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Circle of Fifths Question

Discussion in 'General Instruction [BG]' started by baddarryl, Dec 21, 2008.

  1. baddarryl

    baddarryl Supporting Member

    Oct 26, 2008
    Cape Fear!
    I bought a Mel Bay Essential Music Theory for Electric Bass today. I has a diagram about the Circle of Fifths but very little in the way of explanation. I was able to get more info off the web and have a better understanding now. Here is the question:
    Most Circles have the 5ths running clockwise and the 4ths going counter clockwise. Some go the other way. Is this a problem? At first I thought the book was misprinted until I saw some that were they same way online. Is one way more standard convention than the other?

    Also, what are the notes inside of the Circle correspondent to? For C major you have A minor and for G major is E minor actually inside the circle on the Mel Bay book, but with no explanation. I haven't seen it elsewhere. I understand that these are minor keys I think, but what is the relationship to the major? Thanks.
  2. I made a post about this last week, one moment...
  3. Introduction
    We use key signatures to indicate which major key centre (this is including it's diatonic modes, but we'll get to tonal centres and implied harmony another time) we're deriving our notes from. Rather than write a sharp next to every single F note in an entire song or passage of music in the key of G major, we simply write an F# at the start of the section or song and before the time signature (and usually at the start of each line of notation) to indicate our tonality is G major, or a diatonic relative (ie. a mode such as E Aeolian [minor], which is also known as the relative minor to G Ionian [major]). This then allows both composer and anyone else who reads the music to "think" in G major, automatically sharpening every F note in any octave as they read it. Even if you're not reading the notes, the key signature play a vital role in reading a chord progression, as you can determine the overall implied harmony and not just focus on the chords themselves.

    Note that this all goes beyond just reading music on a musical staff (although I will refer to it now and then) and right into understanding what any given key is doing.

    For the benefits of this post and keeping things as simple as possible, we will be using only major keys.

    Determining Key Signatures
    Circle of Fifths from natural (C major) gives you all you keys with sharps in them
    Cycle of Fourths from natural (again, C major) gives you all your keys with flats in them.

    Note: I've seen it referred to as the Cycle of Fifths and the Circle of Fourths, or both Circle of Fifths and Circle of Fourths, or Cycle of Fifths and Cycle of Fourths. This is all largely irrelavent as the terminology used decribes the exact same thing. In this case I'll apply both terms.

    Circle of Fifths
    The Circle of Fifths, to put simply, is a sequence of major keys, ascending in intervals of fifths.
    Every time we change key, we add a new sharp.

    The order of keys for the circle of fifths is:

    C G D A E B F#

    Remember of course that C contains only natural notes, so there are no sharps.

    The next key in the sequence is of course G major.

    So, starting from C, fifth up we have G. That has one sharp, F#.
    Then, up a fifth from G we go to D. That has two sharps, F# and C#.
    Then up a fifth from D we arrive at A. This has three sharps, F#, C# and G#...

    Can you see a pattern emerging here?

    To check this, go from G major your intervals (TTS, TTTS)

    You'll see your notes are: G A B C D E F#
    D major: D E F# G A B C#
    A major: A B C# D E F# G#

    Each time we go to the next fifth, we add a sharp to the sequence. We build up the sharps in order. An an easy way to figure out which sharp to add to the sequence is simply by going a semitone from the new root note of the next key in the Circle of Fifths.

    So in the case of G, a semitone below is F#
    Then D major you add C# to the F#
    Then for A you add G# to this sequence (F#, C#, G#)
    Then E you have F#, C#, G# and D#...

    ...until we get seven sharps. But, as previously stated by mambo4, as C# is enharmonically the same as Db, and Db has less flats than C# has sharps, we use Db instead much more often than not, as it easier to read five sharps instead of seven sharps.

    Another way we can remember this (perhaps easier for some) is to simply think that we sharpen the dominant seventh of the scale relative to the root. So in the case of G major, F would be the seventh, so we sharpen it to make it a major seventh. D major you add the sharpened C, which is dominant seventh, to create a major seventh.

    Cycle of Fourths
    The Cycle of Fourths is similar to the Circle of Fifths, but as the name implies we ascend using intervals of fourths.
    As we go up a fourth from C, the next key has an extra flat.

    We have an order of keys for the cycle of fourths:

    C F Bb Eb Ab Db Gb

    Again, C major is an all natural key. So no flats used.

    The next is of course F major. Using again (TTS, TTTS) we have:

    F major: F G A Bb C D E
    Bb major: Bb C D Eb F G A
    Eb major: Eb F G Ab Bb C D

    The same rule of going to the next key and adding a flat to the previous sequence applies.

    From C major we have all natural notes, then up a fourth to F major, where we have one flat, and a fourth up is Bb with two flats, etc...

    An easy way to work out the next flat to add, simply take a fourth from the root.

    F major has Bb (an interval of a fourth from the root being F)
    A fourth from the next key (Bb) is Eb, so the order is: Bb, Eb
    A fourth from Eb is Ab, so the order is: Bb, Eb, Ab

    Again, you can see a pattern emerging here.

    Using both circle and cycle (or both circles, or both cycles - depends on what you call them, but despite the labelling the idea remains the same) gives you all 12 keys. Note that F# major is enharmonically the same as Gb major. F# major has six sharps whilst Gb major has six flats... so you could use either one really.

    Determining Keys From the Key Signature
    So... now we can figure out the key signature of any given key, what's next?

    Well, you can now read a key signature and determine the key quickly from there.

    How do we do this? Well, I'm glad you asked...

    Go back to the top and read how we arrived at determining the sharps for the keys of G, D and A. They have one, two and three sharps respectively.

    If we see a key signature of one sharp, this will always mean G major. There is no other possible key that uses the same sequence of notes, other than the diatonic modes associated with G major (this includes it's relative minor, E minor).

    If we see a key signature of two sharps it will always be D major, for the same reasons.

    If we see a key signature of three sharps, it will always be A major.

    Make sense? The same applies for the flats we use.

    Keys With Sharpened Notes
    My grade 12 teacher had a great way of teaching us how to remember the order, as all sharps and/or all flats in a key signature in any given piece of music must follow the same order.

    Remember this little phrase:

    Father Charlie Goes Down And Ends Battle

    So if we see a key signature with three sharps, we count three words along:

    Father Charlie Goes

    So our three sharps in order are: F#, C# and G#. Going a semtione up from the final sharp gives us our key: A major.

    Got that? Ok then...

    Keys With Flattened Notes
    The same goes for flats, only we read the phrase backwards:

    Battle Ends And Down Goes Charlie's Father

    So a key signature with three flats, using the same rules as before, is written in this order: Bb, Eb and Ab. To determine what key we're in, it will be the second last flat. So here the second last flat is Eb. So we're in the key of Eb.

    Make sense?

    Order of Sharps and Flats on the Staff or Stave
    One last thing...

    Remember the phrase for sharps?

    Father Charlie Goes Down And Ends Battle

    The order for writing sharps is the same as the phrase, and the order for writing flats is the same as the phrase reversed.

    Meaning you ALWAYS ALWAYS ALWAYS write a key signature, up to seven sharps, in this order:

    F# C# G# D# A# E# B#

    And same for flats, in reverse phrase order:

    Battle Ends And Down Goes Charlie's Father

    Bb Eb Ab Db Gb Cb Fb

    So for writing the key signature for E major, we would write on the staff: F#, C#, G#, D#
    Writing the key of Eb we would write: Bb Eb Ab

    That's at least a week's worth of classroom theory right there...
    bassman818 likes this.
  4. a_magg


    Sep 23, 2007
    One of the fastest ways I learned key signatures actually applies to what we do as bassists.

    ~Key Signatures with Flats (In order)~
    F Bb Eb Ab Db Gb Cb

    - Ignore the flats for a second... And its the tuning for a 7 string (6 if you memorize that F has 1 flat)

    ~Key Signatures with Sharps~
    Just reverse those above!

    C G D A E B F(#)

    Hope this helps... It really did for me and I wouldn't post it if it didn't :bassist:
  5. onlyclave


    Oct 28, 2005
    The circle of fifths is laid out that way because that is the most common root movement in western music. A Perfect Fifth is an Inversion of a Perfect Fourth, and that's why you see them like that on your chart. If it was the Circle of Thirds the note relationships could be Major Thirds going one direction and Minor Sixths going the other. But Perfect Fifths are the most common root movement in western music (V-I, Perfect Authentic Cadence).

    The other letters inside the circle refer to the Relative Minor Keys. Don't worry about that aeolian crap. Modes are not the key to anything. The relative minor key is always the interval of a minor third below the relative major key.

    A better way to read major key signatures (even though the harmony dictates the key, not the number of sharps or flats on the page) is to use this formula:

    1 flat is F. You have to memorize that one.
    If you have more than 1 flat, look at the penultimate (that means next to last) and the note that it sits on is the major key. 3 flats (Bb Eb Ab) = Eb major. 6 flats (Bb Eb Ab Db Gb Cb) = Gb Major

    If you have any sharps, look at the ultimate (last one) and use the note 1 half-step higher and that is your major key. 1 sharp (F#) + 1 half-step = G major. 4 sharps (F# C# G# D#) + 1 half-step = E major.

    And that is one half-hour of classroom music theory instruction there.
  6. WOW jake of bass, I am slow clapping you, the longest typing post I have EVER seen.
    bassman818 likes this.
  7. DocBop


    Feb 22, 2007
    Los Angeles, CA
    Stare at the source Luke?

    Sometimes just stating at something like the CoF till you see the pattern, and playing the notes and listening to the sound is the best teacher. Working up a good sweat learning something makes the info stick longer and more related discoveries along the way.
  8. Hey man, how's things up north? Weather has been much better these past few weeks after those insane storms we had.

    I have a job as a support worker and I sleep at a house as part of a shift. I couldn't sleep in the middle of the night so I figured I may as well use the time productively...
  9. baddarryl

    baddarryl Supporting Member

    Oct 26, 2008
    Cape Fear!
    My question remains: Does it matter which way the diagram itself is laid out? I have seen it both ways. Thanks for the insight all.
  10. onlyclave


    Oct 28, 2005
    No. Yours is not defective.
  11. DocBop


    Feb 22, 2007
    Los Angeles, CA
    Doesn't really matter the answers are still the same. Fifths one direction and fourths the other. It all about the sound and mathematical relationship.
  12. AlphaMale


    Oct 30, 2006
    Ventura County
    Up a fifth down a fourth

    Start on Bb then F then C then G then A then E then B then Gb then Db then Ab Then Eb then back to Bb flat..

    Play that and you'll realize it man.

    Also play to the tune "autumn leaves" you will definitely have a good example of how to use the circle of fifths.
  13. onlyclave


    Oct 28, 2005
    "All of the Things You Are" is much better example of CoF.
  14. HaVIC5


    Aug 22, 2003
    Brooklyn, NYC
    I wouldn't say much better, both have a lot of CoF action. Autumn leaves is nice because its mostly diatonic CoF and doesn't modulate.
  15. baddarryl

    baddarryl Supporting Member

    Oct 26, 2008
    Cape Fear!
    Thanks guys, it just seemed odd to me that that wouldn't be under some standardized convention. Can be confusing to a newbie.
  16. E2daGGurl


    May 26, 2008
  17. E2daGGurl


    May 26, 2008
    What does this last sentence mean? Can anyone take just that part about "minor third below" and explain it? How does a minor third get below the major key? Isn't the third the third, regardless of whether it's above or below the root? What am I missing?

    And, if anyone can remind me what a relative major key is, please do. I know parallel keys, and I know what a relative minor is - but what's relative major? Relative to what? I'm not near my theory book.
  18. BassChuck

    BassChuck Supporting Member

    Nov 15, 2005
    C major and A minor are 'related' cause they have the same key sig. So... C major is the relative major to A minor. Bb major is the relative major to G minor. etc
  19. E2daGGurl


    May 26, 2008
    Maybe one is for left handed people. No, it doesn't matter in any technical sense, as long as you learn to read one and stick with it.

    If you want to read the one that most other people are using, F will be to the left of C - and to me, that tells me right away that it's the shorter interval,(4th) for some reason left means less to mean - and G should be to the right of C, which is the 5th.

    However, once you realize why it's a circle, you'll see right away that F - back to C, is 5 intervals just as it should be (reading clockwise), and all is right with the world

    I've never seen one that goes in four intervals to the right, but if it did, it would still work (but seem totally backwards in my mind). You'd read it counter-clockwise to find the fifths and clockwise for the fourths. I do not know why you would want to learn it this way though.
  20. onlyclave


    Oct 28, 2005
    All major keys have a relative minor key. It is the same key signature. If you are in the key of C major, its relative minor is A minor. A is a minor 3rd below C (or a major 6th. Whatever you want to think). F major has one flat, it's relative minor (that is, same key signature) is D minor. D is a minor 3rd below F. Ab Major has 4 flats. F minor also has 4 flats. F is a minor 3rd below Ab.

    If you are looking at a minor key signature, and the only way you can tell is by the harmony, it's relative major is a minor third above. C minor has 3 flats. Eb major does too. Eb is a minor 3rd above C. B minor has 2 sharps, so does D major. D is a minor third above B.

    A parallel key is the same notes with a different modality. C minor and C major are parallel. G major and G minor are parallel. They start and end on the same note but they have different key signatures.

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