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Thread: Very basic question about diatonic scales.

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  1. #1
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    Very basic question about diatonic scales.

    Hello, everyone. I'm brand new to guitar. I just got my first on Christmas and my brother has helped me out with learning. I haven't talked with him in a few days as we're both pretty busy and am too anxious to get some answers before we can practice together again. I'm not new to music, I've played drums for just over 9 years now but never really had the opportunity to focus on music scales.

    So, anyway... my question is regarding diatonic scales and their names. I understand the fact that the B and the E don't have any sharps which is why there are natural diatonic scales that hit only the natural notes. I don't mean to imply that the nature of the scales derive from the fact that B and E don't have sharps or visa versa... I'm not trying to create a chicken or egg argument, I'm just speaking on how it would appear to my currently uneducated mind.

    So, with these facts, and the facts that we have these diatonic scales with whole steps and half steps to ensure we always hit the natural notes... It makes me wondering why there are only two (at least only two very popular) scales named major and minor. And why are these scales natural on C and A, respectively? Is there a scale whose natural scale is a B? One that would go "Half, Whole, Whole, Half, Whole, Whole, Whole?" What about scales that are natural in D, E, F, or G? Do they exist? Do they have names?

    Just a little curiosity. I apologize if I've said anything or everything incorrectly. I don't know much about music theory to this point and am greatly interested in learning more.

    Thanks.

  2. #2
    bitter old fool Jed's Avatar
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    A major scale is built up using the following intervals:
    W W H W W W H - where W = Whole-step & H = Half-step

    In the key of C major the notes that result from this sequence of intervals is:
    C (w) D (w) E (h) F (w) G (w) A (w) B (h) C

    A major scale can be built on any of the twelve notes of the chromatic scale (all of the notes from any note to the next octave, excluding the octave)

    There are 15 "standard" major keys based on the following range (arranged from greatest number of flats to greatest number of sharps):

    Cb Gb Db Ab Eb Bb F C G D A E B F# C#

    The rule for writing / naming the notes of any major scale are:
    1) Each letter name can be used once and only once
    2) The sequence of intervals must follow WWHWWWH
    3) Sharps or flats may be used as needed to obtain the required interval.

    Note: The intervallic "distance" from E>F and B>C is a half-step. The intervallic "distance" from C>D, D>E, F>G, G>A and A>B are whole-steps.

    The major scale based on a tonic (root) of G:
    G (w) A (w) B (h) C (w) D (w) E (w) F# (h) G

    The major scale based on a tonic (root) of A:
    A (w) B (w) C# (h) D (w) E (w) F# (w) G# (h) A

    The major scale based on a tonic (root) of Bb:
    Bb (w) C (w) D (h) Eb (w) F (w) G (w) A (h) Bb

    etc, etc
    Last edited by Jed; 01-11-2009 at 04:36 AM.

  3. #3
    Registered User JonR's Avatar
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    Quote Originally Posted by IAmBill
    Hello, everyone. I'm brand new to guitar. I just got my first on Christmas and my brother has helped me out with learning. I haven't talked with him in a few days as we're both pretty busy and am too anxious to get some answers before we can practice together again. I'm not new to music, I've played drums for just over 9 years now but never really had the opportunity to focus on music scales.

    So, anyway... my question is regarding diatonic scales and their names. I understand the fact that the B and the E don't have any sharps which is why there are natural diatonic scales that hit only the natural notes. I don't mean to imply that the nature of the scales derive from the fact that B and E don't have sharps or visa versa... I'm not trying to create a chicken or egg argument, I'm just speaking on how it would appear to my currently uneducated mind.

    So, with these facts, and the facts that we have these diatonic scales with whole steps and half steps to ensure we always hit the natural notes... It makes me wondering why there are only two (at least only two very popular) scales named major and minor. And why are these scales natural on C and A, respectively? Is there a scale whose natural scale is a B? One that would go "Half, Whole, Whole, Half, Whole, Whole, Whole?" What about scales that are natural in D, E, F, or G? Do they exist? Do they have names?

    Just a little curiosity. I apologize if I've said anything or everything incorrectly. I don't know much about music theory to this point and am greatly interested in learning more.

    Thanks.
    Just to expand on Jed's excellent post...

    The "natural" notes (A B C D E F G, or the white notes of the piano) form both the C major scale and the A minor scale, depending on which note you make the "root" (the starting note, but more importantly the final note).
    On guitar, you can see (and play) these scales on 5th string.
    C major = frets 3 5 7 8 10 12 14 15 (sounds like "do re mi fa so la ti do")
    A minor = frets 0 2 3 5 7 8 10 12

    You should play these scales and listen to how they sound. (You may find the minor one clearer when played descending, but play both scales in both directions.)
    The "major" one gets its name from its 3rd step (E) which is 4 frets above C. In the "minor" scale, its 3rd step (C) is only 3 frets above the root (A). This contributes the essential quality to the scale, which most people characterise as "sad".

    Unlike piano, guitar allows you to see the WWHWWWH major scale step structure on the fretboard (and the WHWWHWW minor structure).


    Now, if we want another major scale - starting on another note - we are going to need some of those in-between frets in order to maintain the same whole-half step structure.

    Eg D major (on 5th string) would start at 5th fret and run: 5 7 9 10 12 14 16 17. We have raised two of the notes (8th>9th fret and 15th>16th fret). IOW, we have turned F and C into F# and C#.
    D E F# G A B C# D.

    Working with the same string, we get the A major scale as follows:
    0 2 4 5 7 9 11 12.
    Now we've raised 3 notes: 3>4 (C>C#), 8>9 (F>F#) and 10>11 (G>G#).
    A B C# D E F# G# A

    Supposing we want a scale starting on the 1st fret? That's A# or Bb.
    If you think about it, if we call it A# (and we stick to the rule about 1-of-each-note), we are going to have to raise those 3 notes we already raised, one more fret! (That's getting silly...) So we call our keynote Bb. The WWHWWWH formula runs like this:
    1 3 5 6 8 10 12 13.
    The rule about keeping one of each note letter means we are now lowering 2 notes from the Cmajor/A minor scale: frets 1>2 (B>Bb) and 7>6 (E>Eb).
    So our scale is Bb C D Eb F G A Bb.

    As with C major and A minor, every other major scale has its "relative minor", the root always being 3 frets lower.
    So for D major, the relative minor is B minor;
    For A major, the relative minor is F# minor;
    For Bb major, the relative minor is G minor.

    etc...

    Of course, when we play scales on the guitar normally, we don't play up and down one string! The guitar is tuned in a cunning way which enables up to spread the scale across the strings at 3 notes per string - so we don't have to move our hand up and down the neck. (Clever, huh...?)

  4. #4
    Registered User Malcolm's Avatar
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    Jed and Jon have just outlined the foundation of Western Music. The following charts may help pull all that together. I'm a visual learner and need to see it in a chart format. That helps me see the big picture. Hope you will get some good from these charts.

    Major Scale Notes
    C D E F G A B...............Notice the C scale has no Sharps
    G A B C D E F#.............and the G scale has one, the F#
    D E F# G A B C#...........and the D scale keeps the F# and
    A B C# D E F# G#.........adds the C#. Then the A scale keeps
    E F# G# A B C# D#.......everything and adds the G#. See how
    B C# D# E F# G# A#.....it builds on it's self.
    F# G# A# B C# D# E#
    C# D# E# F# G# A# B#
    F G A Bb C D E.............Look what happens with the flat scales
    Bb C D Eb F G A...........F has one the Bb, then the Bb scale keeps
    Eb F G Ab Bb C D.........it's self and adds the the Eb. Same thing
    Ab Bb C Db Eb F G.......the sharp scales did...
    Db Eb F Gb Ab Bb C
    Gb Ab Bb Cb Db Eb F
    Cb Db Eb Fb Gb Ab Bb

    Memory pegs you will want to memorize.
    See God Destroy All Earth By F#iry C#haos
    Farmer Brown Eats Apple Dumplings Greasely Cooked.
    Fat cats go down alleys eating birds.
    See God is the order of the major scales that have sharps in them.
    Farmer Brown is the order of the major scales that have flats in them.
    Fat cats is the order of the sharps.
    Farmer brown again is the order of the flats.


    Let’s take the Major scale and using the Major Key Formula of I, ii, iii, IV, V, vi viidim make the chords for each key in the Major scale. Upper case numbers become Major chords and lower case numbers become minor chords or the diminished chord.

    Major Scale Notes……..….Chords in that key
    C D E F G A B....................C, Dm, Em, F, G, Am Bdim
    G A B C D E F#..................G, Am, Bm, C, D, Em, F#dim
    D E F# G A B C#................D, Em, F#m, G, A, Bm, C#dim
    A B C# D E F# G#..............A, Bm, C#m, D, E, F#m, G#dim
    E F# G# A B C# D#............E, F#m, G#m, A, B, C#m, D#dim
    B C# D# E F# G# A#..........B, C#m, D#m, E, F#, G#m, A#dim
    F# G# A# B C# D# E#........F#, G#m, A#m, B, C#, D#m, E#dim
    C# D# E# F# G# A# B#......C#, D#m, E#m, F#, G#, A#m, B#dim
    F G A Bb C D E....................F, Gm, Am, Bb, C, Dm, Edim
    Bb C D Eb F G A..................Bb, Cm, Dm, Eb, F, Gm, Adim
    Eb F G Ab Bb C D................Eb, Fm, Gm, Ab, Bb, Cm, Ddim
    Ab Bb C Db Eb F G..............Ab, Abm, Cm, Db, Eb, Fm, Gdim
    Db Eb F Gb Ab Bb C……………..Db, Ebm, Fm, Gb, Ab, Bbm, Ddim
    Gb Ab Bb Cb Db Eb F……………Gb, Abm, Bbm, Cb, Db, Ebm, Fdim
    Cb Db Eb Fb Gb Ab Bb………….Cb, Dbm, Ebm, Fb, Gb, Abm, Bbdim

    Natural Minor Scale
    A B C D E F G .....................Notice how the 6th column of the
    E F# G A B C D....................Major scale becomes the 1st column
    B C# D E F# G A..................in the minor scale and how the 7th
    F# G# A B C# D E................column of the Major scale is now the
    C# D# E F# G# A B.............2nd column in the minor scale. And
    G# A# B C# D# E F#...........yep, the 1st column in the Major scale
    D# E# F# G# A# B C#.........is now the 3rd column, etc. etc.
    A# B# C# D# E# F# G#......Ask your self why?
    D E F G A Bb C
    G A Bb C D Eb F
    C D Eb F G Ab Bb
    F G Ab Bb C Db Eb
    Bb C Db Eb F Gb Ab
    Eb F Gb Ab Bb Cb Db
    Ab Bb Cb Db Eb Fb Gb

    Let’s now take the Natural Minor scale and using the Natural Minor Key Formula of: i, iidim, III, iv, v, VI, VII make the chords for the Natural Minor Key. Again, upper case numbers become Major chords and lower case numbers become minor chords or the diminished chord.

    Natural Minor Scale Notes ……. Chords in that key
    A B C D E F G ......................Am, Bdim, C, Dm, Em, F, G
    E F# G A B C D.....................Em, F#dim, G, Am, Bm, C, D
    B C# D E F# G A...................Bm, C#dim, D, Em, F#m, G, A
    F# G# A B C# D E.................F#m, G#dim, A, Bm, C#m, D, E
    C# D# E F# G# A B...............C#m, D#dim, E, F#m, G#m, A, B
    G# A# B C# D# E F#.............G#m, A#dim, B, C#m, D#m, E, F#
    D# E# F# G# A# B C#...........D#m, E#dim, F#, G#m, A#m, B, C#
    A# B# C# D# E# F# G#.........A#m, B#dim, C#, D#m, E#m, F#, G#
    D E F G A Bb C…………………………Dm, Edim, E, Gm, Am, Bb, C
    G A Bb C D Eb F………………………Gm, Adim, Bb, Cm, Dm, Eb, F
    C D Eb F G Ab Bb…………………….Cm, Ddim, Eb, Fm, Gm, Ab, Bb
    F G Ab Bb C Db Eb…………………..Fm, Gdim, Ab, Bbm, Cm, Db, Eb
    Bb C Db Eb F Gb Ab…………………Bbm, Cdim, Db, Ebm, Fm, Gb, Ab
    Eb F Gb Ab Bb Cb Db……………….Ebm, Fdim, Gb, Abm, Bbm, Cb, Db
    Ab Bb Cb Db Eb Fb Gb…………….Abm, Bbm, Cb, Dbm, Ebm, Fb, Gb

    Chord formula ..... (use the major scale)
    Major = 1-3-5 …….. A Major chord is made up of the 1-3-5 note of the major scale.
    Minor =1-b3-5 …… A Minor chord is made up of the 1-(flatted 3rd) b3-5 note of the major scale. Any minor chord will have a flatted 3rd.
    Augmented = 1-3-#5…… You sharp the 5th to make an augmented chord
    Diminished = 1-b3-b5…The 3rd and 5th are flatted or diminished.
    Diminished Seventh = 1-b3-b5-bb7
    Major 6th = 1-3-5-6
    Minor 6th = 1-b3-5-6
    Seventh = 1-3-5-b7 This one is called the dominant 7th
    Minor seventh = 1-b3-5-b7…… Same as you did to turn a Major.
    Major seventh = 1-3-5-7 ... notice the 3rd is natural, thus major as is the 7th.
    Sus2 = 1-2-5
    Sus4 = 1-4-5
    Fifth = 1-5 Power chord, and notice it’s generic, no 3rd so it can not be minor.
    Sixth = 1-3-5-6
    Ninth = 1-3-5-b7-9
    Add9 = 1-3-5-9

    For more chord detail http://www.smithfowler.org/music/Chord_Formulas.htm

    I suggest you print this string and use it as study material. Too much good information here not to take advantage of it.

    Good luck.
    Last edited by Malcolm; 01-11-2009 at 07:32 PM.

  5. #5
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    Thanks for all of the information, guys. Unfortunately, much of this I already understand and I believe your answers were stemmed from the fact that I did not phrase my question correctly. I am familiar with the 15 major keys and how their key signature is displayed on a music staff. I am also familiar with the fact that B#, E#, Cb, and Fb technically do exist because in some keys they are required to be written in this manor to accommodate the spaces on the music staff. For instance, in the key of Gb, there is is a Cb to accomodate the C space on the treble staff. If there wasn't a Cb then we would have a Bb and a B accomodating the same line on the staff.

    What I was trying to ask is what is the logic behind the W-W-H-W-W-W-H of the major scale and the W-H-W-W-H-W-W of the minor scale? ... or if you would prefer in Solfege, why does Major start on "Do" and minor start on "La?" Naturally the major scale and minor scale represent two different offsets of the same step pattern. My question is whether or not the other offsets of this same pattern are used? If I were to graph it, I guess I'm wondering how these question marks would be filled:

    Code:
    * Bare in mind, "Natural Root" is defined as the key that contains no Sharps
    or Flats
    
    Scale Name	  Natural Root	Step Notation	Solfege Notation
    -----------------------------------------------------------------
    Minor		   A		W-H-W-W-H-W-W	La-Ti-Do-Re-Mi-Fa-So-La
    ?		   B	        H-W-W-H-W-W-W	Ti-Do-Re-Mi-Fa-So-La-Ti
    Major		   C		W-W-H-W-W-W-H	Do-Re-Mi-Fa-So-La-Ti-Do
    ?		   D	        W-H-W-W-W-H-W	Re-Mi-Fa-So-La-Ti-Do-Re
    ?		   E	        H-W-W-W-H-W-W	Mi-Fa-So-La-Ti-Do-Re-Mi
    ?		   F	        W-W-W-H-W-W-H	Fa-So-La-Ti-Do-Re-Mi-Fa
    ?		   G	        W-W-H-W-W-H-W	So-La-Ti-Do-Re-Mi-Fa-So
    Why was B skipped over like Fredo Corleone? It's smart. It's not dumb like everybody says. I guess this is what I'm really wondering... I hope I did a better job of explaining it than I did the first time.

    That said, I greatly, greatly appreciate all the information given. While I am familiar with a lot of it, it's nice to have it clearly defined in writing rather than just a bunch of random facts floating around my brain. I appreciate the help.
    Last edited by IAmBill; 01-11-2009 at 09:01 PM.

  6. #6
    bitter old fool Jed's Avatar
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    Maybe Jon can explain the reasoning for / history of the notes used for C / A minor. But in the meantime, . . . What you are describing are the modes of the major scale / relative natural minor scale. Your Solfege notation assumes Fixed Do, which is fine but more commonly Moveable Do is used. Aeolian = Do Re Me Fa So Le Te Do.

    There's nothing special about "natural roots" since these modes can be built on any root, just as the major and minor scales can be built on any root.

    Code:
    * Bare in mind, "Natural Root" is defined as the key that contains no Sharps or Flats
    
    Mode      Root	       Step Notation	  Solfege Notation
    -----------------------------------------------------------------
    Aeolian	   A		W-H-W-W-H-W-W	La-Ti-Do-Re-Mi-Fa-So-La
    Locrian	   B	        H-W-W-H-W-W-W	Ti-Do-Re-Mi-Fa-So-La-Ti
    Ionian	   C		W-W-H-W-W-W-H	Do-Re-Mi-Fa-So-La-Ti-Do
    Dorian	   D	        W-H-W-W-W-H-W	Re-Mi-Fa-So-La-Ti-Do-Re
    Phrygian   E	        H-W-W-W-H-W-W	Mi-Fa-So-La-Ti-Do-Re-Mi
    Lydian	   F	        W-W-W-H-W-W-H	Fa-So-La-Ti-Do-Re-Mi-Fa
    Mixolydian G	        W-W-H-W-W-H-W	So-La-Ti-Do-Re-Mi-Fa-So
    cheers,
    Last edited by Jed; 01-11-2009 at 10:07 PM.

  7. #7
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    Smile

    The basic set of intervals (offsets) that you refer to have their roots in Harmonic overtones and ratios of each frequency.

    an Octave is double the frequency of the root note. The Third Harmonic overtone is what is labeled as a perfect fifth, the 4th Harmonic overtone is another octave up and the fifth harmonic overtone is on or about a Major third.

    Once you have filled in the gaps between the root note and the octave with some notes that have fairly simple frequency ratios with the Root note you get something like a major scale. Once you have adjusted the methoeds used to space out the notes so that all of the possible keys can be accomodated, you end op with the 12 notes we all know and love.

    The reason that the A and the C (from your example above) got lucky enough to be the Major and the Minor scale is because they work better than the other 5.

    This is a functional Harmony thing that has been tweaked with for about the last 350 years or so.

    pre functional Harmony the pattern of intervals was used from each of the possible starting points in what is reffered to as Modal Harmony, a lot of old folk songs use Modal Harmony, so do a lot of pop songs, but that is just good recycling.

    Your Fred Corleone exampl of B is the most difficult mode of the lot, it is almost impossible to make it sound as if B is the root note. Try it, it usually sounds as if either A or C is in charge of the family

  8. #8
    Registered User JonR's Avatar
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    Quote Originally Posted by Jed
    Maybe Jon can explain the reasoning for / history of the notes used for C / A minor.
    Haha, I wish I could!
    Easy to think they must have called A "A" (and laid out the W-H formula from there) because they liked Aeolian mode. But Aeolian mode didn't exist then.
    I have my own guesses about where it came from, but haven't seen anything to clarify the history.

  9. #9
    Registered User JonR's Avatar
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    Quote Originally Posted by IAmBill
    What I was trying to ask is what is the logic behind the W-W-H-W-W-W-H of the major scale and the W-H-W-W-H-W-W of the minor scale? ... or if you would prefer in Solfege, why does Major start on "Do" and minor start on "La?" Naturally the major scale and minor scale represent two different offsets of the same step pattern. My question is whether or not the other offsets of this same pattern are used?
    Yes - these are the "Modes" as Jed has laid out.

    Briefly, between about 600 and 1500, the European musical system was based on 4 modes:
    Dorian = D E F G A B C D
    Phrygian = E F G A B C D E
    Lydian = F G A B C D E F
    Mixolydian = G A B C D E F G

    These had plagal variants, which meant they ranged from the 5th to the 5th, with the tonic ("final") being in the middle:
    Hypodorian = A B C D E F G A
    Hypophrygian = B C D E F G A B
    Hypolydian = C D E F G A B C
    Hypomixolydian = D E F G A B C D

    (Hypodorian looks like Aeolian or minor, but D is still the "final" (keynote), not A. Likewise, hypolydian looks like the C major scale, but F is actually its "final".)

    In the mid-1500s, Ionian and Aeolian (and their hypo variants) were added, along with the theoretical Locrian (never actually used in practice).

    Over the next century or so (I guess), Ionian and Aeolian took over as the major and minor "key" respectively. Probably because they lent themselves better to the developing art of functional harmony.

    (This is all really an outrageous simplification - with serious omissions - but hopefully will do as an introduction. )

    Here's more:
    http://en.wikipedia.org/wiki/Musical_mode
    http://en.wikipedia.org/wiki/Gregorian_mode
    http://www.midicode.com/tunings/greek.shtml
    http://www.beaufort.demon.co.uk/modes.htm

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    Yep, this is all great information guys. Thanks. I knew Wikipedia would have stuff on this, I was just missing some terminology to get me looking in the right places. This definitely suffices as a starting point in my education of music theory. My brother actually touched on the terms Dorian, Phrygian, Lydian, and Mixolydian but at the time it felt out of context and went right over my head.

    Thanks, again.
    Last edited by IAmBill; 01-12-2009 at 04:54 AM.

  11. #11
    bitter old fool Jed's Avatar
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    Quote Originally Posted by IAmBill
    I understand the fact that the B and the E don't have any sharps which is why there are natural diatonic scales that hit only the natural notes. I don't mean to imply that the nature of the scales derive from the fact that B and E don't have sharps or visa versa... I'm not trying to create a chicken or egg argument, I'm just speaking on how it would appear to my currently uneducated mind.
    What you should be thinking here is that the intervallic distance from B>C and E>F is a half-step. But don't deduce from that fact that there is no such thing as a B# or an E# (or the extension of this flawed logic - that there is no Cb or Fb). Every letter name can have a sharp and flat version.

    For example have a look at the following 15 "standard" major scales:

    Cb major = Cb Db Eb Fb Gb Ab Bb Cb
    Gb major = Gb Ab Bb Cb Db Eb F Gb
    Db major = Db Eb F Gb Ab Bb C Db
    Ab major = Ab Bb C Db Eb F G Ab
    Eb major - Eb F G Ab Bb C D Eb
    Bb major = Bb C D Eb F G A Bb
    F major = F G A Bb C D E F
    C major = C D E F G A B C
    G major = G A B C D E F# G
    A major = A B C# D E F# G# A
    E major = A F# G# A B C# D# E
    B major = B C# D# E F# G# A# B
    F# major = F#, G#, A#, B, C#, D#, E#, F#
    C# major = C# D# E# F# G# A# B# C#

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