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deriving tetratonic scales from the “new notes” on Oleleko

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Let’s have a look at the chord grid for the solo section on Oleleko (the electric piano improvisation happens from 2’02 to 3’35 on the recording):


The following table lists all chord symbols, the parent scales they derive from, and their “new notes,” which is a concept introduced by contemporary jazz pianist and composer Laszlo Gardony (for each chord, we list the notes in the parent scale that were not present in the scale corresponding to the previous chord – this helps to give a sense of forward motion to the music and emphasize the shifts in harmony as we go through the grid):

Bar Chord
Symbol		 Mode
(Parent Scale)		 New
Note(s)?
121 C7 C mixolydian
(F major)		 C D E A
136 D7(#11) D lydian dominant
(A melodic minor)		 F# G# B
137 Eb6 Eb ionian
(Eb major)		 Eb F G Bb
139 Eb7sus Eb mixolydian
(Ab major)		 Db
141 Eb6 Eb ionian
(Eb major)		 D
143 Eb7sus Eb mixolydian
(Ab major)		 Db
144 E7(#11) E lydian dominant
(B melodic minor)		 E F# B D
145 F#6 F# ionian
(F# major)		 D# E#
147 F#7sus F# mixolydian
(B major)		 E
149 F#6 F# ionian
(F# major)		 E#
150 Db7(#11) Db lydian dominant
(Ab melodic minor)		 G

Now let’s find possible tetratonic scales based on those “new notes” (using four-note scales will enable us to limit our melodic choices and create wider, more angular intervals, while including as many of the “new notes” as possible in order to retain the characteristic harmonic shifts in the music):

Bar Chord
Symbol		 Tetratonic
Scale(s)
121 C7 A minor (= A C D E)
136 D7(#11) E major (= E F# G# B)
137 Eb6 Eb major
139 Eb7sus Db major, Bb minor
141 Eb6 Bb major, G minor
143 Eb7sus Db major, Bb minor
144 E7(#11) B minor
145 F#6 C# major, A# minor
147 F#7sus E major, C# minor
149 F#6 C# major, A# minor
150 Db7(#11) Eb major

When there are two tetratonic choices, I simply go with the one I like best (in bold in the table above). By all means, feel free to experiment with both options and chose whichever sounds most satisfying to your ear!

Finally, and for the purpose of practicing, we can further break down these tetratonic sounds into triads: once you feel comfortable improvising using the triads exclusively, it’s easier to play the full tetratonic scales (adding a major second to major triads and a perfect fourth to minor triads to get the corresponding tetratonics).

Bar Chord
Symbol		 Tetratonic
Scale(s)		 Triads
121 C7 A minor A-
136 D7(#11) E major E
137 Eb6 Eb major Eb
139 Eb7sus Bb minor Bb-
141 Eb6 G minor G-
143 Eb7sus Bb minor Bb-
144 E7(#11) B minor B-
145 F#6 C# major C#
147 F#7sus C# minor C#-
149 F#6 C# major C#
150 Db7(#11) Eb major Eb

Complete sheet music for “Oleleko” (from the album Tao, 2019) is available. Please visit the Funnelljazz catalogue for more information.

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finding 5-note 2-hand voicings for half-diminished locrian chords

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While focusing on a section of AfuriKo’s recent arrangement of “Kassai” during practice yesterday, I came across a mi7(b5) chord that calls for the locrian chord scale. Remembering Frank Mantooth’s approach in his Voicings for Jazz Keyboard inspired me to research possible 5-note 2-hand voicings for this chord.

So let’s quickly jot down a major scale and list all possible Quartal (Q), Generic Dominant (GD), and So What (SW) voicings that can be built under each scale degree (top note):

major harmony voicing types screen shot 1

The results are summarized in the table below:

voicing type top note
Quartal 1, 4, 5
Generic Dominant 2, 5
So What 3, 6, 7

The next step is to find suitable candidates to aurally represent our half-diminished locrian chord! It feels natural to go with those that:

  • sound best individually when trying them out against the root (C in the key of Db major) in the low register of the keyboard;
  • sound best in the context of a minor II-V-I.

You’ll notice that most of the eligible voicings include all three guide tones (namely b3, b5, and b7), which seems coherent since these notes characterize the mi7(b5) sound. One of the voicings, however, features b3 and b7 only (no b5), but still sounds strong as a mi7(b5) chord (to my ears…) so I went ahead and included it here, too.

1) The Generic Dominant voicing built underneath scale degree 2 has all four chord tones (C, Eb, Gb, Bb) and the 11th (F). Here it is notated below followed by its four inversions:

major harmony voicing types screen shot 4

Two of these inversions contain the interval of a b9. They sound dissonant and not quite appropriate for a mi7(b5) chord, so let’s go ahead and rule them out. We are left with the following three solid-sounding voicings for Cmi7(b5). From the top note down:

  • Eb Bb F C Gb
  • F C Gb Eb Bb
  • Bb F C Gb Eb

Incidentally (or not!), these notes make up the F insen pentatonic (F Gb Bb C Eb), which reveals itself as a very interesting scale to solo over Cmi7(b5).

2) The So What voicing built underneath scale degree 3 is slightly more adventurous, containing only two of the guide tones (Bb and Eb) and three tensions: the b9th (Db), the 11th (F), and the b13th (Ab). Its inversions don’t seem to function so well (again, these perceptions are of course subjective and there are no hard and fast rules…) as a mi7(b5) chord so let’s just keep the following chord, from the top note down:

  • F Db Ab Eb Bb

Now, it turns out this particular set of notes corresponds to the Db major/Bb minor pentatonic, which is thus also a valid choice to solo over Cmi7(b5).

3) The Generic Dominant voicing built under scale degree 5 contains all four chord tones (C, Eb, Gb, Bb), as well as the b13th (Ab). Here it goes with its inversion:

major harmony voicing types screen shot 6

Two of the those voicings (labeled Ab7 above) have a very distinct dominant color, but we can definitely use the other three as strong sounding half-diminished locrian chords. Spelling them from top to bottom, we have:

  • Ab Eb Bb Gb C
  • C Ab Eb Bb Gb
  • Gb C Ab Eb Bb

These notes (Ab Bb C Eb Gb) constitute the Ab dominant pentatonic scale.

4) The Quartal voicing built under scale degree 4 and the So What voicing built under scale degree 6 are in fact inversions of each other:

major harmony voicing types screen shot 5

Although the Db here creates the interval of a b9 with the underlying root (C), it is OK to go ahead and list all inversions for this chord as possible mi7(b5) voicings because b2 is a characteristic note of the locrian mode. From the top note down, we have the following five additional possibilities for Cmi7(b5):

  • Gb Db Ab Eb Bb
  • Ab Eb Bb Gb Db
  • Bb Gb Db Ab Eb
  • Db Ab Eb Bb Gb
  • Eb Bb Gb Db Ab

This last set of notes uncovers the Gb major/Eb minor pentatonic, yet another option to solo over Cmi7(b5).

To sum up, here are all twelve previously found half-diminished locrian voicings:

major harmony voicing types screen shot 8

And finally, let’s put them back in context! I have chosen minor II-V-Is with either V7(b9) or V7alt as the dominant chord:

major harmony voicing types screen shot 7

ADDENDUM

29 Oct. 2019

The in pentatonic scale (E F A B D) is also contained within the major scale and can also be used effectively to derive 5-note 2-hand voicings for half-diminished locrian chords (Bmi7(b5) in this case). The way to do it is to play the first scale degree (E), skip the second scale degree (F), play the third scale degree (A), skip the fourth scale degree (B), etc… until you’re playing all five notes simultaneously, divided between both hands. You will end up with the voicing E A D F B, and its inversions (F B E A D, A D F B E, B E A D F, and D F B E A). Some of these include the interval of a b9 within the voicing (between the notes E and F) but this doesn’t matter (in my opinion and experience) as the flatted second scale degree is a characteristic note of the locrian mode.

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pentatonic possibilities 1: major and minor pentatonics

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Pentatonics are 5-note scales. Technically, any ordered sequence of 5 notes can be called a pentatonic. But the most common and widely used pentatonic is without doubt the one obtained by reordering a series of 5 notes stacked on top of each other in fifths (for example, the series “C G D A E” gives us “C D E G A” once reordered). This particular pentatonic comes in its “major” form (C D E G A), and its relative “minor” form (A C D E G).

So, what do I mean by “pentatonic possibilities?” Well, pentatonics tend to break up the diatonic quality of 7-note major and minor scales because of their intervallic content. So, to create fresh melodic shapes and give a more edgy feel to your lines while improvising over changes, you might ask yourself: what pentatonic scales can I use over these chords? Chords derive from modes, and modes from harmony types, so the question may be rephrased as: what pentatonic scales can be extracted from the various harmony types?

For the purpose of this particular post, I will limit myself to what I call the “common” or “global” pentatonic scale (the one discussed in the first paragraph). Let’s have a look at major harmony first. The pentatonics listed in the first and last column of the table shown below are extracted from the key of C major (C D E F G A B). Their “major” forms are listed in the left-hand side of the table along with their relative “minor” forms on the right-hand side, and the roman numerals represent the scale degrees for each pentatonic:

major harmony pentatonic possibilities
C D E G A I Maj. pent. <=> VI min. pent. A C D E G
F G A C D IV Maj. pent. <=> II min. pent. D F G A C
G A B D E V Maj. pent. <=> III min. pent. E G A B D

Natural minor harmony is equivalent to the Aeolian mode. Therefore, the pentatonic possibilities in natural minor are the same as in major harmony (the roman numerals indicating the scale degrees, however, would have to change due to the shift to relative minor).

Now, let’s have a look at melodic minor harmony. It turns out only one pentatonic scale can be extracted from this harmony type. It is shown in the table below in the key of C melodic minor (C D Eb F G A B):

melodic minor harmony pentatonic possibilities
F G A C D IV Maj. pent. <=> II min. pent. D F G A C

Finally, neither harmonic minor nor harmonic major harmony bear common pentatonic possibilities, due to a flatted 6th scale degree in both instances. However, some interesting “exotic” pentatonics can be derived from those harmony types…

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