Why all the interval sequences in your book, Ari?

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Hi Ari,
On page 36 of your book “Music Theory for the Bass Player”, there are two interesting statements about minor and major thirds.

When repeating minor thirds, you reach the starting note after four minor thirds, creating three unique interval sequences:

[diatonic naming, meaning Bbb is called A for practical purposes]

  1. C – Eb – Gb – A – C 
  2. C# – E – G – Bb – C#
  3. D – F – Ab – B – D

When repeating major thirds, you reach the starting note after three major thirds, creating four unique sequences: 

  1. C – E – G# – C
  2. Db – F – A – Db
  3. D – F# – Bb – D
  4. Eb – G – B – Eb

What is interesting or important about these ”unique sequences”? Why are they worth calling out and listing in your book? What use can be made of them?

Thanks,
Robert

Thanks for the question, Robert. The easiest way to find the answer is to just play these interval sequences on the bass using consistent fingerings. What emerges is helpful on so many levels – here are just six that I can think of just off the top of my head:

1 • Because it is crucial to understand how notes relate to each other.

Before we go into your thirds intervals, Robert, let’s take a step back because in the book I actually do this “repeat-the-interval” business with every single interval. Most commonly this is done with the fifth.

There are 12 unique pitches. Most commonly we organize them in descending fifths or ascending fourths, meaning the Cycle of Fifths in both directions.

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

Here you have repeated the interval of an ascending fourth or descending fifth (you know I prefer it when you call it “descending fifths” rather than “ascending fourths”!) and you have touched on every single pitch there is, which is pretty magical and unique. It is also helpful because if you play a major scale off of each of these notes you only change one note at a time. And it occurs in songs a ton. And it is smooth sounding, like a resolution. And it tells you the exact note-naming.

And more magic about fifths here:

Fifths are also great for practicing something in all keys, see below!

There is only one other interval that does that, and that is the half step or minor second.

But back to thirds.

  • 4 times 3 half steps (minor third!) or
  • 3 times 4 half steps (major third!)

is twelve.

  • When you jump in minor thirds – three notes change (from C major to Eb major for example, you add three flats.)
  • When you jump in major thirds – four notes change (from C major to E major you add four sharps.)

2 • The Fretboard 

Build the intervals on the fretboard and see how notes relate across strings.

The fretboard helps you see this if you finger it consistently (instructions are in the book).

Learn and practice this sequence with good fingering, ascending and descending, all over the fretboard as described and that interval is yours forever and everywhere.

3 • Chords

These stacked intervals actually make up chords!

  • C+ – all major thirds 
  • Co7 – all minor thirds

What to do with this:

  • Arpeggiate these chords over at least two octaves
  • In all keys
  • Have good fingering ready as described
  • Play it in a walking bass when you come across one of these chords!
  • Use for soloing. You can even play
    • a + chord over a Dominant 7 flat 13
    • or a o7 over a diminished dominant (which makes it a b9, #9 #11 natural 13)
  • Make a groove from it

4 – Chord progressions

Songs move in thirds constantly. Know how to move in thirds, major and minor. If it is under your fingers and if you recognize it in the chord changes, no mystery!


5 – Reading 

Stop spot placing notes. Know how to read intervals and the fretboard is yours without constantly having to look at it (since thrids are now under your fingers).

6 – Systematic Practice

Practice everything you do in sequences of all intervals. Hopefully, you are already practicing all shapes in fifths. Now practice them through the cycles of thirds!

 

To sum it up, there is symmetry everywhere in music!

Understanding this has practical application for playing music, cracking theory and for mastering the fretboard. If you feel these shapes under your fingers they mean something. They are no longer just abstract concepts. They are sounds that “feel” a certain way on the instrument. Experiencing that fosters learning.

Comments(3)

  • Carol crumlish
    September 19, 2019, 14:47  Reply

    This is brilliant, Ari. Thanks for taking the time to map out these ideas so clearly.

  • Joe
    September 27, 2019, 16:36  Reply

    Hi Ari,

    Is there a particular video that demonstrates this “Songs move in thirds constantly” theory within your Music Theory for the Bass Player book?

    • September 27, 2019, 22:31

      Joe, it is not a theory. Play a I – Vi – II – V chord progression and there is your thirds movement (from the I to the VI). (Oodles of Jazz standards, or songs like “Oh won’t you stay…”.
      Play All of me – I chord to the III chord.
      The song “Giant Steps” is famously all about major third movements.
      Rock? How about Smoke on the Water, first two chords. It is everywhere!

      Take any song you are playing and look for a major or minor third movement either up or down between any two chords. It is everywhere.
      And to be fit in all situations a great way is to practice this stuff systematically, just isolating that interval, up and down, major and minor, in all directions.

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