A pentatonic scale has five notes, which in the C Major pentatonic scale are as follows:
C – D – E – G- A
Take a look at the notes and intervals, and think about what’s missing. The C Major pentatonic scale is the C Major Scale with the fourth (F) and seventh (B) scale tones removed. By removing these tones, we also remove the intervals of a minor 2nd (semitone) and diminished 5th (tritone). The dissonance of these intervals is what creates much of the tension in traditional Western music.
By removing the most dissonant intervals, pentatonic scales can evoke a more relaxed, even dreamy feeling. They are commonly used in Asian music, and are often referred to as having “no wrong notes.” This also makes them popular for improvising in rock, blues, or jazz. Pentatonic scales were used in ancient Greece, in folk music from all over the world, and are a near universal part of our musical language, as Bobby McFerrin demonstrated at the World Science Festival last year.
By combining what we learned in how to Build Piano Chords with our knowledge of Basic Intervals, we are ready to move beyond the triad. First stop: seventh chords.
Take a basic triad and add a note that is a seventh above the root to form a seventh chord. There are several different types of seventh chords, distinguished by both the type of triad and the type of seventh used. Here’s how to form the most common seventh chords in root position.
Major Seventh chord = major triad + major seventh
Seventh(or “dominant seventh”) chord = major triad + minor seventh
Minor Seventh chord = minor triad + minor seventh
Half-diminished Seventh chord = diminished triad + minor seventh
Diminished Seventh chord = diminished triad + diminished seventh (half step lower than a minor seventh)
An easy way to remember where each seventh is:
The major seventh is one half step below the octave.
The minor seventh is one half step below the major seventh.
The diminished seventh is one half step below the minor seventh.
You can step through each of the above seventh chords by starting with the major seventh and dropping one note a half step for each type: [click to continue…]
For those of you in a hurry, we’ll give away the ending first: take any interval (x), subtract it from 9, and you are left with the inversion of that interval. Now let’s review:
All of this prepares us for the information you have been waiting for!
How to Invert an Interval
Find middle C on the piano
Play a perfect fifth above middle C (i.e., G)
Move the G down an octave
You have inverted a perfect fifth, which results in a perfect fourth
By moving the top note of an interval down an ocatave, you invert that interval. It also works in reverse: if you start over with C and G, and move the bottom note up an octave, you again end up with a perfect fourth. Try it!
Now take 9, subtract the original interval, and you end up with the inversion: 9 – 5 = 4. Our original formula gives us the following results: [click to continue…]
Since our Scales and the Circle of Fifths article has been floating into the top five posts on MMT, we decided it’s time to delve a little deeper.
The Mersenne Star (Click to Enlarge)
On our first visit, we skipped along the outer edge of the circle, which displays the Major keys arranged in intervals of a fifth. Going clockwise around the circle, each successive key has one more sharp (or one less flat).
With just a straight edge and compass, Marin Mersenne (yes, thatMarin Mersenne) produced the drawing shown at right. The Mersenne Star, from his HARMONICORUM LIBRI XII published in 1648, shows the harmonies and disharmonies between intervals arranged as a circle of fifths.
That’s all well and good for 1648, but today we want more. And the Circle of Fifths as drawn below delivers.
Here, in addition to a visual display of the sharps and flats, the inner circle shows the relative minor for each major key. How are they related? They share the same key signature. G Major has one sharp (F#), as does E minor. So they have the same notes in their scales, they just start in different places.
And just like the major scales, all minor scales are made of the same sequence of whole steps (W) and half steps (H). A half-step, sometimes referred to as a semitone, is the interval between any two adjacent keys on the piano. A whole step equals two half-steps. The sequence for a natural minor scale is: W-H, W-W-H, W-W.
The relative minor is always three half-steps down from (or a minor third below) the major key. So the relative minor of C Major is A minor. Just like C Major, there are no sharps or flats, so it is played on all white keys. Starting from A, it is a whole step to B, then a half-step to C. Then there are two whole steps followed by another half-step: a whole step to D, another to E, then a half step to F. Then there are two whole steps to complete the scale: F to G, and G to A.
Got it? Whole-Half, Whole-Whole-Half, Whole-Whole Now play that sequence starting anywhere on the piano, and you know all your minor scales.
Fingering: the proper fingering for the A minor scale (and many others) is to start with the thumb of your right hand on A. Your index finger plays B, middle finger plays C, then cross your thumb under to strike the D key and continue up the scale. You will end with your little finger on A. Reverse the procedure to come back down the scale.
There are 8 notes in the scale, so on the way up, remember 3 + 5 = 8. On the way down: 5 + 3 = 8. The left hand uses the same sequence, just upside-down. Try it, you’ll see. Start with your little finger on the A, and it’s 5 +3 on the way up, and 3 + 5 on the way down.
From our last post on Building Piano Chords, you should be able to form root position chords in any key. Root position simply means that the chord is played with the root as the lowest note. (The root is the reference note for a chord: the tone the chord is built on and named after. The tonic is the reference note for a scale.)
For a C Major chord, the root position has C as the lowest (or bass) note. This is the normal form of a chord — for example, C, E. G.
When a note other than the root is in the lowest position, the chord is said to be inverted. The first inversion of a C chord has E as the bottom note, for example, E, G, C. The second inversion has G in the bass, e.g., G, C, E. These are labeled as examples because the notes above the bass note can be in any order, it is the lowest note that defines the chord form.
Mario Ajero does a nice job of showing inversions, and teaches you the intro to “Let It Be” along the way.
Here’s Nate again, this time with a lesson on building chords in the key of G Major. From the last lesson on scales and the circle of fifths, you’ll remember that the key of G Major has one sharp: F#. So the scale runs as follows: G-A-B-C-D-E-F#-G.
The most basic chord is a triad, which consists of three notes stacked in thirds. To build a Major chord, start with a major 3rd, then stack a minor third on top. The G Major chord is a triad consisting of notes G, B, and D. G to B is a major 3rd, and B to D is a minor 3rd. In the lesson you’ll see that you can build chords by playing every other note in a scale.
Moving up a whole step and playing A, C, and E simultaneously produces an A minor chord. As you approach the top of the scale, extend it another octave to fill out the chords. For example, to form a D Major chord, you would press D (skip E), F# (skip G), and A.
Now for the good stuff. Take what you learned and move it down to C. Starting with notes 1, 3, and 5 (C-E-G), move the shape up the keyboard until you reach the C Major chord one octave higher. By playing every other note on just the white keys, you will play the following chord progression: C Major, D minor, E minor, F Major, G Major, A minor, and B diminished.
This progression of Major, minor, and diminished chords is the same for every major scale. The chords are often referred to by their position in the scale, and indicated by the corresponding Roman numeral.
Chord Symbols, Chords, Scale Degrees, Notes and Intervals in the Key of C Major
Roman numeral
I
ii
iii
IV
V
vi
vii°
Chords
C
D minor
E minor
F
G
A minor
B dim
Scale degrees
tonic
supertonic
mediant
subdominant
dominant
submediant
leading tone
Scale Notes
C
D
E
F
G
A
B
Interval from C
Perfect
unison
Major
2nd
Major
3rd
Perfect
4th
Perfect
5th
Major
6th
Major
7th
Harmony in Western music relies mainly on the primary triads: those built on the tonic (I), subdominant (VI), and dominant (V) scale degrees noted above. The chords themselves are often referred to by the Roman numerals I, IV, and V, which in the key of C would be C Major, F Major, and G Major.
While it’s not important to immediately memorize all of the names and nuances of notation, it is critical to understand the relationships between keys, chords, and scale degrees. Just knowing I, IV, V will take you a long way, since most popluar music is based on these three chords, sometimes with one or two others mixed in. Once you are comfortable building chords in common keys, it’s time to move on to chord progressions.
While keyboard players typically begin their scale studies with C Major, guitarists should consider starting out with the A minor pentatonic scale. Justin Sandercoe offers an excellent introduction to a scale that is used the world over in all different kinds of music. In America, this scale is most closely identified with the blues. It [...]
Now comes the exciting part! I knew it was hard to make scales exciting, but trying to find a good tutorial on YouTube tells me it may be impossible. There are some high quality demonstrations of individual scales on pianolessons.com, but the introduction is missing some key information. Go ahead and watch it, then come [...]
This is an excellent series of podcasts on Guitar Music Theory available for free on iTunes. Taught by Desi Sarna, the author of Fretboard Theory, they are best for intermediate and advanced players. Lessons include pentatonic and major scale patterns, chord inversions and arpeggio patterns with the CAGED system.
Type “music intervals” into Google and you get over 5 million results, most of them useless. They are either too long or too complicated or of poor quality or just plain wrong. The best introduction to intervals I found was at pianolessons.com. The YouTube video is below, or you can see the video along with [...]
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