that I'm not finished simply because I know that C Major is the only scale with no sharps or flats - so I know this isn't complete - and that it will end up with at least one sharp or flat - it has to. But as we go forward - keep in mind that we cannot change any of those letters. We already know they must be there in that order. So - next rule...

RULE #4 -Every Major Scale is a specific sequence of half-steps and whole-steps.
- W W h W W W h (whole whole half whole whole whole half)

I used to remember it this way: "a major scale is all whole steps except from the third degree to the fourth degree and the seventh to the eighth which are half steps. Or Mi to Fa and Ti to Do. (3 to 4 and 7 to 8)

  • Back to our D Major -so far we have: D E F G A B C D
  • And let's just remind ourselves where the half steps go:
  • 3-4 and 7-8 which is F to G and C to D! We'll get to them in a minute...

At his point we have to analyze each 'pair' of notes - in order from left to right - by asking "what the interval is now", what interval do we want it to be - and do we need to change anything or can we move on... Here we go:

  • D to E is a whole step, I want a whole step, move on.
  • E to F is a half step, I want a whole step - now what?
  • I can't change any letter - I already now those are correct.
  • So what's a whole step above E? Not F - it's only a half step!
  • We can't change the E because that would mess up the D to E interval which we already confirmed is correct.
  • So we have to change the F. Not the letter!
  • Just the distance it is from the E. Or more accurately - what "F" is a whole step above E?
  • How about F#? Well that works - and look what it does with the G coming up:

We've got D w E w F# h G So check it out - the F# not only fixed the E to F issue - it also took care of our 3 to 4 issue where we needed a half step (F# to G!)

Now let's speed things up:

  • D to E = W
  • E to F# = W
  • F# to G = H
  • G to A = W
  • A to B = W
  • B to C = H
  • C to D = W

Hold on! Did you notice my problem? Right now we have W W h W W h W The B to C is a half step (we need a whole step) and the C to D is a whole step where we need a half step. So like before with the E F G thing, one change will fix both issues: let's raise the C to a C# and now we have a major scale:

  • D E F# G A B C# D - or - W W h W W W h

And to review the rules:

  • We started and ended on the same note - which there are 8 of.
  • We used every other letter of the musical alphabet 1 time in alphabetical order.
  • And we have the required sequence of half steps and whole steps.

Which tells us why the key of D Major has two sharps (F# and C#).

And finally - Double Trouble with Double Sharps and Double Flats

So let's quickly name the notes of the D# Major Scale shall we?

Start and end on the root with all other musical letters here once in alphabetical order:

  • D# E F G A B C D#

Analyze the pairs:

  • D# to E is a half step, I need a whole step so I have to change it to:
  • D# to E# (are you starting to see a problem already? me too!)
  • E# to F is - uh - Unison! - and I need a whole step! I really don't have a choice:
  • D# to E# to F* to G# to A# to B# to C* to D#

    • If i follow the rules - the two double sharps are necessary... However, this really isn't used in practice - it's a "theoretical scale" and although not impossible I suppose - I have never seen a double sharp or flat in a key signature. The main reason?

Well, in this case - we would use the enharmonic scale of Eb - which only has two flats!

  • Eb F G A Bb C D Eb

So - that accomplishes the same thing much easier - and we like easy.

Anyway - I've shown here a valid reason for needing double sharps and double flats - to follow the rules of major scale construction - the more common use of double sharps and double flats would be to indicate the "job" or "role" of the note in it's specific context. For example, if I'm playing a song in G major but then start noticing the use of D# regularly I can usually safely assume that we've modulated to the relative minor key of Em and the D# is being used as a leading tone as in the E Harmonic Minor scale. A 'raised seventh' in E minor - or an 'augmented fifth' in the context of G major. So - same example - but let's start in B Major and modulate to the relative minor of G#m and now we want a raised seventh degree of the G#m scale - that's an F double sharp - the leading tone - by 'raising the seventh degree a half step from F# to F double sharp. G natural might be easier to deal with - but it wouldn't be a 'raised seventh'.

hope this helped!

stay in tune and keep the groove, brad

  • Do believe this could be (needs to be) condensed. Brad, it's your first attempt on this site - take a look at the more upvoted answers to glean some ideas of being succinct. – Tim Jun 20 '18 at 13:38
  • Probably worth mentioning I did read through music.stackexchange.com/help/how-to-answer and - being long winded by nature (yeah I admit it) - I took the following to heart: "Brevity is acceptable, but fuller explanations are better." Brevity vs. Fuller is not the same as Succinct vs. Long-Winded to be sure, but anyway... – bradpikemusic Jun 20 '18 at 17:28
  • Brad, far and away yours is the best answer. In fact I scrolled through the entire page of answer before selecting yours because it was the longest and after reading I will offer that 'hand-holding' statements like "Hold on! Did you notice my problem?" aren't relating information. In that instance you could, one option, say "Notice that ... " – Randy Zeitman Jun 20 '18 at 21:29
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Using G# harmonic minor as an example: the natural minor consists of G#, A#, B, C#, D#, E and F#. In order to create a harmonic minor, the 7th note, in this case F#, must be raised. This means that F# becomes Fx because in raising, the note preceeding the accidental symbol must remain the same - in other words, you can't have a G and a G# in the same scale because all letters are used and only once in every scale out there.

The purpose of double sharps and flats in key signatures is to represent this scale in the way it is written, and avoid constant use of accidentals on a note - as per the example switching between G and G#. The purpose of double sharps and flats within the piece is for presentation; in order to show a section is written from - and can be thought of as - a different scale. For example, in bar 34 of the 1st movement of Beethoven's Moonlight Sonata, double sharps are used to show the broken chord series consists of notes in G# harmonic minor, while the piece is written in E major.

1

How would you propose we raise the leading tone of a# minor if not with the use of a double sharp? Sometimes notes with sharps in front of them also have to be raised by a semitone and this is where double sharps come in.

1

One benefit of using F x instead of G Natural in a key where G is sharp (e.g., A Major) is that if you mark the G Natural it stays natural throughout the bar, and you may want the G to be played as a G # in the rest of the bar. It would be unfortunate to write G Natural, then G# again in the same bar. Better to write the F x and leave the subsequent G notes alone, i.e., they are already sharp as per the key signature.

  • An example of this is on page 5 of the song "My Grandmother's Watch" (see loc.gov/resource/sm1878.09874.0/?sp=5 second measure) . The piece is in G major (one sharp) but there's a B major chord (major III) which contains a D#. Each D# within the measure is preceded by a grace note a half step below. Alternating between D natural and D sharp would be rather more awkward than alternating between C double-sharp and D sharp. – supercat Feb 8 '17 at 18:08
  • There is a case where you'd actually have to write the G as Gnat., then put the accidental back for G#, depending on what the Gnat. signified. If it was supposed to be m7, you certainly would not write it as Fx. – Tim May 2 '18 at 7:08
0

From a music theory point of view the double sharps and flats are necessary to preserve the relationship between the notes and the key. I'll explain by example.

The degrees of the major scale are numbers {1, 2, 3, 4, 5, 6, 7, 8 (octave)}. In the key of C maj these notes (by letter name) are {C, D, E, F, G, A, B, C}. The formula for building chords is to stack thirds (every other note). C maj is {1, 3, 5} or {C, E, G}, and C min would be {1, b3, 5} or {C, Eb, G}. In the key of C flat the Cb min chord would be built as {Cb, Ebb, Gb}. In equal tempered tuning this is enharmonic to {Cb, D, Gb} but the context is lost with these notes. The musician who plays {Cb, D, Gb} on a piano will hear Cb min, but looking at the stacking of notes on sheet music it would not be immediately apparent that this is a minor triad.

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