15 Keys?

[Yank]

In one of my bass books, it has the circle of fifths, but 3 of the twelve it gives both enharmonic equivilents. It lists both B and C flat, D flat and C sharp, and F sharp and G flat. Why these three keys? I also don't find much music written in these keys. Is this just an intellectual exercise?

[Dood]

Although I am sure there are better resources, this one does a good job of explaining!

[url="http://musicnotation.org/tutorials/enharmonic-equivalents/"]http://musicnotation...ic-equivalents/[/url]

Off the top of my head, I think Whitney Houston's 'I Wanna Dance With Somebody' is in C#, but for pop and rock, I can't think of any in Cb right now!

Edited April 18, 2017 by dood

[Dood]

[quote name='dood' timestamp='1492511784' post='3280781']
but for pop and rock, I can't think of any in Cb right now!
[/quote]

Unless the song was originally played in C physically but on guitars dropped to Eb I suppose!

Edited April 18, 2017 by dood

[Steve Woodcock]

[quote name='Yank' timestamp='1492509157' post='3280749']
In one of my bass books, it has the circle of fifths, but 3 of the twelve it gives both enharmonic equivilents. It lists both B and C flat, D flat and C sharp, and F sharp and G flat. Why these three keys?
[/quote]

Have a look at the diagram below, you will see as you go clockwise (up a perfect fifth) you add one sharp to the key signature - [b]there are only 7 notes in a key therefore the most alterations a key signature can contain is 7[/b]. If you go clockwise around the circle (up a perfect fourth) you add one flat to the key signature - again, the maximum you can have is 7.

[attachment=243332:Circle of Fifths.jpg]

As you have noted three of the keys are enharmonic equivalents of each other:

B (5 sharps) and Cb (7 flats)
F# (6 sharps) and Gb (6 flats)
C# (7 sharps) and Db (5 flats)

F# and Gb both have the same number of alterations (6 each) however B and Cb, and Db and C# have 5 versus 7 alterations - which is easier to read, 5 right?

[dlloyd]

[quote name='Steve Woodcock' timestamp='1492519430' post='3280863'][b]there are only 7 notes in a key therefore the most alterations a key signature can contain is 7[/b]
[/quote]

Just to be pedantic, there is no theoretical limit to 7 sharps or flats.

Just going through the sharp keys:

G = 1 sharp, F#
D = 2 sharps, F#, C#
A = 3 sharps, F#, C#, G#
E = 4 sharps, F#, C#, G#, D#
B = 5 sharps, F#, C#, G#, D#, A#
F# = 6 sharps, F#, C#, G#, D#, A#, E# (we're really at the limits of most practical usage here)
C# = 7 sharps, F#, C#, G#, D#, A#, E#, B#
G# = 8 sharps, Fx, C#, G#, D#, A#, E#, B#
D# = 9 sharps, Fx, Cx, G#, D#, A#, E#, B#

etc.

Fx is "F double sharp" = G natural. Triple sharps are given the symbol "#x". I have never seen one in the wild.

Believe it or not, there is music out there written in G# major.

The situation for flat keys is similar... Double flats get the symbol "bb"

Fb major has Bbb, Eb, Ab, Db, Gb, Cb, Fb

[Trueno]

Never seen a double sharp or double flat as a key, although I have seen it in music where it aids the playing of the music (or at least it does for woodwind).

[dlloyd]

[quote name='Trueno' timestamp='1492859806' post='3283694']
Never seen a double sharp or double flat as a key, although I have seen it in music where it aids the playing of the music (or at least it does for woodwind).
[/quote]

Obvious places to find a double sharp within a score would be in G# minor, where the F# is sharpened to Fx, but yeah, I started to see them around grade 6 clarinet.

There's a few examples of scores written in G# major here:

https://en.wikipedia.org/wiki/G-sharp_major

Not common at all.

[Steve Woodcock]

[quote name='dlloyd' timestamp='1492858552' post='3283686']
Just to be pedantic, there is no theoretical limit to 7 sharps or flats.
[/quote]

[i]Theoretical [/i]being the key word there, it really is an academic exercise and of no practical use.

[dlloyd]

[quote name='Steve Woodcock' timestamp='1492872898' post='3283815']
[i]Theoretical [/i]being the key word there, it really is an academic exercise and of no practical use.
[/quote]

There are real pieces of music that are written in keys that fall outside of the limitations you're claiming, but sure, they are few and far between.

It's important to understand that G# is not the same as Ab in use, even if they sound exactly the same on a fixed pitch instrument. There are solid reasons why a composer would use G# major rather than Ab major, for example a modulation from C# major to G# major is far easier for orchestral instrumentalists to deal with than rewriting everything after the key change to Ab major.

For most of us though, we'll never have to deal with thinking about these things. And I confess... on my grade 7 clarinet exam I cheated and played a Db major scale when I was asked for C# major.

[Steve Woodcock]

[quote name='dlloyd' timestamp='1492887868' post='3283969']
There are real pieces of music that are written in keys that fall outside of the limitations you're claiming, but sure, they are few and far between.

It's important to understand that G# is not the same as Ab in use, even if they sound exactly the same on a fixed pitch instrument. There are solid reasons why a composer would use G# major rather than Ab major, for example a modulation from C# major to G# major is far easier for orchestral instrumentalists to deal with than rewriting everything after the key change to Ab major.
[/quote]

Not my limitations, rather those of traditional music notation practices.

You are correct that a modulation to the dominant of C# major would be written in G# major rather than Ab major as to avoid mixing numerous sharps and flats, however my point was that a [i]key signature[/i] with a double accidental is never used and is therefore a theoretical concept.

[dlloyd]

[quote name='Steve Woodcock' timestamp='1493174879' post='3286230']
Not my limitations, rather those of traditional music notation practices.

You are correct that a modulation to the dominant of C# major would be written in G# major rather than Ab major as to avoid mixing numerous sharps and flats, however my point was that a [i]key signature[/i] with a double accidental is never used and is therefore a theoretical concept.
[/quote]

That's what I thought too. However John Fould's World Requiem ([url="https://en.wikipedia.org/wiki/A_World_Requiem"]https://en.wikipedia...A_World_Requiem[/url]) apparently has a section written in G# major with the double sharp in the key signature. I have never seen the score.

Edit: And here's one in the key of Fb: http://www.enspub.com/pages/sku93503.htm

Edited April 26, 2017 by dlloyd

[Steve Woodcock]

[quote name='dlloyd' timestamp='1493237165' post='3286862']
That's what I thought too. However John Fould's World Requiem ([url="https://en.wikipedia.org/wiki/A_World_Requiem"]https://en.wikipedia...A_World_Requiem[/url]) apparently has a section written in G# major with the double sharp in the key signature. I have never seen the score.

Edit: And here's one in the key of Fb: [url="http://www.enspub.com/pages/sku93503.htm"]http://www.enspub.co...es/sku93503.htm[/url]
[/quote]

I can't find a copy of World Requiem however I have just found the Ewald score - this is the first score in over 20 years of study where I have seen this written! I still maintain this is highly unusual as there is no reference of such practice in Gardner Read's bible on score writing, [i]Music Notation: A Manual of Modern Practice [/i](Gollancz, 1974); the only mention I could find was from composer Paul Hindemith, who also denounces their usage:

[indent=1]But in practice, while keys containing more than 7 sharps or flats are occasionally used (as a result of modulations in the course of simpler keys), they are never indicated in signatures.[/indent]
[indent=16][i]Elementary Training for Musicians ([/i]Schott, 1949)[/indent]


Fascinating stuff.

[Bilbo]

I think it is worth saying that there comes a point in all of this where there is insufficient frequency or consistency in the use of certain theories to allow is to use terms like right or wrong, normal or conventional. There are idiosyncratic approaches to notation in every situation and it often falls to the musicians and MD in any given case to seek to establish consensus regarding the intentions of the composer or transcriber.

[paul_c2]

There's 15 keys because there's (in diatonic stuff and related) 7 notes in a scale, so the range of possible keys can be 1-7 sharps (7 of these), 1-7 flats (7 of these) and the one with no sharps or flats. 7+7+1 = 15.

The reason you don't see music with more than 7 sharps or flats in the key signature is convention - by convention, keys can only contain up to 7 sharps/flats, thus don't need to use double sharps or flats. BUT certainly music can be in a "key" with double sharps or flats if it modulates from one key to another. For example, a piece in Gb (6 flats) modulates to the fourth (Cb), then again to the fourth (Fb, which includes Bbb), then Bbb (which includes Ebb), etc etc without changing the key signature but by using accidentals.

I would expect a piece that changes key and key signature, such that it might end up with >7 sharps/flats, to go from eg having lots of flats, to having lots of sharps (or vice versa). For example a major-minor modulation might take you from Db major (5 flats) to C# minor (4 sharps).

Edited June 20, 2017 by paul_c2