Little revelation about sharps and flats

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vizviz Frets: 5678
edited November 6 in Theory
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?


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  • sev112sev112 Frets: 690
    How many flats in E sharp? ;)
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  • mgawmgaw Frets: 3286
    extremely!!!   can I pre-order the book please :)
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  • BranshenBranshen Frets: 1105
    edited November 8
    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!
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  • vizviz Frets: 5678
    edited November 8
    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.)
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  • droflufdrofluf Frets: 201
    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 :)
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  • martmart Frets: 3655
    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.
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  • 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

    It's not a competition.
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  • vizviz Frets: 5678
    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#!
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  • BarneyBarney Frets: 424
    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


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  • HAL9000HAL9000 Frets: 5163
    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.
    It might look like I'm listening to you, but in my head I'm playing my guitar.
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  • vizviz Frets: 5678
    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!!!!
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  • HAL9000HAL9000 Frets: 5163
    edited November 9
    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).
    It might look like I'm listening to you, but in my head I'm playing my guitar.
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  • vizviz Frets: 5678
    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
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  • sev112sev112 Frets: 690
    I love it
    but I still don’t see how it works with F to F flat
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  • vizviz Frets: 5678
    edited November 10

    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)
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  • sev112sev112 Frets: 690
    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 ;) 

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  • vizviz Frets: 5678
    edited November 10
    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


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  • HAL9000HAL9000 Frets: 5163
    edited November 10
    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.

    It might look like I'm listening to you, but in my head I'm playing my guitar.
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  • vizviz Frets: 5678
    edited November 10
    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)

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  • sev112sev112 Frets: 690
    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?
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  • vizviz Frets: 5678
    edited November 10
    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. 

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  • sev112sev112 Frets: 690
    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?
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  • vizviz Frets: 5678
    edited November 10
    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. 
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  • vizviz Frets: 5678
    edited November 12
    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. 

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  • sev112sev112 Frets: 690
    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, :)
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  • vizviz Frets: 5678
    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 :)
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  • uncledickuncledick Frets: 341
    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.
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  • vizviz Frets: 5678
    edited November 11
    uncledick 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. 
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  • uncledickuncledick Frets: 341
    viz said:
    uncledick 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.
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  • vizviz Frets: 5678
    uncledick said:
    viz said:
    uncledick 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!
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