20 Hz ~ 20 kHz

Now it gets interesting – if a C major scale is a lightly salted soda cracker, consider the whole-tone scale a wheat thin, and the octatonic scale is some tasty ciabatta with olive oil. This next mode of limited transposition might very well be “The Burger.” Messiaen himself invented the remaining five modes of limited transposition and, in my humble opinion, this particular one is quite possibly one of the most beautiful things birthed by human beings in the past century – human beings themselves notwithstanding. (Perhaps Messiaen’s mother, or Cleopatra’s nose, really deserve credit, but this is a very different topic). This mode has a total of four transpositions before it is enharmonically repeated, and employs the following pattern of whole-steps and half-steps (w and h, respectively):

w  h  h  w  h  h  w  h  h

This mode translates very nicely to guitar. Behold the fretboard diagrams, this time with each mode written out in standard notation as well:

Consider the first transposition: C  D  E♭  E♮  G♭  G♮  A♭  B♭  B♮  C

And the following tonal triads which are native to it: dominant seventh chords are denoted with the seventh in parenthesis.

  C               E              G♯
  C               E              G♮             (B♭)
  C               E♭             G
  C               E♭             G♭
          D                F♯             A♯
                  E♭             G               B♮
                  E♭             G               B♭       (D♭)
                  E♭             G♭             B♭
                  E♮             G♯              B♯
                  E               G♯              B♮         (D)
                  E               G♮             B
                  E               G               B♭
                                  G♭             B♭          D
                                  G♮             B♭          D                                                B♭          D
                                  G               B♮          D
                                          A♭            C           E♮
                                          A♭            C           E♭       (G♭)
                                          A♭            C♭         E♭
                                          A♭            C♭         E 𝄫
B♭           D               F♯
B♮           D               F♯
B            D♯               F♯          (A)

Similar to the octatonic scale, these chords can be used to modulate into and out of the mode. They also give it a certain tonal ubiquitousness -no particular key is emphasized, but many of these triads are not distant from each other and can hint towards particular tonal regions if the composer so chooses. There are even a few traditional tonic-dominant relationship (C – G or A♭-E♭or E♮-B♮).

The mode itself is divided into three symmetrical groups of four notes:

C                   D                  E♭                 E♮
E♮     whole       G♭      half       G♮      half       A♭
A♭     step        B♭      step       B♮      step       C

It is symmetrical along an augmented fifth – this basically means that C is equivalent to G♯ (A♭), which is itself equivalent to E♮. It will sound the same if you start the mode on C, G♯ or E♮, since each of these notes is followed by a whole-step and two half-steps. This symmetry is what gives these modes their unique character – the chromatic and whole-tone scales are such because all intervals in them are homogeneous, the symmetry is an almost immaterial byproduct of the nature of these scales. The octatonic scale is slightly more complex, as it alternates whole and half steps, but is still only has two variations: it either begins with a half step or a whole step. The third mode is symmetrical in a less obvious way: it folds over itself in thirds, and each third is equivalent.

The guitar is particularly well suited for observing these unique characteristics – perhaps moreso than the piano because of the fretboard’s logical chromatic layout.  Arbitrary placement of white and black keys don’t detract from the relatively simple underlying patterns. For example, look again at the first transposition – the pattern on the first fret repeats itself exactly on frets 5, 9, 13, 17, 21…. etc. You really only need to memorize the fingering patterns for four frets to play the mode up and down the entire neck! It’s almost deceptively simple when applied to guitar.

No worries if you haven’t been able to follow all of the theory so far – just take the first transposition and play around with it, and all of these relationships will fall into place. It’s so much easier and more effective to just soak it up in a purely musical sense than to try to explain things with feeble words and theory. I can’t stress it enough – this mode is awesome. Invest an hour to learn at least one transposition and mess around with it.