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Introduction to Scale and Chord Theory

Discussion in 'Lessons & Articles' started by TalkBass, Apr 26, 2004.

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  1. TalkBass

    TalkBass News & Features Posting Account Gold Supporting Member

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    <p><font face="Verdana, Arial, Helvetica, sans-serif" size="2"><br>
    <p align="center"><font size="4"><b><font size="5">Introduction to Scale and Chord
    Theory</font></b></font></p><p align="center"><i>by TalkBass Member <a href="http://www.talkbass.com/forum/member.php?s=&action=getinfo&userid=8215">"Jazzbo"</a></i></p>
  2. TalkBass

    TalkBass News & Features Posting Account Gold Supporting Member

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    <p><b>The Chromatic Scale</b> </p>
    <p>Music is music, and is pretty wide opened, but learning the language of Western
    Tonal music is based in learning scales. The chromatic scale is a scale that
    uses all 12 possible pitches, (also known as tones, or notes).
    Those pitches are:</p><p>A -- A# (Bb) -- B -- C -- C# (Db) -- D -- D# (Eb) -- E -- F -- F# (Gb) -- G
    -- G# (Ab) -- a</p>
    <p><img src="http://www.talkbass.com/images/lessons/chromscale.gif" width="500" height="189"></p>
    <p>(Lower case letters denote the next octave).</p>
    <p>Also note that the scale is a cycle, continuing in a circular fashion.</p>
    <p>So, I have two lists of the pitches. Those notes listed in parentheses next
    to another note are known as enharmonics. An <b>enharmonic</b> is a note that
    can be written two different ways, but whose tone is the same. A# is said to
    be an enharmonic of Bb. D# and Eb are enharmonics.<br>
    <br>
    Out of these twelve pitches, comes all of the music you're used to hearing.
    In my opinion, the best way to become familiar with these, is from a piano or
    keyboard. </p>
    <p><img src="http://www.talkbass.com/images/lessons/keyboard.gif" width="400" height="202"></p>
    <p> </p>
    <p><br>
    <b>What is a Chromatic Scale?</b></p>
    <p>Scales create a pattern of pitches. They talk about the distance between pitches,
    and how they relate. The distance between pitches is known as <b>intervals</b>.
    Look back at the list of all 12 pitches. The distance between A to A# is just
    one note, eh? This is known as a <b>semi-tone</b> (or half-step). The distance
    between A to B is two notes. This is known as a <b>tone</b> (or whole-step).
    So now we have two different intervals we know, semi-tones and whole-tones.
    Knowing just this information, the 12 pitches and semi- and whole-tones, we
    can learn about scales.</p>
    <p>A chromatic scale is always 12 pitches, and each pitch is a semi-tone away
    from the other. This is an important scale; however, I'm going to speak more
    in-depth about another type of scale. The <b>diatonic</b> scale is a very important
    scale to start from. More commonly, it is referred to as the <b>major</b> scale.
    So, how do we figure out what a major scale is. </p>
    <p><b>The Major Scale</b></p>
    <p>A major scale is just a formula used to create a certain musical language from
    the 12 pitches. Let's start with any pitch, let's say "C." So if we
    start from "C" and build a major/diatonic scale, we are said to be
    in the <b>key of C</b>.</p>
    <p>How do you build that scale? Here's the formula:</p>
    <p align="center"><u><b>tone - tone - semitone - tone - tone - tone - semitone</b></u></p>
    <p>So, from C, we move up one tone, to D, another tone to E, a semitone to F,
    another tone to G, a tone to A, a tone to B, and another semitone, back to C
    (an octave higher).</p>
    <p>So, using the above formula of (<b>t-t-s-t-t-t-s</b>), a major scale in the
    key of C, will look like:</p>
    <p align="center">C - D - E - F - G - A - B - c</p>
    <p>The key of the scale, C, is also said to be the root.</p>
    <p>So, we've discovered how to make a C Major scale. Congrats. What you really
    have to do at this point, is take that same formula, and learn the scale for
    all 12 pitches. The best way to do this is through the <b>Circle of Fifths</b>
    (aka Cycle of Fourths). There is a thread in the Miscellaneous forum, by <a href="http://www.talkbass.com/forum/member.php?s=&action=getinfo&userid=1601">Gard</a>,
    about this. </p>
    <p>To reinforce the theory behind building a scale, let's choose another key.
    For example, how 'bout Fmaj? So, here are our possible pitches again:</p>
    <p align="center">A - A# - B - C - C# - D - D# - E - F - F# - G - G# - a</p>
    <p>This is the A <b>chromatic</b> scale if you recall. Just to get back to chromatics
    again, the chromatic scale is a scale of 12 pitches, from root to octave, that
    are each a semi-tone apart. So a D# chromatic scale, would look like this:</p>
    <p align="center">D# - E - F - F# - G - G# - A - A# - B - C - C# - D - d#</p>
    <p>Easy, right? It is important to note the intervals, or distance between each
    pitch. The chromatic scale is simple because it's just all the tones. So let's
    get back to Fmaj. The formula for a <b>major scale</b> again is "t-t-s-t-t-t-s."
    Where "t" stands for "tone" and "s" stands for
    "semi-tone." To reiterate, a <b>tone</b> is a distance of one full
    step, a <b>semi-tone</b> is a half-step. Now, why is a full step really like
    two steps? I think the best way to explain this is from looking at a keyboard.
    If you find F on the keyboard, then the next white key is G. That's a full step,
    which is a distance of two pitches. F# (or Gb) is between those two pitches,
    a black key, but it is just a half step. Weird. Have I confused myself well
    enough yet?</p>
    <p>Okay, <b>Fmaj</b>.</p>
    <p>F, then using the formula, find the pitch one tone away, which is G. The next
    step is another tone, which is A. The next step asks for a semi-tone, which
    is A# right? Now we run into a problem. A major scale, when written, can only
    be represented by each pitch letter once. So what I mean, is that you can't
    have two As, even if one is A (without a sharp or flat, it's A <b>natural</b>),
    another is Ab, and another is A#. But Bb is the same as A#, no?</p>
    <p>So, so far, we have:</p>
    <p align="center">F - G - A - Bb</p>
    <p>We have done the t-t-s part of the formula to get G - A - Bb. No we have to
    move another whole tone from Bb to what? C. No another whole tone to D, another
    whole tone to E, and a semi-tone, which gets you back to the octave, F. Here's
    our scale:</p>
    <p align="center">F - G - A - Bb - C - D - E - f</p>
    <p>No we have an Fmaj. scale. Try and do it for Gmaj. You should come up with:</p>
    <p align="center">G - A - B - C - D - E - F# - g</p>
    <p>If you don't, look through it again and figure out what went wrong. </p>
    <p>From understanding where a major scale comes from, you can understand all the
    <b>modes</b>, including the minor scale. And even more importantly, you can
    understand the triads derived from a scale. </p>
    <p>Additional scales that I didn't mention are: <b>pentatonic, blues, melodic
    minor, harmonic minor</b>, and many many more.</p>
    <p><br>
    <b>Triads</b></p>
    <p>What's a triad? Well, it's a type of chord. So, what's a chord? A <b>chord</b>
    is usually a group of 3 or more <b>notes</b> (pitches) played in unison. Now
    I know what you're thinking to yourself. Where can I learn to play me some of
    dem phat pitches? Okay, maybe you're not, never mind. </p>
    <p>A <b>triad</b> is a chord consisting of 3 notes wherein the intervals are root,
    3rd, 5th. Back to those tricky intervals. So, an <b>interval</b> being the distance
    between two notes, we've learned about a semi-tone (minor 2nd) and a whole-tone
    (major 2nd). I'm not going to get too much into intervals, Harvard's Music Dictionary
    has an <b>excellent</b> definition, but I am going to introduce two other important
    intervals. </p>
    <p>· The <b>major 3rd</b> is an interval wherein the two pitches are 2
    whole-tones apart.</p>
    <p>· The minor 3rd is an interval wherein the two pitches are 1 1/2 whole-tones
    (one whole-tone, one semi-tone) apart.</p>
    <p>Now, you actually have the basis to build all your chords.</p>
    <blockquote>
    <p> <i>My original bass teacher used to try and have me think about major and
    minor 3rds when I was away from my bass. So if I was driving my car, or in
    a really boring class, I would think, okay, what's a minor 3rd from Bb, or
    a major 3rd from E, or a major 3rd from F? Really, you should do this as much
    as possible. </i></p>
    <p><i>Some examples:</i></p>
    <p><i>E up a major 3rd is G#<br>
    E up a minor 3rd is G<br>
    C up a major 3rd is E<br>
    C up a minor 3rd is Eb</i></p>
    </blockquote>
    <p>So, WHAT DOES IT ALL MEAN?! Knowing major and minor 3rds gives you the tools
    to build triads. </p>
    <p>Here are the triads that appear naturally in a major scale. I'll explain in
    a few minutes what it means for a triad to appear in the major scale. </p>
    <p>·<b> Major chord</b>: Root + Major 3rd + minor 3rd<br>
    · <b>Minor chord</b>: Root + minor 3rd + Major 3rd<br>
    · <b>Diminished chord</b>: Root + minor 3rd + minor 3rd</p>
    <p>So, using that information, <b>let's construct a Major chord</b>. <u>The root
    is also the <b>name of the chord</b></u><b>.</b> Let's stay with C. So, a Cmaj
    chord will take the root, C, move up a Major 3rd, E, then up a minor 3rd, G.
    </p>
    <p align="center"><b>Cmaj. chord = C - E - G</b></p>
    <p>How 'bout a minor chord. C, the root, up a minor 3rd, or Eb, up a Major 3rd,
    which is G.</p>
    <p align="center"><b>Cmin. chord = C - Eb - G</b></p>
    <p>And a diminished chord. C, the root, up a minor 3rd, or Eb, up a minor 3rd
    again, which is Gb.</p>
    <p align="center"><b>Cdim. chord = C - Eb - Gb</b></p>
    <p>Congrats. 3 chords constructed. How does this relate to the major scale?</p>
    <p>Back to Cmaj: C - D - E - F - G - A - B - c</p>
    <p>Let's use some backwards thinking from what we just learned, and build chords
    with each scale degree, using the notes of the scale. To do this, the easy way
    to think of it, is to take the root and use every other note, as every other
    note in the major scale is a 3rd from the other. Whether it's a minor 3rd or
    Major 3rd is what we'll figure out. Confused, yet? It gets better.</p>
    <p>So, let's do that.</p>
    <p>First note of the scale = C. The scale gives us every other note as C - E -
    G. (Look familiar?)</p>
    <p>C being the root (roman numeral I), E is a Major 3rd from C, and G is a minor
    3rd from E. What chord has a root, then Major 3rd, then minor 3rd? Major chord.
    </p>
    <p><b>The chord found naturally from the root (I) of a major scale, is a major
    chord.</b></p>
    <p>The second scale position (ii) is D. Using the scale, the chord we would find
    is D - F - A. D being the root, F is a minor 3rd from D, and A is a Major 3rd
    from F. Root + minor 3rd + Major 3rd = minor chord.</p>
    <p><b>The chord found naturally from the ii of a major scale, is a minor chord.</b></p>
    <p>Do the same for each position, next with E (E - G - B), then F (F - A - C),
    then G (G - B - D), then A (A - C - E), then finally B (B - D - F). You should
    get:</p>
    <table width="75" border="1" align="center"><tr><td>C</td><td>D</td><td>E</td><td>F</td><td>G</td><td>A</td><td>B</td><td>c</td></tr><tr><td>I</td><td>ii</td><td>iii</td><td>IV</td><td>V</td><td>vi</td><td>vii</td><td>I</td></tr><tr><td>Maj.</td><td>min.</td><td>min</td><td>Maj</td><td>Maj</td><td>min</td><td>dim</td><td>Maj</td></tr></table>
    <p>Notice the Roman number <b>scale degrees</b>. Also notice that the major chords
    are capitalized, and the minor chords (or diminished) are lower-case. You'll
    find this common in most musical notation. </p>
    <p>What this tells us, is that in <u>every single</u> major scale, the first note
    of the scale (the I, or root, position) is going to be a major key. Here's what
    this would look like for Fmaj.</p>
    <table width="75" border="1" align="center"><tr><td>F</td><td>G</td><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td><td>f</td></tr><tr> <td>I</td><td>ii</td><td>iii</td><td>IV</td><td>V</td><td>vi</td><td>vii</td><td>I</td></tr><tr> <td>Maj.</td><td>min.</td><td>min</td><td>Maj</td><td>Maj</td><td>min</td><td>dim</td><td>Maj</td></tr></table>
    <p>The "I" chord from Fmaj, is F - A - C, a major chord. Also, didja
    notice that this chord also appears as the "IV" position of Cmaj?
    Neat, eh? The Cmaj. triad is found as the root of the C major chord, but also
    as the fourth scale position of the F major scale.</p>
    <p></p>
    <p><b>Applying this to the Bass</b></p>
    <p>Remember that the principles that I'm outlining are basic music theory principles.
    I haven't mentioned how they relate to a particular instrument yet. I really
    believe the piano is the best instrument for first learning scales and chords,
    seeing how intervals form, and what they mean, but you can apply this to any
    instrument. Which would, of course, include the bass.</p>
    <p>So put away the things I've been speaking of so far, and look at the bass.
    </p>
    <p align="center"><img src="http://www.talkbass.com/images/lessons/Bass%20Fretboard.gif" width="464" height="96">
    </p>
    <p>The strings are tuned E-A-D-G from lowest to highest. What you may notice is
    that the strings are spaced a fourth apart. Then each individual string's pitch
    can be manipulated by fretting. Starting with the E string, when you fret from
    the first fret, you raise the pitch by one semitone. Then if you fret the second
    fret, you raise the pitch a semitone from F, which would be F# (Gb). Going forward
    all the way to the 12th fret, you get:</p>
    <p align="center">
    E -- F -- F# -- G -- G# -- A -- A# -- B -- C -- C# -- D -- D# -- e </p>
    <p>This is a chromatic scale. We're used to seeing it begin at C, per my earlier
    examples. This just happens to begin at E. Doing the same thing for the other
    string, you're fretboard should look like this:</p>
    <p align="center"><b>G - G# - A - A# - B - C - C# - D - D# - E - F - F# - G<br>
    D - D# - E - F - F# - G - G# - A - A# - B - C - C# - D<br>
    A - A# - B - C - C# - D - D# - E - F - F# - G - G# - A<br>
    E - F - F# - G - G# - A - A# - B - C - C# - D - D# - E</b></p>
    <p> </p>
    <p>The trick now is to be able to<b> identify a major scale on your own</b>. The
    fretboard itself is not designed to naturally show the major scale. However,
    as the intervals between the strings are the same, transposing on a stringed
    instrument is fabulously simple. If you look for Cmaj, (C-D-E-F-G-A-B-c), starting
    with the E string, you'll find your scale by playing (in tab form):</p>
    <p>G: 2 - 4 <b>5</b><br>
    D: 2 3 - 5<br>
    A: 2 <b>3</b> - 5<br>
    E: - 3 - 5</p>
    <p>These are all the possible notes of the Cmaj scale in a four-fret position
    at the lowest point on the neck (to play a complete scale). The lowest note
    I show is the 3rd fret of the E string (G), the fifth of the scale. It's a possible
    note of the scale, but many people prefer to only show the notes on the A-D-G
    strings because you can play one full octave of the scale that way. That's fine
    too, I just wanted to show you where all the notes in that finger position are.
    So you'll notice the 3rd fret of the A string is C, and the 5th fret of the
    G string is C. If you play that pattern with that beginning and end point, you've
    played one octave of Cmaj. </p>
    <p>If you wanted to play a Db major scale, let's use the t-t-s-t-t-t-s formula
    to get the Dbmaj. scale, which would be:</p>
    <p align="center">Db - Eb - F - Gb - Ab - Bb - C - db</p>
    <p>And to show, in tab form, that scale on the fretboard, you would have:</p>
    <p>G: 3 - 5 6<br>
    D: 3 4 - 6<br>
    A: 3 4 - 6<br>
    E: - 4 - 6</p>
    <p>Notice how the pattern just moved one step higher on the fretboard? The root
    of the first scale was C. The root of the second scale was Db, which is a semi-tone
    higher than C, eh? So just move the pattern one semi-tone higher.</p>
    <p>Personally, I think memorizing patterns is fine, but it's better to memorize
    the notes of the scale, or the intervals, and discover patterns on your own,
    it will make you very familiar with the fretboard.</p>
    <p><b>The Minor Scale (Natural or Pure Minor)</b></p>
    <p>So I haven't talked about minor scales yet. There's been some talk of the major
    scale and triads, but nothing about the minor scale. </p>
    <p>The <b>natural minor</b> scale is built from a similar formula of intervals
    as the major scale. Instead of the formula we're used to of "t-t-s-t-t-t-s,"
    the order of tones and semitones for minor scales is:</p>
    <p align="center"><b>t-s-t-t-s-t-t</b></p>
    <p>So, let's use as an example, C again, for a C minor scale.</p>
    <p>Start with C, then move one whole tone to D, then a semitone to Eb, then a
    whole tone to F, then another whole tone to G, then a semitone to Ab, then a
    tone to Bb, then another tone back to c (the octave). This gives us a C minor
    scale:</p>
    <p align="center"><b>C - D - Eb - F - G - Ab - Bb - c</b></p>
    <p>So let's look at everyone's favorite major scale; Cmajor.</p>
    <p align="center"><b>C - D - E - F - G - A - B - c</b></p>
    <p>Every scale has it's <b>RELATIVE NATURAL MINOR</b>. The relative minor is the
    minor scale built from a major scale. It's considered one of the scale's <b>modes</b>,
    which essentially is simply playing the same scale from different root points
    within the scale. (Maybe I'll do modes later). So, play a C major scale with
    A, (the sixth position of the scale), as the root:</p>
    <p align="center"><b>A - B - C - D - E - F - G - a</b></p>
    <p>This isn't a major scale right? Notice it does follow the format of a minor
    scale. <u>Amin is the <b>relative minor scale</b> to C Major</u>. The <b>Sixth</b>
    position of a major scale is the relative minor. You can also note that the
    relative minor root is a minor 3rd lower than the Major root. A is a minor 3rd
    lower than C. </p>
    <p>With major scales, we have a series of triads that naturally occur:</p>
    <table width="100" border="1" align="center"><tr><td>C</td><td>D</td><td>E</td><td>F</td><td>G</td><td>A</td><td>B</td></tr><tr> <td>I</td><td>ii</td><td>iii</td><td>IV</td><td>V</td><td>vi</td><td>vii</td></tr></table>
    <p> </p>
    <p><i>(Note the trend that Major triads are represented by a capital Roman numeral,
    and that minor triads are associated with a lower case Roman numeral).</i></p>
    <p>This is just to illustrate how the order of the notes changes, but when building
    triads, each one retains it's interval value.</p>
    <p>Play a C major scale, then a C minor scale. Try and hear the differences between
    the two scales, the feel of them, the flavors. Major scales and minor scales
    have no instructions as to when or apply them. It's up to you to know them,
    understand them, and get the feel in you to decide how you want to use the notes
    from these scales.</p>
  3. TalkBass

    TalkBass News & Features Posting Account Gold Supporting Member

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    <p>In practicing, I strongly advice to become just as familiar with the minor
    scales for all pitches, as you are with the major scales for all pitches. Also,
    understand the relative minors to each scale. The best way to do this, I feel,
    is through the <b>Circle of Fifths</b>.</p>
    <p><b>The Pentatonic Scale</b></p>
    <p>Ah, the Pentatonic Scale. The crutch of the rock guitarist. The cliff notes
    of tonal theory. The scale responsible for making Eric Clapton a millionare!
    Okay, kidding.</p>
    <p>The <b>pentatonic scale</b> is just another type of scale, similar to the major
    or minor. As such, a major and minor pentatonic scale exists. So, how 'bout
    we have a good look at those today. </p>
    <p>Let's look at the diatonic scales (major and minor) again, and look at the
    <b>intervals</b> a little differently than we were. I was introducing them as
    either (t-t-s-t-t-t-s) or (t-s-t-t-s-t-t), for major and minor, respectively.
    Here's another way to look at it. </p>
    <p>Let's take C major again (are we getting sick of this scale, hmmmmm?)</p>
    <p>C - D - E - F - G - A - B</p>
    <p>Start with the root, and another way to think of the scale is </p>
    <p><b>Root - 2 - 3 - 4 - 5 - 6 - 7</b></p>
    <p>Okay, boring. Whatever. Look at Cminor and you'll notice where I'm going with
    these intervals.</p>
    <p>C - D - Eb - F - G - Ab - Bb</p>
    <p><b>Root - 2 - b3 - 4 - 5 - b6 - b7</b></p>
    <p>Okay! Now do you see where I'm going with this? <u>A minor scale is just a
    major scale with a lowered 3rd, 6th, and 7th.</u></p>
    <p>Now, how can we use this information for evil? Well.....wait, wrong thread.
    Sorry.</p>
    <p>Anyhoo, looking at the scale as a whole group of intervals, in relation to
    the root, can be easier than thinking, "okay, Eb, um....minor, okay, first
    um, tone, then um....a....semitruck, um, tone, then....um....wait!" See
    what I mean?</p>
    <p>I like this approach when I'm looking at the fingerboard. If you understand
    the intervalic relationship on your fingerboard, playing any scale will be easier,
    knowing the intervals of the scale from the root.</p>
    <p>So how does this pentatonic stuff fit in? Like I said, it's just another type
    of scale. There's nothing more special, or less special, about it, in comparison
    to the diatonic scale. </p>
    <p>Okay, here's <b>Pentatonic Major</b>: (director's cut):</p>
    <p>t - t - 1.5t - t - 1.5t</p>
    <p>Um....what?</p>
    <p>Okay, humor me. C Pentatonic Major. Start with the root, C. Move up a tone,
    D. Move up another tone, E. Now, one and a half tones to G, then another tone
    to A.</p>
    <p>C Pentatonic Major = <b>C - D - E - G - A - c</b></p>
    <p>Here's how I like to think about it:</p>
    <p><b>Root - 2 - 3 - 5 - 6</b></p>
    <p>Ahhhhh, so root = C. Then a second, D. A third, is E. What's a fifth from C,
    why, it's G! Then a 6th, A. </p>
    <p>While I'm thinking of it..... <b>C Pentatonic minor:</b></p>
    <p>1.5t - t - t - 1.5t - t</p>
    <p>Ummmm.........</p>
    <p>C Pentatonic Minor. Start with C. Follow the formular, um....C, then Eb, then
    F, G, Bb.</p>
    <p>Here's how I like to think about this one:</p>
    <p><b>Root - b3 - 4 - 5 - b7</b></p>
    <p>C - Eb - F - G - Bb - c</p>
    <p>Pentatonic Major and Minor. So, what do you do with them? Why jeez boy, the
    same thing you do with every scale, you play it and play it and play it. You
    play it ascending and descending. You play it for two octaves, then 3. You play
    it out of sequence. You doodle around in using only scale tones. You figure
    out the triads in those scales, you play those. You let your ears get the flavor
    of the scale. You let your fingers know them inside and out. You solo in them.</p>
    <p>Pentatonic scales are the lifeblood of rock music. Listen very closely to the
    differences between the Pentatonic Scales and the Diatonic Scales. It's just
    a matter of letting your ear here what is different. <u>What is a Pentatonic
    Major scale but a Diatonic scale without the 4 or 7? </u></p>
    <p><u>What is the Pentatonic Minor scale but a Diatonic minor scale without the
    2 or 6?</u></p>
    <p>A good question to ask yourself is, why take out those notes to build a scale?
    What is so special about those notes? Now, I could give you some answers as
    to what is accepted in music circles, but really, it's more important to listen
    to the differences of those scales, and <b><u>LET YOUR EARS</u></b> tell you
    the differences, so that <u>you can make up your own mind</u> about how you
    want to use these scales, and how you want to play them. I can't encourage that
    enough.</p>
    <p><br>
    <b>Scales for all Keys</b></p>
    <p>Okay, so now we've seen the <b>major and minor scales, pentatonic scales, and
    building triads.</b></p>
    <p>We've seen the "formula" for creating scales is a system of using
    whole tones and semi-tones (whole steps and half steps). I also mentioned that
    there are twelve different tones (or notes) in music, so we have scales for
    twelve different keys. Let's look at the notes of the major scales for all twelve
    keys. Remember, we start with the tonal center, or root, and use the formula
    of t-t-s-t-t-t-s, which is also 1-2-3-4-5-6-7 as discussed in another post.</p>
    <p>So, here we go:</p>
    <p><b>C:</b> C - D - E - F - G - A - B - c<br>
    <b>F:</b> F - G - A - Bb - C - D - E - f<br>
    <b>Bb:</b> Bb - C - D - Eb - F - G - A - bb<br>
    <b>Eb</b>: Eb - F - G - Ab - Bb - C - D - eb<br>
    <b>Ab:</b> Ab - Bb - C - Db - Eb - F - G - ab<br>
    <b>Db:</b> Db - Eb - F - Gb - Ab - Bb - C - db<br>
    <b>Gb:</b> Gb - Ab - Bb - Cb - Db - Eb - F - gb<br>
    <b>B</b>: B - C# - D# - E - F# - G# - A# - b<br>
    <b>E:</b> E - F# - G# - A - B - C# - D# - e<br>
    <b>A</b>: A - B - C# - D - E - F# - G# - a<br>
    <b>D</b>: D - E - F# - G - A - B - C# - d<br>
    <b>G</b>: G - A - B - C - D - E - F# - g</p>
    <p>Now that we see all of the major keys, we know that the <b>relative natural
    minor</b> for all of these keys is the sixth position (<b>Aeolian</b>) of the
    major scale. So for Cmaj, the minor key is:</p>
    <p align="center">(A minor)<br>
    A - B - C - D - E - F - G - a</p>
    <p>For Gmaj, we have:</p>
    <p align="center">(E minor)<br>
    E - F# - G - A - B - C - D - e</p>
    <p>Go through all twelve keys, like I did for the major keys, and get the natural
    minor key. So build the natural minor, <b>t-s-t-t-s-t-t</b>, or (1-2-b3-4-5-b6-b7).
    Do this for all keys.</p>
    <p>I like the manner of deriving the scale from the intervallic relationship.
    Instead of thinking tones and semitones, remember that your whole scale is your
    1-2-3-4-5-6-7, and to get a minor scale, lower the 3, 6, and 7. Take <u>A Major</u>.
    Here's the major scale:</p>
    <p align="center">A - B - C# - D - E - F# - G# - a</p>
    <p>Lower the 3, 6, and 7 for the minor key:</p>
    <p align="center">A - B - <b>C</b> - D - E - <b>F</b> - <b>G</b> - a</p>
    <p><br>
    <b>7th Chords</b></p>
    <p>Building chords is a system of 3rds. I've discussed some of these intervals
    before in talking about <b>Major, Minor, and Diminished Triads</b>, all which
    appear naturally in the major and minor scales. </p>
    <p>To refresh, a 3rd is an interval, a distance from one note to another. </p>
    <p><b>· A Major 3rd is a distance of 2 whole steps, (or two whole tones)<br>
    <br>
    · A Minor 3rd is a distance of 1.5 steps, (or one whole tone and one
    semitone) </b></p>
    <p>Again, here's the chromatic scale:</p>
    <p align="center">C -- C# -- D -- D# -- E -- F -- F# -- G -- G# -- A -- A# --
    B</p>
    <p>From D, a major 3rd is F#<br>
    From E, a major 3rd is G#<br>
    From G, a major 3rd is B</p>
    <p>From E, a minor 3rd is G<br>
    From C, a minor 3rd is Eb<br>
    From F, a minor 3rd is Ab</p>
    <p>Again, when away from your instrument, a great exercise is to go over these
    in your head. What's a major 3rd from G? What's a minor 3rd from B? Do this
    over and over. Get it in your head.</p>
    <blockquote>
    <blockquote>
    <p><i>Note: Notice how from C a minor 3rd is Eb, not D#. Although Eb and D#
    are enharmonics, (the same note), the note is written as Eb, not D#. In
    intervals, the notes are chosen by their distance from one another. From
    C, a 3rd will always be E. If it's a major 3rd, we know it's E natural.
    If it's a minor 3rd it's Eb. If it's an augmented (raised) 3rd, then it's
    E#. If we want to go to another interval, a 2nd, then from C, we go to D.
    If it's a major 2nd, then it's D natural. If it's a minor 2nd, then it's
    Db. If it's an augmented 2nd, then the note is D#. Notice that an augmented
    2nd, is the same as a minor 3rd, but they're written differently. Take some
    time reviewing this concept. </i></p>
    </blockquote>
    </blockquote>
    <p></p>
    <p></p>
    <p></p>
    <p></p>
    <p></p>
    <p></p>
    <p>Now, recall the three triads found in a major scale:</p>
    <p><b>Major:</b> Root + Major 3rd + minor 3rd<br>
    <b>Minor</b>: Root + minor 3rd + Major 3rd<br>
    <b>Diminished</b>: Root + minor 3rd + minor 3rd</p>
    <p>Incidentally, here's another triad. It does not appear naturally in the major
    scale:</p>
    <p><b>Augmented</b>: Root + Major 3rd + Major 3rd</p>
    <p>Let's build <b>TRIADS</b> from the scale. Once again, constructing chords from
    a major scale, let's say Cmaj, we use intervals of 3rds. I've placed the scale
    position, in Roman numerals, underneath each scale tone. We take every other
    note to build our triads.</p>
    <p align="center"><b>C - D - E - F - G - A - B</b></p>
    <p>C= C,E,G<br>
    D= D,F,A<br>
    E= E,G,B<br>
    F= F,A,C<br>
    G= G,B,D<br>
    A= A,C,E<br>
    B= B,D,F</p>
    <p>The first chord is <b>C-E-G</b>. This chord has C, the root, followed by E,
    a major 3rd, to G, a minor 3rd from E, which means it's a major chord.</p>
    <p>So we have:</p>
    <p><b>C: (I) : C-E-G : C Major<br>
    D: (ii) : D-F-A : D minor<br>
    E: (iii) : E-G-B : E minor<br>
    F: (IV) : F-A-C : F Major<br>
    G: (V) : G-B-D : G Major<br>
    A: (vi) : A-C-E : A minor<br>
    B: (vii) : B-D-F : B diminished</b></p>
    <p>These chords are <b>TRIADS</b>, because they're chords built from 3rds, containing
    a total of 3 notes. </p>
    <p><b>7th chords are the logical extensions</b>. 7th chords, still using 3rds,
    add a forth note, the 7th!</p>
    <p>Here are your common 7th chords:</p>
    <p><b>Major 7th</b>: Root + Major 3rd + Minor 3rd + Major 3rd<br>
    <b>Minor 7th</b>: Root + minor 3rd + Major 3rd + minor 3rd<br>
    <b>Dominant 7th</b>: Root + Major 3rd + minor 3rd + minor 3rd<br>
    <b>Minor 7th (flat 5)</b>: Root + minor 3rd + minor 3rd + Major 3rd</p>
    <p>Let's build one of each 7th chords for C.</p>
    <p><u>C Major 7th:</u> C to a Major 3rd is E. E to a minor 3rd is G. G to a major
    3rd is B. <b>C-E-G-B</b>.</p>
    <p><u>C Minor 7th:</u> C to a minor 3rd is Eb. Eb to a Major 3rd is G. G to a
    minor 3rd is Bb. <b>C-Eb-G-Bb</b>.</p>
    <p><u>C Dominant 7th</u>: C to a major 3rd is E. E to a minor 3rd is G. G to a
    minor 3rd is Bb. <b>C-E-G-Bb</b> </p>
    <p><u>C Minor 7 (flat 5):</u> C to a minor 3rd is Eb. Eb to a minor 3rd is Gb.
    Gb to a Major 3rd is Bb. <b>C-Eb-Gb-Bb</b> </p>
    <p>Let's build <b>7th chords</b> from the scale. Yet again, constructing chords
    from a major scale, let's say Cmaj, we use intervals of 3rds. I've placed the
    scale position, in Roman numerals, underneath each scale tone. We take every
    other note to build our triads.</p>
    <p align="center"><b>C - D - E - F - G - A - B</b></p>
    <p>C= C,E,G,B<br>
    D= D,F,A,C<br>
    E= E,G,B,D<br>
    F= F,A,C,E<br>
    G= G,B,D,F<br>
    A= A,C,E,G<br>
    B= B,D,F,A</p>
    <p>Look at the first chord we've constructed from this scale, which is C-E-G-B.
    Look at the intervals. E is a Major 3rd from C. G is a minor 3rd from E. B is
    a Major 3rd from G. So what 7th chord is Root + Major 3rd + minor 3rd + Major
    3rd? A Major 7th. Do the same for all of the chords, and we have:</p>
    <p><b>C: (I) : C-E-G-B : C Major7<br>
    D: (ii) : D-F-A-C : D minor7<br>
    E: (iii) : E-G-B-D : E minor7<br>
    F: (IV) : F-A-C-E : F Major7<br>
    G: (V) : G-B-D-F : G Dominant7<br>
    A: (vi) : A-C-E-G : A minor7<br>
    B: (vii) : B-D-F-A : B minor7 (b5)</b></p>
    <p>Ahhhh, dear 7th chords. Now, the trick is to play all the major 7th, minor
    7th, dominant 7th, and minor7b5 chords for all 12 tones. Listen to the chords
    and play them at a piano if you can, so you really hear the chord voiced. </p>
    <p><b>Vocabulary</b></p>
    <p>Here are some definitions of some "need-to-know" terms. Some of these
    are straight from <i><b>THE HARVARD CONCISE DICTIONARY OF MUSIC</b></i>, a must
    have for anyone serious in learning theory. I've paraphrased, added, or rewritten
    where I thought it made it easier to understand.</p>
    <p><b>PITCH</b>: The perceived highness or lowness of a sound. It is a function
    primarily of frequency, though at some etremes of frequency, intensity may also
    affect the perception of pitch.</p>
    <p>There are twelve pitches (or pitch classes) in Western tonal music, each of
    which is represented in each octave of the entire range of pitches.</p>
    <p>In slang: "D**n girl, dem be some crazy pitches! Get them pitches out
    my face!, knowuti'msayin?</p>
    <p><b>NOTE</b>: The signs with which music is written on a staff. Colloquially,
    see PITCH.</p>
    <p><b>SCALE:</b> The underlying tonal material of some particular music, arranged
    in an order or rising pitches. The basic scale is the diatonic scale, usually
    referred to as the major scale, as distinguished from the pure minor scale.
    Both major and minor scales may be transposed to start on any one of the twelve
    pitches (pitch classes). Thus there are twelve major scales and twelve minor
    scales, on in each key.</p>
    <p><b>KEY</b>: In a song (composition), the main pitch or "tonal center"
    to which all of the composition's pitches are related; by extension, the entire
    tonal material itself in relation to its center. Key is practically synonymous
    with tonality, since one may describe a composition as being the key of, e.g.,
    C.</p>
    <p><b>TONALITY:</b> A system of organizing pitch in which a single pitch (or tone,
    call the tonic), is made central. "Key" is the more popular term.
    Tonality being rarely used.</p>
    <p><b>CHROMATIC:</b> An adjective applied to the scale that includes all of the
    12 pitches (and thus all of the 12 semitones) contained in an octave, (as opposed
    to the diatonic scale).</p>
    <p><b>MAJOR SCALE</b>: Consists of 5 whole tones (t) and 2 semitones (s) in the
    following arrangement: t-t-s-t-t-t-s, where the first tone is the key or tonal
    center.</p>
    <p><b>MINOR SCALE:</b> Consists of 5 whole tones (t) and 2 semitones (s) in the
    following arrangement: t-s-t-t-s-t-t, also where the first tone is the key or
    tonal center.</p>
    <p><b>CHORD:</b> Three or more tones sounded simultaneously, two simultaneous
    tones usually being designated as an interval. The most basic chords are the
    major and minor triads and their inversions. Other chords that play an important
    role are the seventh chord, ninth chord, the augmented sixth chord, and the
    diminished triad.</p>
    <p><b>ARPEGGIO:</b> The notes of a chord played one after another instead of simultaneously.
    (Important for bassists, as bassists played arpeggios more often than not).</p>
    <p><b>INTERVAL:</b> The distance (in terms of pitch) between two pitches. Intervals
    are named according to (1) the number of diatonic scale degrees comprised, as
    represented in the letter names of the two pitches, and (2) the number of semitones
    between the two pitches. </p>
    <p>I'm not going to get into this definition that well. Harvard's dictionary has
    a table which demonstrates it exceptionally well, but took me several reads
    to fully understand. As stated in a previous post, the only important intervals,
    for now, are the major 3rd (2 whole tones) and minor 3rd (1.5 whole tones).</p>
    <p><b>TRIAD:</b> A chord of three pitches consisting of a pitch called the root
    and the pitches a third and fifth above it. There are four kinds of triad, depending
    on the exact sizes of the intervals combined: major, minor, diminished, augmented.</p>
    <p><b>DIMINISHED TRIAD</b>: A chord consisting of the root, a minor 3rd, and then
    another minor 3rd. Example: C - Eb - Gb. C being the root, Eb a minor 3rd (1.5
    whole tones) from the root, and Gb being a minor 3rd from Eb. This chord is
    said to be dissonant. It appears naturally in a major scale in the 7th position.</p>
    <p><b>AUGMENTED:</b> A chord consisting of the root, a major 3rd, and then another
    major 3rd. Example: D - F# - A#. D being the root, F# a major 3rd (2 whole tones)
    from D, and A# a major 3rd from F#. This chord is also said to be dissonant,
    and does not appear naturally in the diatonic scale.</p>
    <p><b>CONSONANCE / DISSONANCE:</b> Popularly, a combination of pitches that are
    pleasing or displeasing. More accurately, consonances are those combinations
    of pitches that have been used in Western tonal music as suitable points of
    at least momentary repose and not necessarily requiring resolution. Dissonances
    are those combinations that, in Western tonal music, do not serve as points
    or repose but require, instead, resolution to some consonance.</p>
    <p>This is an extremely subjective issue. The best way to understand this is to
    hear consance versus dissonance. Major and minor triads are said to be consanant
    while augmented and diminished triads are said to be dissonant. Play both on
    a piano. First play a diminished chord, then a major just after. Now try it
    the other way around. Listen very carefully to the sound of both, and listen
    how, in the first example, the diminished chord resolves to the major (if you're
    in the same key with both chords). Dissonant should never be confused with "bad."
    Many composers have used dissonance to make very "pleasing" music.
    The best example I think, is Stravinsky's "Rite of Spring." I am not
    going to touch on this subject much more for now. </p>
    <p><b>ENHARMONIC:</b> Tones that are actually one and the same degree of the chromatic
    scale, but are named and written differently, e.g., G# and Ab, which are thus
    said to be "enharmonically equivalent." Other examples include, F#
    and Gb, A# and Bb, B# and C, E# and F.</p>
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