Little revelation about sharps and flats

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vizviz Frets: 10647
edited November 2019 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?


Roland said: Scales are primarily a tool for categorising knowledge, not a rule for what can or cannot be played.
Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
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Comments

  • sev112sev112 Frets: 2739
    How many flats in E sharp? ;)
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  • mgawmgaw Frets: 5239
    extremely!!!   can I pre-order the book please :)
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  • BranshenBranshen Frets: 1222
    edited 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!
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  • vizviz Frets: 10647
    edited 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.)
    Roland said: Scales are primarily a tool for categorising knowledge, not a rule for what can or cannot be played.
    Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
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  • droflufdrofluf Frets: 3616
    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: 5205
    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: 10647
    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#!
    Roland said: Scales are primarily a tool for categorising knowledge, not a rule for what can or cannot be played.
    Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
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  • BarneyBarney Frets: 614
    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: 9551
    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.
    I play guitar because I enjoy it rather than because I’m any good at it
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  • vizviz Frets: 10647
    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!!!!
    Roland said: Scales are primarily a tool for categorising knowledge, not a rule for what can or cannot be played.
    Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
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  • HAL9000HAL9000 Frets: 9551
    edited 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).
    I play guitar because I enjoy it rather than because I’m any good at it
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  • vizviz Frets: 10647
    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
    Roland said: Scales are primarily a tool for categorising knowledge, not a rule for what can or cannot be played.
    Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
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  • sev112sev112 Frets: 2739
    I love it
    but I still don’t see how it works with F to F flat
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  • vizviz Frets: 10647
    edited 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)
    Roland said: Scales are primarily a tool for categorising knowledge, not a rule for what can or cannot be played.
    Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
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  • sev112sev112 Frets: 2739
    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: 10647
    edited 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


    Roland said: Scales are primarily a tool for categorising knowledge, not a rule for what can or cannot be played.
    Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
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  • HAL9000HAL9000 Frets: 9551
    edited 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.

    I play guitar because I enjoy it rather than because I’m any good at it
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  • vizviz Frets: 10647
    edited 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)

    Roland said: Scales are primarily a tool for categorising knowledge, not a rule for what can or cannot be played.
    Supportact said: [my style is] probably more an accumulation of limitations and bad habits than a 'style'.
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  • sev112sev112 Frets: 2739
    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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