Music theory for banjoheads, pt. 3, building triads

Kind of off the subject - You might notice that in various examples I'm pretty much leaving out the fifth string (and will probably continue to do so). There are a few reasons for this: one is that people have different ways of using it; another is that it adds another skrillion to the bazillion ways of playing anything on the banjo; and probably most importantly, there is only one music writing software program I know of that takes into account the proper TAB numbering, 0,6,7,8,9, etc. for the 5th string but I don't really like to use it, as it's sort of clunky and doesn't look any good. You can look on chat threads for Finale, and see complaints about this back to 2002!! The only thing they did on the banjo part of the latest version is get the written range wrong. Whenever I mention it to support they say "I'll pass this on the the developers..." and I'm like oh haha, April fool to you too. OK, back to theory.

First, the answers to the "homework."

m2 from C# = D

M2 from B = C#

m3 from G = Bb

m3 from A = C

m3 from Eb = Gb

M3 from E = G#

P4 from F = Bb

A4 from C = F#

d5 from C = Gb

P5 from C = G

P5 from D = A

P5 from E = B

P5 from F = C

P5 from G = D

P5 from A = E

P5 from Bb = F

P5 from B = F#

A5 from Db = A

M6 from F# = D#

m7 from Ab = Gb

M7 from B = A#

There's a reason I gave you a few extra ones for P5's. A lot of stuff happens in the so-called "circle of fifths" (though every time I try to write one for my students it comes out as kind of "the pear of fifths"). If you start on any note and go in perfect fifths, you hit all twelve notes of the chromatic scale before you repeat one. so:

F C G D A E B F# C# G# D# A# E# B# - go back to F#, turn it into Gb:

Gb Db Ab Eb Bb F...

So one way of working on something in all the keys is to do it in "the cycle." And you'll see that a lot of chord progressions follow the cycle of fourths, which is just a matter of running the cycle/circle of fifths from right to left.

You might have noticed this: Except for knowing Bb - F and B - F#, knowing the cycle is just a matter of counting on your fingers and matching the accidentals, or lack thereof. Look:

F C G D A E B

(Fb Cb) Gb Db Ab Eb Bb - the ones in parentheses you just aren't going to see that often.

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

Time for some CHORD CONSTRUCTION. I'm going to do the same thing as with the last post, having also previously written about this, but there'll be a lot of banjo chords. It won't be an exhaustive compendium, but should give you a way to figure out and practice your own chord voicings.

Here are two major triads on the banjo. These are in "root position," meaning the root is in the bass of the chord.The voicing is root-third-fifth. Play these (you may already know them) and before looking ahead, try figuring out the minor, augmented and diminished versions of these voicings. Hint: starting with the major triad, lower the third, you have minor. Raising the fifth of the major triad will give you the augmented. Lowering the fifth of the minor triad will give you the diminished. Do them all even if you're thinking "when am I gonna use an augmented triad?" These things will all come up in ways we can't anticipate!

Of course you probably recognize these as being the bottom part of an F-position chord, and the top part of a bar-position one, so:

Of course the big thing in these posts is to get you spelling all these things properly, so now do some triad arithmetic by spelling the following triads:

Major: Bb,  F  D   Ab

now turn them to augmented: Bb+  F+  D+  Ab+

minor:  C#m   Gm    Bm     Em

now turn minor to diminished:  C#dim   Gdim    Bdim    Edim

(the answers to everything will be at the end of this post)

You probably know the closed D and Dm chords - "D-position" - now work out the augmented and diminished versions of the D-position chord (I'll show you at the end). 

Um, these are four note chords...are they still triads? I'm not sure actually... What they definitely are though, is triadic harmony, since there are only (get ready for it) 3 "pitch classes" in play. In other words, whether you play it on a banjo or a London Symphony, an F-chord contains just F's, A's and C's regardless of octave or doubling, or the pitch classes F, A, and C.

The chords built on each scale degree are called "the one chord, the two chord," etc. and are indicated using Roman numerals. So in the key of C:

I - CEG

II- DFA

III - EGB

IV - FAC

V - GBD

VI - ACE

VII - BDF

This pattern is true for every major scale, always! You already knew that I, IV, and V are major right? In G, your I-IV-V is G-C-D. In C, C-F-G.

(answers at the end!)

Let's apply this to the banjo neck. We'll take a D-chord (D-position, see measure 1) break it into two triads (measure 2), then run each one up the neck in the key of D, changing major to minor or diminished as needed.

Running triads up the neck diatonically (ie., in a scale) is a always a useful study.Notice that you now have three ways of voicing a chord: root position - root in the bass; 1st inversion - third in the bass; 2nd inversion - 5th in the bass. This can, but doesn't have to parallel what the bass player is doing.

OK, the answers.

Major: Bb: Bb-D-F  F: F-A-C  D: D-F#-A   Ab: Ab-C-Eb

augmented: Bb+: Bb-D-F#    F+: F-A- C#   D+: D-F#-A#   Ab+: Ab-C-E

minor:  C#m: C#-E-G#   Gm : G-Bb-D   Bm: B-D-F#    Em: E-G-B

diminished:  C#dim: C#-E-G    Gdim: G-Bb-Db    Bdim: B-D-F    Edim: E-G-Bb

Triads in scales:

D Em F#m G A Bm C#dim

G Am Bm C D Em F#dim

A Bm C#m D E F#m G#dim

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

Gb Abm Bbm Cb (yes! not B!) Db Ebm Fdim

Ab Bbm Cm Db Eb Fm Gdim

You get this? You start by constructing the major scale, as in the first part of this series, then I IV and V are major, II III and Vi are minor, VII is diminished. Every time.

Triads are extremely important and useful even if the harmony isn't triadic, so we'll do some more with them later. But for now, it's on to SEVENTH CHORDS. See ya.