There seems to be confusion amongst musicians, and others who play an instrument, in that the role and function of the double and even triple sharp/flat is misunderstood or even dismissed as irrelevant. But the simple truth is that both the double and triple accidental are messengers of the underlying truth that is occurring in the music.
First, the double sharp. The most common role the double sharp has is to announce to the performer or reader that the music is heading into the relative minor key via the use of the Harmonic minor scale. The first time the double sharp accidental appears in music is usually in the key of B Major:
B Major = B C# D# E F# G# A#
A change from the Major to its relative minor is most easily accomplished via the raising of the root of its Mixolydian mode:
F# Mixolydian = F# G# A# B C# D# E (+1) = F## G# A# B C# D# E = F## Alt bb7
You can see that the sharpening of the F# to F## (I apologise for the two sharp signs instead of a double sharp sign but that is the limitation of this font) converts the F# Mixolydian mode into the F## Alt bb7 mode, which is mode VII of G# Harmonic minor. So, the double sharp is simply used to announce the shift into the relative minor key and scale.
The second most common appearance of the double sharp is when the music is in the key of F# Major. In this key there are two simple opportunities for it to occur, namely the modulation to the relative minor as outlined above, using the Mixolydian mode to get from F# Major to D# minor, and also the modulation to the minor key on the second degree, using the Ionian mode, which is where the Melodic scale comes in. Both ways of introducing the double sharp in F# Major are shown below:
C# Mixolydian = C# D# E# F# G# A# B (+1) = C## Alt bb7 C## D# E# F# G# A# B (Mode VII of D# Harmonic minor)
F# Ionian = F# G# A# B C# D# E# (+1) = F## G# A# B C# D# E# = F## Altered/ Superlocrian (Mode VII of G# Melodic)
There are more ways of getting the double sharp into music, but these are the most common and easiest to do. It is very useful to know this fact and to understand more broadly how a single alteration affects the music you are playing or listening to. The shift to another key or scale often comes down to a single accidental, so being able to recognize it is of fundamental importance.
The first time that a double sharp can actually occur, in terms of possibilities, is when the music is in the key of A Major:
A Major = A B C# D E F# G#
The only sharpened note that can be raised again is the F#. The mode on F# in the key of A Major is F# Aeolian, so by raising the F# to F## we get the first possible double sharp in music:
F# Aeolian = F# G# A B C# D E (+1) = F## G# A B C# D E = F## Alt bb367
The mode F## Alt bb367 (1 b2 bb3 b4 b5 bb6 bb7) is mode VII of the G# Locrian natural 7 scale. This scale is used in music from the baroque period all the way through to now, but most people are unaware of it as well as most other scales.
Double flats. Not as common as its sibling, but still in a lot of music. The reason why is that the common modulations, relative minor, parallel minor, back and forward a fifth are all best accomplished with the raising of notes. Flattening a note leads to more unusual scale changes such as Dorian (-1) = Lydian +#26 (Harmonic Major #4 mode VI) which is more complicated to use.
The first time a double flat can occur is in the key of Eb Major (Eb F G Ab Bb C D). The Bb can be flattened again to Bbb and the mode on Bb is again, Mixolydian, mode V of Eb Major:
Bb Mixolydian (-1) = Bbb Super Lydian Augmented (S.L.A.) = Mode V of Bb Ionian b5
So, the first double flat leads to the Ionian b5 scale and the first double sharp leads to the Locrian natural 7 scale, both of which occur in music from the last three hundred years right up to the present.
If you are interested in the use of triple sharps and flats, here is a post to my article on that very thing:
Thanks for reading. Don't forget, the second printing of my book is still available at the moment.
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