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EMC's Functional Harmony Thread (or, How i learned to love the circle of 5ths)

Discussion in 'Tab & Music Forum' started by dogletnoir, Mar 9, 2020.

  1. dogletnoir

    dogletnoir V----V Strat-Talk Supporter

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    Instead of piggybacking this material onto other threads such as the Q & A sticky,
    i thought i should probably start my own, and so... here we are.

    Welcome to my Functional Harmony thread!
    :D
    Many of the concepts we will be discussing here are things that i have
    attempted to incorporate in the Practical Jazz and Practical Music Workshops
    that i've hosted personally, so please excuse any repeated information if it's
    something you've already seen and have internalized.

    This first post will definitely duplicate what i've posted elsewhere but since it's really
    the basis for everything else we'll be talking about here, its reiteration is not a bad thing.

    i'm just going to leave this here for future reference:

    Screen Shot 2020-03-09 at 6.33.28 PM.png

    It is the 'key' to unlocking so much of functional harmony.
    Study it, figure out the various patterns it contains...
    and you will travel far along the path of musical righteousness.
    :D

    First step:
    Look at the circle of 5ths diagram above.
    The Outer Circle spells out the 12 diatonic Major Keys.
    Starting from the key of C at the top, as we rotate clockwise,
    we move upwards by the interval of a perfect 5th each time,

    and each new key adds one more accidental, which will be a sharp (#)...

    C (no sharps), then G (one sharp, which occurs on the 7th scale degree), so
    G A B C D E F# and then back to G, the 8th scale degree, or octave.

    The D Major scale would be the next in line, and we retain the F# from the previous key,
    and add one more sharp on the 7th scale degree of our new key:
    D E F#G A B C# D.

    In A major we would carry over both sharps from the previous key,
    and add one more on the 7th degree once again, so we now have:
    A B C# D E F# G# A

    The Major scale pattern is always the same, with half steps occurring between steps 3 and 4 and between 7 and 8.

    If we look at the diagram again and move counterclockwise from C this time, we are still ascending
    (this is the tricky part visually and conceptually), but by the interval of a perfect 4th now,
    and each click in that counterclockwise direction adds one flat (b).

    C (no flats, the only 'natural' major key), then F Major (one flat):
    F G A Bb C D E F.
    For the next key, we keep the Bb (obviously, since it's now the root or 'tonic' of our new key, LOL),
    and add one more flat on the new key's 4th step to arrive at Bb Major:
    Bb C D Eb F G A Bb

    The next counterclockwise key is Eb Major, and guess what we're going to do?
    That's right, the previous key's 4th step has again become our new tonic , and now
    we'll carry over our previous flats, and add another one to the new key's 4th step:
    Eb F G Ab Bb C D Eb

    Next key: Ab Major:
    Ab Bb C Db Eb F G Ab

    Are you starting to see the patterns?
    Each new clockwise key moves to the 5th, keeps any previous sharps, and adds a sharp to the new key's 7th scale degree.
    Each new counterclockwise key moves to the 4th, keeps any previous flats, and adds a flat to the new 4th scale degree.
    At the bottom of the circle is F#, which is also enharmonic Gb (in equal temperament, of course, LOL again).

    "Ahh, but if I'm counting backwards, aren't I going down 5 steps, not 4?", i hear you saying.

    Yes, in fact you are... welcome to the world of inversions.

    A lot of basic music theory is actually just simple math.
    Any given interval plus its inversion gives a sum of 9.
    So up 5 steps will give you the same pitch name as down 4.
    Conversely, up 4 steps will give you the same pitch name as down 5.
    And up 6 will give you the same pitch name as down 3.
    Try it:
    C D E F G A B C...
    move up 6 steps starting from C, and you will arrive at A.
    Count back 3 steps from C, and you get back to... wait for it... A again.
    Count up 3 scale degrees from the C and you arrive at E.
    Count down 6 scale degrees from C and you are back at E once more.
    Add 6 + 3, and the sum is... 9.
    9 is our magic number when it comes to inversions.

    Major intervals invert to minor ones, and minor intervals invert to major ones.
    A to C is an interval of a minor 3rd, while C to A is an interval of a major 6th.
    The exception to this: 4ths and 5ths are 'perfect' intervals, so they stay major either way.
    We'll look at inversions a bit more closely when we get into chord construction later on.


    Stay tuned... next we'll enter the 'Inner Circle'...
    but we've already received the 'key' to the door.
     
    Last edited: Mar 10, 2020
  2. Dadocaster

    Dadocaster Dr. Stratster Strat-Talk Supporter

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  3. duzie

    duzie Senior Stratmaster

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    Thank you for posting this !
     
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  4. dogletnoir

    dogletnoir V----V Strat-Talk Supporter

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    Don't worry... it's all just patterns, man.
    Just patterns.
    If you can memorize linear patterns (i.e. scales &/or chord shapes) on your fingerboard,
    you're capable of memorizing circular ones around the cycle of 5ths diagram too!
    You'll see... as long as you're willing to try.
    :D
     
    Last edited: Mar 10, 2020
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  5. Antstrat

    Antstrat Senior Stratmaster

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    Thank you :thumb:
     
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  6. 3bolt79

    3bolt79 Most Honored Senior Member

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    Nice! Thanks for the crash course! I think I actually had to know this at one time, when I was a kid, and then like so many other things in life, what I wasn’t using was dumped from my brain.
     
  7. fezz parka

    fezz parka Duke of Dilligaf Strat-Talk Supporter

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    :D
     
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  8. dogletnoir

    dogletnoir V----V Strat-Talk Supporter

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    i'm grateful to and thankful for all of you that have joined me on this journey so far.

    Now it's time to look at the Inner Circle, which spells out the 12 diatonic minor keys.

    Screen Shot 2020-03-09 at 6.33.28 PM.png
    The first important point is this:
    Every major key has a 'relative' minor key, which uses the same pitches but in a different order.
    On the diagram, each major key on the outer circle is paired with its relative minor on the inner one

    ( C Major's relative minor is A minor, G Major's relative minor is E minor, and so on around the circle),
    and the same sharps or flats are added to each new key for the relative minor as for the major one.

    As we've seen in the first post, C Major has no sharps or flats: C D E F G A B C
    To find the relative minor key of C Major, we can simply look at the chart to see that C Major is paired with
    A minor
    , the minor key which also contains no sharps or flats.
    A B C D E F G A
    But we can also find the relative minor by counting scale steps
    ; down three steps from the root, or up six.
    Remember the 'sum of an interval and its inversion will always be 9' thing from the first post?
    So, count down three scale degrees from C or up six, and either way we get A as the tonic of the relative minor of the key of C.

    The minor scale pattern is basically an offset of the major scale one,
    with half steps occurring between the 2nd and 3rd step, and between the 5th and 6th step
    this time.
    Moving clockwise around the inner circle, we will still retain any previous sharps and add one more,
    but this time to the 2nd scale degree of our new key.
    E minor, one sharp: E F# G A B C D E
    B minor, two sharps: B C# D E F# G A B
    F# Minor, three sharps: F#
    G# A B C# D E F#

    As we move counterclockwise around the circle, we keep any previous flats,
    and add one flat to each successive new key center's 6th scale degree:
    D Minor, one flat:
    D E F G A Bb C D
    G Minor, two flats: G A Bb C D Eb F G
    C Minor, three flats: C D Eb F G Ab Bb C


    etc etc etc.
    Again, it's just a couple of repeating patterns...
    are you still with me?

    i hope so, because we're going to do some pretty cool stuff with this thingie as we get further into it!!!




     
    Last edited: Mar 10, 2020
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  9. dogletnoir

    dogletnoir V----V Strat-Talk Supporter

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    The next step in making the Circle of 5ths an incredibly useful tool is understanding 'enharmonic equivalence'.
    In 12 tone equal temperament tuning systems (basically piano based tuning, which is what our western ears are most accustomed
    to hearing) every flat has an equivalent sharp one pitch name below it.
    Here are the enharmonic equivalents:
    C# = Db
    D# = Eb
    E# = F
    (this one is more theoretical than practical, but i'll note it anyhow)
    F# = Gb
    G# = Ab
    A# = Bb
    B# = C
    (again, more theoretical)
    We'll be using this info when we start using the Circle as a tool to build chords.
     
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  10. AxemanVR

    AxemanVR I appreciate, therefore I am... Strat-Talk Supporter

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    `
    I discovered this "interactive" Circle of Fifths online awhile back:

    https://randscullard.com/CircleOfFifths/

    Just another great visual tool to help someone grasp how things relate - I especially like how the "Mode" charts are included.

    Try this: Notice how the Key of C Major and the Key of D Dorian have the same chords, but their "functions" (Roman Numerals) are different:

    z Circle 5ths C Major - C Dorian.JPG

    Below is a piano piece I wrote which has all the chords from the Key of B Major except for the B Major chord!

    z Circle 5ths C# Dorian.JPG

    The A# diminished chord was also changed to A# minor in my piece. It starts on A#m and ends on C#m, so it's more or less written in C# Dorian.

    *This is a stripped down version with the vocal and orchestra parts removed (thus has a couple of "pregnant pauses"):



    Here are the basic chords, whose roots generally steps downwards as the song progresses, but it's the Melody that really makes it want to resolve to C# minor instead of B Major...

    Inner Piano Chords b.jpg


    `


    `
     
    Last edited: Mar 12, 2020
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  11. BallisticSquid

    BallisticSquid Most Honored Senior Member

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    I understand the words you are saying. I'm curious to see how this is applied. Following.
     
  12. dogletnoir

    dogletnoir V----V Strat-Talk Supporter

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    Cool stuff; thanks for linking it!!!
    This brings me to one of our next important tools, the harmonized major scale!
    I will post something that my dear friend @fezz parka has already posted so many times before:

    It's just counting to 7.

    CDEFGAB. 7 notes

    Here are the 7 modes derived from the parent major scale in C.

    Ionian. 1st
    CDEFGAB
    Dorian. 2nd
    DEFGABC
    Phrygian. 3rd
    EFGABCD
    Lydian. 4th
    FGABCDE
    Mixolydian. 5th
    GABCDEF
    Aeolian. 6th
    ABCDEFG
    Locrian. 7th.
    BCDEFGA

    7 modes. 7 notes.

    Now using the 1st, 3rd, 5th, and 7th modal degrees (in bold above), you can harmonize that parent scale, building the C major chord progression.
    (my NB: you construct the chord by going down each stack vertically, and skipping a line each time...)

    I - Cma7 - CEGB
    ii - Dm7 - DFAC
    iii - Em7 - EGBD
    IV - Fmaj7 - FACE
    V - G7 - GBDF
    vi - Am7 - ACEG
    vii° - Bm7b5 - BDFA


    7 notes. 7 modes. 7 chords.

    7.

    If you can count to seven...and know the formula...you can harmonize the major (parent) scale.

    -----------------------------------------------------------------------------------------------------------
    Back to me again now...

    Because the major scale pattern (half steps between scale degrees 3 and 4 and between 7 and 8)
    always stays the same no matter which tonic you begin on, the harmonized major scale always yields
    the same sequence of chords:
    I (major)
    ii (minor)
    iii (minor)
    IV (major)
    V (major / dominant in 4 voice chords)
    vi (minor)
    vii° (diminished / minor 7 b5 a/k/a 'half diminished' in 4 voice chords)

    This sequence of chords will remain the same for any major key.

    And guess what? Since we already know that the minor scale sequence is just an offset
    of the major scale one, it follows logically that the sequence of chords based on a harmonized
    minor scale is the same, only offset.

    That's the 'relative minor' key (or scale, or chord... it works for all those things).

    Let's go back to our C major scale for the sake of clarity.
    If we refer to the Circle of 5ths diagram above, we see that the paired relative minor is A minor.
    That A minor scale is comprised of the same pitches as the C major scale, but starting on A this time
    (the 'offset').
    A B C D E F G A

    Therefore, the harmonized chord sequence is also offset (the vi chord is now the tonic, or i)
    A mi7 = i
    B mi7b5 = ii°
    C Maj7 = III
    D mi7 = iv
    E mi7 = v
    F Maj7 = VI
    G 7 = VII7
    (mnemnonic aid - in a minor key, the seventh chord is a 7th chord)


    Let's pick a different key to work this out in... how about Eb major?
    The scale is Eb F G Ab Bb C D Eb, so when we arrange those pitches vertically, we get:
    Eb - I - Eb Maj 7(Eb G Bb D)
    F - ii - F mi 7 (F Ab C Eb)
    G - iii - G mi 7 (G Bb D F)
    Ab - IV - Ab Maj 7(Ab C Eb G)
    Bb - V7 - Bb7 (Bb D F Ab)
    C - vi - C mi 7 (C Eb G Ab)
    D - vii° - D mi7b5 (D F Ab C)

    What's the relative minor of Eb? C minor!
    Screenshot 2020-03-09 08.31.41.png
    We know this because the two are paired on the Circle diagram, and it's also the vi chord of our harmonized major scale.

    Now if the vi turns out to be the i (not 9, sorry Jimi, LOL) ...
    the chords in the key of C minor are the same as the ones for Eb major... with that same offset.
    i = C mi7
    ii° = D mi7b5
    III = Eb Maj 7
    iv = F mi7
    v = G mi7
    VI = Ab Maj7
    VII7 = Bb7

    So far, so good, right?
     
    Last edited: Mar 12, 2020
  13. Agtronic

    Agtronic Strat-Talker

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    I could never understand this stuff. I've tried so many times. I get so confused between thinking in terms of intervals vs. thinking in notes. I get so angry with myself. I don't get why it just doesn't make any sense to me. It's as if my brain has a bad sector that is needed for this stuff to just click. Yet I can code software without issue. I don't even fully understand what this applies to, chords of a key or scales? Or is that the same thing?

    I'll try and go back to this when I get home tonight.

    Thanks for your efforts by the way.
     
  14. davidKOS

    davidKOS sheltered Strat-Talk Supporter

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    It can get confusing; and, to make you feel better, I can understand music theory up-and-down but am horrible with computer code. :p:D

    Thinking in notes, as in specific pitches, is concrete - these are the notes in such-and such a chord, these are the notes in such and such a scale, etc.

    Thinking in intervals is more abstract, in that it gives the formulae for deriving chords, scales, etc. In other words, it's more of a pattern than a specific example.

    "Or is that the same thing"

    Scales can be harmonized to produce chords ; chords imply the scales from which they are derived. Melodies can imply scales and chords; chord tones can suggest melodies.

    It's like the chicken and the egg. Neither really comes first, it's the 2 sides of the same coin. (3 if you include the side rim !)

    Scales and intervals are written with Arabic numerals; functional chords are written with Roman numerals, upper case for major and lower case for minor.

    So our C scale is:

    C - D - E - F -G - A - B

    the scale degrees are

    1 -2 - 3 - 4 - 5 - 6 - 7

    Intervals are sort of like fractions:

    from C to E is a maj3rd, from E to G is a min3rd, often written as M3rd and m3rd.

    As in https://www.strat-talk.com/members/dogletnoir.40400/'s post,

    chords are given in Roman numerals

    Cmaj7 = Imaj7

    Dm7 = iim7, etc.

    I hope this helps clear things up a bit for you.
     
  15. albala

    albala Most Honored Senior Member Strat-Talk Supporter

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    Understanding The Circle has eluded me for years but THIS TIME I’m ready to absorb and use it

    Thanks dog
     
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  16. AxemanVR

    AxemanVR I appreciate, therefore I am... Strat-Talk Supporter

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    You don't have to understand every intricate detail of it to benefit from it (or Music Theory as a whole for that matter), since just knowing that something exists is half the battle!

    Plus, knowing that there's always something else waiting around the corner to discover makes it all that more exciting - like reading a suspense novel where you can't wait to turn the next page.

    If you look at the Circle of Fifths like the proverbial "layer of onions", then you'll realize that the more you learn, the more there is still left to learn! It's a virtual cornucopia of music structure knowledge...

    Good Luck!

    il_570xN.843010483_ik97.jpg

    `
     
    Last edited: Mar 11, 2020
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  17. albala

    albala Most Honored Senior Member Strat-Talk Supporter

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    I was introduced to the circle in the early '90s and I've had a decent understanding of theory since then, but tbh, I never put the time in to learning, understanding, and applying the circle of 5ths in my playing...but I'm ready now and so far, it makes perfect sense.
     
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  18. AxemanVR

    AxemanVR I appreciate, therefore I am... Strat-Talk Supporter

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    I would look at the Circle of Fifths as a "reference" that still requires further "self study" in other areas.

    Knowing what scales and chords fit into a certain Key is nice, but that doesn't really tell you how to use them. Harmony and Melody are the other layers of the onion I was referring to. Going back and forth, using the Circle of Fifths to "check your Math" so to speak.

    One example is "Parallel Keys".

    For example, C Major and C minor are considered to be Parallel Keys, because they share the same "Tonic", which is "C".

    If you look at the Circle of Fifths it should be obvious that C major has no sharps or flats. Compare that to C minor, which has three flats (Bb, Eb and Ab). *I'll be using the Bb Major chord in my next example:

    z Circle 5ths C Major - C minor.JPG

    Another term you might come across is "borrowed chord".

    A Borrowed Chord is sometimes described as a chord which does not fit in a certain key but can be found in a parallel key. For instance, lets say you are playing in the Key of C Major and are using a Bb Major chord, like this:

    C - Bb - G - C

    Sounds okay, right? But how does that stinkin' Bb Major chord fit in the Key of C Major? Well, if you look at the chords in the Key of C minor you can see a Bb Major just sitting there waiting to be used! So Bb Major is a chord that can be "borrowed" from the Key of C minor and used in the Key of C Major. Neat huh? Give the Eb Major and Ab Major chords a try as well.

    Anyway, my greater point is the "layer of onions" thing and the little nuggets of gold you'll find as you keep looking...

    ...and once again... Good Luck!


    `
     
    Last edited: Mar 11, 2020
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  19. tukoztukoz

    tukoztukoz Strat-Talker

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    I was just thinking these days about finding a better way for me to memorize the circle of fifths, without using a sentence. Something faster than a sentence. I think I’ve found something that works for me. We certainly talk about this later...
     
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  20. AxemanVR

    AxemanVR I appreciate, therefore I am... Strat-Talk Supporter

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    I just memorized these "letter patterns" years ago and they somehow stuck with me:

    untitled.JPG

    *SIDE NOTE: Not all Key Signatures are practical or necessary, since Cb Major is exactly the same as B Major for instance - but the fact that they are the same patterns (with one reversed) is the main take away here.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

    For sharps it's like, what's the Key of E Major?: F# C# G# D# then "E" (stop at the note which is a 1/2 step before the Key Note). So the Key of E Major has four sharps: F# C# G# D#.

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    FLATS: B E A D G C F

    Flats are a little different. It's easier to just remember that F Major has one flat, which is Bb. MEMORIZE IT NOW!

    The rest are "The Key Note" + "The next note past the Key Note"...

    What's the Key of Ab Major? B E "A" + D = the Key of Ab Major (Bb Eb Ab Db)

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    So memorizing the Sharp and Flat patterns is the main challenge, but after that it's (more or less) a breeze!




    `
     
    Last edited: Mar 12, 2020
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