Little revelation about sharps and flats

viz · November 2019

While writing my ‘book’ on music theory it suddenly occurred to me:

Like a die where any pair of opposite sides add up to 7, sharps and flats follow a similar rule.

If you know how many sharps a key has, you can immediately tell the flats of the neighbouring flat key, and vice versa.

D has 2 sharps so Db has 5 flats
Eb has 3 flats so E has 4 sharps
C has zero sharps or flats, so C# has 7 sharps and Cb has 7 flats.

Neat, huh?

sev112 · November 2019

How many flats in E sharp?

mgaw · November 2019

extremely!!! can I pre-order the book please

Branshen · November 2019

Ok, it works for C and Cb, does this work for F and Fb? Cracking my head over this. Gonna have to work this out in my own time.

This is cool, but knowing the number of sharps and flats would not be really useful unless you memorised which notes are sharped/flatted.

Edit: I guess this is where your little "Father Charles goes down and ends battle" phrase comes in. This will be an excellent book. Will pre-order it!

viz · November 2019

Branshen said:

Ok, it works for C and Cb, does this work for F and Fb?

Well F is already a flat key (it’s on the left of C in the c of 5) so it’s:

F (1 flat) - F# (6 sharps)

so it’s

G (1 sharp) - Gb (6 flats)
D (2 sharps) - Db (5 flats)
A (3 sharps) - Ab (4 flats)
E (4 sharps) - Eb (3 flats)
B (5 sharps) - Bb (2 flats)
F# (6 sharps) - F (1 flat)
and
C (0) - C# (7 sharps), Cb (7 flats)

Most people find it easier to remember the order of the sharp keys. Especially bassists. They have it easy: their 1st string is G with 1 sharp. Their 2nd string is D with 2 sharps, etc. My little revelation helps them immediately know the corresponding flat key’s flats.

(Fb major, if it existed, would be at 4 o’clock and have 6 flats and a double flat, Bbb. Instead it’s called E and has 4 sharps.)

drofluf · November 2019

sev112 said:

How many flats in E sharp?

5. 2 on the ground floor, 2 on the first an a penthouse on the top floor.

HTH

mart · November 2019

It’s a neat trick, and means you can transpose a piece from, say, E to Eb, just by changing the key signature, not moving any of the black dots.

What I initially found confusing was knowing which pairs of adjacent keys obeyed this rule, e.g. D and D# don’t. But the simple answer is that a key with sharps in the key signature works with the key immediately beneath it with flats.

Cb/C/C# is the one place you get three consecutive keys that do this, because of the unique role of C in having no flats or sharps.

stratman3142 · November 2019

Another neat trick for common guitar keys is:

'D' has 2 sharps the letter 'D' can be written with 2 lines
'A' has 3 sharps and the letter A can be written with 3 lines
'E' has 4 sharps and the letter 'E' can be written with 4 lines
'B' has 5 sharps and the letter 'B' can be written with 5 lines

viz · November 2019

mart said:

What I initially found confusing was knowing which pairs of adjacent keys obeyed this rule, e.g. D and D# don’t. But the simple answer is that a key with sharps in the key signature works with the key immediately beneath it with flats.

Exactly, basically because D# is actually Eb, which has 3 flats. D# would be D# E# F## G# A# B# C## D#!

Barney · November 2019

I find it helpful using the guitar fretboard as a guide like below

...3....G ..1 sharp
...3...D...2
...2...A ...3
...2...E...4
...2..B....5
...2...F#..6

The for the b of these make them add up to 7 like @viz says

HAL9000 · November 2019

viz said:

While writing my ‘book’ on music theory it suddenly occurred to me:

Like a die where any pair of opposite sides add up to 7, sharps and flats follow a similar rule.

If you know how many sharps a key has, you can immediately tell the flats of the neighbouring flat key, and vice versa.

D has 2 sharps so Db has 5 flats
Eb has 3 flats so E has 4 sharps
C has zero sharps or flats, so C# has 7 sharps and Cb has 7 flats.

Neat, huh?

Neat. I guess it’s simply explained in that flattening a scale by a semitone means all the naturals will become flats and all the sharps will become naturals thus preserving your ‘seven rule’ (due to there being seven notes in a scale). It’s impossible for it not to work.

viz · November 2019

HAL9000 said:

viz said:

While writing my ‘book’ on music theory it suddenly occurred to me:

Like a die where any pair of opposite sides add up to 7, sharps and flats follow a similar rule.

If you know how many sharps a key has, you can immediately tell the flats of the neighbouring flat key, and vice versa.

D has 2 sharps so Db has 5 flats
Eb has 3 flats so E has 4 sharps
C has zero sharps or flats, so C# has 7 sharps and Cb has 7 flats.

Neat, huh?

Neat. I guess it’s simply explained in that flattening a scale by a semitone means all the naturals will become flats and all the sharps will become naturals thus preserving your ‘seven rule’ (due to there being seven notes in a scale). It’s impossible for it not to work.

When you explain it like that it seems so obvious I wish I’d never mentioned it!!!!

HAL9000 · November 2019

Not at all obvious. You discovered it - not me. I've got a little bit of an interest in math and logic puzzles and wanted to know why it worked (and if it worked in all cases since you might expect F and C to be somehow different).

viz · November 2019

HAL9000 said:

Not at all obvious. You discovered it - not me. I've got a little bit of an interest in math and logic puzzles and wanted to know why it worked (and if it worked in all cases since you might expect F and C to be somehow different).

Maybe we’re both awesome

sev112 · November 2019

I love it
but I still don’t see how it works with F to F flat

viz · November 2019

sev112 said:

I love it
but I still don’t see how it works with F to F flat

Well it doesn’t you see, because Fb isn’t a key. Look at your guitar. We use E major, not Fb major. Fb would need the note Bbb.

It works from F# to F at the bottom of this list:

G (1 sharp) - Gb (6 flats)
D (2 sharps) - Db (5 flats)
A (3 sharps) - Ab (4 flats)
E (4 sharps) - Eb (3 flats)
B (5 sharps) - Bb (2 flats)
F# (6 sharps) - F (1 flat)

sev112 · November 2019

viz said:

sev112 said:

I love it
but I still don’t see how it works with F to F flat

Well it doesn’t you see, because Fb isn’t a key. Look at your guitar. We use E major, not Fb major. Fb would need the note Bbb.

It works from F# to F at the bottom of this list:

G (1 sharp) - Gb (6 flats)
D (2 sharps) - Db (5 flats)
A (3 sharps) - Ab (4 flats)
E (4 sharps) - Eb (3 flats)
B (5 sharps) - Bb (2 flats)
F# (6 sharps) - F (1 flat)

It so “is” a key

viz · November 2019

sev112 said:

viz said:

sev112 said:

I love it
but I still don’t see how it works with F to F flat

Well it doesn’t you see, because Fb isn’t a key. Look at your guitar. We use E major, not Fb major. Fb would need the note Bbb.

It works from F# to F at the bottom of this list:

G (1 sharp) - Gb (6 flats)
D (2 sharps) - Db (5 flats)
A (3 sharps) - Ab (4 flats)
E (4 sharps) - Eb (3 flats)
B (5 sharps) - Bb (2 flats)
F# (6 sharps) - F (1 flat)

It so “is” a key

Ok! if you like double sharps then why not! It’s just that as you play the guitar which is tuned to E I thought you might prefer it

I think B# major must be the silliest key

HAL9000 · November 2019

I think the point is that F is already a 'flat' key in that it contains Bb. So moving to the equivalent flat key (Fb) breaks the original criterion of moving from a key containing any combination of sharps and naturals to its equivalent flat key. However, if you think of the Bb in the key of F as actually being an A# then it all works perfectly.

viz · November 2019

HAL9000 said:

I think the point is that F is already a 'flat' key in that it contains Bb. So moving to the equivalent flat key (Fb) breaks the original criterion of moving from a key containing any combination of sharps and naturals to its equivalent flat key. However, if you think of the Bb in the key of F as actually being an A# then it all works perfectly.

Yes, and/or if you just go round the c of clockwise you hit F# at the bottom, which matches F. Don’t go through the alphabet, go clockwise round the circle. G D A E B F#. The purpose is to marry the sharps-side of the circle with its equivalent flattened note on the flat-side (the blues to their greens)

https://i.imgur.com/a6F98YN.jpg

sev112 · November 2019

Ah that’s an interesting way of looking at it

So the Key of F is actually F#flat, because it contains flats (I.e the Bflat)

does anyone one know how to type a correct ”flat” symbology a keyborad?

viz · November 2019

sev112 said:

Ah that’s an interesting way of looking at it

So the Key of F is actually F#flat, because it contains flats (I.e the Bflat)

does anyone one know how to type a correct ”flat” symbology a keyborad?

Flat is just written as a small b - use that.

The key of F is not the key of F#b “F sharp flat” - that doesn’t make sense.

Look at the circle of 5ths. From the top, C; clockwise in blue you have all the “sharp keys” - in other words the keys that deploy one or more sharps. F# is at the bottom.

G (1 sharp)
D (2 sharps)
A (etc)
E
B
F# (6 sharps)
C#

Anticlockwise, in green, you have all the “flat keys” - the ones that deploy at least 1 flat. F is just to the left of C and has one flat, as you rightly said.

F (1 flat)
Bb (2 flats)
Eb (etc)
Ab
Db
Gb
Cb

my original ‘rule of 7’ is that if you know the number of sharps in, say, D (2), you can calculate the number of flats in Db (5).

By the time you get round the SHARPS to F# (6), that means that the key of F has 1 flat.

Or vice versa, if you know that F has 1 FLAT, then F# must have 6 SHARPS.

sev112 · November 2019

Flats aren’t lower case b - they have an angularity and a bit of curve - not the same as “b”. Is there actually a way of typing it?

viz · November 2019

sev112 said:

Flats aren’t lower case b - they have an angularity and a bit of curve - not the same as “b”. Is there actually a way of typing it?

Understood and I managed to get it on my keyboard - look at my pic of the circle of fifths. But you can’t get it on an i-phone. Even if you type it on a keyboard I’m not sure it will come through as a character on the forum software.

But nothing else in music uses the lower case b so most people just use that. Oh here it is:♭

viz · November 2019

Here’s a dodecahedron die to demonstrate it. It has the sharps from 1-6 and the flats from 1-6.

As each face is a pentagon it can only accommodate 5 sharps or flats (1 at each corner) so you have to include the actual sharp or flat of the key-name in the centre of the pentagon when counting. Eg F# has 6 sharps.

https://i.imgur.com/h77TjNr.jpg

sev112 · November 2019

viz said:

sev112 said:

Flats aren’t lower case b - they have an angularity and a bit of curve - not the same as “b”. Is there actually a way of typing it?

Understood and I managed to get it on my keyboard - look at my pic of the circle of fifths. But you can’t get it on an i-phone. Even if you type it on a keyboard I’m not sure it will come through as a character on the forum software.

But nothing else in music uses the lower case b so most people just use that.

PS don’t get me wrong, I think your first post is a work of genius - it is so obvious when you pointed it out, but can’t believe I or anyone else had not spotted it before,

viz · November 2019

sev112 said:

viz said:

sev112 said:

Flats aren’t lower case b - they have an angularity and a bit of curve - not the same as “b”. Is there actually a way of typing it?

Understood and I managed to get it on my keyboard - look at my pic of the circle of fifths. But you can’t get it on an i-phone. Even if you type it on a keyboard I’m not sure it will come through as a character on the forum software.

But nothing else in music uses the lower case b so most people just use that.

PS don’t get me wrong, I think your first post is a work of genius - it is so obvious when you pointed it out, but can’t believe I or anyone else had not spotted it before,

No prob dude. I just bought a dodecahedron - will video it when it’s made

uncledick · November 2019

stratman3142 said:

Another neat trick for common guitar keys is:

'D' has 2 sharps the letter 'D' can be written with 2 lines
'A' has 3 sharps and the letter A can be written with 3 lines
'E' has 4 sharps and the letter 'E' can be written with 4 lines
'B' has 5 sharps and the letter 'B' can be written with 5 lines

Thanks for adding a post I can understand. I should've known better than to look in the Theory section and just stuck to looking at pictures of shiny guitars. Joking apart, who might find this revelation useful? Session musician? Song-writer? I'm trying to envisage someone sitting at home thinking 'my life just got easier.'

Genuinely no offence meant, @viz clearly knows his stuff.

viz · November 2019

uncledick said:

stratman3142 said:

Another neat trick for common guitar keys is:

'D' has 2 sharps the letter 'D' can be written with 2 lines
'A' has 3 sharps and the letter A can be written with 3 lines
'E' has 4 sharps and the letter 'E' can be written with 4 lines
'B' has 5 sharps and the letter 'B' can be written with 5 lines

Thanks for adding a post I can understand. I should've known better than to look in the Theory section and just stuck to looking at pictures of shiny guitars. Joking apart, who might find this revelation useful? Session musician? Song-writer? I'm trying to envisage someone sitting at home thinking 'my life just got easier.'

Genuinely no offence meant, @viz clearly knows his stuff.

None taken, it’s helpful for anyone who learns classical music, or anyone who reads or writes music, or anyone who’s interested in how music works. That’s it really.

My interest in theory isn’t abstract, it’s grown as I’ve needed it, in reading music, in communicating with other musicians, even just in having effective guitar lessons.

uncledick · November 2019

viz said:

uncledick said:

stratman3142 said:

Another neat trick for common guitar keys is:

'D' has 2 sharps the letter 'D' can be written with 2 lines
'A' has 3 sharps and the letter A can be written with 3 lines
'E' has 4 sharps and the letter 'E' can be written with 4 lines
'B' has 5 sharps and the letter 'B' can be written with 5 lines

Thanks for adding a post I can understand. I should've known better than to look in the Theory section and just stuck to looking at pictures of shiny guitars. Joking apart, who might find this revelation useful? Session musician? Song-writer? I'm trying to envisage someone sitting at home thinking 'my life just got easier.'

Genuinely no offence meant, @viz clearly knows his stuff.

None taken, it’s helpful for anyone who learns classical music, or anyone who reads or writes music, or anyone who’s interested in how music works. That’s it really.

My interest in theory isn’t abstract, it’s grown as I’ve needed it, in reading music, in communicating with other musicians, even just in having effective guitar lessons.

It's interesting how music can be so many things to so many people. When I first joined up on here and started reading about Dorian/Mixolydian etc. I mentioned it to a friend of my daughter, who was just completing his music A level and he said "I know what you're talking about, but they don't teach it that way any more!" I get by on guitar and I'm fortunate in that I play in a band where we all have similar ambitions and abilities which fits with my ethos of 'if you're enjoying it, you're doing it right.'

My niece is studying music at Goldsmith's and has started doing a few film scores so this will be an interesting conversation when we have our Christmas get-together. We sometimes have a family 'jam' and she plays a mean fiddle.

viz · November 2019

uncledick said:

viz said:

uncledick said:

stratman3142 said:

Another neat trick for common guitar keys is:

'D' has 2 sharps the letter 'D' can be written with 2 lines
'A' has 3 sharps and the letter A can be written with 3 lines
'E' has 4 sharps and the letter 'E' can be written with 4 lines
'B' has 5 sharps and the letter 'B' can be written with 5 lines

Thanks for adding a post I can understand. I should've known better than to look in the Theory section and just stuck to looking at pictures of shiny guitars. Joking apart, who might find this revelation useful? Session musician? Song-writer? I'm trying to envisage someone sitting at home thinking 'my life just got easier.'

Genuinely no offence meant, @viz clearly knows his stuff.

None taken, it’s helpful for anyone who learns classical music, or anyone who reads or writes music, or anyone who’s interested in how music works. That’s it really.

My interest in theory isn’t abstract, it’s grown as I’ve needed it, in reading music, in communicating with other musicians, even just in having effective guitar lessons.

It's interesting how music can be so many things to so many people. When I first joined up on here and started reading about Dorian/Mixolydian etc. I mentioned it to a friend of my daughter, who was just completing his music A level and he said "I know what you're talking about, but they don't teach it that way any more!"

Yup, modal music is so comparatively rare in classical music it can be totally skipped by many musicians. But keys and 4ths and 5ths can’t!

Howdy, Stranger!

Categories

In this Discussion

Become a Subscriber!

Little revelation about sharps and flats

Comments